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 𝒫 then it is dictatorial if it satisfies the Pareto criterion and (W) If f is Arrovian with domain 𝒫 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.
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Received: 23 October 2001/Accepted: 19 March 2002
We thank our two referees for their suggestions for improving the exposition.
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Campbell, D., Kelly, J. On the Arrow and Wilson impossibility theorems. Soc Choice Welfare 20, 273–281 (2003). https://doi.org/10.1007/s003550200181
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DOI: https://doi.org/10.1007/s003550200181