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Equilibrium and effectiveness of two-parameter scoring rules

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  • Giles, Adam
  • Postl, Peter

Abstract

We study a cardinal model of voting with three alternatives where voters’ von Neumann Morgenstern utilities are private information. We consider voting protocols given by two-parameter scoring rules, as introduced by Myerson (2002). For these voting rules, we show that all symmetric Bayes Nash equilibria are sincere, and have a very specific form. These equilibria are unique for a wide range of model parameters, and we can therefore compare the equilibrium performance of different rules. Computational results regarding the effectiveness of different scoring rules (where effectiveness is captured by a modification of the effectiveness measure proposed in Weber, 1978) suggest that those which most effectively represent voters’ preferences allow for the expression of preference intensity, in contrast to more commonly used rules such as the plurality rule, and the Borda Count. While approval voting allows for the expression of preference intensity, it does not maximize effectiveness as it fails to unambiguously convey voters’ ordinal preference rankings.

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  • Giles, Adam & Postl, Peter, 2014. "Equilibrium and effectiveness of two-parameter scoring rules," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 31-52.
    • Handle: RePEc:eee:matsoc:v:68:y:2014:i:c:p:31-52
    DOI: 10.1016/j.mathsocsci.2013.12.003
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    Cited by:

    1. Ahn, David S. & Oliveros, Santiago, 2016. "Approval voting and scoring rules with common values," Journal of Economic Theory, Elsevier, vol. 166(C), pages 304-310.
    2. Marcus Pivato, 2016. "Statistical Utilitarianism," Studies in Political Economy, in: Maria Gallego & Norman Schofield (ed.), The Political Economy of Social Choices, pages 187-204, Springer.
    3. Semin Kim, 2016. "Ordinal Versus Cardinal Voting Rules: A Mechanism Design Approach," Working papers 2016rwp-94, Yonsei University, Yonsei Economics Research Institute.
    4. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," GLO Discussion Paper Series 185, Global Labor Organization (GLO).
    5. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which “Almost” Rule is Optimal?," Group Decision and Negotiation, Springer, vol. 27(1), pages 129-151, February.
    6. Marcus Pivato, 2016. "Asymptotic utilitarianism in scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 431-458, August.
    7. Eyal Baharad & Leif Danziger, 2018. "Voting in Hiring Committees: Which "Almost" Rule is Optimal?," CESifo Working Paper Series 6851, CESifo.
    8. Baharad, Eyal & Danziger, Leif, 2018. "Voting in Hiring Committees: Which "Almost" Rule Is Optimal?," IZA Discussion Papers 11287, Institute of Labor Economics (IZA).
    9. Kim, Semin, 2017. "Ordinal versus cardinal voting rules: A mechanism design approach," Games and Economic Behavior, Elsevier, vol. 104(C), pages 350-371.
    10. Postl, Peter, 2017. "Évaluation et comparaison des règles de vote derrière le voile de l’ignorance : Tour d'horizon sélectif et analyse des règles de scores à deux paramètres," L'Actualité Economique, Société Canadienne de Science Economique, vol. 93(1-2), pages 249-290, Mars-Juin.

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