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Unanimity overruled: Majority voting and the burden of history

Author

Listed:
  • Klaus Nehring

    (Department of Economics, University of California, Davis, USA)

  • Marcus Pivato

    (THEMA, Université de Cergy-Pontoise, France)

  • Clemens Puppe

    (Department of Economics and Management, Karlsruhe Institute of Technology, Germany)

Abstract

Sequential majority voting over interconnected binary decisions can lead to the overruling of unanimous consensus. We characterize, within the general framework of judgement aggregation, when this happens for some sequence of decisions. The large class of aggregation spaces for which this vulnerability is present includes the aggregation of preference orderings over at least four alternatives, the aggregation of equivalence relations over at least four objects, resource allocation problems, and most committee selection problems. We also ask whether it is possible to design respect for unanimity by choosing appropriate decision sequences (independently from the ballot). Remarkably, while this is not possible in general, it can be accomplished in some interesting special cases. Generalizing and sharpening a classic result by Shepsle and Weingast, we show that respect for unanimity can indeed be thus guaranteed in the cases of the aggregation of weak preference orderings, linear preference orderings, and equivalence relations. By contrast, impossibility results can be obtained for the aggregation of acyclic relations and separable preference orderings. As a key technical tool, we introduce the notion of a covering fragment that serves as a counterpart and generalization of the notions of covering relation/uncovered set in voting theory.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jothpo:v:28:y:2016:i:4:p:552-597
    DOI: 10.1177/0951629815586884
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    1. 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.
    2. Nehring, Klaus & Pivato, Marcus, 2019. "Majority rule in the absence of a majority," Journal of Economic Theory, Elsevier, vol. 183(C), pages 213-257.
    3. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    4. 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.
    5. Andreas Darmann & Julia Grundner & Christian Klamler, 2017. "Consensus in the 2015 Provincial Parliament Election in Styria, Austria: Voting Rules,Outcomes, and the Condorcet Paradox," Graz Economics Papers 2017-13, University of Graz, Department of Economics.
    6. 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.
    7. Darmann, Andreas & Grundner, Julia & Klamler, Christian, 2019. "Evaluative voting or classical voting rules: Does it make a difference? Empirical evidence for consensus among voting rules," European Journal of Political Economy, Elsevier, vol. 59(C), pages 345-353.

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