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<title>Measures of Cognitive Distance and Diversity.</title>
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<h1 class="title">Measures of Cognitive Distance and Diversity.</h1>
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<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#sec-1">1 Introduction</a></li>
<li><a href="#sec-2">2 Causal Beliefs and Joint Distributions</a></li>
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<h2 id="sec-1"><span class="section-number-2">1</span> Introduction</h2>
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<p>
An understanding of the conditions for collective wisdom and the mechanisms that enable collectives to become wiser, are at the core of what we might hope to call a science of sustainable development. Most decisions that are relevant to sustainable development, however we may define it, are at least indirectly influenced by human collectives (i.e. committees, congress, corporate boards etc.). One important set of machanisms relates the diversity of individual minds within a collection to the wisdom with which it solves its problems (collective decision and collective action). In economics and political science much has been done to uncover important mechanisms with respect to heterogenous preferences, information asymmetries and even the diversity of received signals (information) when beliefs are homogenous, in market settings and strategic games. However, the situation in which information and goals are the same among members of a collection but beliefs are heterogenous (such as in a team), has to my knowledge not been given much attention and neither have those situations, which are likely to be quite common in our world, where both beliefs and goals, or both beliefs and information-selection are diverse (people endogenously select their sources). Climate change discussions at all scales (from local to global) for example, are likely to draw attendees with highly diverse goals and beliefs, who also are exposed to very different information.
</p>
<p>
Starting with Condorcet's jury theorem, (Marquis de Condorcet, 1785)<sup><a class="footref" name="fnr.1" href="#fn.1">1</a></sup>, there have been various arguments with different degrees of sophistication, that, depending also on the organizational scheme of the collective, many thinkers together will on average come to wiser conclusions than any individual could on her own. In general, in these arguments the implied reason is that the greater the number of people, the greater is the variance in insights (the cognitive heterogeneity and diversity is higher in larger groups, by assumption) and it is this diversity of minds and not the sheer number of people that is believed to lead to better collective decisions<sup><a class="footref" name="fnr.2" href="#fn.2">2</a></sup>. Analogous with the definition of bio-diversity as the amount of genetic information that is available to the system (for greater functional diversity under a greater range of circumstances), an organization's cognitive diversity can be defined as the collective's current available theoretical tool kit and it should thus increase the degree of accuracy with which the collective will judge the workings of the world, under a greater number of contingencies<sup><a class="footref" name="fnr.3" href="#fn.3">3</a></sup>. This, in turn, should improve the collective interaction of the organization with the world; particularly if the world of interest is constantly changing. Models of the world (to be made precise below) that had been inaccurate previously, might have more explanatory power as circumstances change, while those models that once furnished the best explanations might fade in relevance. For a thorough discussion and overview of the literatures on and related to collective wisdom, distributed intelligence/cognition or the wisdom of crowds, see "Collective Wisdom: Principles and Mechanisms" (edited by Landemore and Elster, 2012).
</p>
<p>
In much, but not all of this and related work, the number of people in a group of thinkers acts as a proxi for diversity in the absence of a direct measure, which leaves open all questions concerning the differential cognitive diversity in groups with more or less the same fixed number of members. Although diversification of investment in resources and capital has long been standard advise in portfolio theory, not much is known or recommended in terms of the diversification of investment in human resources, with the notable exception of some recent theoretical work by Hong and Page (2004) which has inspired the present work. Additionally, this research direction could give rise to some nuanced and unorthodox policy recommendations for the educational sector. For example, it may result in the advise to expose different students (at all ages and levels) to varying educational opportunities, suited to their own individual needs and desires.
</p>
<p>
Socially constructed measures of diversity (along ethnic, gender and religious dimensions, for example), the definitions of which are highly sensitive to context and interpretation, have become a common public agenda of firms and organizations. This diversity agenda is promoted mostly for ethical and esthetic reasons or as a result of political pressures, while perhaps the most relevant form of diversity, for the success and robustness of collectives, is related to cognition and beliefs. I content that the current lack of a natural measure of cognitive diversity stands in the way of constructing falsifiable theories directly relating the cognitive diversity of a collective to its collective wisdom and that this lack leads to an impasse which helps to explain the current dirth in the theory and empirics of this important subject. Note however, that, depending on the context, socially constructed measures of diversity might be highly correlated with cognitive diversity, and thus they may serve as more applicable proxies of cognitive diversity than membership size which is often constrained. Thus, a focus on these often more easily apparent forms of diversity might be justifiable not only on ethical or esthetic grounds, but also on grounds of organizational efficacy and robustness, if cognitive diversity can indeed be scientifically shown to have such benefits. As a requisite for such scientific work, however, adequate and theoretically well-motivated measures of <i>cognitive distance</i> (between any two individuals) and <i>cognitive diversity</i> (for a collection of individuals) are needed<sup><a class="footref" name="fnr.4" href="#fn.4">4</a></sup>. Thus, this paper concerns itself with such measures. The here advanced cognitive distance metric is the square root of a measure known as the Jensen-Shannon Divergence (henceforth JSD). JSD is an important information theoretic quantity that will here be derived from recent work in cognitive science on how humans uncover causal structure in their universe of concern (Tenenbaum & Griffiths, 2001, Griffiths & Tenenbaum, 2005). JSD is then generalized and the square-root of the resulting quantity (known as the \(n\)-point JSD, or generalized JSD), with the apropriate normalization, is argued to be a meaningful metric of group level cognitive diversity.
</p>
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<h2 id="sec-2"><span class="section-number-2">2</span> Causal Beliefs and Joint Distributions</h2>
<div class="outline-text-2" id="text-2">
<p>
Underlying many of the important discussions in business, politics and sustainable development are matters of causality and causal reasoning. Thus, as a preliminary step, this paper restricts itself to the causal domain, although it is acknowledged that other forms of reasoning (ontological, deontic, deontological, etc.) quite often play important roles and must be incorporated to account completely for the diversity of individual reasoning within a collective. Here, "reasoning" replaces "cognition" to temporarily draw attention to the fact that the measures of cognitive distance and diversity are constructed not from data of cognition per se, as cognition at this scale is unobservable, but from observable reasoning. Either interviews or transcriptions of speeches/debates are used to elicit statements of the form "CO\(_2\) causes Climate Change," which are then encoded as directed signed arcs of the graph representing a particular speaker's belief system as depicted in Figure <a href="#fig-animals">animals</a>:
</p>
<div id="footnotes">
<h2 class="footnotes">Footnotes: </h2>
<div id="text-footnotes">
<p class="footnote"><sup><a class="footnum" name="fn.1" href="#fnr.1">1</a></sup> Although since Waldron (1995) there has been widespread argreement among scholars that in \textit{Politics} Aristotle had already espoused a theory of ``The Wisdom of the Multitude'', which implicitly was synonymous with a theory of the social benefits of Diversity, Cammack (2013) convincingly dispelled this interpretation of Aristotle's text and showed that Aristotle, very likely, had something very different in mind.
</p>
<p class="footnote"><sup><a class="footnum" name="fn.2" href="#fnr.2">2</a></sup> In the case of Condorcet's jury theorem the argument is simply numerical and has little to do with people's cognition at all.
</p>
<p class="footnote"><sup><a class="footnum" name="fn.3" href="#fnr.3">3</a></sup> Whether and to what degree this is true for any given organization must depend also on the organization's opinion aggregation scheme, just as the benefits of bio-diversity depend on the structure of the food web.
</p>
<p class="footnote"><sup><a class="footnum" name="fn.4" href="#fnr.4">4</a></sup> If the mechanisms by which cognitive diversity impacts performance and robustness can then be sufficiently isolated and it can be shown that this form of diversity indeed correlates with the other forms, it may be found simpler and more convenient to use more easily visable proxies in actual practice (for example, in human resource departments of firms).
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<div id="postamble">
<p class="date">Date: 2013-11-01 16:32:06 EDT</p>
<p class="author">Author: Johannes Castner</p>
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