Handbook of Social Choice and Voting
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Handbook of Social Choice and Voting

Edited by Jac C. Heckelman and Nicholas R. Miller

This Handbook provides an overview of interdisciplinary research related to social choice and voting that is intended for a broad audience. Expert contributors from various fields present critical summaries of the existing literature, including intuitive explanations of technical terminology and well-known theorems, suggesting new directions for research.
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Chapter 9: Condorcet jury theorems

Bryan C. McCannon


Consider the following dilemma. A decision needs to be made to adopt one of two options. We have common preferences in that one option is objectively better for all of us. Unfortunately, the problem is that we do not know precisely which option is the one to implement. How should the choice be made? The seminal contribution, known as the Condorcet Jury Theorem (hereafter CJT), provides guidance. The result is that a group using simple majority voting to make a decision is more likely to make the correct choice than would any individual member of the group. Additionally, as the size of the group expands, the likelihood of the majority decision being correct increases and approaches certainty in the limit. Thus, there is wisdom in the crowds. This powerful result has spurred numerous investigations that generalize its theoretical assumptions, and has been applied to various decision-making contexts. The result is named for Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet (1743–1794), the French mathematician who outlined the argument in the essay Essai sur l‘Application de l’Analyse à la Probabilité des Décisions Rendues à la Pluralté des Voix (1785). An enthusiastic activist for democracy, Condorcet was a political leader during the French Revolution (McLean and Hewitt 1994).

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