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A necessary and sufficient condition for Wilson's impossibility theorem with strict non-imposition

Author

Listed:
  • Yasuhito Tanaka

    (Faculty of Law, Chuo University)

Abstract

Wilson's impossibility theorem (Wilson(1972)) about Arrovian social welfare functions (Arrow(1963)) states that there exists a dictator or an inverse-dictator for any non-null social welfare function which satisfies the conditions of unrestricted domain, non-imposition and independence of irrelevant alternatives (IIA). Among these conditions IIA is very strong and controversial. We will show that, under the condition of strict non-imposition which is stronger than non-imposition, IIA can be replaced by weaker condition. We call this condition "monotonicity". We will also show that under strict non-imposition it is necessary and sufficient condition for Wilson''s theorem, that is, it is equivalent to dictatorship or inverse-dictatorship of Arrovian social welfare functions under unrestricted domain and strict non-imposition.

Suggested Citation

  • Yasuhito Tanaka, 2003. "A necessary and sufficient condition for Wilson's impossibility theorem with strict non-imposition," Economics Bulletin, AccessEcon, vol. 4(17), pages 1-8.
    • Handle: RePEc:ebl:ecbull:eb-02d70020
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    References listed on IDEAS

    as
    1. k. g. binmore, 1976. "Social Choice and Parties," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 459-464.
    2. Vincenzo DenicolÔ, 1998. "Independent Decisiveness and the Arrow theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 563-566.
    3. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
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    Cited by:

    1. Donald Campbell & Jerry Kelly, 2014. "Universally beneficial manipulation: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 329-355, August.

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    More about this item

    Keywords

    inverse monotonicity;

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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