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Arrovian juntas

Author

Listed:
  • Eisermann, Michael

Abstract

This article explicitly constructs and classifies all arrovian voting systems on three or more alternatives. If we demand orderings to be complete, we have, of course, Arrow's classical dictator theorem, and a closer look reveals the classification of all such voting systems as dictatorial hierarchies. If we leave the traditional realm of complete orderings, the picture changes. Here we consider the more general setting where alternatives may be incomparable, that is, we allow orderings that are reflexive and transitive but not necessarily complete. Instead of a dictator we exhibit a junta whose internal hierarchy or coalition structure can be surprisingly rich. We give an explicit description of all such voting systems, generalizing and unifying various previous results.

Suggested Citation

  • Eisermann, Michael, 2006. "Arrovian juntas," MPRA Paper 81, University Library of Munich, Germany, revised 03 Oct 2006.
  • Handle: RePEc:pra:mprapa:81
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    File URL: https://mpra.ub.uni-muenchen.de/81/1/MPRA_paper_81.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Bernard Monjardet, 2005. "Social choice theory and the “Centre de Mathématique Sociale”: some historical notes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 433-456, December.
    4. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    5. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    6. Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    rank aggregation problem; Arrow's impossibility theorem; classification of arrovian voting systems; partial ordering; partially ordered set; poset; dictator; oligarchy; junta;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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