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The Condorcet set: Majority voting over interconnected propositions

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  • Nehring, Klaus
  • Pivato, Marcus
  • Puppe, Clemens

Abstract

Judgement aggregation is a model of social choice in which the space of social alternatives is the set of consistent evaluations (‘views’) on a family of logically interconnected propositions, or yes/no issues. However, simply complying with the majority opinion in each issue often yields a logically inconsistent collective view. Thus, we consider the Condorcet set: the set of logically consistent views which agree with the majority on a maximal subset of issues. The elements of this set turn out to be exactly those that can be obtained through sequential majority voting, according to which issues are sequentially decided by simple majority unless earlier choices logically force the opposite decision. We investigate the size and structure of the Condorcet set for several important classes of judgement aggregation problems. While the Condorcet set verifies a version of McKelvey's (1979) celebrated ‘chaos theorem’ in a number of contexts, in others it is shown to be very regular and well-behaved.

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  • Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
    • Handle: RePEc:eee:jetheo:v:151:y:2014:i:c:p:268-303
    DOI: 10.1016/j.jet.2013.12.013
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    Citations

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    Cited by:

    1. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part one: general agendas," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 747-786, April.
    2. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    3. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    4. Franz Dietrich & Kai Spiekermann, 2021. "Social Epistemology," Post-Print halshs-02431971, HAL.
    5. Nehring, Klaus & Pivato, Marcus, 2019. "Majority rule in the absence of a majority," Journal of Economic Theory, Elsevier, vol. 183(C), pages 213-257.
    6. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    7. Baumeister, Dorothea & Erdélyi, Gábor & Erdélyi, Olivia J. & Rothe, Jörg, 2015. "Complexity of manipulation and bribery in judgment aggregation for uniform premise-based quota rules," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 19-30.
    8. Klaus Nehring & Marcus Pivato, 2022. "The median rule in judgement aggregation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 1051-1100, June.
    9. Klaus Nehring & Marcus Pivato & Clemens Puppe, 2016. "Unanimity overruled: Majority voting and the burden of history," Journal of Theoretical Politics, , vol. 28(4), pages 552-597, October.
    10. Jérôme Lang & Gabriella Pigozzi & Marija Slavkovik & Leendert Torre & Srdjan Vesic, 2017. "A partial taxonomy of judgment aggregation rules and their properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 327-356, February.
    11. Pivato, Marcus & Soh, Arnold, 2020. "Weighted representative democracy," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 52-63.

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    More about this item

    Keywords

    Judgement aggregation; Social choice; Condorcet set; Sequential majority voting; Path-dependence; Indeterminacy;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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