Arrow's Theorem, countably many agents, and more visible invisible dictators
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.
|Date of creation:||06 May 1997|
|Date of revision:||07 May 1997|
|Note:||Journal of Mathematical Economics (1999) 32: 267 |287|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
- Kelly, Jerry S., 1988. "Social choice and computational complexity," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 1-8, February.
- H. Reiju Mihara, 1997.
"Arrow's Theorem and Turing computability,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 257-276.
- Ehud Kalai, 1987. "Bounded Rationality and Strategic Complexity in Repeated Games," Discussion Papers 783, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Spear, Stephen E, 1989. "Learning Rational Expectations under Computability Constraints," Econometrica, Econometric Society, vol. 57(4), pages 889-910, July.
- Barton L. Lipman, 1993.
"Information Processing and Bounded Rationality: A Survey,"
872, Queen's University, Department of Economics.
- Barton L. Lipman, 1995. "Information Processing and Bounded Rationality: A Survey," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 42-67, February.
- Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
- Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
- Lewis, Alain A., 1988. "An infinite version of arrow's theorem in the effective setting," Mathematical Social Sciences, Elsevier, vol. 16(1), pages 41-48, August.
- KIRMAN, Alan P. & SONDERMANN, Dieter, .
"Arrow's theorem, many agents, and indivisible dictators,"
CORE Discussion Papers RP
118, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
- Elisha A. Pazner & Eugene Wesley, 1978. "Cheatproofness Properties of the Plurality Rule in Large Societies," Review of Economic Studies, Oxford University Press, vol. 45(1), pages 85-91.
- Anderlini, L. & Felli, L., 1993.
"Incomplete Written Contracts: Undescribable States of Nature,"
183, Cambridge - Risk, Information & Quantity Signals.
- Luca Anderlini & Leonardo Felli, 1994. "Incomplete Written Contracts: Undescribable States of Nature," The Quarterly Journal of Economics, Oxford University Press, vol. 109(4), pages 1085-1124.
- H. Reiju Mihara, 2001.
"Existence of a coalitionally strategyproof social choice function: A constructive proof,"
Social Choice and Welfare,
Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 543-553.
- H. Reiju Mihara, 1996. "Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof," Public Economics 9604002, EconWPA, revised 20 Sep 1996.
This item is featured on the following reading lists or Wikipedia pages:
- Ultrafilter in Wikipedia English ne '')
- الگو:Cite doi/10.1016.2FS0304-4068.2898.2900061-5 in Wikipedia Persian ne '')
- Txantiloi:Cite doi/10.1016.2FS0304-4068.2898.2900061-5 in Wikipedia Basque ne '')
- Arrow's impossibility theorem in Wikipedia English ne '')
- User:Theorist2/Unused stuffs in Wikipedia English ne '')
- Template:Cite doi/10.1016.2FS0304-4068.2898.2900061-5 in Wikipedia Japanese ne '')
- アローの不可能性定理 in Wikipedia Japanese ne '')
- フィルター (数学) in Wikipedia Japanese ne '')
- قالب:Cite doi/10.1016.2FS0304-4068.2898.2900061-5 in Wikipedia Arabic ne '')
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwppe:9705001. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.