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Axiomatizing collective judgment sets in a minimal logical language

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Abstract

We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula \(\square \varphi\) expresses that\(\varphi\) is collectively accepted, or that\(\varphi\) is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where\(\square \varphi\) holds if a majority of individuals accepts\(\varphi\), consensus voting, where\(\square \varphi\) holds if all individuals accept\(\varphi\), and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures.

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Article 22 July 2014

Jeffrey Sanford Russell, John Hawthorne & Lara Buchak

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Authors and Affiliations

  1. Department of Philosophy, Stanford University, Stanford, USA

    Marc Pauly

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  1. Marc Pauly
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Correspondence to Marc Pauly.

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Pauly, M. Axiomatizing collective judgment sets in a minimal logical language. Synthese 158, 233–250 (2007). https://doi.org/10.1007/s11229-006-9079-z

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  • DOI: https://doi.org/10.1007/s11229-006-9079-z

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