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May’s Theorem with an infinite population

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  • Mark Fey

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    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

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    Bibliographic Info

    Article provided by Springer in its journal Social Choice and Welfare.

    Volume (Year): 23 (2004)
    Issue (Month): 2 (October)
    Pages: 275-293

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    Handle: RePEc:spr:sochwe:v:23:y:2004:i:2:p:275-293

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    Cited by:
    1. Kumabe, Masahiro & Mihara, H. Reiju, 2006. "Computability of simple games: A characterization and application to the core," MPRA Paper 437, University Library of Munich, Germany.
    2. Frederik Herzberg, 2014. "Aggregating infinitely many probability measures," Working Papers 499, Bielefeld University, Center for Mathematical Economics.
    3. Susumu Cato, 2011. "Pareto principles, positive responsiveness, and majority decisions," Theory and Decision, Springer, vol. 71(4), pages 503-518, October.
    4. 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.

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