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Limits of acyclic voting

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  • Duggan, John

Abstract

Assuming three or more alternatives, there is no systematic rule for aggregating individual preferences that satisfies acyclicity and the standard independence and Pareto axioms, that avoids making some voter a weak dictator, and that is minimally responsive to changes in voter preferences. The latter axiom requires that a preference reversal in the same direction by roughly one third of all voters is sufficient to break social indifference. This result substantially strengthens classical acyclicity theorems of Mas-Colell and Sonnenschein (1972) and Schwartz (1986). When the set of alternatives is large, cycles become intuitively easier to construct, the acyclicity axiom has greater bite, and the responsiveness threshold can be increased to two less than the number of individuals, which yields the weakest logically possible responsiveness axiom.

Suggested Citation

  • Duggan, John, 2016. "Limits of acyclic voting," Journal of Economic Theory, Elsevier, vol. 163(C), pages 658-683.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:658-683
    DOI: 10.1016/j.jet.2016.02.004
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    References listed on IDEAS

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    4. Le Breton, Michel & Weymark, John A., 2011. "Chapter Seventeen - Arrovian Social Choice Theory on Economic Domains," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 17, pages 191-299, Elsevier.
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    Cited by:

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    2. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.
    3. John Duggan, 2019. "Weak rationalizability and Arrovian impossibility theorems for responsive social choice," Public Choice, Springer, vol. 179(1), pages 7-40, April.
    4. McMorris, F.R. & Mulder, Henry Martyn & Novick, Beth & Powers, Robert C., 2021. "Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 164-174.

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    More about this item

    Keywords

    Acyclicity; Voting; Preference aggregation; Arrow's theorem; Positive responsiveness;
    All these keywords.

    JEL classification:

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

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