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Anonymity in large societies

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Author Info

  • Andrei Gomberg

    ()

  • César Martinelli

    ()

  • Ricard Torres

    ()

Abstract

In a social choice model with an infinite number of agents, there may occur "equal size" coalitions that a preference aggregation rule should treat in the same manner. We introduce an axiom of equal treatment with respect to a measure of coalition size and explore its interaction with common axioms of social choice. We show that, provided the measure space is sufficiently rich in coalitions of the same measure, the new axiom is the natural extension of the concept of anonymity, and in particular plays a similar role in the characterization of preference aggregation rules.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s0355-005-0051-5
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Bibliographic Info

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

Volume (Year): 25 (2005)
Issue (Month): 1 (October)
Pages: 187-205

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Handle: RePEc:spr:sochwe:v:25:y:2005:i:1:p:187-205

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References

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  1. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
  2. Armstrong, Thomas E., 1985. "Precisely dictatorial social welfare functions : Erratum and Addendum to `arrows theorem with restricted coalition algebras'," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 57-59, February.
  3. Luc Lauwers, 1997. "Topological aggregation, the case of an infinite population," Social Choice and Welfare, Springer, vol. 14(2), pages 319-332.
  4. Jeffrey Banks & John Duggan & Michel Le Breton, . "Social Choice in the General Spatial Model of Politics," Wallis Working Papers WP26, University of Rochester - Wallis Institute of Political Economy.
  5. H. Reiju Mihara, 1997. "Anonymity and neutrality in Arrow's Theorem with restricted coalition algebras," Social Choice and Welfare, Springer, vol. 14(4), pages 503-512.
  6. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
  7. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, vol. 10(2), pages 257-276.
  8. Schmitz, Norbert, 1977. "A further note on arrow's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 189-196, August.
  9. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
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Citations

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Cited by:
  1. 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.
  2. Kari Saukkonen, 2007. "Continuity of social choice functions with restricted coalition algebras," Social Choice and Welfare, Springer, vol. 28(4), pages 637-647, June.
  3. H. Reiju Mihara, 2003. "Nonanonymity and sensitivity of computable simple games," Game Theory and Information 0310006, EconWPA, revised 01 Jun 2004.
  4. Ricard Torres, 2002. "Smallness of Invisible Dictators," Working Papers 0213, Centro de Investigacion Economica, ITAM, revised Sep 2003.
  5. Torres, Ricard, 2005. "Limiting Dictatorial rules," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 913-935, November.

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