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Arrow's Theorem and Turing Computability

 
Paper:ewp-pe/9408001
From:    
Date: Tue, 23 Aug 94 02:25:52 -0500
Date (revised): Tue, 23 Aug 94 03:19:50 -0500
Date (revised): Mon, 26 Aug 1996 18:16:13 +0900
Date (revised): Thu, 6 Aug 1998 22:12:54 +0900

Abstract:
A social welfare function for a denumerable society satisfies {Pairwise Computability} if for each pair (x, y) of alternatives, there exists an algorithm that can decide from any description of each profile on {x,y} whether the society prefers x to y. I prove that if a social welfare function satisfying Unanimity and Independence also satisfies Pairwise Computability, then it is dictatorial. This result severely limits on practical grounds Fishburn's resolution~(1970) of Arrow's impossibility. I also give an interpretation of a denumerable ``society.'' {Keywords} Arrow impossibility theorem, Hayek's knowledge problem, algorithms, recursion theory, ultrafilters.

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EconWPA began as a conversation between Bob Parks and Larry Blume on January 28, 1993. I located Paul Ginsparg's archive (then xxx.lanl.gov) and he graciously installed his software on a Sun Sparc system which was supporting the department of economics email and computation. EconWPA began accepting papers July 1, 1993 and had ftp, email, gopher and web interfaces. The web interface for submissions was engineered into existence in July 1995. A complete and catastrophic machine failure in 1999 caused the loss of EconWPA's email new paper announcment service at which time there were over 15,000 subscriptions with over 8,000 unique email addresses.

In 2005, Arts and Sciences commandeered the computing services that I had provided to the Department of Economics since 1987. Some might say that the department was sold out, others would (erroneously) claim that centralization is efficient, and still others would claim that I have few marketing skills.

I was told that I could keep operating EconWPA (as well as many other services including rfe.wustl.edu, barnett.wustl.edu, and three RePEc servers) but I would receive no support (hardware, software, or anthing else) and (as had been the case) no compensation. At that point, given the apparent low valuation of my activities by the department, and university, it made no sense for me to continue operating EconWPA or other services.

Thanks to all who have supported EconWPA in the past.

A Chinese curse states May you live in intersting times. I have. Bob Parks - Jan 2006