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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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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 68 (2014)
Issue (Month): C ()
Pages: 31-52

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Handle: RePEc:eee:matsoc:v:68:y:2014:i:c:p:31-52

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Web page: http://www.elsevier.com/locate/inca/505565

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  1. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-819, November.
  2. Jose Apesteguia & Miguel A. Ballester & Rosa Ferrer, 2011. "On the Justice of Decision Rules," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 1-16.
  3. Schmitz, Patrick W. & Tröger, Thomas, 2012. "The (sub-)optimality of the majority rule," Games and Economic Behavior, Elsevier, vol. 74(2), pages 651-665.
  4. Tilman Börgers & Peter Postl, 2008. "Efficient Compromising," Discussion Papers 06-11R, Department of Economics, University of Birmingham.
  5. Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
  6. André Blais, 2002. "Why Is there So Little Strategic Voting in Canadian Plurality Rule Elections?," Political Studies, Political Studies Association, vol. 50(3), pages 445-454, 08.
  7. Robert J. Weber, 1978. "Comparison of Public Choice Systems," Cowles Foundation Discussion Papers 498, Cowles Foundation for Research in Economics, Yale University.
  8. Roger B. Myerson, 2000. "Comparison of Scoring Rules in Poisson Voting Games," Econometric Society World Congress 2000 Contributed Papers 0686, Econometric Society.
  9. Wade D. Cook & Moshe Kress, 1985. "Ordinal Ranking with Intensity of Preference," Management Science, INFORMS, vol. 31(1), pages 26-32, January.
  10. Postl Peter, 2011. "Strategy-Proof Compromises," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-37, October.
  11. Matthew O Jackson & Hugo F Sonnenschein, 2007. "Overcoming Incentive Constraints by Linking Decisions -super-1," Econometrica, Econometric Society, vol. 75(1), pages 241-257, 01.
  12. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
  13. Buenrostro, Lucia & Dhillon, Amrita, 2004. "Scoring Rule Voting Games And Dominance Solvability," The Warwick Economics Research Paper Series (TWERPS) 698, University of Warwick, Department of Economics.
  14. Miralles, Antonio, 2012. "Cardinal Bayesian allocation mechanisms without transfers," Journal of Economic Theory, Elsevier, vol. 147(1), pages 179-206.
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Cited by:
  1. Pivato, Marcus, 2013. "Statistical utilitarianism," MPRA Paper 49561, University Library of Munich, Germany.

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