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Variable-population voting rules

  • Pivato, Marcus

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 rule' F 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 of 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 is 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). We also discuss the sense in which the balance or scoring representation of F is unique. Finally, we provide a characterization of two scoring rules: `formally utilitarian' voting and `range voting'. a

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 31896.

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Date of creation: 28 Jun 2011
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Handle: RePEc:pra:mprapa:31896
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  1. DHILLON, Amrita & MERTENS, Jean-François, 1993. "Relative Utilitarianism," CORE Discussion Papers 1993048, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  3. Gaertner, Wulf & Xu, Yongsheng, 2012. "A general scoring rule," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 193-196.
  4. Itzhak Gilboa & David Schmeidler, 2002. "Inductive Inference: An Axiomatic Approach," Levine's Working Paper Archive 391749000000000544, David K. Levine.
  5. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
  6. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
  7. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, vol. 40(2), pages 581-630, February.
  8. Donald Saari, 2010. "Systematic analysis of multiple voting rules," Social Choice and Welfare, Springer, vol. 34(2), pages 217-247, February.
  9. Young, H Peyton, 1974. "A Note on Preference Aggregation," Econometrica, Econometric Society, vol. 42(6), pages 1129-31, November.
  10. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
  11. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
  12. Chun-Hsien Yeh, 2008. "An efficiency characterization of plurality rule in collective choice problems," Economic Theory, Springer, vol. 34(3), pages 575-583, March.
  13. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer, vol. 15(4), pages 521-542.
  14. Carlos Alós-Ferrer, 2006. "A Simple Characterization of Approval Voting," Social Choice and Welfare, Springer, vol. 27(3), pages 621-625, December.
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