THE HEX GAME THEOREM AND THE ARROW IMPOSSIBILITY THEOREM: THE CASE OF WEAK ORDERS

Yasuhito Tanaka

Metroeconomica, 2009, vol. 60, issue 1, pages 77-90

Abstract: The Arrow impossibility theorem when individual preferences are weak orders is equivalent to the HEX game theorem. Because Gale showed that the Brouwer fixed point theorem is equivalent to the HEX game theorem, this paper indirectly shows the equivalence of the Brouwer fixed point theorem and the Arrow impossibility theorem. Chichilnisky showed the equivalence of her impossibility theorem and the Brouwer fixed point theorem, and Baryshnikov showed that the impossibility theorem by Chichilnisky and the Arrow impossibility theorem are very similar. Thus, Chichilnisky and Baryshnikov are precedents for the result-linking the Arrow impossibility theorem to a fixed point theorem. Copyright © 2008 The Author. Journal compilation © 2008 Blackwell Publishing Ltd.

Date: 2009

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