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On the Arrow and Wilson impossibility theorems

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  • Donald E. Campbell
  • Jerry S. Kelly

Abstract

A social welfare function is Arrovian if it is transitive-valued and satisfies IIA. We examine the logical relation between the statements (A) If f is Arrovian with domain F then it is dictatorial if it satisfies the Pareto criterion and (W) If f is Arrovian with domain F then it is dictatorial or inversely dictatorial if it is non-null and satisfies non-imposition. We exhibit a class of domains on which W implies A and another on which A implies W. We also present examples of domains on which one of the statements is true and the other is false. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Donald E. Campbell & Jerry S. Kelly, 2003. "On the Arrow and Wilson impossibility theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(2), pages 273-281, March.
    • Handle: RePEc:spr:sochwe:v:20:y:2003:i:2:p:273-281
    DOI: 10.1007/s003550200181
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    Cited by:

    1. Kruger, Justin & Sanver, M. Remzi, 2021. "The relationship between Arrow’s and Wilson’s theorems on restricted domains," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 95-97.
    2. Susumu Cato & Yohei Sekiguchi, 2012. "A generalization of Campbell and Kelly’s trade-off theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 237-246, February.
    3. 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.
    4. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.

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