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Smallness of Invisible Dictators

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Author Info
Ricard Torres () (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM), Universitat de Girona)
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 Format: application/pdf
File Function: First version, 2002
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Publisher Info
Paper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0213.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
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;

Find related papers by JEL classification:
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
C69 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Other

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Andrei Gomberg & Cesar Martinelli & Ricard Torres, 2002. "Anonymity in Large Societies," Working Papers 0211, Centro de Investigacion Economica, ITAM. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!] (restricted)
  3. Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003. "Social Choice and Electoral Competition in the General Spatial Model," IDEI Working Papers 188, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
    Other versions:
  4. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March. [Downloadable!] (restricted)
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This page was last updated on 2009-11-25.

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