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On the probability of the Condorcet Jury Theorem or the Miracle of Aggregation

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  • 'Alvaro Romaniega

Abstract

The Condorcet Jury Theorem or the Miracle of Aggregation are frequently invoked to ensure the competence of some aggregate decision-making processes. In this article we explore an estimation of the prior probability of the thesis predicted by the theorem (if there are enough voters, majority rule is a competent decision procedure). We use tools from measure theory to conclude that, prima facie, it will fail almost surely. To update this prior either more evidence in favor of competence would be needed or a modification of the decision rule. Following the latter, we investigate how to obtain an almost sure competent information aggregation mechanism for almost any evidence on voter competence (including the less favorable ones). To do so, we substitute simple majority rule by weighted majority rule based on some weights correlated with epistemic rationality such that every voter is guaranteed a minimal weight equal to one.

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  • 'Alvaro Romaniega, 2021. "On the probability of the Condorcet Jury Theorem or the Miracle of Aggregation," Papers 2108.00733, arXiv.org, revised Jun 2022.
  • Handle: RePEc:arx:papers:2108.00733
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    References listed on IDEAS

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    1. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
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    4. Bezalel Peleg & Shmuel Zamir, 2012. "Extending the Condorcet Jury Theorem to a general dependent jury," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 91-125, June.
    5. Daniel Berend & Jacob Paroush, 1998. "When is Condorcet's Jury Theorem valid?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 481-488.
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