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May’s Theorem with an infinite population

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  • Mark Fey

Abstract

In this paper, we investigate majority rule with an infinite number of voters. We use an axiomatic approach and attempt to extend May’s Theorem characterizing majority rule to an infinite population. The analysis hinges on correctly generalizing the anonymity condition and we consider three different versions. We settle on bounded anonymity as the appropriate form for this condition and are able to use the notion of asymptotic density to measure the size of almost all sets of voters. With this technique, we define density q-rules and show that these rules are characterized by neutrality, monotonicity, and bounded anonymity on almost all sets. Although we are unable to provide a complete characterization applying to all possible sets of voters, we construct an example showing that our result is the best possible. Finally, we show that strengthening monotonicity to density positive responsiveness characterizes density majority rule on almost all sets. Copyright Springer-Verlag 2004

Suggested Citation

  • Mark Fey, 2004. "May’s Theorem with an infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 275-293, October.
    • Handle: RePEc:spr:sochwe:v:23:y:2004:i:2:p:275-293
    DOI: 10.1007/s00355-003-0264-4
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    Cited by:

    1. Knoblauch, Vicki, 2016. "Elections generate all binary relations on infinite sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 105-108.
    2. Yariv, Leeat & Bartholdi, Laurent & Hann-Caruthers, Wade & Josyula, Maya & Tamuz, Omer, 2018. "Equitable Voting Rules," CEPR Discussion Papers 13316, C.E.P.R. Discussion Papers.
      • Laurent Bartholdi & Wade Hann-Caruthers & Maya Josyula & Omer Tamuz & Leeat Yariv, 2018. "Equitable voting rules," Papers 1811.01227, arXiv.org, revised Aug 2020.
    3. Surekha, K. & Bhaskara Rao, K.P.S., 2010. "May's theorem in an infinite setting," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 50-55, January.
    4. Kari Saukkonen, 2007. "Continuity of social choice functions with restricted coalition algebras," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 637-647, June.
    5. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 348-366, February.
    6. Susumu Cato, 2011. "Pareto principles, positive responsiveness, and majority decisions," Theory and Decision, Springer, vol. 71(4), pages 503-518, October.
    7. Laurent Bartholdi & Wade Hann‐Caruthers & Maya Josyula & Omer Tamuz & Leeat Yariv, 2021. "Equitable Voting Rules," Econometrica, Econometric Society, vol. 89(2), pages 563-589, March.
    8. Frederik Herzberg, 2015. "Aggregating infinitely many probability measures," Theory and Decision, Springer, vol. 78(2), pages 319-337, February.
    9. Bossert, Walter & Cato, Susumu, 2020. "Acyclicity, anonymity, and prefilters," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 134-141.

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