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<title>Schulze-Methode</title>

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<h1 id="firstHeading" class="firstHeading mw-first-heading">Schulze-Methode</h1>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr">Die Schulze-Methode (nach Markus Schulze) ist ein <a href="Wahlsystem" title="Wahlsystem">Wahlverfahren</a> aus der Familie der <a href="Vorzugswahl" class="mw-redirect" title="Vorzugswahl">Vorzugswahlen</a>, mit dem ein einzelner Sieger bestimmt wird. Es ist die derzeit verbreitetste Methode, um Wahlen durchzuführen, bei welchen der Wähler Kandidaten nach Rang ordnet.

Die Schulze-Methode ist eine <a href="Condorcet-Methode" title="Condorcet-Methode">Condorcet-Methode</a>, d. h., dass sie einen Kandidaten, der im paarweisen Vergleich jeden anderen Kandidaten besiegen würde, als Sieger auswählt, sofern ein solcher existiert.

Markus Schulze hat die Methode 1997 entwickelt. Die ersten Veröffentlichungen datieren von 2003 und 2006.<a href="#cite_note-1">[1]</a><a href="#cite_note-2">[2]</a><a href="#cite_note-3">[3]</a> Verwendet wurde die Schulze-Methode erstmals 2003 (von <a href="Software_in_the_Public_Interest" title="Software in the Public Interest">Software in the Public Interest</a>), 2003 (von <a href="Debian" title="Debian">Debian</a>) und 2005 (von <a href="Gentoo_Linux" title="Gentoo Linux">Gentoo Linux</a>).

<div class="mw-heading mw-heading2"><h2 id="Erklärung">Erklärung</h2></div>

Jeder Wähler erhält eine komplette Liste aller <a href="Kandidat" title="Kandidat">Kandidaten</a>. Er reiht die Kandidaten, indem er ihnen Zahlen zuordnet. Eine kleine Zahl ist besser als eine größere, jedoch zählt nur die Reihenfolge. Kandidaten mit gleicher Zahl sind an gleicher Stelle gereiht. Kandidaten ohne Zahl sind gemeinsam an letzter Stelle – so als ob der Wähler ihnen jeweils die größtmögliche Zahl zugeschrieben hätte.

<div class="mw-heading mw-heading3"><h3 id="Anzahl_der_Wähler">Anzahl der Wähler</h3></div>

Die Anzahl der Wähler, die den Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> dem Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

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<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> vorziehen (d. h. die bei <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> eine kleinere Zahl als bei <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

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<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> vermerkt haben), wird durch <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[A,B]}">

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<annotation encoding="application/x-tex">{\displaystyle d[A,B]}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/90754a949acd09b1949fbf9d7ad13151b5bfb62d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.051ex; height:2.843ex;" alt="{\displaystyle d[A,B]}" loading="lazy"> ausgedrückt.

Der Wert von <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}">

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<annotation encoding="application/x-tex">{\displaystyle d}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e85ff03cbe0c7341af6b982e47e9f90d235c66ab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}" loading="lazy"> wird aus den Stimmabgaben gezählt

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<annotation encoding="application/x-tex">{\displaystyle d[A,B]}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/90754a949acd09b1949fbf9d7ad13151b5bfb62d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.051ex; height:2.843ex;" alt="{\displaystyle d[A,B]}" loading="lazy"> ist die Zahl der Wähler, die Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> besser als <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

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<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> finden.</li>

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<annotation encoding="application/x-tex">{\displaystyle d[B,A]}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f7c4893d3d24c03ccc0943be763b24167736aea1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.051ex; height:2.843ex;" alt="{\displaystyle d[B,A]}" loading="lazy"> ist die Zahl der Wähler, die Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

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<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> besser als <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> finden.</li></ul>

Für diese Werte ist es unerheblich, ob noch andere Kandidaten existieren und ob diese besser oder schlechter als <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

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<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> oder zwischen beiden eingestuft werden.

<div class="mw-heading mw-heading3"><h3 id="Definition">Definition</h3></div>

Die Schulze-Methode ist folgendermaßen definiert:

<dl><dd>Ein Weg (<a href="Englische_Sprache" title="Englische Sprache">englisch</a> path) vom Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}">

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<annotation encoding="application/x-tex">{\displaystyle X}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/68baa052181f707c662844a465bfeeb135e82bab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" loading="lazy"> zum Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}">

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<annotation encoding="application/x-tex">{\displaystyle Y}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/961d67d6b454b4df2301ac571808a3538b3a6d3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}" loading="lazy"> der Stärke <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}">

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<annotation encoding="application/x-tex">{\displaystyle z}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bf368e72c009decd9b6686ee84a375632e11de98.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" loading="lazy"> ist eine Sequenz von Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{1},\dots ,C_{n}}">

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<annotation encoding="application/x-tex">{\displaystyle C_{1},\dots ,C_{n}}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/cc72696c6524f0377453cb2a973cdd45d80a27c8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.775ex; height:2.509ex;" alt="{\displaystyle C_{1},\dots ,C_{n}}" loading="lazy"> mit den folgenden Eigenschaften:</dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle C_{1}=X}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/509a5a709d8652f7877dca8dc18dba60271cb778.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.795ex; height:2.509ex;" alt="{\displaystyle C_{1}=X}" loading="lazy">, d. h. der Weg beginnt bei <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}">

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<annotation encoding="application/x-tex">{\displaystyle X}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/68baa052181f707c662844a465bfeeb135e82bab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" loading="lazy">.</li>

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</mrow>

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<annotation encoding="application/x-tex">{\displaystyle C_{n}=Y}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/37fb255ccc04b976fac3077349d85911e192304e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.752ex; height:2.509ex;" alt="{\displaystyle C_{n}=Y}" loading="lazy">, d. h. der Weg endet bei <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}">

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<annotation encoding="application/x-tex">{\displaystyle Y}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/961d67d6b454b4df2301ac571808a3538b3a6d3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}" loading="lazy">.</li>

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<annotation encoding="application/x-tex">{\displaystyle \forall i<n.\ d[C_{i},C_{i+1}]>d[C_{i+1},C_{i}]}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d6805b33d6e8427875d49844051c160ad378ef77.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.435ex; height:2.843ex;" alt="{\displaystyle \forall i<n.\ d[C_{i},C_{i+1}]>d[C_{i+1},C_{i}]}" loading="lazy">, d. h. jeder Kandidat auf dem Weg gewinnt den paarweisen Vergleich gegen den auf ihn folgenden Kandidaten.</li>

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<annotation encoding="application/x-tex">{\displaystyle \forall i<n.\ d[C_{i},C_{i+1}]\geq z}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b8aa074f623bfb2f1d709af5ea886f4df335ea65.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.956ex; height:2.843ex;" alt="{\displaystyle \forall i<n.\ d[C_{i},C_{i+1}]\geq z}" loading="lazy">, d. h. jeder Kandidat auf dem Weg wird gegenüber dem auf ihn folgenden Kandidaten von mindestens <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}">

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<annotation encoding="application/x-tex">{\displaystyle z}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bf368e72c009decd9b6686ee84a375632e11de98.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" loading="lazy"> Wählern bevorzugt.</li>

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<annotation encoding="application/x-tex">{\displaystyle \exists i<n.\ d[C_{i},C_{i+1}]=z}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/99ce36caa509702e780af366cd9dd7cd385f71f1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.956ex; height:2.843ex;" alt="{\displaystyle \exists i<n.\ d[C_{i},C_{i+1}]=z}" loading="lazy">, d. h. wenigstens einer dieser Vergleiche wird von (nur) genau <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}">

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<annotation encoding="application/x-tex">{\displaystyle z}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bf368e72c009decd9b6686ee84a375632e11de98.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" loading="lazy"> Wählern gestützt.</li></ol></dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle C_{1},\dots ,C_{n}}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/cc72696c6524f0377453cb2a973cdd45d80a27c8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.775ex; height:2.509ex;" alt="{\displaystyle C_{1},\dots ,C_{n}}" loading="lazy"> die Stärke <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}">

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<annotation encoding="application/x-tex">{\displaystyle z}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bf368e72c009decd9b6686ee84a375632e11de98.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" loading="lazy">, so werden die Bögen dieses Weges, für die <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d[C_{i},C_{i+1}]=z}">

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<annotation encoding="application/x-tex">{\displaystyle d[C_{i},C_{i+1}]=z}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/65d69c892867a6447c351eae5345b5f754afbda9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.754ex; height:2.843ex;" alt="{\displaystyle d[C_{i},C_{i+1}]=z}" loading="lazy"> gilt, kritische Siege genannt. Bei ihnen handelt es sich um die schwächsten Siege auf dem Weg.</dd></dl>

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<annotation encoding="application/x-tex">{\displaystyle p[A,B]}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2db36f2c916152b48d8c762329032136698cd2f1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:7.094ex; height:2.843ex;" alt="{\displaystyle p[A,B]}" loading="lazy">, die Stärke des stärksten Weges vom Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> zum Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

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<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">, ist der größte Wert, so dass es einen Weg dieser Stärke vom Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> zum Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

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<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> gibt. Falls es überhaupt keinen Weg von <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> nach <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> gibt, wird <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[A,B]=0}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[A,B]=0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e1012483d213c4cce23e162a1707bc628281af06.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:11.354ex; height:2.843ex;" alt="{\displaystyle p[A,B]=0}" loading="lazy"> gesetzt.</dd></dl>

<dl><dd>Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> ist besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> genau dann, wenn <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[A,B]>p[B,A]}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[A,B]>p[B,A]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2521bee8b78629227931636d389fbcc41bc97155.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:17.196ex; height:2.843ex;" alt="{\displaystyle p[A,B]>p[B,A]}" loading="lazy"> ist.</dd></dl>

<dl><dd>Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> ist ein potentieller Sieger genau dann, wenn <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[A,B]\geq p[B,A]}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[A,B]\geq p[B,A]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fff3c5648c8a56ed003a0c6331949f3de87c0922.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:17.196ex; height:2.843ex;" alt="{\displaystyle p[A,B]\geq p[B,A]}" loading="lazy"> ist für jeden anderen Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">.</dd></dl>

Es lässt sich zeigen, dass die besser-Relation <a href="Transitive_Relation" title="Transitive Relation">transitiv</a> ist. Es existiert somit stets mindestens ein potentieller Sieger.

<div class="mw-heading mw-heading3"><h3 id="Beispiel_1">Beispiel 1</h3></div>

<th>1

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

</td></tr>

<tr>

<th>2

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td></tr>

<tr>

<th>3

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td></tr>

<tr>

<th>4

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td></tr>

<tr>

<th>5

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td></tr>

<tr>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 5}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/29483407999b8763f0ea335cf715a6a5e809f44b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 5}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 5}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/29483407999b8763f0ea335cf715a6a5e809f44b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 5}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 8}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1aaa997e6ad67716cfaa9a02c4df860bf60a95b5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 8}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 3}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/991e33c6e207b12546f15bdfee8b5726eafbbb2f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 3}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 7}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ee716ec61382a6b795092c0edd859d12e64cbba8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 7}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/901fc910c19990d0dbaaefe4726ceb1a4e217a0f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 2}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 7}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ee716ec61382a6b795092c0edd859d12e64cbba8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 7}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 8}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1aaa997e6ad67716cfaa9a02c4df860bf60a95b5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 8}" loading="lazy">

</th></tr></tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Paarweise_Matrix">Paarweise Matrix</h4></div>

Tabelle, die jeden Kandidaten mit jedem anderen vergleicht. Die rot markierten Felder werden weiter benutzt. Z. B. wurde Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> von <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 25}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 25}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a8acf6937f13156a1301ebb614c5364d16597e42.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.325ex; height:2.176ex;" alt="{\displaystyle 25}" loading="lazy"> Stimmen gegenüber <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> bevorzugt.

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,A]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f6062742a166ebfc42f5ff4aff3fabea69088657.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.449ex; height:2.843ex;" alt="{\displaystyle d[\ast ,A]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,B]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2c65778ead47b0e225f4f935e7b7e3b4f99415b8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.47ex; height:2.843ex;" alt="{\displaystyle d[\ast ,B]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,C]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c64abe95f34fedcd6d020d31a7309b53540ef871.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.472ex; height:2.843ex;" alt="{\displaystyle d[\ast ,C]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,D]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9926ef38a63d9aa7d2570640a43f285b2604095e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.63ex; height:2.843ex;" alt="{\displaystyle d[\ast ,D]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,E]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/72d9262da3be9d71bd42152b30c004e8361113f5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.482ex; height:2.843ex;" alt="{\displaystyle d[\ast ,E]}" loading="lazy">

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[A,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a0f251b147701d4dc2dafe247f041ba89dc80bf3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.449ex; height:2.843ex;" alt="{\displaystyle d[A,\ast ]}" loading="lazy">

</td>

<td>22

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[B,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a7eada643990df89fbfb801de5e0126260a1c4f6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.47ex; height:2.843ex;" alt="{\displaystyle d[B,\ast ]}" loading="lazy">

</td>

<td>18

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[C,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/37cbd9510f311633ddd7350d99b1ea8e17fe576f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.472ex; height:2.843ex;" alt="{\displaystyle d[C,\ast ]}" loading="lazy">

</td>

<td style="background:#FEDBCA; color:#202122;">24

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[D,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fa6173aecb39b531d5fa915a2bc827340f5ead36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.63ex; height:2.843ex;" alt="{\displaystyle d[D,\ast ]}" loading="lazy">

</td>

<td>14

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[E,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ee4397d4bf37a23964ea4a7c6cf981fab5f1b614.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.482ex; height:2.843ex;" alt="{\displaystyle d[E,\ast ]}" loading="lazy">

</td>

</td></tr></tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Paarweiser_Graph">Paarweiser Graph</h4></div>

Graph mit gewichteten Pfeilen aus der Tabelle von oben. Man sieht den Pfeil von Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> zu Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> mit dem Gewicht von <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 25}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 25}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a8acf6937f13156a1301ebb614c5364d16597e42.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.325ex; height:2.176ex;" alt="{\displaystyle 25}" loading="lazy"> aus der obigen Tabelle.

<div class="mw-heading mw-heading4"><h4 id="Die_stärksten_Wege">Die stärksten Wege</h4></div>

Von den Verbindungen zwischen Kandidaten wird diejenige gesucht, bei der das schwächste Glied am stärksten ist. Bildlich gesprochen wird die stärkste Kette gesucht. Wie kommt man von <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> nach <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">?

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> über <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"> nach <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> ist das schwächste Glied von <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> nach <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"> mit <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 26}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 26}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/95afbbb0014a068ce8ff3db0c90da36a5b1b2fa1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.325ex; height:2.176ex;" alt="{\displaystyle 26}" loading="lazy">.</li>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> über <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"> und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"> nach <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> ist das schwächste Glied <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"> nach <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"> mit <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 28}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 28}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c88f99b6131febe59de9aeeb35f429c94fa36e78.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.325ex; height:2.176ex;" alt="{\displaystyle 28}" loading="lazy">. Diese Kette ist stärker und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 28}">

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<annotation encoding="application/x-tex">{\displaystyle 28}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c88f99b6131febe59de9aeeb35f429c94fa36e78.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.325ex; height:2.176ex;" alt="{\displaystyle 28}" loading="lazy"> wird nachfolgend verwendet.</li></ul>

Man kann sich den Vorgang beispielsweise aus Sicht eines Transportunternehmens vorstellen, das möglichst viele Pakete auf einmal von einer Stadt in die andere transportieren möchte (egal wie lang der Weg ist). Ohne Zwischenlager kann natürlich nur so viel transportiert werden wie das Fassungsvermögen des kleinsten Transportmittels, das am Weg verwendet wird: Wenn die Pakete zuerst per <a href="F%C3%A4hre" title="Fähre">Fähre</a>, dann per <a href="Lastkraftwagen" title="Lastkraftwagen">Lastkraftwagen</a> und zuletzt per <a href="G%C3%BCterzug" title="Güterzug">Güterzug</a> transportiert werden, dann ist wahrscheinlich der Lastkraftwagen am kleinsten. Im Vergleich zu einer anderen Route (die z. B. einen <a href="Pick-up" title="Pick-up">Pickup-Truck</a> enthält) ist der Lastkraftwagen damit das schwächste Glied der stärksten Kette.

Oft wird dieses schwächste Glied der stärksten Kette auch kritischer Sieg genannt. Die kritischen Siege der stärksten Wege sind unterstrichen.

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> …

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<annotation encoding="application/x-tex">{\displaystyle A{\overset {30}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle A{\overset {30}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/009dc1d56cbf21e20832dad917266390b3ab6233.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.045ex; height:3.843ex;" alt="{\displaystyle A{\overset {30}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle A{\overset {\underline {30}}{\longrightarrow }}D}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/90e3a11907b79ae678abd868d0eaf69a1e5a1642.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.473ex; height:3.843ex;" alt="{\displaystyle A{\overset {\underline {30}}{\longrightarrow }}D}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle A{\overset {30}{\longrightarrow }}D{\overset {28}{\longrightarrow }}C{\overset {\underline {24}}{\longrightarrow }}E}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2537b7daa93e51ff49a5905c90b0b108d65a7b64.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.626ex; height:3.676ex;" alt="{\displaystyle A{\overset {30}{\longrightarrow }}D{\overset {28}{\longrightarrow }}C{\overset {\underline {24}}{\longrightarrow }}E}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> …

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<annotation encoding="application/x-tex">{\displaystyle B{\overset {\underline {25}}{\longrightarrow }}A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7cdcea6092a39ce7fa135b0740e53256eb6da783.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.313ex; height:3.843ex;" alt="{\displaystyle B{\overset {\underline {25}}{\longrightarrow }}A}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle B{\overset {33}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/dff604035045096aaf75e2977b31e8cb370f9832.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.066ex; height:3.843ex;" alt="{\displaystyle B{\overset {33}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle B{\overset {\underline {33}}{\longrightarrow }}D}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6967472834dab42357e577bd8dca5046dd82de87.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.494ex; height:3.843ex;" alt="{\displaystyle B{\overset {\underline {33}}{\longrightarrow }}D}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle B{\overset {33}{\longrightarrow }}D{\overset {28}{\longrightarrow }}C{\overset {\underline {24}}{\longrightarrow }}E}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6d39f9f6691808830cbf7084ab4d0a4ae9634e2d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.647ex; height:3.676ex;" alt="{\displaystyle B{\overset {33}{\longrightarrow }}D{\overset {28}{\longrightarrow }}C{\overset {\underline {24}}{\longrightarrow }}E}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"> …

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<annotation encoding="application/x-tex">{\displaystyle C{\overset {29}{\longrightarrow }}B{\overset {\underline {25}}{\longrightarrow }}A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9e334b604e5f1d6661550125574434333739984a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.885ex; height:3.843ex;" alt="{\displaystyle C{\overset {29}{\longrightarrow }}B{\overset {\underline {25}}{\longrightarrow }}A}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle C{\overset {\underline {29}}{\longrightarrow }}B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8e78368d739bc15627ae361c43a7cb1b209a7d16.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.336ex; height:3.843ex;" alt="{\displaystyle C{\overset {\underline {29}}{\longrightarrow }}B}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle C{\overset {\underline {29}}{\longrightarrow }}B{\overset {33}{\longrightarrow }}D}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/73e89998ae6305736debcaa1ad45625f1e62fc02.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.066ex; height:3.843ex;" alt="{\displaystyle C{\overset {\underline {29}}{\longrightarrow }}B{\overset {33}{\longrightarrow }}D}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle C{\overset {\underline {24}}{\longrightarrow }}E}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/dbf53b6bed87b75e711f9710d51eb7d367ce3f9f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.348ex; height:3.676ex;" alt="{\displaystyle C{\overset {\underline {24}}{\longrightarrow }}E}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"> …

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<annotation encoding="application/x-tex">{\displaystyle D{\overset {28}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B{\overset {\underline {25}}{\longrightarrow }}A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b7f109fb74b96de2eb43913bc0f4e49db7b4dfb8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.614ex; height:3.843ex;" alt="{\displaystyle D{\overset {28}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B{\overset {\underline {25}}{\longrightarrow }}A}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle D{\overset {\underline {28}}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0e547455df9f5196f52f7b839c138775489ed228.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.066ex; height:3.843ex;" alt="{\displaystyle D{\overset {\underline {28}}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle D{\overset {\underline {28}}{\longrightarrow }}C}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4ce09d24062dd757dd4eb76f7b2d698ea1256a81.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.496ex; height:3.843ex;" alt="{\displaystyle D{\overset {\underline {28}}{\longrightarrow }}C}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle D{\overset {28}{\longrightarrow }}C{\overset {\underline {24}}{\longrightarrow }}E}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c9711378e514a08591a7e42a4c2f19a6f2578d49.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.077ex; height:3.676ex;" alt="{\displaystyle D{\overset {28}{\longrightarrow }}C{\overset {\underline {24}}{\longrightarrow }}E}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy"> …

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<annotation encoding="application/x-tex">{\displaystyle E{\overset {31}{\longrightarrow }}D{\overset {28}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B{\overset {\underline {25}}{\longrightarrow }}A}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/56f5bfa1fd1ce00d8b14c0c00d3f9cda12bc91ac.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:24.196ex; height:3.843ex;" alt="{\displaystyle E{\overset {31}{\longrightarrow }}D{\overset {28}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B{\overset {\underline {25}}{\longrightarrow }}A}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle E{\overset {31}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d5efae29e6013d772eb624296746e231e1e008c2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.647ex; height:3.843ex;" alt="{\displaystyle E{\overset {31}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C{\overset {29}{\longrightarrow }}B}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle E{\overset {31}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b5100c6efdb4232a1a5310a3bb88c67de9a0d54b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.077ex; height:3.843ex;" alt="{\displaystyle E{\overset {31}{\longrightarrow }}D{\overset {\underline {28}}{\longrightarrow }}C}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle E{\overset {\underline {31}}{\longrightarrow }}D}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/01477bf5a28fbb49ad68857ceaa0832a94149da6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.505ex; height:3.843ex;" alt="{\displaystyle E{\overset {\underline {31}}{\longrightarrow }}D}" loading="lazy">

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<div class="mw-heading mw-heading4"><h4 id="Die_Stärken_der_stärksten_Wege">Die Stärken der stärksten Wege</h4></div>

Das schwächste Glied der stärksten Verbindung, wie oben gefunden, wird in eine Tabelle eingetragen. Dann wird wieder paarweise verglichen, wer wen schlägt, in der Tabelle unten wieder rot markiert.

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<annotation encoding="application/x-tex">{\displaystyle p[\ast ,A]}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/64543e94893b8fb7fcd6c455b050437e7efd901b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.492ex; height:2.843ex;" alt="{\displaystyle p[\ast ,A]}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle p[\ast ,B]}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bb52f6befa12a3cbb439f9c66a95f47f96bb665a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.513ex; height:2.843ex;" alt="{\displaystyle p[\ast ,B]}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle p[\ast ,C]}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/54a7f8388d2513be26fa4776f99c62c7820a94ef.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.515ex; height:2.843ex;" alt="{\displaystyle p[\ast ,C]}" loading="lazy">

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<annotation encoding="application/x-tex">{\displaystyle p[\ast ,D]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e2713ac9b56506837d245fdaf8a8b5e3c922a942.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.673ex; height:2.843ex;" alt="{\displaystyle p[\ast ,D]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[\ast ,E]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6aeb2ba9c1f69c1f8ee353ae11e554ecc6a45201.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.525ex; height:2.843ex;" alt="{\displaystyle p[\ast ,E]}" loading="lazy">

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[A,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fce5d7fb73342e63b38107e1d5c6815c65866056.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.492ex; height:2.843ex;" alt="{\displaystyle p[A,\ast ]}" loading="lazy">

</td>

<td>24

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[B,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4968bf66785ab349f834dc9a249541b7f240231f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.513ex; height:2.843ex;" alt="{\displaystyle p[B,\ast ]}" loading="lazy">

</td>

<td>24

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[C,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e3b49c713f23c45dcd344fedc26b81b9e3dcf4e2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.515ex; height:2.843ex;" alt="{\displaystyle p[C,\ast ]}" loading="lazy">

</td>

<td>24

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[D,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7e429092865c294b0a414cf5f96a28d8b2900a39.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.673ex; height:2.843ex;" alt="{\displaystyle p[D,\ast ]}" loading="lazy">

</td>

<td>24

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[E,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/075b96909b349497d02f85afcaebe921a3c84c3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.525ex; height:2.843ex;" alt="{\displaystyle p[E,\ast ]}" loading="lazy">

</td>

</td></tr></tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Ergebnis">Ergebnis</h4></div>

Sieger nach der Schulze-Methode ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy">, da <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p[E,X]\geq p[X,E]}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[E,X]\geq p[X,E]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a93b3547fa268c146f1723b3c2327d148e926562.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:17.693ex; height:2.843ex;" alt="{\displaystyle p[E,X]\geq p[X,E]}" loading="lazy"> ist für jeden anderen Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle X}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/68baa052181f707c662844a465bfeeb135e82bab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" loading="lazy">.

<ul><li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 25=p[E,A]>p[A,E]=24}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 25=p[E,A]>p[A,E]=24}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/90c70f8584d160aff5bad99f5dda787a4d19a086.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.977ex; height:2.843ex;" alt="{\displaystyle 25=p[E,A]>p[A,E]=24}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 28=p[E,B]>p[B,E]=24}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 28=p[E,B]>p[B,E]=24}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5a409218d6067bbea5ad3813f915a00732fb3687.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.019ex; height:2.843ex;" alt="{\displaystyle 28=p[E,B]>p[B,E]=24}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 28=p[E,C]>p[C,E]=24}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 28=p[E,C]>p[C,E]=24}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d25dff02044ad50e6b0419565a3f2107587a449c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.023ex; height:2.843ex;" alt="{\displaystyle 28=p[E,C]>p[C,E]=24}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 31=p[E,D]>p[D,E]=24}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 31=p[E,D]>p[D,E]=24}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/359d06cba39e66d1c14629ecbcf95c4b3bb32ed5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.339ex; height:2.843ex;" alt="{\displaystyle 31=p[E,D]>p[D,E]=24}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 28=p[A,B]>p[B,A]=25}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 28=p[A,B]>p[B,A]=25}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/202a48ebaf3818f6ac78891b505db624df809a77.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.954ex; height:2.843ex;" alt="{\displaystyle 28=p[A,B]>p[B,A]=25}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 28=p[A,C]>p[C,A]=25}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 28=p[A,C]>p[C,A]=25}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0fbf7e3be97ad00d3835d2da3951d64f93959329.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.958ex; height:2.843ex;" alt="{\displaystyle 28=p[A,C]>p[C,A]=25}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 30=p[A,D]>p[D,A]=25}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 30=p[A,D]>p[D,A]=25}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/112271a7e5ce2d599148141a5109810a682be019.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.274ex; height:2.843ex;" alt="{\displaystyle 30=p[A,D]>p[D,A]=25}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 29=p[C,B]>p[B,C]=28}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 29=p[C,B]>p[B,C]=28}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0c485ad393e48f81f4df4dd72b347d6bd2bdc476.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28ex; height:2.843ex;" alt="{\displaystyle 29=p[C,B]>p[B,C]=28}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 29=p[C,D]>p[D,C]=28}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 29=p[C,D]>p[D,C]=28}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3ce53dafa2b7780f157f856729c71d84c5c807e2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.32ex; height:2.843ex;" alt="{\displaystyle 29=p[C,D]>p[D,C]=28}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">.</li>

<li>Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 33=p[B,D]>p[D,B]=28}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 33=p[B,D]>p[D,B]=28}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/df686be9440c8a2d75bb4a8baec0cdc1dcd673de.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.316ex; height:2.843ex;" alt="{\displaystyle 33=p[B,D]>p[D,B]=28}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">.</li></ul>

Das Schulze-Ranking ist somit <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E>A>C>B>D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E>A>C>B>D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9d9993c0f931bc4720f09a14584e42559d0a0d1b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:21.367ex; height:2.176ex;" alt="{\displaystyle E>A>C>B>D}" loading="lazy">.

<div class="mw-heading mw-heading3"><h3 id="Beispiel_2">Beispiel 2</h3></div>

<th>1

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td></tr>

<tr>

<th>2

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td></tr>

<tr>

<th>3

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td></tr>

<tr>

<th>4

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td></tr>

<tr>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 3}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/991e33c6e207b12546f15bdfee8b5726eafbbb2f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 3}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/901fc910c19990d0dbaaefe4726ceb1a4e217a0f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 2}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/901fc910c19990d0dbaaefe4726ceb1a4e217a0f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 2}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/901fc910c19990d0dbaaefe4726ceb1a4e217a0f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 2}" loading="lazy">

</th></tr></tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Paarweise_Matrix_2">Paarweise Matrix</h4></div>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,A]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f6062742a166ebfc42f5ff4aff3fabea69088657.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.449ex; height:2.843ex;" alt="{\displaystyle d[\ast ,A]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,B]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2c65778ead47b0e225f4f935e7b7e3b4f99415b8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.47ex; height:2.843ex;" alt="{\displaystyle d[\ast ,B]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,C]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c64abe95f34fedcd6d020d31a7309b53540ef871.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.472ex; height:2.843ex;" alt="{\displaystyle d[\ast ,C]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[\ast ,D]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9926ef38a63d9aa7d2570640a43f285b2604095e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.63ex; height:2.843ex;" alt="{\displaystyle d[\ast ,D]}" loading="lazy">

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[A,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a0f251b147701d4dc2dafe247f041ba89dc80bf3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.449ex; height:2.843ex;" alt="{\displaystyle d[A,\ast ]}" loading="lazy">

</td>

<td>3

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[B,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a7eada643990df89fbfb801de5e0126260a1c4f6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.47ex; height:2.843ex;" alt="{\displaystyle d[B,\ast ]}" loading="lazy">

</td>

<td style="background:#FEDBCA; color:#202122;">5

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[C,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/37cbd9510f311633ddd7350d99b1ea8e17fe576f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.472ex; height:2.843ex;" alt="{\displaystyle d[C,\ast ]}" loading="lazy">

</td>

<td style="background:#FEDBCA; color:#202122;">5

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d[D,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fa6173aecb39b531d5fa915a2bc827340f5ead36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.63ex; height:2.843ex;" alt="{\displaystyle d[D,\ast ]}" loading="lazy">

</td>

</td></tr></tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Paarweiser_Graph_2">Paarweiser Graph</h4></div>

<div class="mw-heading mw-heading4"><h4 id="Die_stärksten_Wege_2">Die stärksten Wege</h4></div>

Die kritischen Siege der stärksten Wege sind unterstrichen.

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"> …

</td>

</td>

<td>

<mover>

</munder>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A{\overset {\underline {5}}{\longrightarrow }}B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6ef30dda22f625cd0f7b6f889cdedea0bd1d03f4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.313ex; height:3.843ex;" alt="{\displaystyle A{\overset {\underline {5}}{\longrightarrow }}B}" loading="lazy">

</td>

<td>

<mover>

</munder>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A{\overset {\underline {5}}{\longrightarrow }}C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f5f01f56ea57f1c8996710e01820d23a2dcd9198.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.315ex; height:3.843ex;" alt="{\displaystyle A{\overset {\underline {5}}{\longrightarrow }}C}" loading="lazy">

</td>

<td>

<mover>

</munder>

</mover>

</mrow>

<mover>

</munder>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A{\overset {\underline {5}}{\longrightarrow }}B{\overset {\underline {5}}{\longrightarrow }}D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6c3f01e39dcb237ab321ab75f7e161ad10603205.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.042ex; height:3.843ex;" alt="{\displaystyle A{\overset {\underline {5}}{\longrightarrow }}B{\overset {\underline {5}}{\longrightarrow }}D}" loading="lazy">

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> …

</td>

<td>

<mover>

</munder>

</mover>

</mrow>

<mover>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B{\overset {\underline {5}}{\longrightarrow }}D{\overset {6}{\longrightarrow }}A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/509b4df377b980bdb7b36a4bda2a5aeeeb3a9d26.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.042ex; height:3.843ex;" alt="{\displaystyle B{\overset {\underline {5}}{\longrightarrow }}D{\overset {6}{\longrightarrow }}A}" loading="lazy">

</td>

</td>

<td>

<mover>

</munder>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B{\overset {\underline {7}}{\longrightarrow }}C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/10d3b77fd9def1c36bcd43236417fc5216f175da.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.336ex; height:3.843ex;" alt="{\displaystyle B{\overset {\underline {7}}{\longrightarrow }}C}" loading="lazy">

</td>

<td>

<mover>

</munder>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B{\overset {\underline {5}}{\longrightarrow }}D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b099297a32d4722d50a84e0ef5365df297ed6a4d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.494ex; height:3.843ex;" alt="{\displaystyle B{\overset {\underline {5}}{\longrightarrow }}D}" loading="lazy">

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy"> …

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<mover>

</munder>

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<mover>

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</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C{\overset {\underline {5}}{\longrightarrow }}D{\overset {6}{\longrightarrow }}A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/22775a29d0225ecdbcff573ccf17b03ecc5afdfd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.045ex; height:3.843ex;" alt="{\displaystyle C{\overset {\underline {5}}{\longrightarrow }}D{\overset {6}{\longrightarrow }}A}" loading="lazy">

</td>

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<mover>

</munder>

</mover>

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<mover>

</mover>

</mrow>

<mover>

</munder>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle C{\overset {\underline {5}}{\longrightarrow }}D{\overset {6}{\longrightarrow }}A{\overset {\underline {5}}{\longrightarrow }}B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/67f4aa5005904f6492b161090a708e0a1c1373f8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:18.614ex; height:3.843ex;" alt="{\displaystyle C{\overset {\underline {5}}{\longrightarrow }}D{\overset {6}{\longrightarrow }}A{\overset {\underline {5}}{\longrightarrow }}B}" loading="lazy">

</td>

</td>

<td>

<mover>

</munder>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C{\overset {\underline {5}}{\longrightarrow }}D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/60aba3b1f20592491bf11d6600cdaf1147ed5458.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.496ex; height:3.843ex;" alt="{\displaystyle C{\overset {\underline {5}}{\longrightarrow }}D}" loading="lazy">

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"> …

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<mover>

</munder>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle D{\overset {\underline {6}}{\longrightarrow }}A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1276038c553d1833ffa2812118458f482391a52a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.473ex; height:3.843ex;" alt="{\displaystyle D{\overset {\underline {6}}{\longrightarrow }}A}" loading="lazy">

</td>

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<mover>

</mover>

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<mover>

</munder>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D{\overset {6}{\longrightarrow }}A{\overset {\underline {5}}{\longrightarrow }}B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1316172652ff5101f0a86b846b1b16ded229ead9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.042ex; height:3.843ex;" alt="{\displaystyle D{\overset {6}{\longrightarrow }}A{\overset {\underline {5}}{\longrightarrow }}B}" loading="lazy">

</td>

<td>

<mover>

</mover>

</mrow>

<mover>

</munder>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D{\overset {6}{\longrightarrow }}A{\overset {\underline {5}}{\longrightarrow }}C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/56e41d066c18eef298f308fff870025d538b8903.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.045ex; height:3.843ex;" alt="{\displaystyle D{\overset {6}{\longrightarrow }}A{\overset {\underline {5}}{\longrightarrow }}C}" loading="lazy">

</td>

</td></tr></tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Die_Stärken_der_stärksten_Wege_2">Die Stärken der stärksten Wege</h4></div>

Das schwächste Glied der stärksten Verbindung wie oben gefunden, wird in eine Tabelle eingetragen. Dann wird wieder paarweise verglichen, wer wen schlägt, in der Tabelle unten wieder rot markiert. Violett markiert ist jeder Gleichstand.

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[\ast ,A]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/64543e94893b8fb7fcd6c455b050437e7efd901b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.492ex; height:2.843ex;" alt="{\displaystyle p[\ast ,A]}" loading="lazy">

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[\ast ,B]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bb52f6befa12a3cbb439f9c66a95f47f96bb665a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.513ex; height:2.843ex;" alt="{\displaystyle p[\ast ,B]}" loading="lazy">

</td>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[\ast ,C]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/54a7f8388d2513be26fa4776f99c62c7820a94ef.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.515ex; height:2.843ex;" alt="{\displaystyle p[\ast ,C]}" loading="lazy">

</td>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[\ast ,D]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e2713ac9b56506837d245fdaf8a8b5e3c922a942.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.673ex; height:2.843ex;" alt="{\displaystyle p[\ast ,D]}" loading="lazy">

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[A,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fce5d7fb73342e63b38107e1d5c6815c65866056.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.492ex; height:2.843ex;" alt="{\displaystyle p[A,\ast ]}" loading="lazy">

</td>

<td>5

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[B,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4968bf66785ab349f834dc9a249541b7f240231f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.513ex; height:2.843ex;" alt="{\displaystyle p[B,\ast ]}" loading="lazy">

</td>

<td style="background:#DBCAFE; color:#202122;">5

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[C,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e3b49c713f23c45dcd344fedc26b81b9e3dcf4e2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.515ex; height:2.843ex;" alt="{\displaystyle p[C,\ast ]}" loading="lazy">

</td>

<td style="background:#DBCAFE; color:#202122;">5

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[D,\ast ]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7e429092865c294b0a414cf5f96a28d8b2900a39.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:6.673ex; height:2.843ex;" alt="{\displaystyle p[D,\ast ]}" loading="lazy">

</td>

</td></tr></tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Ergebnis_2">Ergebnis</h4></div>

Potentielle Sieger nach der Schulze-Methode sind somit Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> und Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy">, da

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[B,X]\geq p[X,B]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/dcd5cf182826609851efd633c7b4858f72de3c17.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:17.67ex; height:2.843ex;" alt="{\displaystyle p[B,X]\geq p[X,B]}" loading="lazy"> ist für jeden anderen Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle X}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/68baa052181f707c662844a465bfeeb135e82bab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}" loading="lazy"> und</dd>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle p[D,Y]\geq p[Y,D]}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0f280c4aa8eb3b9c5008909e6db1fb9dd388b733.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:17.577ex; height:2.843ex;" alt="{\displaystyle p[D,Y]\geq p[Y,D]}" loading="lazy"> ist für jeden anderen Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Y}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/961d67d6b454b4df2301ac571808a3538b3a6d3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}" loading="lazy">.</dd></dl>

Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 7=p[B,C]>p[C,B]=5}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 7=p[B,C]>p[C,B]=5}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/783ea1b818fa1c7021dc3015f070c32f6c559d3f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.675ex; height:2.843ex;" alt="{\displaystyle 7=p[B,C]>p[C,B]=5}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/47136aad860d145f75f3eed3022df827cee94d7a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4fc55753007cd3c18576f7933f6f089196732029.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}" loading="lazy">.

Wegen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 6=p[D,A]>p[A,D]=5}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 6=p[D,A]>p[A,D]=5}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/713cae1404d14a749e93cb7cd7297001c27b9c0f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.949ex; height:2.843ex;" alt="{\displaystyle 6=p[D,A]>p[A,D]=5}" loading="lazy"> ist Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f34a0c600395e5d4345287e21fb26efd386990e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle D}" loading="lazy"> besser als Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy">.

Mögliche Schulze-Rankings sind somit

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B>C>D>A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/938577e6a260ba9941c2a5e99012ee3610df0c5a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.493ex; height:2.176ex;" alt="{\displaystyle B>C>D>A}" loading="lazy">,</li>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B>D>A>C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e66dcae781eb427019ffda763b19060c6f516c48.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.493ex; height:2.176ex;" alt="{\displaystyle B>D>A>C}" loading="lazy">,</li>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle B>D>C>A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/44bd97b1f8955776d8fad6cad3c946214f3d918a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.493ex; height:2.176ex;" alt="{\displaystyle B>D>C>A}" loading="lazy">,</li>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D>A>B>C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8df99ce8521298ec3d5f24665d77034140b85db7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.493ex; height:2.176ex;" alt="{\displaystyle D>A>B>C}" loading="lazy">,</li>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D>B>A>C}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/dcc0841cd00120471e466c9169867600d1b4829e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.493ex; height:2.176ex;" alt="{\displaystyle D>B>A>C}" loading="lazy"> und</li>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle D>B>C>A}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f291f923cee063ed8f6168598de16ab08b97d4cc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.493ex; height:2.176ex;" alt="{\displaystyle D>B>C>A}" loading="lazy">.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Implementierung">Implementierung</h2></div>

Sei <code>C</code> die Anzahl der Kandidaten. Dann lassen sich die Stärken der stärksten Wege mit Hilfe des <a href="Algorithmus_von_Floyd_und_Warshall" title="Algorithmus von Floyd und Warshall">Algorithmus von Floyd und Warshall</a> berechnen.

Input: <code>d[i,j]</code> ist die Anzahl der Wähler, die den Kandidaten <code>i</code> dem Kandidaten <code>j</code> strikt vorziehen.

Output: <code>p[i,j]</code> ist die Stärke des stärksten Weges vom Kandidaten <code>i</code> zum Kandidaten <code>j</code>.

<div class="mw-heading mw-heading3"><h3 id="Beispiel_einer_Implementierung_in_Pascal">Beispiel einer Implementierung in Pascal</h3></div>

<div class="mw-highlight mw-highlight-lang-pascal mw-content-ltr" dir="ltr"><pre>for i := 1 to C do

begin

for j := 1 to C do

begin

if ( i <> j ) then

begin

if ( d[i,j] > d[j,i] ) then

begin

p[i,j] := d[i,j]

end

else

begin

p[i,j] := 0

end

end

for i := 1 to C do

begin

for j := 1 to C do

begin

if ( i <> j ) then

begin

for k := 1 to C do

begin

if ( i <> k ) then

begin

if ( j <> k ) then

begin

p[j,k] := max ( p[j,k], min ( p[j,i], p[i,k] ) )

end

end

</pre></div>

<div class="mw-heading mw-heading2"><h2 id="Heuristiken_und_Eigenschaften">Heuristiken und Eigenschaften</h2></div>

Spezielle <a href="Heuristik" title="Heuristik">Heuristiken</a> der Schulze-Methode sind auch bekannt unter den Namen Beatpath, Beatpaths, Beatpath Method, Beatpath Winner, Path Voting, Path Winner, Schwartz Sequential Dropping (SSD) und Cloneproof Schwartz Sequential Dropping (CSSD).

Die Schulze-Methode erfüllt die folgenden Kriterien<a href="#cite_note-4">[4]</a><a href="#cite_note-5">[5]</a> (Zur Erläuterung der wichtigsten Kriterien siehe <a href="Sozialwahltheorie#Qualitätskriterien" title="Sozialwahltheorie">Abschnitt Qualitätskriterien</a> im Artikel Sozialwahltheorie):

<ol><li>Majority criterion</li>

<li>Mutual majority criterion</li>

<li>Monotonicity criterion (auch bezeichnet als non-negative responsiveness, mono-raise)</li>

<li>Pareto criterion</li>

<li><a href="Condorcet-Methode#Condorcet-Kriterium" title="Condorcet-Methode">Condorcet-Kriterium</a></li>

<li><a href="Condorcet-Methode#Condorcet-Verliererkriterium" title="Condorcet-Methode">Condorcet-Verlierer-Kriterium</a></li>

<li>Smith criterion (auch bezeichnet als Generalized Condorcet criterion)</li>

<li>Local independence from irrelevant alternatives</li>

<li><a href="Schwartz-Menge" title="Schwartz-Menge">Schwartz-Kriterium</a></li>

<li>Strategy-Free criterion</li>

<li>Generalized Strategy-Free criterion</li>

<li>Strong Defensive Strategy criterion</li>

<li>Weak Defensive Strategy criterion</li>

<li>Summability criterion</li>

<li>Independence of clones</li>

<li><a href="Arrow-Theorem" title="Arrow-Theorem">nicht-diktatorisch</a></li>

<li><a href="Arrow-Theorem" title="Arrow-Theorem">Universalität</a></li>

<li>Woodall’s plurality criterion</li>

<li>Woodall’s CDTT criterion</li>

<li>Minimal Defense criterion</li>

<li>Resolvability</li>

<li>Reversal symmetry</li>

<li>mono-append</li>

<li>mono-add-plump</li></ol>

Die Schulze-Methode verletzt

<ol><li>das <a href="Majority_Judgment#Konsistenzkriterium" title="Majority Judgment">Konsistenzkriterium</a>,</li>

<li>das Partizipationskriterium,</li>

<li>die Unabhängigkeit von irrelevanten Alternativen</li>

<li>sowie das Favorite-betrayal-Kriterium.</li></ol>

<div class="mw-heading mw-heading2"><h2 id="Anwendungen">Anwendungen</h2></div>

Die Schulze-Methode wird derzeit nicht in staatlichen Wahlen angewandt. Sie findet jedoch mehr und mehr Anwendung in Privatorganisationen. Sie ist u. a. in folgenden Organisationen benutzt worden:

<ul><li><a href="Wikimedia" class="mw-redirect" title="Wikimedia">Wikimedia Foundation</a><a href="#cite_note-6">[6]</a></li>

<li><a href="Piratenpartei_Deutschland" title="Piratenpartei Deutschland">Piratenpartei Deutschland</a><a href="#cite_note-7">[7]</a></li>

<li><a href="Piratpartiet" title="Piratpartiet">Piratenpartei Schweden</a><a href="#cite_note-8">[8]</a></li>

<li><a href="Piratenpartei_%C3%96sterreichs" title="Piratenpartei Österreichs">Piratenpartei Österreichs</a><a href="#cite_note-9">[9]</a></li>

<li><a href="Debian" title="Debian">Debian</a><a href="#cite_note-10">[10]</a></li>

<li><a href="Ubuntu_(Betriebssystem)" title="Ubuntu (Betriebssystem)">Ubuntu</a><a href="#cite_note-11">[11]</a></li>

<li><a href="Software_in_the_Public_Interest" title="Software in the Public Interest">Software in the Public Interest</a><a href="#cite_note-12">[12]</a></li>

<li><a href="Gentoo_Linux" title="Gentoo Linux">Gentoo Foundation</a></li>

<li><a href="Sender_Policy_Framework" title="Sender Policy Framework">Sender Policy Framework</a><a href="#cite_note-13">[13]</a></li>

<li><a href="Free_Software_Foundation_Europe" title="Free Software Foundation Europe">Free Software Foundation Europe (FSFE)</a><a href="#cite_note-14">[14]</a></li>

<li>Kingman Hall<a href="#cite_note-16">[16]</a></li>

<li>TopCoder</li>

<li><a href="GNU_Privacy_Guard" title="GNU Privacy Guard">GNU Privacy Guard</a><a href="#cite_note-17">[17]</a></li>

<li>Golden Geek Award<a href="#cite_note-18">[18]</a></li>

<li>Studierendenrat der <a href="Albert-Ludwigs-Universit%C3%A4t_Freiburg" title="Albert-Ludwigs-Universität Freiburg">Albert-Ludwigs-Universität Freiburg</a><a href="#cite_note-19">[19]</a></li>

<li><a href="Berufsverband_der_Kinder-_und_Jugend%C3%A4rzte" title="Berufsverband der Kinder- und Jugendärzte">Berufsverband der Kinder- und Jugendärzte</a><a href="#cite_note-20">[20]</a></li>

<li><a href="Deutsche_Sch%C3%BClerAkademie#Alumniorganisation" title="Deutsche SchülerAkademie">Club der Ehemaligen der Deutschen SchülerAkademien e. V.</a><a href="#cite_note-21">[21]</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Siehe_auch">Siehe auch</h2></div>

<ul><li><a href="Ranked_Pairs" title="Ranked Pairs">Ranked Pairs</a></li>

<li><a href="Sozialwahltheorie" title="Sozialwahltheorie">Sozialwahltheorie</a></li>

<li><a href="Condorcet-Paradoxon" title="Condorcet-Paradoxon">Condorcet-Paradoxon</a></li>

<li><a href="LiquidFeedback" title="LiquidFeedback">LiquidFeedback</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>

<ul><li>Christoph Börgers: <a rel="nofollow" class="external text" href="http://books.google.de/books?id=dccBaphP1G4C&pg=PA37">Mathematics of Social Choice: Voting, Compensation, and Division.</a> SIAM 2009, ISBN 0-89871-695-0.</li>

<li>Saul Stahl, Paul E. Johnson: <a rel="nofollow" class="external text" href="http://books.google.de/books?id=CMLL9sVGLb8C&pg=PA119">Understanding Modern Mathematics.</a> Jones & Bartlett Publishing, London u. a. 2007, ISBN 0-7637-3401-2, S. 119 ff.</li>

<li><a href="Nicolaus_Tideman" title="Nicolaus Tideman">Nicolaus Tideman</a>: <a rel="nofollow" class="external text" href="http://books.google.de/books?id=RN5q_LuByUoC&pg=PA228">Collective Decisions and Voting: The Potential for Public Choice.</a> Ashgate Publishing, 2006, ISBN 0-7546-4717-X, S. 228 ff.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>

<div class="sisterproject" style="margin:0.1em 0 0 0;"><div class="noresize noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"></div><a class="external text" href="https://commons.wikimedia.org/wiki/Schulze_method?uselang=de">Commons: Schulze method</a> – Album mit Bildern, Videos und Audiodateien</div>

<ul><li>Rosa Camps, Xavier Mora, Laia Saumell: <a rel="nofollow" class="external text" href="http://mat.uab.cat/~xmora/articles/crating.pdf">A Continuous Rating Method for Preferential Voting.</a> (PDF; 1,76 MB)</li>

<li>Paul E. Johnson: <a rel="nofollow" class="external text" href="http://pj.freefaculty.org/Ukraine/PJ3_VotingSystemsEssay.pdf">Voting Systems.</a> (PDF; 324 kB)</li>

<li>Rob LeGrand: <a rel="nofollow" class="external text" href="https://rob-legrand.github.io/ranked-ballot-voting-calculator/old/desc.html">Descriptions of ranked-ballot voting methods.</a></li>

<li>Rob Loring: <a rel="nofollow" class="external text" href="http://accuratedemocracy.com/voting_rules.htm">Accurate Democracy.</a></li>

<li>James D. McCaffrey: <a rel="nofollow" class="external text" href="http://msdn.microsoft.com/de-de/magazine/dd148646.aspx">Testlauf: Gruppenentscheidungen bei Softwaretests.</a> MSDN</li>

<li>Tommi Meskanen, Hannu Nurmi: <a rel="nofollow" class="external text" href="https://www.researchgate.net/profile/Hannu_Nurmi/publication/31597053_Distance_from_Consensus_A_Theme_and_Variations/links/09e415085728bc86ba000000/Distance-from-Consensus-A-Theme-and-Variations.pdf">Distance from Consensus: a Theme and Variations.</a> (PDF; 170 kB) In: Bruno Simeone, Friedrich Pukelsheim (Hrsg.): Mathematics and democracy: recent advances in voting systems and collective choice. Studies in choice and welfare. Springer, Berlin u. a. 2006, ISBN 3-540-35603-7, S. 117–132, hier S. 120 ff.</li>

<li>Massimo Narizzano, Luca Pulina, Armando Tacchella: <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/221153297_Ranking_and_Reputation_Systems_in_the_QBF_Competition">Ranking and Reputation Systems in the QBF Competition.</a> (PDF; 455 kB) In: AI*IA ’07 Proceedings of the 10th Congress of the Italian Association for Artificial Intelligence on AI*IA 2007: Artificial Intelligence and Human-Oriented Computing. Springer, Berlin / Heidelberg 2007, ISBN 978-3-540-74781-9.</li>

<li>Markus Schulze: <a rel="nofollow" class="external text" href="https://arxiv.org/pdf/1804.02973.pdf">Schulze-Methode FAQ</a></li>

<li>Markus Schulze: <a rel="nofollow" class="external text" href="http://www.votingmatters.org.uk/ISSUE17/I17P3.PDF">A New Monotonic and Clone-Independent Single-Winner Election Method.</a> (PDF; 74 kB) In: Voting Matters, 17, 2003, S. 9–19.</li>

<li>Kevin Venzke: <a rel="nofollow" class="external text" href="http://nodesiege.tripod.com/elections/">Election Methods and Criteria.</a></li>

<li>Jochen Voss: <a rel="nofollow" class="external text" href="https://www.seehuhn.de/pages/vote.html">The Debian Voting System.</a></li>

<li>Barry Wright: <a rel="nofollow" class="external text" href="https://services.math.duke.edu/~bray/Courses/49s/Senior%20Theses/Barry%20Wright/Barry%20Wright%27s%20Thesis.pdf">Objective Measures of Preferential Ballot Voting Systems.</a> (PDF; 289 kB) Abschlussarbeit Duke University, Durham NC 2009.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>

<li id="cite_note-1"><a href="#cite_ref-1">↑</a> <a rel="nofollow" class="external text" href="http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-October/001570.html">Condorcet sub-cycle rule</a>, Election-Methods-Mailingliste, 3. Oktober 1997

</li>

<li id="cite_note-2"><a href="#cite_ref-2">↑</a> Markus Schulze: <a rel="nofollow" class="external text" href="http://www.votingmatters.org.uk/ISSUE17/I17P3.PDF">A new monotonic and clone-independent single-winner election method.</a> (PDF; 75 kB) In: Voting Matters, issue 17, 2003, S. 9–19

</li>

<li id="cite_note-3"><a href="#cite_ref-3">↑</a> Nicolaus Tideman: Collective Decisions and Voting: The Potential for Public Choice. Ashgate Publishing, 2006. Saul Stahl, Paul E. Johnson: Understanding Modern Mathematics. Jones & Bartlett Publishing, 2006

</li>

<li id="cite_note-4"><a href="#cite_ref-4">↑</a> Markus Schulze: <a rel="nofollow" class="external text" href="http://m-schulze.9mail.de/schulze1.pdf">A new monotonic, clone-independent, reversal symmetric, and Condorcet-consistent single-winner election method.</a> (PDF; 1,4 MB) Juli 2007 (englisch)

</li>

<li id="cite_note-5"><a href="#cite_ref-5">↑</a> D. R. Woodall: <a rel="nofollow" class="external text" href="http://www.votingmatters.org.uk/ISSUE3/P5.HTM">Properties of Preferential Election Rules.</a> Dezember 1994 (englisch)

</li>

<li id="cite_note-6"><a href="#cite_ref-6">↑</a> <a class="external text" href="https://lists.wikimedia.org/pipermail/foundation-l/2008-May/043134.html">Board election to use preference voting, Mai 2008</a>

</li>

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</style><a class="external text" href="https://redirecter.toolforge.org/?url=http%3A%2F%2Fbremen.piratenpartei.de%2FBlog%2F2010-8-13%2Fpiraten-starten-grossversuch-zu-direkter-demokratie%2F">Originals</a> vom 29. Mai 2011 im <a href="Internet_Archive" title="Internet Archive">Internet Archive</a>)  Info: Der Archivlink wurde automatisch eingesetzt und noch nicht geprüft. Bitte prüfe Original- und Archivlink gemäß Anleitung und entferne dann diesen Hinweis.<a rel="nofollow" class="external text" href="http://IABotmemento.invalid/http://bremen.piratenpartei.de/Blog/2010-8-13/piraten-starten-grossversuch-zu-direkter-demokratie/">@1</a><a rel="nofollow" class="external text" href="http://bremen.piratenpartei.de/Blog/2010-8-13/piraten-starten-grossversuch-zu-direkter-demokratie/">@2</a>Vorlage:Webachiv/IABot/bremen.piratenpartei.de, August 2010

</li>

<li id="cite_note-8"><a href="#cite_ref-8">↑</a> <a rel="nofollow" class="external text" href="http://viktualiebrodern.wordpress.com/2010/01/26/probewahl-der-schwedischen-piraten-ergebnis/">Probewahl der schwedischen Piraten</a>, Januar 2010

</li>

<li id="cite_note-9"><a href="#cite_ref-9">↑</a> <a rel="nofollow" class="external text" href="https://wiki.piratenpartei.at/wiki/BGV2013-01/Protokoll/Wahlergebnisse">wiki.piratenpartei.at</a>

</li>

<li id="cite_note-10"><a href="#cite_ref-10">↑</a> <a rel="nofollow" class="external text" href="http://www.debian.org/devel/constitution">Verfassung für das Debian-Projekt, Anhang A6</a>

</li>

<li id="cite_note-11"><a href="#cite_ref-11">↑</a> <a rel="nofollow" class="external text" href="https://lists.ubuntu.com/archives/ubuntu-irc/2012-May/001538.html">Ubuntu IRC Council Position</a>, Mai 2012

</li>

<li id="cite_note-12"><a href="#cite_ref-12">↑</a> <a rel="nofollow" class="external text" href="http://www.spi-inc.org/corporate/resolutions/2003/2003-01-06.wta.1/">Process for adding new board members, Januar 2003</a>

</li>

<li id="cite_note-13"><a href="#cite_ref-13">↑</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110716065154/http://www.openspf.org/Council_Election">Council Election Procedures</a> (<a href="Webarchivierung#Begrifflichkeiten" title="Webarchivierung">Memento</a> vom 16. Juli 2011 im <a href="Internet_Archive" title="Internet Archive">Internet Archive</a>)

</li>

<li id="cite_note-14"><a href="#cite_ref-14">↑</a> § 6 Absatz 3 der <a rel="nofollow" class="external text" href="http://www.fsfeurope.org/about/legal/Constitution.de.pdf">Satzung</a> (PDF; 112 kB)

</li>

<li id="cite_note-15"><a href="#cite_ref-15">↑</a> Artikel 3.4.1 der <a rel="nofollow" class="external text" href="http://ev.kde.org/rules/online_voting.php">Rules of Procedures for Online Voting</a>

</li>

<li id="cite_note-16"><a href="#cite_ref-16">↑</a> <a rel="nofollow" class="external text" href="http://zestyping.livejournal.com/111588.html">Kingman adopts Condorcet voting, April 2005</a>

</li>

<li id="cite_note-17"><a href="#cite_ref-17">↑</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20061216125859/http://logo-contest.gnupg.org/results.html">GnuPG Logo Vote, November 2006</a> (<a href="Webarchivierung#Begrifflichkeiten" title="Webarchivierung">Memento</a> des <a class="external text" href="https://redirecter.toolforge.org/?url=http%3A%2F%2Flogo-contest.gnupg.org%2Fresults.html">Originals</a> vom 16. Dezember 2006 im <a href="Internet_Archive" title="Internet Archive">Internet Archive</a>)  Info: Der Archivlink wurde automatisch eingesetzt und noch nicht geprüft. Bitte prüfe Original- und Archivlink gemäß Anleitung und entferne dann diesen Hinweis.<a rel="nofollow" class="external text" href="http://IABotmemento.invalid/http://logo-contest.gnupg.org/results.html">@1</a><a rel="nofollow" class="external text" href="http://logo-contest.gnupg.org/results.html">@2</a>Vorlage:Webachiv/IABot/logo-contest.gnupg.org

</li>

<li id="cite_note-18"><a href="#cite_ref-18">↑</a> <a rel="nofollow" class="external text" href="http://boardgamegeek.com/thread/851248/2012-golden-geek-awards-nominations-open-for-boa">Golden Geek Awards</a>

</li>

<li id="cite_note-19"><a href="#cite_ref-19">↑</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20250608044834/https:/www.stura.uni-freiburg.de/gremien/studierendenrat/go/at_download/file/Stura-GO_Stand_06_06_2019.pdf">Geschäftsordnung des Studierendenrats der Albert-Ludwigs-Universität Freiburg.</a> (PDF FDP; 55 kB) In: stura.uni-freiburg.de. 6. Juni 2019, abgerufen am 22. Mai 2025.<span style="display: none;" class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rfr_id=info%3Asid%2Fde.wikipedia.org%3ASchulze-Methode&rft.title=Gesch%C3%A4ftsordnung+des+Studierendenrats+der+Albert-Ludwigs-Universit%C3%A4t+Freiburg&rft.description=Gesch%C3%A4ftsordnung+des+Studierendenrats+der+Albert-Ludwigs-Universit%C3%A4t+Freiburg&rft.identifier=https%3A%2F%2Fweb.archive.org%2Fweb%2F20250608044834%2Fhttps%3A%2Fwww.stura.uni-freiburg.de%2Fgremien%2Fstudierendenrat%2Fgo%2Fat_download%2Ffile%2FStura-GO_Stand_06_06_2019.pdf&rft.date=2019-06-06">

</li>

<li id="cite_note-20"><a href="#cite_ref-20">↑</a> <a rel="nofollow" class="external text" href="http://www.bvkj.de/der-bvkj/satzung/">Satzung des BVKJ</a>

</li>

<li id="cite_note-21"><a href="#cite_ref-21">↑</a> <a rel="nofollow" class="external text" href="https://db.cde-ev.de/doc/Realm_Assembly_Voting-Details.html#id2">Voting Details</a>

</li>

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