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Variable-population voting rules

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  • Pivato, Marcus

Abstract

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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Bibliographic Info

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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Keywords: reinforcement; scoring rule; balance rule; linearly ordered abelian group; formal utilitarian; range voting;

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References

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  1. Gilboa, I. & Schmeidler, D., 2001. "Inductive Inference: An Axiomatic Approach," Papers 2001-19, Tel Aviv.
  2. Pivato, Marcus, 2011. "Voting rules as statistical estimators," MPRA Paper 30292, University Library of Munich, Germany.
  3. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-41, November.
  4. Young, H Peyton, 1974. "A Note on Preference Aggregation," Econometrica, Econometric Society, vol. 42(6), pages 1129-31, November.
  5. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
  6. Gaertner, Wulf & Xu, Yongsheng, 2012. "A general scoring rule," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 193-196.
  7. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer, vol. 15(4), pages 521-542.
  8. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
  9. Carlos Alós-Ferrer, 2006. "A Simple Characterization of Approval Voting," Social Choice and Welfare, Springer, vol. 27(3), pages 621-625, December.
  10. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
  11. Chun-Hsien Yeh, 2008. "An efficiency characterization of plurality rule in collective choice problems," Economic Theory, Springer, vol. 34(3), pages 575-583, March.
  12. Donald Saari, 2010. "Systematic analysis of multiple voting rules," Social Choice and Welfare, Springer, vol. 34(2), pages 217-247, February.
  13. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
  14. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
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Cited by:
  1. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer, vol. 42(4), pages 873-911, April.
  2. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, vol. 40(2), pages 581-630, February.
  3. Pivato, Marcus, 2014. "Formal utilitarianism and range voting," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 50-56.
  4. Núñez Matias & Valleta Giacomo, 2012. "The informational simplicity of scoring rules," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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