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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Monoculture (computer science)</span></span>

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<p>In <a href="Computer_science" title="Computer science">computer science</a>, a <b>monoculture</b> is a community of <a href="Computers" class="mw-redirect" title="Computers">computers</a> that all run identical software. All the computer systems in the community thus have the same vulnerabilities, and, like agricultural <a href="Monoculture" title="Monoculture">monocultures</a>, are subject to catastrophic failure in the event of a successful attack.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

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

<p>With the global trend of increased usage and reliance on computerized systems, some vendors supply solutions that are used throughout the industry (such as <a href="Microsoft_Windows" title="Microsoft Windows">Microsoft Windows</a>) - this forms algorithmic monocultures. Monocultures form naturally since they utilize <a href="Economies_of_scale" title="Economies of scale">economies of scale</a>, where it is cheaper to manufacture and distribute a single solution - savings that are typically passed on to end-users. Furthermore, by being used by a large community means that bugs are typically discovered and addressed faster.

</p><p>Like <a href="Monoculture#Risks" title="Monoculture">agricultural monocultures</a>, algorithmic monocultures are not diverse, thus susceptible to correlated failures - a failure of many parts participating in the monoculture. In complete non-monocultures, where the outcome of all components are mutually <a href="Independence_(probability_theory)" title="Independence (probability theory)">independent</a>, thus un-correlated. The chance of catastrophic event (failure of all the parts in the monoculture) is the multiplication of each component failure probability (exponentially decreasing).

</p><p>On the other end, perfect monocultures are completely correlated, thus have a single point of failure. This means that the chance of a catastrophic event is typically higher, as a failure of a single component can have widespread ramifications.

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

<p>Since <a href="Operating_system" title="Operating system">operating systems</a> are used in almost every workstation, they form monocultures. For example, <a href="Dan_Geer" title="Dan Geer">Dan Geer</a> has argued that <a href="Microsoft" title="Microsoft">Microsoft</a> is a monoculture, since a majority of the overall number of workstations connected to the Internet are running versions of the <a href="Microsoft_Windows" title="Microsoft Windows">Microsoft Windows</a> operating system, many of which are vulnerable to the same attacks.

</p><p>Large monocultures can also arise from <a href="Library_(computing)" title="Library (computing)">software libraries</a>, for example the <a href="Log4Shell" title="Log4Shell">Log4Shell</a> exploit in the popular Log4j library estimated to affect hundreds of millions of devices.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Individual_level_concerns">Individual level concerns</h2></div>

<p>The concept is significant when discussing <a href="Computer_security" title="Computer security">computer security</a> and <a href="Computer_virus" title="Computer virus">viruses</a>, the main threat is exposure to security vulnerabilities. Since monocultures are not diverse, any vulnerability found exists in all the individual members of the monoculture increasing the risk of exploitation.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> An example to that is <a href="Patch_Tuesday#Exploit_Wednesday" title="Patch Tuesday">exploit Wednesday</a> in which after <a href="Windows" class="mw-redirect" title="Windows">Windows</a> security patches are released there is an increase exploitation events on not updated machines.

</p><p><a href="Clifford_Stoll" title="Clifford Stoll">Clifford Stoll</a> wrote in 1989 after dealing with the <a href="Morris_worm" title="Morris worm">Morris worm</a>:<sup id="cite_ref-stoll1989_4-0" class="reference"><a href="#cite_note-stoll1989-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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</style><blockquote class="templatequote"><p>A computer virus is specialized: a virus that works on an <a href="IBM_PC" class="mw-redirect" title="IBM PC">IBM PC</a> cannot do anything to a <a href="Macintosh" class="mw-redirect" title="Macintosh">Macintosh</a> or a <a href="Unix" title="Unix">Unix</a> computer. Similarly, the <a href="Arpanet" class="mw-redirect" title="Arpanet">Arpanet</a> virus could only strike at systems running <a href="Berkeley_Unix" class="mw-redirect" title="Berkeley Unix">Berkeley Unix</a>. Computers running other operating systems—like <a href="AT%26T_Unix" class="mw-redirect" title="AT&T Unix">AT&T Unix</a>, <a href="OpenVMS" title="OpenVMS">VMS</a>, or <a href="DOS" title="DOS">DOS</a>—were totally immune.

</p><p>Diversity, then, works against viruses. If all the systems on the Arpanet ran Berkeley Unix, the virus would have disabled all fifty thousand of them. Instead, it infected only a couple thousand. Biological viruses are just as specialized: we can't catch the flu from dogs.

</p><p>

Bureaucrats and managers will forever urge us to standardize on a single type of system: "Let's only use Sun workstations" or "Only buy IBM systems." Yet somehow our communities of computers are a diverse population—with <a href="Data_General" title="Data General">Data General</a> machines sitting next to <a href="VAX" title="VAX">Digital Vaxes</a>; IBMs connected to <a href="Sony#Computing" title="Sony">Sonys</a>. Like our neighborhoods, electronic communities thrive through diversity.</p></blockquote>

<p>Another main concern is increased spread of <a href="Algorithmic_bias" title="Algorithmic bias">algorithmic bias</a>. In the light of increased usage of <a href="Machine_learning" title="Machine learning">machine learning</a> there is a growing awareness of the biases introduced by algorithms. The nature of monocultures exacerbate this problem since it makes the bias systemic and spreading unfair decisions.

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<div class="mw-heading mw-heading2"><h2 id="Social_level_concerns">Social level concerns</h2></div>

<p>Monocultures may lead to <a href="Braess's_paradox" class="mw-redirect" title="Braess's paradox">Braess's</a> like paradoxes in which introducing a "better option" (such as a more accurate algorithm) leads to suboptimal monocultural convergence - a monoculture whose correlated nature results in degraded overall quality of the decisions. Since monocultures form in areas of high-stakes decisions such as credit scoring and automated hiring, it is important to achieve optimal decision making.

</p><p>This scenario can be studied through the lens of <a href="Mechanism_design" title="Mechanism design">mechanism design</a>, in which agents are choosing between a set of algorithms, some of which return correlated outputs. The overall impact of the decision making is measured by <a href="Social_welfare" class="mw-redirect" title="Social welfare">social welfare</a>.

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<div class="mw-heading mw-heading3"><h3 id="Suboptimal_monocultures_convergence_in_automated_hiring">Suboptimal monocultures convergence in automated hiring</h3></div>

<p>This section demonstrates the concern of suboptimal monoculture convergence using automated hiring as a case study. Hiring is the process of ranking a group of candidates and hiring the top-valued. In recent years <a href="Artificial_intelligence_in_hiring#Interviews" title="Artificial intelligence in hiring">automated hiring</a> (automatically ranking candidates based on their interaction with an AI powered system) became popular.

</p><p>As shown by <a href="Jon_Kleinberg" title="Jon Kleinberg">Kleinberg</a>,<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> under some assumptions, suboptimal automated hiring monocultures naturally form, namely, choosing the correlated algorithm is a <a href="Dominant_strategy" class="mw-redirect" title="Dominant strategy">dominant strategy</a>, thus converging to monoculture that leads suboptimal social welfare.

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

<p>In this scenario we will consider two firms and a group <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}">

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

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</math></span><img src="./4611d85173cd3b508e67077d4a1252c9c05abca2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}" loading="lazy"></span> of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">

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

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</math></span><img src="./a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span> candidate with hidden utilities of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}}">

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

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</math></span><img src="./e87000dd6142b81d041896a30fe58f0c3acb2158.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle x_{i}}" loading="lazy"></span>. For hiring process - each firm will produce a noisy-ranking of the candidates, then each firm (in a random order) hires the first available candidate in their ranking. Each firm can choose to use either an independent human rankers or use a common algorithmic ranking.

</p><p>The ranking algorithm <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}_{\theta }}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}_{\theta }}</annotation>

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</math></span><img src="./3196c71bb72ce23cf8cdb17be6b49ba04c4ed2ee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.674ex; height:2.509ex;" alt="{\displaystyle {\mathcal {F}}_{\theta }}" loading="lazy"></span> is modeled as a noisy distribution above <a href="Permutations" class="mw-redirect" title="Permutations">permutations</a> of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}">

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

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</math></span><img src="./4611d85173cd3b508e67077d4a1252c9c05abca2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}" loading="lazy"></span> parametrized by an accuracy parameter <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta >0}">

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

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</math></span><img src="./0b0ac07626379d065418cc158ce6be9aeccf33b9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.351ex; height:2.176ex;" alt="{\displaystyle \theta >0}" loading="lazy"></span>.

</p><p>In order for <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}_{\theta }}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}_{\theta }}</annotation>

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</math></span><img src="./3196c71bb72ce23cf8cdb17be6b49ba04c4ed2ee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.674ex; height:2.509ex;" alt="{\displaystyle {\mathcal {F}}_{\theta }}" loading="lazy"></span> to make sense it should satisfy these conditions:

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<ol><li><b>Differentiability:</b> The probability of each permutation <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }">

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

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</math></span><img src="./9be4ba0bb8df3af72e90a0535fabcc17431e540a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }" loading="lazy"></span> is continues and differentiable in <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

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

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</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span></li>

<li><b>Asymptotic optimality:</b> For the true ranking <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi ^{*}}">

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

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</math></span><img src="./f44ad69ec033a9a86437b2edaf620ea0b2c3f494.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.388ex; height:2.343ex;" alt="{\displaystyle \pi ^{*}}" loading="lazy"></span>: <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{\theta \to \infty }Pr[\pi ^{*}]=1}">

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<annotation encoding="application/x-tex">{\displaystyle \lim _{\theta \to \infty }Pr[\pi ^{*}]=1}</annotation>

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</math></span><img src="./bb098ce9bde7ce7ce504ab850ae567305e8bb754.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.182ex; height:4.009ex;" alt="{\displaystyle \lim _{\theta \to \infty }Pr[\pi ^{*}]=1}" loading="lazy"></span></li>

<li><b>Monotonicity:</b> The expected utility of the top-ranked candidate gets better as <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

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

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</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span> increases, even if any subset of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}">

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

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</math></span><img src="./4611d85173cd3b508e67077d4a1252c9c05abca2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}" loading="lazy"></span> is removed.</li></ol>

<p>These conditions state that a firm should always prefer higher values of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

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

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</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span>, even if it is not first in the selection order.

</p><p>Both the algorithmic and human ranking methods are of the form of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}_{\theta }}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}_{\theta }}</annotation>

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</math></span><img src="./3196c71bb72ce23cf8cdb17be6b49ba04c4ed2ee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.674ex; height:2.509ex;" alt="{\displaystyle {\mathcal {F}}_{\theta }}" loading="lazy"></span> and differ by the accuracy parameters <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{A},\theta _{H}}">

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

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</math></span><img src="./75199ca2165fafc636c8548594782172221f61af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.371ex; height:2.509ex;" alt="{\displaystyle \theta _{A},\theta _{H}}" loading="lazy"></span>. The algorithmic ranking output is corotated - it always outputs the same permutation. In contrast, a human ranked premutation is drawn from <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}_{\theta _{H}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}_{\theta _{H}}}</annotation>

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</math></span><img src="./4b55b15f8d04495271e2566d24a7f3749c2bb5ae.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.023ex; height:2.843ex;" alt="{\displaystyle {\mathcal {F}}_{\theta _{H}}}" loading="lazy"></span> independently for each of firms.

</p><p>For <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{1},s_{2}\in \{A,H\}}">

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<annotation encoding="application/x-tex">{\displaystyle s_{1},s_{2}\in \{A,H\}}</annotation>

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</math></span><img src="./c2946aca75c1431696745456f06a1f34bb57c39f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.33ex; height:2.843ex;" alt="{\displaystyle s_{1},s_{2}\in \{A,H\}}" loading="lazy"></span> strategies of the first and second firm, Social welfare <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{s_{1},s_{2}}}">

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<annotation encoding="application/x-tex">{\displaystyle W_{s_{1},s_{2}}}</annotation>

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</math></span><img src="./891a6191bc42110cddb241a58c7482a34fb15f70.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.089ex; height:2.843ex;" alt="{\displaystyle W_{s_{1},s_{2}}}" loading="lazy"></span> is defied as the sum of utilities of the hired candidates.

</p>

<div class="mw-heading mw-heading4"><h4 id="Conditions_to_suboptimal_convergence">Conditions to suboptimal convergence</h4></div>

<p>The Braess's like paradox in this framework is suboptimal monocultures converges. That is, using the algorithmic ranking is dominant strategy thus converging toward monoculture yet it yields suboptimal welfare <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W_{A,A}<W_{H,H}}">

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

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</math></span><img src="./d500f0f07e07c079b4b4c2750e17f1883e9ab74a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.249ex; height:2.843ex;" alt="{\displaystyle W_{A,A}<W_{H,H}}" loading="lazy"></span> (welfare in a world without algorithmic ranking is higher).

</p><p>The main theorem proved by Kleinberg<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> of this model is that for any <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{H}}">

<msub>

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

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</math></span><img src="./6cf0885e8c63d224218150753f6e15fcdb7a3689.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.782ex; height:2.509ex;" alt="{\displaystyle \theta _{H}}" loading="lazy"></span> and any noisy ranking family <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}_{\theta }}">

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}_{\theta }}</annotation>

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</math></span><img src="./3196c71bb72ce23cf8cdb17be6b49ba04c4ed2ee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.674ex; height:2.509ex;" alt="{\displaystyle {\mathcal {F}}_{\theta }}" loading="lazy"></span> that satisfy these conditions:

</p>

<ol><li><b>Preference for the first position:</b> For all <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta >0}">

</mstyle>

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

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</math></span><img src="./0b0ac07626379d065418cc158ce6be9aeccf33b9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.351ex; height:2.176ex;" alt="{\displaystyle \theta >0}" loading="lazy"></span> if <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi ,\sigma \sim {\mathcal {F}}_{\theta }}">

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \pi ,\sigma \sim {\mathcal {F}}_{\theta }}</annotation>

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</math></span><img src="./ff5fa0afdb418c7216c65152b98d980d40f3782d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.469ex; height:2.509ex;" alt="{\displaystyle \pi ,\sigma \sim {\mathcal {F}}_{\theta }}" loading="lazy"></span> then <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {E} [\pi _{1}-\pi _{2}|\pi _{1}\neq \sigma _{1}]>0}">

</mrow>

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<annotation encoding="application/x-tex">{\displaystyle \mathbb {E} [\pi _{1}-\pi _{2}|\pi _{1}\neq \sigma _{1}]>0}</annotation>

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</math></span><img src="./72f487a3307f3b073a613afcb5bd542aafe35136.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.21ex; height:2.843ex;" alt="{\displaystyle \mathbb {E} [\pi _{1}-\pi _{2}|\pi _{1}\neq \sigma _{1}]>0}" loading="lazy"></span>.</li>

<li><b>Preference for weaker competition:</b> For all <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{1}>\theta _{2},\sigma \sim {\mathcal {F}}_{\theta _{1}}and\ \pi ,\tau \sim {\mathcal {F}}_{\theta _{2}}:\mathbb {E} [\pi _{1}^{(-\sigma _{1})}]<\mathbb {E} [\pi _{1}^{(-\tau _{1})}]}">

<msub>

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</msubsup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \theta _{1}>\theta _{2},\sigma \sim {\mathcal {F}}_{\theta _{1}}and\ \pi ,\tau \sim {\mathcal {F}}_{\theta _{2}}:\mathbb {E} [\pi _{1}^{(-\sigma _{1})}]<\mathbb {E} [\pi _{1}^{(-\tau _{1})}]}</annotation>

</semantics>

</math></span><img src="./5a73ccbee7b6ce25bb8934b394211de29dbd2359.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:53.242ex; height:3.676ex;" alt="{\displaystyle \theta _{1}>\theta _{2},\sigma \sim {\mathcal {F}}_{\theta _{1}}and\ \pi ,\tau \sim {\mathcal {F}}_{\theta _{2}}:\mathbb {E} [\pi _{1}^{(-\sigma _{1})}]<\mathbb {E} [\pi _{1}^{(-\tau _{1})}]}" loading="lazy"></span>.</li></ol>

<p>there exists a <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta _{A}>\theta _{H}}">

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

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

</semantics>

</math></span><img src="./13c15af46e32cffe999920a3a07850a07d914fd3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.436ex; height:2.509ex;" alt="{\displaystyle \theta _{A}>\theta _{H}}" loading="lazy"></span> such that both firms prefer using the sherd algorithmic ranking even though the social welfare is higher when both use the human evaluators. In other words - regardless of the accuracy of the human rankers there exists a more accurate algorithm whose introduction leads to suboptimal monoculture convergence.

</p><p>The implications of this theorem is that under these conditions, firms will choose to use the algorithmic ranking even though that the correlated nature of algorithmic monocultures degrades total social welfare. Even though algorithmic rankings are more accurate.

</p><p>The first condition on <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}_{\theta }}">

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}_{\theta }}</annotation>

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</math></span><img src="./3196c71bb72ce23cf8cdb17be6b49ba04c4ed2ee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.674ex; height:2.509ex;" alt="{\displaystyle {\mathcal {F}}_{\theta }}" loading="lazy"></span> (Preference for the first position) is equivalent to a preference of firms to have independent ranking (in our setting - non algorithmic). This means that a firm should prefers independent ranking methods given all else is equal.

</p><p>The intuition behind preference for weaker competition is that when a candidate is removed (hired by a different firm), the best remaining candidate is better in expectation when the removed candidate is chosen based on a less accurate ranking. Thus, a firm should always prefer that its competitors would be less accurate.

</p><p>These conditions are met for <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {F}}_{\theta }}">

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\mathcal {F}}_{\theta }}</annotation>

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</math></span><img src="./3196c71bb72ce23cf8cdb17be6b49ba04c4ed2ee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.674ex; height:2.509ex;" alt="{\displaystyle {\mathcal {F}}_{\theta }}" loading="lazy"></span> that is the Mallows Model distributions and some types of random utility models (Gaussian or Laplacian noise).

</p>

<ul><li><a href="Comparison_of_DOS_operating_systems" title="Comparison of DOS operating systems">Comparison of DOS operating systems</a></li>

<li><a href="Influence_of_the_IBM_PC_on_the_personal_computer_market#Domination_of_the_clones" title="Influence of the IBM PC on the personal computer market">Domination of the clones</a></li>

<li><a href="History_of_computing_hardware_(1960s%E2%80%93present)" title="History of computing hardware (1960s–present)">History of computing hardware (1960s–present)</a></li>

<li><a href="IBM_PC_compatible" title="IBM PC compatible">IBM PC compatible</a></li>

<li><a href="Open_architecture" title="Open architecture">Open architecture</a></li>

<li><a href="Software_diversity" title="Software diversity">Software diversity</a></li>

<li><a href="Timeline_of_DOS_operating_systems" title="Timeline of DOS operating systems">Timeline of DOS operating systems</a></li>

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

<li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=eUJ2fWRVDpE">Researcher lecture about suboptimal monocultures convergence</a></li></ul>

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

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</style><cite id="CITEREFGoth2003" class="citation journal cs1">Goth, G. (2003). "Addressing the monoculture". <i>IEEE Security & Privacy</i>. <b>1</b> (6): <span class="nowrap">8–</span>10. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Fmsecp.2003.1253561">10.1109/msecp.2003.1253561</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1540-7993">1540-7993</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16965084">16965084</a>.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFMurphy2021" class="citation news cs1">Murphy, Hannah (2021-12-14). <a rel="nofollow" class="external text" href="https://www.ft.com/content/d3c244f2-eaba-4c46-9a51-b28fc13d9551">"Hackers launch more than 1.2m attacks through Log4J flaw"</a>. <i><a href="Financial_Times" title="Financial Times">Financial Times</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-12-17</span></span>.</cite></span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFStamp2004" class="citation journal cs1">Stamp, Mark (2004). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://dl.acm.org/doi/10.1145/971617.971650">"Risks of monoculture"</a></span>. <i>Communications of the ACM</i>. <b>47</b> (3): 120. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F971617.971650">10.1145/971617.971650</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0001-0782">0001-0782</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16746625">16746625</a>.</cite></span>

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<li id="cite_note-stoll1989-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-stoll1989_4-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFStoll,_Clifford1989" class="citation book cs1"><a href="Clifford_Stoll" title="Clifford Stoll">Stoll, Clifford</a> (1989). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/cuckooseggtracki00stol"><i>The Cuckoo's Egg</i></a></span>. Doubleday. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/cuckooseggtracki00stol/page/320">320–321</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-307-81942-0</bdi>.</cite></span>

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<li id="cite_note-:0-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFKleinberg2021" class="citation journal cs1">Kleinberg, Jon (2021). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8179131">"Algorithmic monoculture and social welfare"</a>. <i>Proceedings of the National Academy of Sciences</i>. <b>118</b> (22). <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2101.05853">2101.05853</a></span>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021PNAS..11818340K">2021PNAS..11818340K</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.2018340118">10.1073/pnas.2018340118</a></span>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8179131">8179131</a></span>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/34035166">34035166</a>.</cite></span>

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