# Arrow's Theorem and Turing Computability

*H. Reiju Mihara*

Public Economics from EconWPA

**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.

**JEL-codes:** D71 C69 D89 (search for similar items in EconPapers)

**New Economics Papers:** this item is included in nep-cdm, nep-pbe and nep-pub

**Date:** 1994-08-23, Revised 1998-08-06

**Note:** LaTeX2.09 file; Appeared in Economic Theory 10, 257--276 (1997)

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**Related works:**

Journal Article: Arrow's Theorem and Turing computability (1997)

Working Paper: Arrow's Theorem and Turing Computability (1994)

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**Persistent link:** http://EconPapers.repec.org/RePEc:wpa:wuwppe:9408001

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