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Approval voting under dichotomous preferences: A catalogue of characterizations

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  • Brandl, Florian
  • Peters, Dominik

Abstract

Approval voting allows every voter to cast a ballot of approved alternatives and chooses the alternatives with the largest number of approvals. Due to its simplicity and superior theoretical properties, it is a serious contender for use in real-world elections. We support this claim by giving eight characterizations of approval voting. All our results involve the consistency axiom, which requires choices to be consistent across different electorates. In addition, we consider strategyproofness, agreement with majority opinions, independence of cloned alternatives, and invariance under removing inferior alternatives. We prove our results by reducing them to a single base theorem, for which we give a simple and intuitive proof.

Suggested Citation

  • Brandl, Florian & Peters, Dominik, 2022. "Approval voting under dichotomous preferences: A catalogue of characterizations," Journal of Economic Theory, Elsevier, vol. 205(C).
    • Handle: RePEc:eee:jetheo:v:205:y:2022:i:c:s0022053122001223
    DOI: 10.1016/j.jet.2022.105532
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    References listed on IDEAS

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    1. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
    2. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    3. Norihisa Sato, 2014. "A characterization result for approval voting with a variable set of alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 809-825, December.
    4. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2009. "Size approval voting," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1187-1210, May.
    5. Jordi Massó & Marc Vorsatz, 2008. "Weighted approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 129-146, July.
    6. Sanver, M. Remzi, 2002. "Scoring rules cannot respect majority in choice and elimination simultaneously," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 151-155, March.
    7. Sato, Norihisa, 2019. "Approval voting and fixed electorate with dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 51-60.
    8. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
    9. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    10. Bogomolnaia, Anna & Moulin, Herve & Stong, Richard, 2005. "Collective choice under dichotomous preferences," Journal of Economic Theory, Elsevier, vol. 122(2), pages 165-184, June.
    11. Marc Vorsatz, 2008. "Scoring rules on dichotomous preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 151-162, June.
    12. Felix Brandt, 2015. "Set-monotonicity implies Kelly-strategyproofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 793-804, December.
    13. Ceron, Federica & Gonzalez, Stéphane, 2021. "Approval voting without ballot restrictions," Theoretical Economics, Econometric Society, vol. 16(3), July.
    14. Lackner, Martin & Skowron, Piotr, 2021. "Consistent approval-based multi-winner rules," Journal of Economic Theory, Elsevier, vol. 192(C).
    15. Young, H. P., 1988. "Condorcet's Theory of Voting," American Political Science Review, Cambridge University Press, vol. 82(4), pages 1231-1244, December.
    16. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    17. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    18. Alós-Ferrer, Carlos & Buckenmaier, Johannes, 2019. "Strongly sincere best responses under approval voting and arbitrary preferences," Games and Economic Behavior, Elsevier, vol. 117(C), pages 388-401.
    19. Fishburn, Peter C., 1972. "Lotteries and social choices," Journal of Economic Theory, Elsevier, vol. 5(2), pages 189-207, October.
    20. Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, July.
    21. Carlos Alós-Ferrer & Ðura-Georg Granić, 2012. "Two field experiments on Approval Voting in Germany," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 171-205, June.
    22. Sertel, Murat R., 1988. "Characterizing approval voting," Journal of Economic Theory, Elsevier, vol. 45(1), pages 207-211, June.
    23. Malik, Komal & Mishra, Debasis, 2021. "Pareto efficient combinatorial auctions: Dichotomous preferences without quasilinearity," Journal of Economic Theory, Elsevier, vol. 191(C).
    24. Jean-François Laslier & Karine Straeten, 2008. "A live experiment on approval voting," Experimental Economics, Springer;Economic Science Association, vol. 11(1), pages 97-105, March.
    25. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, January.
    26. Alcalde-Unzu, Jorge & Vorsatz, Marc, 2014. "Non-anonymous ballot aggregation: An axiomatic generalization of Approval Voting," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 69-78.
    27. Baigent, Nick & Xu, Yongsheng, 1991. "Independent necessary and sufficient conditions for approval voting," Mathematical Social Sciences, Elsevier, vol. 21(1), pages 21-29, February.
    28. Pivato, Marcus, 2013. "Variable-population voting rules," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 210-221.
    29. Brandt, Felix & Saile, Christian & Stricker, Christian, 2022. "Strategyproof social choice when preferences and outcomes may contain ties," Journal of Economic Theory, Elsevier, vol. 202(C).
    30. Jean-François Laslier, 2011. "And the loser is... Plurality Voting," Working Papers hal-00609810, HAL.
    31. Marc Vorsatz, 2007. "Approval Voting on Dichotomous Preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 127-141, January.
    32. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
    33. Yongsheng Xu, 2010. "Axiomatizations of Approval Voting," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 91-102, Springer.
    34. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
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    Cited by:

    1. Susumu Cato & Stéphane Gonzalez & Eric Rémila & Philippe Solal, 2022. "Approval voting versus proportional threshold methods: so far and yet so near," Working Papers halshs-03858356, HAL.
    2. Chris Dong & Patrick Lederer, 2023. "Characterizations of Sequential Valuation Rules," Papers 2302.11890, arXiv.org.

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    More about this item

    Keywords

    Approval voting; Dichotomous preferences; Consistency with variable electorates; Strategyproofness; Condorcet consistency; Variable agendas;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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