Smallness of Invisible Dictators
AbstractFishburn (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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0213.
Length: 24 pages
Date of creation: Nov 2002
Date of revision: Sep 2003
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; Programming Models; Mathematical and Simulation Modeling - - - Other
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.:
- Andrei Gomberg & César Martinelli & Ricard Torres, 2005.
"Anonymity in large societies,"
Social Choice and Welfare,
Springer, vol. 25(1), pages 187-205, October.
- 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.
- 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.
- 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.
- Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Diego Dominguez).
If references are entirely missing, you can add them using this form.