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<title>Condorcet-Methode</title>

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

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Condorcet-Methoden (nach <a href="Marie_Jean_Antoine_Nicolas_Caritat%2C_Marquis_de_Condorcet" class="mw-redirect" title="Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet">Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet</a>) sind <a href="Pr%C3%A4ferenzwahl" title="Präferenzwahl">Präferenzwahlen</a>, bei denen ein Kandidat zumindest dann gewinnt, wenn er jedem anderen Kandidaten im direkten Vergleich vorgezogen wird.

Jeder Wähler ordnet die Kandidaten nach Rang, wobei mehrere Kandidaten auf demselben Rang möglich sind. Bei der Auswertung werden aus den Daten der Stimmabgaben Zweikämpfe simuliert, in denen jeder Kandidat gegen jeden anderen Kandidaten antritt. Dazu wird gezählt, wie oft ein Kandidat über seinem Gegner angeordnet ist. Wer jeden dieser Kämpfe gewinnt, ist Condorcet-Sieger.

Alle Condorcet-Methoden sind sich vollkommen einig über den Gewinner, wenn jemand Condorcet-Sieger ist. Sie unterscheiden sich darin, wen sie als Gewinner festlegen, wenn es keinen Condorcet-Sieger gibt.

Die <a href="Sozialwahltheorie" title="Sozialwahltheorie">Sozialwahltheorie</a> untersucht und vergleicht u. a. unterschiedliche Aggregationsverfahren und deren Probleme und Vorzüge.

Dabei wird die Möglichkeit von taktischem Abstimmungsverhalten der Wähler mit dem Ziel, das für einen selbst bestmögliche Wahlergebnis durchzusetzen, nicht berücksichtigt. („Zwar wäre mir Kandidat A am liebsten, aber da er keine Aussicht hat zu gewinnen, stimme ich für Kandidat B, der für mich der zweitbeste ist.“) Derartige Überlegungen können bei realen Abstimmungen nicht ausgeschlossen werden.

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

Gegeben sei eine Menge von Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K=\{k_{1},\dots ,k_{n}\}}">

<msub>

</mrow>

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</mrow>

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</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9cb5b1081bd31c222d417c0d179b8d0b49768378.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.363ex; height:2.843ex;" alt="{\displaystyle K=\{k_{1},\dots ,k_{n}\}}" loading="lazy">. Jeder teilnehmende Wähler <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"> bringt nun diese Kandidaten in eine Präferenz-Totalordnung <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leq _{X}}">

<msub>

</mrow>

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</mstyle>

</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/781e8e2efb254f21328c1997107169cc5f814166.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.44ex; height:2.343ex;" alt="{\displaystyle \leq _{X}}" loading="lazy">, d. h. gibt an, welche Kandidaten er welchen anderen gegenüber bevorzugt bzw. welche er gleich einstuft. Wie üblich wird <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\geq y}">

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</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/aded94d634c48071188bf96a76a4d3b7dfb28470.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.343ex;" alt="{\displaystyle x\geq y}" loading="lazy"> für <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y\leq x}">

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</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7de6a6e4f44d9dfcbfaadbdcf388d4b8a6fed109.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.343ex;" alt="{\displaystyle y\leq x}" loading="lazy"> geschrieben, sowie <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x<y}">

</mstyle>

</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/aeb239de6fee56ea8b6a65f7858d95b87632069f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.176ex;" alt="{\displaystyle x<y}" loading="lazy"> für <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\leq y}">

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</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c07a0bc023490be1c08e6c33a9cdc93bec908224.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.343ex;" alt="{\displaystyle x\leq y}" loading="lazy"> und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\neq y}">

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</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f51b711ca7f932963cdb268b0817dc72d6258733.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.584ex; height:2.676ex;" alt="{\displaystyle x\neq y}" loading="lazy"> und zuletzt <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x>y}">

</mstyle>

</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6e8432c5c4451b66818abae111d41f27d6de8623.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.176ex;" alt="{\displaystyle x>y}" loading="lazy"> für <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y<x}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4052851a7a0fd170365775f6fc8ad079d274ee55.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.176ex;" alt="{\displaystyle y<x}" loading="lazy">.

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

Ein Kandidat <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{i}}">

<msub>

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</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f29138ed3ad54ffce527daccadc49c520459b0b0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.011ex; height:2.509ex;" alt="{\displaystyle k_{i}}" loading="lazy"> wird einem Kandidaten <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{j}\neq k_{i}}">

<msub>

</mrow>

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<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle k_{j}\neq k_{i}}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f7f28cd0322bfe3eeee40ab0a80cf338a70af3cc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.23ex; height:2.843ex;" alt="{\displaystyle k_{j}\neq k_{i}}" loading="lazy"> gegenüber bevorzugt, falls es mehr Wähler <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"> gibt, für die <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{i}>_{X}k_{j}}">

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</mrow>

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</mstyle>

</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f003572dea46409f3333c2dc0318b6baa23f4392.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.863ex; height:2.843ex;" alt="{\displaystyle k_{i}>_{X}k_{j}}" loading="lazy"> ist als Wähler mit <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{i}<_{X}k_{j}}">

<msub>

</mrow>

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<msub>

</mrow>

</msub>

<msub>

</mrow>

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</mstyle>

</mrow>

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

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b52d43416b112fbcc54df45df3ffba273c5371f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.863ex; height:2.843ex;" alt="{\displaystyle k_{i}<_{X}k_{j}}" loading="lazy">, also falls

<dl><dd><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left|\{\,X\;|\;k_{i}>_{X}k_{j}\,\}\right|>\left|\{\,X\;|\;k_{i}<_{X}k_{j}\,\}\right|}">

<mrow>

<mrow>

</mrow>

<msub>

</mrow>

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<msub>

</mrow>

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<mrow>

<mrow>

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<msub>

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</mrow>

</msub>

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</mrow>

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</mrow>

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</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \left|\{\,X\;|\;k_{i}>_{X}k_{j}\,\}\right|>\left|\{\,X\;|\;k_{i}<_{X}k_{j}\,\}\right|}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ee543920f36fbc187366d5aab981208bd409c762.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:37.444ex; height:3.009ex;" alt="{\displaystyle \left|\{\,X\;|\;k_{i}>_{X}k_{j}\,\}\right|>\left|\{\,X\;|\;k_{i}<_{X}k_{j}\,\}\right|}" loading="lazy"></dd></dl>

gilt.

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

Wenn es einen Kandidaten gibt, der jeden anderen Kandidaten in einer paarweisen Abstimmung besiegt, wird dieser der Condorcet-Sieger genannt. (Einen solchen muss es nicht notwendigerweise geben, siehe unten.)

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

Wenn es einen Kandidaten gibt, dem gegenüber alle anderen Kandidaten bevorzugt werden, ist dieser der Condorcet-Verlierer. (Auch diesen muss es nicht notwendigerweise geben.)

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

Ein Wahlverfahren (allgemein) erfüllt das Condorcet-Kriterium, wenn in den Fällen, wo es einen Condorcet-Sieger gibt, dieser auch Wahlsieger ist.

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

Ein Wahlverfahren (allgemein) erfüllt das Condorcet-Verliererkriterium, falls in den Fällen, in denen es einen Condorcet-Verlierer gibt, dieser sicher nicht gewählt wird.

<div class="mw-heading mw-heading2"><h2 id="Allgemeines_Beispiel_bei_drei_Kandidaten">Allgemeines Beispiel bei drei Kandidaten</h2></div>

Es gebe die drei Kandidaten oder Optionen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

</mrow>

<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">, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}">

</mstyle>

</mrow>

<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"> und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}">

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</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">. Die Wähler müssen nun eine Präferenzliste angeben. Das Wahlergebnis sei:

<th>1

</th>

</mstyle>

</mrow>

<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">

</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>

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</mrow>

<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">

</td>

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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">

</td>

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</mrow>

<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">

</td>

</mstyle>

</mrow>

<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">

</td></tr>

<tr>

<th>2

</th>

</mstyle>

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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">

</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>

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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">

</td>

</mstyle>

</mrow>

<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">

</td>

</mstyle>

</mrow>

<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">

</td></tr>

<tr>

<th>3

</th>

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</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>

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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">

</td>

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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">

</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 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 u}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}" loading="lazy">

</th>

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e07b00e7fc0847fbd16391c778d65bc25c452597.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}" loading="lazy">

</th>

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}" loading="lazy">

</th>

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/87f9e315fd7e2ba406057a97300593c4802b53e4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" loading="lazy">

</th>

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b8a6208ec717213d4317e666f1ae872e00620a0d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" loading="lazy">

</th>

</mstyle>

</mrow>

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

</semantics>

</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">

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

Also: <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}" loading="lazy"> Personen wollten <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"> lieber als <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 <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"> lieber als <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">, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e07b00e7fc0847fbd16391c778d65bc25c452597.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}" loading="lazy"> Personen haben die Präferenzliste <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A>C>B}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2ae75b9e582edc703e7efd4bbbd1be85ac0a964d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.47ex; height:2.176ex;" alt="{\displaystyle A>C>B}" loading="lazy">, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}" loading="lazy"> Personen wollen <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B>A>C}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fd0f3336c97405a897a497fe4e3caac368bf9759.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.47ex; height:2.176ex;" alt="{\displaystyle B>A>C}" loading="lazy"> und so weiter. Dann ist <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"> genau dann Sieger, wenn:

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle u+v+y>w+x+z}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/87e504d47fc5214aa6ca4a98cd702c526bd8efa8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.155ex; height:2.343ex;" alt="{\displaystyle u+v+y>w+x+z}" loading="lazy">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle u+v+w>x+y+z}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f5b307ec1f9422d58f9204878b6b20ba16f4ba36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.155ex; height:2.343ex;" alt="{\displaystyle u+v+w>x+y+z}" loading="lazy">.</dd></dl>

Die erste <a href="Ungleichung" title="Ungleichung">Ungleichung</a> heißt, dass <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"> gegenüber <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"> bevorzugt wird (denn <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}" loading="lazy">, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e07b00e7fc0847fbd16391c778d65bc25c452597.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}" loading="lazy"> und <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/b8a6208ec717213d4317e666f1ae872e00620a0d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" loading="lazy"> werten <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"> vor <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">, die anderen nicht), die zweite besagt, dass <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"> auch <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"> schlägt.

Wenn zum Beispiel <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u=5}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7d4b46d77400b9dc9fb8b261c8250f329267406f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.591ex; height:2.176ex;" alt="{\displaystyle u=5}" loading="lazy">, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=3}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/17e2b0628eaafa5ee70f2f79e52006c4788049bf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.389ex; height:2.176ex;" alt="{\displaystyle v=3}" loading="lazy">, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w=2}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/79829ff5e0566f20aebb3a56955e308fb768aa65.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.925ex; height:2.176ex;" alt="{\displaystyle w=2}" loading="lazy"> und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=y=z=1}">

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/584efd316f44e0edb556b01e89840997cb940426.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.031ex; height:2.509ex;" alt="{\displaystyle x=y=z=1}" loading="lazy"> wären, wäre <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"> Sieger, denn

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 9>4}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9831bb4771198188c632802dcfbe20b894037004.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.423ex; height:2.176ex;" alt="{\displaystyle 9>4}" loading="lazy">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 9}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/32d3d1e1f9dfe0254c628379e69a69711fe4eabd.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 9}" loading="lazy"> Leute sehen <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"> vor <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">, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 4}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/295b4bf1de7cd3500e740e0f4f0635db22d87b42.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 4}" loading="lazy"> sehen <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"> vor <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">) und</dd></dl></dd>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 10>3}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5ce8c87d3cc1081e6ac06e4acd0512b35deffab9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.586ex; height:2.176ex;" alt="{\displaystyle 10>3}" loading="lazy">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 10}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4ec811eb07dcac7ea67b413c5665390a1671ecb0.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 10}" loading="lazy"> Leute sehen <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"> vor <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">, nur <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3}">

</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"> sehen <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"> vor <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">).</dd></dl></dd></dl>

Für den Fall, dass <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u=x=y>0}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle u=x=y>0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/23afe9bd767368279ef01972a10f97c2fc381018.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.273ex; height:2.509ex;" alt="{\displaystyle u=x=y>0}" loading="lazy"> und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=w=z=0}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v=w=z=0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a25c9db2afbdec99ebb4229b1cd8ece5f34abc5a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.338ex; height:2.176ex;" alt="{\displaystyle v=w=z=0}" loading="lazy">, ergibt sich das <a href="Condorcet-Paradoxon" title="Condorcet-Paradoxon">Condorcet-Paradoxon</a>.

<div class="mw-heading mw-heading2"><h2 id="Paradoxe_Eigenheiten">Paradoxe Eigenheiten</h2></div>

Es ist möglich, dass sich sowohl jeweils eine Mehrheit findet, die 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"> gegenüber <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"> bevorzugt, sowie <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"> gegenüber <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"> als auch <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"> 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">. Diese „zyklische Mehrheit“ nennt man das <a href="Condorcet-Paradoxon" title="Condorcet-Paradoxon">Condorcet-Paradoxon</a>. Condorcet-Verteidiger führen an, dass dieser Widerspruch nicht aus einem Defekt der Wahlmethode resultiert, sondern dass Condorcet lediglich real existierende, sich verschieden zusammensetzende (und damit gar nicht so paradoxe) Mehrheiten aufzeigt.

Ein weiterer der Intuition widersprechender Aspekt ist die geringe Wichtigkeit der Erstwahl im Vergleich mit einer anderen Ranglistenmethode, <a href="Instant-Runoff-Voting" class="mw-redirect" title="Instant-Runoff-Voting">Instant-Runoff-Voting</a> (IRV). Es ist durchaus möglich, dass der Condorcet-Sieger von niemandem auf den ersten Platz gewählt wurde.

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

Es gebe <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 100}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 100}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0572cd017c6d7936a12737c9d614a2f801f94a36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.487ex; height:2.176ex;" alt="{\displaystyle 100}" loading="lazy"> Wähler und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3}">

</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"> Kandidaten <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">, <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 <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">.

<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 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></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 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 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 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 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 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 40}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/686d435c2512a705c6680b84e9d172f259941f7a.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 40}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2aae8864a3c1fec9585261791a809ddec1489950.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 0}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2aae8864a3c1fec9585261791a809ddec1489950.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 0}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 35}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2d9e1349d41046b756a2984168e74dec26cdcf2a.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 35}" loading="lazy">

</th>

</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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2aae8864a3c1fec9585261791a809ddec1489950.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 0}" loading="lazy">

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

Der Vergleich von Kandidatenpaaren:

</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 über <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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 65>35}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/513f5104d68b6ba223051e512b3869169e879b55.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 65>35}" 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"> bevorzugt 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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 75>25}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/932eb59de8b35bd4d3204a16aaf891b6254c439d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 75>25}" 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"> bevorzugt über <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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 60>40}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4efd67e7eb55529ea734a40ba6830293e09c7cc1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 60>40}" loading="lazy">

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

Ein Condorcet-Paradoxon. Da der Sieg von <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"> über <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"> am unspektakulärsten ist, bietet sich an, diesen zu ignorieren. Dann ist <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"> der Sieger.

Wenn ein Kandidat über die Hälfte Erstplatzierungen erhält, gewinnt dieser auch jeden Zweikampf. Wenn dem Wähler erlaubt ist, mehreren Kandidaten denselben Rang zu geben (und Condorcet-Fürsprecher treten dafür ein) und es mehrere Kandidaten mit über die Hälfte der Erstplatzierungen gibt, kommt der Sieger aus ebendieser Gruppe. Aber es ist dann nicht unbedingt der mit den meisten Erstplatzierungen, wie folgendes Beispiel mit <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 100}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 100}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0572cd017c6d7936a12737c9d614a2f801f94a36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.487ex; height:2.176ex;" alt="{\displaystyle 100}" loading="lazy"> Wählern und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3}">

</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"> Kandidaten <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">, <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 <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"> zeigt:

<th>1

</th>

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/96c3298ea9aa77c226be56a7d8515baaa517b90b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.541ex; height:2.509ex;" alt="{\displaystyle A,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>

</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></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 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>

</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></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 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 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 60}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5cef1e5bbfe2c0fea5bd36788b3970ff98b9617c.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 60}" loading="lazy">

</th>

</mstyle>

</mrow>

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

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/92d98b82a3778f043108d4e20960a9193df57cbf.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 1}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2aae8864a3c1fec9585261791a809ddec1489950.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 0}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2aae8864a3c1fec9585261791a809ddec1489950.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 0}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 0}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2aae8864a3c1fec9585261791a809ddec1489950.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 0}" loading="lazy">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 39}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7c7989bcad346b9bcc5df585eb98363b34265a8c.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 39}" loading="lazy">

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

Der Vergleich von Kandidatenpaaren:

</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 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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 61>39}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2403aeda6e67007317c3f65dc2c662e5097235c3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 61>39}" 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"> bevorzugt 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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 60>40}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4efd67e7eb55529ea734a40ba6830293e09c7cc1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 60>40}" 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"> bevorzugt über <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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 39>1}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9437fc629e003da04fc9364d0549ca877717e017.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.586ex; height:2.176ex;" alt="{\displaystyle 39>1}" loading="lazy">

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

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"> wird zweimal über andere Optionen bevorzugt und gewinnt. Das liegt daran, dass Gleichplatzierungen im Prinzip wie Enthaltungen gewertet werden.

Wenn kein Kandidat mehr als die Hälfte der Erstplatzierungen erreicht, kann auch jemand ohne eine einzige Erstplatzierung zum Sieger werden. Ein besonders drastisches Beispiel mit <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 100}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 100}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0572cd017c6d7936a12737c9d614a2f801f94a36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.487ex; height:2.176ex;" alt="{\displaystyle 100}" loading="lazy"> Wählern und <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 4}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/295b4bf1de7cd3500e740e0f4f0635db22d87b42.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 4}" loading="lazy"> Kandidaten <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">, <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">, <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"> und <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">:

<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 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>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 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 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>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 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 49}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4e854adb3d39762b45aea9e0b4df5188127c7a74.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 49}" loading="lazy">

</th>

</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">

</th>

</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">

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

Von den <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4!=24}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 4!=24}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6b31e59bf87c098f00b2c9aad48fe5f85fc86263.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.233ex; height:2.176ex;" alt="{\displaystyle 4!=24}" loading="lazy"> möglichen Wahlentscheidungen werden hier nur die gezeigt, die Wählerstimmen erhalten. Der Vergleich von Kandidatenpaaren ergibt:

</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"> bevorzugt über <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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 51>49}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/030bd3deeed572a6a7e5769587e3aa48b5db8b8a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 51>49}" 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"> bevorzugt über <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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 51>49}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/030bd3deeed572a6a7e5769587e3aa48b5db8b8a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 51>49}" 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"> bevorzugt über <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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 51>49}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/030bd3deeed572a6a7e5769587e3aa48b5db8b8a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 51>49}" 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"> bevorzugt 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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 74>26}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/275d0d20e2ac759e547b3bec128833bf9a2acb55.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 74>26}" 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"> bevorzugt 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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 75>25}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/932eb59de8b35bd4d3204a16aaf891b6254c439d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 75>25}" 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"> bevorzugt 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">

</th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 75>25}</annotation>

</semantics>

</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/932eb59de8b35bd4d3204a16aaf891b6254c439d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.748ex; height:2.176ex;" alt="{\displaystyle 75>25}" loading="lazy">

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

</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"> gewinnt jedes Duell. <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

</mstyle>

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<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"> verliert jedes Duell.

Diese im Vergleich zu IRV sehr geringe Gewichtung der Erstplatzierungen bedeutet, dass der Wähler einem deutlich geringeren Druck ausgesetzt ist, einen Kompromiss mit guten Chancen über einen Favoriten mit schlechten Chancen zu stellen (geringer <a href="Spoilereffekt" title="Spoilereffekt">Spoilereffekt</a>).

<div class="mw-heading mw-heading2"><h2 id="Verschiedene_Condorcet-Methoden">Verschiedene Condorcet-Methoden</h2></div>

Die derzeit am weitesten verbreitete Condorcet-Methode ist die <a href="Schulze-Methode" title="Schulze-Methode">Schulze-Methode</a>. Sie wird unter anderem von der <a href="Piratenpartei_Deutschland" title="Piratenpartei Deutschland">Piratenpartei Deutschland</a>, <a href="Debian" title="Debian">Debian</a>, <a href="Gentoo_Linux" title="Gentoo Linux">Gentoo</a>, <a href="Software_in_the_Public_Interest" title="Software in the Public Interest">Software in the Public Interest (SPI)</a> und <a href="Sender_Policy_Framework" title="Sender Policy Framework">Sender Policy Framework (SPF)</a> benutzt.

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

<ul><li><a rel="nofollow" class="external text" href="https://citizensassembly.arts.ubc.ca/resources/submissions/csharman-10_0409201706-143.pdf">A New Monotonic and Clone-Independent Single-Winner Election Method.</a> (PDF; 601 kB)</li>

<li><a rel="nofollow" class="external text" href="https://www.wahlrecht.de/lexikon/condorcet.html">Condorcet-Paradoxon, Condorcet-Sieger und Condorcet-Verfahren</a> bei <a href="Wahlrecht.de" title="Wahlrecht.de">Wahlrecht.de</a></li></ul></div><div><div class="zim-footer">

Dieser Artikel wurde von <a class="external text" title="Zuletzt bearbeitet am 2025-03-02" href="https://de.wikipedia.org/wiki/?title=Condorcet-Methode&oldid=253813958">Wikipedia</a> herausgegeben. Der Text ist unter <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.de">Creative Commons Attribution-Share Alike 4.0</a> verfügbar, sofern nicht anders angegeben. Für die Mediendateien können zusätzliche Bedingungen gelten.

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