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

*H. Reiju 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

**References:** View references in EconPapers View complete reference list from CitEc

**Citations** View citations in EconPapers (8) Track citations by RSS feed

**Downloads:** (external link)

http://econwpa.repec.org/eps/pe/papers/9705/9705001.pdf (application/pdf)

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

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

Access Statistics for this paper

More papers in Public Economics from EconWPA

Series data maintained by EconWPA ().