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

*H. Mihara*

Public Economics from EconWPA

**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 fs 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 goracle h resolves Mihara fs 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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**Citations** View citations in EconPapers (6) Track citations by RSS feed

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**Persistent link:** http://EconPapers.repec.org/RePEc:wpa:wuwppe:9705001

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