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 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.
|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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- H. Reiju Mihara, 1996.
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276, Minnesota - Center for Economic Research.
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- Barton L. Lipman, 1993.
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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.
- KIRMAN, Alan P. & SONDERMANN, Dieter, .
"Arrow's theorem, many agents, and indivisible dictators,"
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-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.
- Armstrong, Thomas E., 1980. "Arrow's theorem with restricted coalition algebras," Journal of Mathematical Economics, Elsevier, vol. 7(1), pages 55-75, March.
- Pazner, Elisha A & Wesley, Eugene, 1978. "Cheatproofness Properties of the Plurality Rule in Large Societies," Review of Economic Studies, Wiley Blackwell, vol. 45(1), pages 85-91, February.
- 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.
- Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
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