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Smallness of Invisible Dictators

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  • Ricard Torres

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

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    Abstract

    Fishburn (1970) showed that in an infinite society Arrow's axioms for a preference aggregation rule do not necessarily imply a dictator. Kirman and Sondermann (1972) showed that, in this case, nondictatorial rules imply an invisible dictator that, whenever the agent set is an atomless finite measure space, can be viewed as the limit of coalitions of arbitrarily small size. We show first that, when admissible coalitions are restricted to an algebra, there are two sorts of invisible dictators. We next show that, in most cases of interest, we do not need to resort to measures on the agent space to give a precise meaning to the statement that invisible dictators are the limit of arbitrarily small decisive coalitions.

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    File URL: http://ftp.itam.mx/pub/academico/inves/torres/02-13.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 0213.

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    Length: 24 pages
    Date of creation: Nov 2002
    Date of revision: Sep 2003
    Handle: RePEc:cie:wpaper:0213

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    Related research

    Keywords: Preference aggregation; Arrow´s Theorem; Invisible Dictators; Ultrafilter Property; Strict Neutrality;

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    1. 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.
    2. 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.
    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. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers 0211, Centro de Investigacion Economica, ITAM.
    5. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
    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.
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