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Strongly sincere best responses under approval voting and arbitrary preferences

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  • Alós-Ferrer, Carlos
  • Buckenmaier, Johannes

Abstract

Approval voting allows voters to support as many candidates as they wish. One advantage is that voters have weak or no incentives to vote insincerely. However, the exact meaning of this statement depends on how the voters' preferences over candidates are extended to sets. We show that, under a combination of standard, well-established assumptions on extended preferences, voters always have a strongly sincere best response (a best response ballot such that every approved candidate is strictly preferred to every disapproved one) given other voters' ballots. An analogous result for sincere best responses obtains under weaker conditions. The results hold for arbitrary preferences over candidates, allowing for indifferences but covering the extreme cases of dichotomous or strict preferences. As a corollary, we show that the classical strategy-proofness result for dichotomous preferences (Brams and Fishburn, 1978) holds for a larger class of preferences on sets than originally assumed.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:388-401
    DOI: 10.1016/j.geb.2019.07.005
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    References listed on IDEAS

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    1. Wolitzky, Alexander, 2009. "Fully sincere voting," Games and Economic Behavior, Elsevier, vol. 67(2), pages 720-735, November.
    2. 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.
    3. Ulle Endriss, 2013. "Sincerity and manipulation under approval voting," Theory and Decision, Springer, vol. 74(3), pages 335-355, March.
    4. 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.
    5. 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.
    6. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    7. Steven J. Brams & Peter C. Fishburn, 2010. "Going from Theory to Practice: The Mixed Success of Approval Voting," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 19-37, Springer.
    8. Eyal Baharad & Shmuel Nitzan, 2005. "Approval voting reconsidered," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 619-628, October.
    9. Jean-François Laslier, 2009. "The Leader rule: a model of strategic approval voting in a large electorate," Post-Print hal-00363218, HAL.
    10. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    11. Laslier, Jean-François & Núñez, Matías & Pimienta, Carlos, 2017. "Reaching consensus through approval bargaining," Games and Economic Behavior, Elsevier, vol. 104(C), pages 241-251.
    12. Baigent, Nick & Xu, Yongsheng, 1991. "Independent necessary and sufficient conditions for approval voting," Mathematical Social Sciences, Elsevier, vol. 21(1), pages 21-29, February.
    13. Barberà, Salvador & Coelho, Danilo, 2010. "On the rule of k names," Games and Economic Behavior, Elsevier, vol. 70(1), pages 44-61, September.
    14. Myerson, Roger B., 2002. "Comparison of Scoring Rules in Poisson Voting Games," Journal of Economic Theory, Elsevier, vol. 103(1), pages 219-251, March.
    15. Merrill, Samuel & Nagel, Jack, 1987. "The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules," American Political Science Review, Cambridge University Press, vol. 81(2), pages 509-524, June.
    16. 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.
    17. Francesco Sinopoli & Bhaskar Dutta & Jean-François Laslier, 2006. "Approval voting: three examples," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(1), pages 27-38, December.
    18. Nitzan, Shmuel I. & Pattanaik, Prasanta K., 1984. "Median-based extensions of an ordering over a set to the power set: An axiomatic characterization," Journal of Economic Theory, Elsevier, vol. 34(2), pages 252-261, December.
    19. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    20. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    21. Sen, Amartya, 1991. "Welfare, preference and freedom," Journal of Econometrics, Elsevier, vol. 50(1-2), pages 15-29, October.
    22. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Anja Achtziger & Carlos Alós-Ferrer & Alexander Ritschel, 2020. "Cognitive load in economic decisions," ECON - Working Papers 354, Department of Economics - University of Zurich.

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    More about this item

    Keywords

    Approval voting; Manipulation; Preferences among sets; Strong sincerity;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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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