Weber, Tjark (2009): Alternatives vs. Outcomes: A Note on the Gibbard-Satterthwaite Theorem.
Download (130Kb) | Preview
The Gibbard-Satterthwaite theorem is a well-known theorem from the field of social choice theory. It states that every voting scheme with at least 3 possible outcomes is dictatorial or manipulable. Later work on the Gibbard-Satterthwaite theorem frequently does not distinguish between alternatives and outcomes, thereby leading to a less general statement that requires the voting scheme to be onto. We show how the Gibbard-Satterthwaite theorem can be derived from the seemingly less general formulation.
|Item Type:||MPRA Paper|
|Original Title:||Alternatives vs. Outcomes: A Note on the Gibbard-Satterthwaite Theorem|
|Keywords:||Gibbard-Satterthwaite theorem; infeasible alternatives|
|Subjects:||D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice; Clubs; Committees; Associations|
|Depositing User:||Tjark Weber|
|Date Deposited:||13. Oct 2009 04:33|
|Last Modified:||08. Jan 2014 07:16|
Kenneth J. Arrow. A difficulty in the concept of social welfare. Journal of Political Economy, 58(4):328-346, August 1950.
Salvador Barbera. Strategy-proofness and pivotal voters: A direct proof of the Gibbard-Satterthwaite theorem. International Economic Review, 24(2):413-417, 1983.
Jean-Pierre Benoit. The Gibbard-Satterthwaite theorem: a simple proof. Economics Letters, 69(3):319-322, December 2000.
John Duggan and Thomas Schwartz. Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized. Social Choice and Welfare, 17(1):85-93, January 2000.
Allan M. Feldman and Roberto Serrano. Welfare Economics and Social Choice Theory. Birkhäuser, 2006.
Peter Gärdenfors. A concise proof of a theorem on manipulation of social choice functions. Public Choice, 32:137-142, 1977.
Allan Gibbard. Manipulation of voting schemes: a general result. Econometrica, 41(4):587-601, July 1973. Reprinted in Charles K. Rowley, ed., Social Choice Theory (Cheltenham: Edward Elgar, 1993).
Eitan Muller and Mark A. Satterthwaite. The equivalence of strong positive association and strategy-proofness. Journal of Economic Theory, 14(2):412-418, April 1977.
Tobias Nipkow. Social choice theory in HOL: Arrow and Gibbard-Satterthwaite. Journal of Automated Reasoning, 2009. To appear.
Paramesh Ray. Independence of irrelevant alternatives. Econometrica, 41(5):987-991, September 1973.
Philip J. Reny. Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach. Economics Letters, 70(1):99-105, January 2001.
Mark A. Satterthwaite. Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10:187-217, April 1975.
D. Schmeidler and H. Sonnenschein. Two proofs of the Gibbard-Satterthwaite theorem on the possibility of a strategy-proof social choice function. In H. Gottinger and W. Leinfellner, editors, Decision Theory and Social Ethics: Issues in Social Choice, pages 227-234. D. Reidel Publishing Company, Dordrecht, 1978.
Lars-Gunnar Svensson. The proof of the Gibbard-Satterthwaite theorem revisited. Working Papers from Lund University, Department of Economics, 1, 1999.
Alan D. Taylor. Social Choice and the Mathematics of Manipulation. Outlooks. Cambridge University Press, 2005.
Wikipedia. Gibbard-Satterthwaite theorem. In Wikipedia, The Free Encyclopedia. 2009. Retrieved September 1, 2009, from http://en.wikipedia.org/w/index.php?title=Gibbard% E2%80%93Satterthwaite_theorem&oldid=292659871.