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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

Suggested Citation

  • Pivato, Marcus, 2011. "Variable-population voting rules," MPRA Paper 31896, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:31896
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    References listed on IDEAS

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    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
    3. Carlos Alós-Ferrer, 2006. "A Simple Characterization of Approval Voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 621-625, December.
    4. Young, H Peyton, 1974. "A Note on Preference Aggregation," Econometrica, Econometric Society, vol. 42(6), pages 1129-1131, November.
    5. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    6. Ching, Stephen, 1996. "A Simple Characterization of Plurality Rule," Journal of Economic Theory, Elsevier, vol. 71(1), pages 298-302, October.
    7. repec:cup:apsrev:v:72:y:1978:i:03:p:831-847_15 is not listed on IDEAS
    8. Marcus Pivato, 2014. "Additive representation of separable preferences over infinite products," Theory and Decision, Springer, vol. 77(1), pages 31-83, June.
    9. Donald Saari, 2010. "Systematic analysis of multiple voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(2), pages 217-247, February.
    10. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    11. Gaertner, Wulf & Xu, Yongsheng, 2012. "A general scoring rule," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 193-196.
    12. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    13. Chun-Hsien Yeh, 2008. "An efficiency characterization of plurality rule in collective choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 575-583, March.
    14. Fishburn, Peter C., 1978. "Axioms for approval voting: Direct proof," Journal of Economic Theory, Elsevier, vol. 19(1), pages 180-185, October.
    15. Amrita Dhillon, 1998. "Extended Pareto rules and relative utilitarianism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 521-542.
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    Citations

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    Cited by:

    1. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    2. Franz Dietrich, 2014. "Scoring rules for judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 873-911, April.
    3. repec:eee:matsoc:v:88:y:2017:i:c:p:49-54 is not listed on IDEAS
    4. Pivato, Marcus, 2014. "Formal utilitarianism and range voting," Mathematical Social Sciences, Elsevier, vol. 67(C), pages 50-56.
    5. repec:eee:mateco:v:72:y:2017:i:c:p:51-69 is not listed on IDEAS
    6. Núñez Matias & Valleta Giacomo, 2012. "The information simplicity of scoring rules," Research Memorandum 011, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Pivato, Marcus, 2017. "Epistemic democracy with correlated voters," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 51-69.

    More about this item

    Keywords

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

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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