Weber, Tjark (2009): Alternatives vs. Outcomes: A Note on the GibbardSatterthwaite Theorem.

PDF
MPRA_paper_17836.pdf Download (133kB)  Preview 
Abstract
The GibbardSatterthwaite theorem is a wellknown 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 GibbardSatterthwaite 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 GibbardSatterthwaite theorem can be derived from the seemingly less general formulation.
Item Type:  MPRA Paper 

Original Title:  Alternatives vs. Outcomes: A Note on the GibbardSatterthwaite Theorem 
Language:  English 
Keywords:  GibbardSatterthwaite theorem; infeasible alternatives 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice; Clubs; Committees; Associations 
Item ID:  17836 
Depositing User:  Tjark Weber 
Date Deposited:  13. Oct 2009 04:33 
Last Modified:  08. Jan 2014 07:16 
References:  Kenneth J. Arrow. A difficulty in the concept of social welfare. Journal of Political Economy, 58(4):328346, August 1950. Salvador Barbera. Strategyproofness and pivotal voters: A direct proof of the GibbardSatterthwaite theorem. International Economic Review, 24(2):413417, 1983. JeanPierre Benoit. The GibbardSatterthwaite theorem: a simple proof. Economics Letters, 69(3):319322, December 2000. John Duggan and Thomas Schwartz. Strategic manipulability without resoluteness or shared beliefs: GibbardSatterthwaite generalized. Social Choice and Welfare, 17(1):8593, 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, 32:137142, 1977. Allan Gibbard. Manipulation of voting schemes: a general result. Econometrica, 41(4):587601, 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 strategyproofness. Journal of Economic Theory, 14(2):412418, April 1977. Tobias Nipkow. Social choice theory in HOL: Arrow and GibbardSatterthwaite. Journal of Automated Reasoning, 2009. To appear. Paramesh Ray. Independence of irrelevant alternatives. Econometrica, 41(5):987991, September 1973. Philip J. Reny. Arrow's theorem and the GibbardSatterthwaite theorem: a unified approach. Economics Letters, 70(1):99105, January 2001. Mark A. Satterthwaite. Strategyproofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory, 10:187217, April 1975. D. Schmeidler and H. Sonnenschein. Two proofs of the GibbardSatterthwaite theorem on the possibility of a strategyproof social choice function. In H. Gottinger and W. Leinfellner, editors, Decision Theory and Social Ethics: Issues in Social Choice, pages 227234. D. Reidel Publishing Company, Dordrecht, 1978. LarsGunnar Svensson. The proof of the GibbardSatterthwaite 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. GibbardSatterthwaite 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. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/17836 