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Anonymity in Large Societies

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  • Andrei Gomberg

    (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))

  • Cesar Martinelli

    ()
    (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))

  • Ricard Torres

    (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM), Universitat de Girona)

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.

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File URL: http://ftp.itam.mx/pub/academico/inves/martinelli/02-11.pdf
File Function: First version, 2002
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Bibliographic Info

Paper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0211.

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Length: 24 pages
Date of creation: Nov 2002
Date of revision:
Handle: RePEc:cie:wpaper:0211

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References

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  1. 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.
  2. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer, vol. 10(2), pages 257-276.
  3. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
  4. Schmitz, Norbert, 1977. "A further note on arrow's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 189-196, August.
  5. 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.
  6. Luc Lauwers, 1997. "Topological aggregation, the case of an infinite population," Social Choice and Welfare, Springer, vol. 14(2), pages 319-332.
  7. 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.
  8. 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.
  9. 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.
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Citations

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

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