A geometric proof of Gibbard's random dictatorship theorem |
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Authors: | John Duggan |
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Institution: | (1) Division of the Humanities and Social Sciences, Caltech, 91125 Pasadena, CA, USA;(2) Present address: Department of Economics, Queen's University, K7L 3N6 Kingston, Ont., Canada |
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Abstract: | Summary Gibbard has shown that a social choice function is strategy-proof if and only if it is a convex combination of dictatorships and pair-wise social choice functions. I use geometric techniques to prove the corollary that every strategy-proof and sovereign social choice function is a random dictatorship.I thank Kim Border for several useful discussions and many insightful comments. |
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