# Arrow's Theorem and Turing Computability

*H. Reiju Mihara*

Public Economics from University Library of Munich, Germany

**Abstract:**
A social welfare function for a denumerable society satisfies {Pairwise Computability} if for each pair (x, y) of alternatives, there exists an algorithm that can decide from any description of each profile on {x,y} whether the society prefers x to y. I prove that if a social welfare function satisfying Unanimity and Independence also satisfies Pairwise Computability, then it is dictatorial. This result severely limits on practical grounds Fishburn's resolution~(1970) of Arrow's impossibility. I also give an interpretation of a denumerable ``society.'' {Keywords} Arrow impossibility theorem, Hayek's knowledge problem, algorithms, recursion theory, ultrafilters.

**JEL-codes:** D71 C69 D89 (search for similar items in EconPapers)

**Date:** 1994-08-23, Revised 1998-08-06

**New Economics Papers:** this item is included in nep-cdm, nep-pbe and nep-pub

**Note:** LaTeX2.09 file; Appeared in Economic Theory 10, 257--276 (1997)

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

**Citations:** View citations in EconPapers (2) Track citations by RSS feed

**Downloads:** (external link)

https://econwpa.ub.uni-muenchen.de/econ-wp/pe/papers/9408/9408001.tex (application/x-tex)

https://econwpa.ub.uni-muenchen.de/econ-wp/pe/papers/9408/9408001.pdf (application/pdf)

https://econwpa.ub.uni-muenchen.de/econ-wp/pe/papers/9408/9408001.ps.gz (application/postscript)

**Related works:**

Journal Article: Arrow's Theorem and Turing computability (1997)

Working Paper: Arrow's Theorem and Turing Computability (1994)

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:** https://EconPapers.repec.org/RePEc:wpa:wuwppe:9408001

Access Statistics for this paper

More papers in Public Economics from University Library of Munich, Germany

Bibliographic data for series maintained by EconWPA ().