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Variable-population voting rules

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  • Pivato, Marcus

Abstract

Let X be a set of social alternatives, and let V be a set of ‘votes’ or ‘signals’. (We do not assume any structure on X or V.) A variable population voting ruleF takes any number of anonymous votes drawn from V as input, and produces a nonempty subset of X as output. The rule F satisfies reinforcement if, whenever two disjoint sets of voters independently select some subset Y⊆X, the union of these two sets will also select Y. We show that F satisfies reinforcement if and only if F is a balance rule. If F satisfies a form of neutrality, then F satisfies reinforcement if and only if F is a scoring rule (with scores taking values in an abstract linearly ordered abelian group R); this generalizes a result of Myerson (1995).

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  • Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:3:p:210-221
    DOI: 10.1016/j.jmateco.2013.02.001
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    Cited by:

    1. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    2. Jac C. Heckelman & Robi Ragan, 2021. "Symmetric Scoring Rules And A New Characterization Of The Borda Count," Economic Inquiry, Western Economic Association International, vol. 59(1), pages 287-299, January.
    3. Pivato, Marcus, 2014. "Formal utilitarianism and range voting," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 50-56.
    4. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    5. Macé, Antonin, 2018. "Voting with evaluations: Characterizations of evaluative voting and range voting," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 10-17.
    6. Chris Dong & Patrick Lederer, 2023. "Refined Characterizations of Approval-based Committee Scoring Rules," Papers 2312.08799, arXiv.org, revised Mar 2024.
    7. Martínez, Ricardo & Moreno, Bernardo, 2017. "Qualified voting systems," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 49-54.
    8. Federica Ceron & Stéphane Gonzalez, 2019. "A characterization of Approval Voting without the approval balloting assumption," Working Papers halshs-02440615, HAL.
    9. Lederer, Patrick, 2024. "Bivariate scoring rules: Unifying the characterizations of positional scoring rules and Kemeny's rule," Journal of Economic Theory, Elsevier, vol. 218(C).
    10. Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    11. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.
    12. Martin Lackner & Piotr Skowron, 2017. "Consistent Approval-Based Multi-Winner Rules," Papers 1704.02453, arXiv.org, revised Oct 2019.
    13. Nuñez, M. & Valletta, G., 2012. "The information simplicity of scoring rules," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. Wesley H. Holliday & Eric Pacuit, 2023. "Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilers," Public Choice, Springer, vol. 197(1), pages 1-62, October.

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    More about this item

    Keywords

    Voting; Reinforcement; Scoring rule; Ordered abelian group;
    All these keywords.

    JEL classification:

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

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