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

Yasuhito Tanaka

Metroeconomica, 2009, vol. 60, issue 1, 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.

Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/j.1467-999X.2008.00332.x

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:metroe:v:60:y:2009:i:1:p:77-90

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0026-1386

Access Statistics for this article

Metroeconomica is currently edited by Heinz D. Kurz and Neri Salvadori

More articles in Metroeconomica from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().