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

Authors

  • Yasuhito Tanaka

    1. Doshisha University
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      I would like to thank two anonymous referees for their valuable comments which substantially improved the quality of this paper. Of course any remaining errors are mine. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid in Japan.


Yasuhito Tanaka
Department of Faculty of Economics
Kamigyo-ku
Kyoto 602-8580
Japan
E-mail: yatanaka@mail.doshisha.ac.jp

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.

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