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THE HEX GAME THEOREM AND THE ARROW IMPOSSIBILITY THEOREM: THE CASE OF WEAK ORDERS
Author(s) -
Tanaka Yasuhito
Publication year - 2009
Publication title -
metroeconomica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.256
H-Index - 29
eISSN - 1467-999X
pISSN - 0026-1386
DOI - 10.1111/j.1467-999x.2008.00332.x
Subject(s) - arrow's impossibility theorem , impossibility , fixed point theorem , brouwer fixed point theorem , kakutani fixed point theorem , fundamental theorem , equivalence (formal languages) , mathematical economics , mathematics , arrow , social choice theory , discrete mathematics , schauder fixed point theorem , computer science , political science , law , programming language
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.