Arrow's Theorem and Turing Computability

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Arrow's Theorem and Turing Computability

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Center for Economic Research, Department of Economics, University of Minnesota


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A social welfare function for an infinite society satisfies Pairwise Computability if for each pair (x, y) of alternatives, there exists an algorithm that can decide from a description of a 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 must be dictatorial. This result severely limits on practical grounds Fishburn's resolution (1970) of Arrow's impossibility. An interpretation of an infinite "society" is also given.


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Mihara, H.R., (1994), "Arrow's Theorem and Turing Computability", Discussion Paper No. 276, Center for Economic Research, Department of Economics, University of Minnesota.

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Mihara, H. Reiju. (1994). Arrow's Theorem and Turing Computability. Retrieved from the University Digital Conservancy,

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