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Arrow's Theorem, countably many agents, and more visible invisible dictators

H. Reiju Mihara

Public Economics from University Library of Munich, Germany

Abstract: For infinite societies, Fishburn (1970), Kirman and Sondermann (1972), and Armstrong (1980) gave a nonconstructive proof of the existence of a social welfare function satisfying Arrow's conditions (Unanimity, Independence, and Nondictatorship). This paper improves on their results by (i) giving a concrete example of such a function, and (ii) showing how to compute, from a description of a profile on a pair of alternatives, which alternative is socially preferred under the function. The introduction of a certain "oracle" resolves Mihara's impossibility result (1997) about computability of social welfare functions.

Keywords: Arrow impossibility theorem; Turing computability; recursion theory; oracle algorithms; free ultrafilters (search for similar items in EconPapers)
JEL-codes: C69 C71 D71 (search for similar items in EconPapers)
Date: 1997-05-06, Revised 2004-06-01
Note: Journal of Mathematical Economics (1999) 32: 267-287
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