Arrow's Theorem, countably many agents, and more visible invisible dictators
AbstractFor infinite societies, Fishburn (1970), Kirman and Sondermann (1972), and Armstrong (1980) gave a nonconstructive proof of the existence of a social welfare function satisfying Arrowfs 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 goracleh resolves Miharafs impossibility result (1997) about computability of social welfare functions.
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Bibliographic InfoPaper provided by EconWPA in its series Public Economics with number 9705001.
Date of creation: 06 May 1997
Date of revision: 07 May 1997
Note: Journal of Mathematical Economics (1999) 32: 267|287
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Arrow impossibility theorem; Turing computability; recursion theory; oracle algorithms; free ultrafilters;
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- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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