Arrow's Theorem and Turing Computability
1994-08
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Arrow's Theorem and Turing Computability
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1994-08
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Center for Economic Research, Department of Economics, University of Minnesota
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Working Paper
Abstract
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, https://hdl.handle.net/11299/55723.
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