Arrow's Theorem, countably many agents, and more visible invisible dictators
H. Reiju Mihara
Public Economics from University Library of Munich, Germany
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: D71 C69 C71 (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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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwppe:9705001
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