Abstract
This paper proves stronger versions of the Gibbard random dictatorship theorem using induction on the number of voters. It shows that when there are at least three voters, every random social choice function defined on a domain satisfying a Free Triple at the Top property and satisfying a weak form of strategy-proofness called Limited-Comparison Strategy-proofness and Unanimity, is a random dictatorship provided that there are at least three alternatives. The weaker notion of strategy-proofness requires truth-telling to maximize a voter’s expected utility only for a limited class of von Neumann–Morgenstern utility representations of the voter’s true preference ordering. In the case of two voters, an even weaker condition on the domain and a weaker notion of strategy-proofness are sufficient for the random dictatorship result.
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References
Aswal N, Chatterji S, Sen A (2003) Dictatorial domains. Econ Theory 22: 45–62
Barberà S (1977) The Manipulation of social choice functions that do not leave “Too Much” to chance. Econometrica 45: 1573–1588
Barberà S (1979) Majority and positional voting in a probabilistic framework. Rev Econ Stud 46: 379–389
Chatterji S, Sen A (2010) Tops-only domains. Econ Theory (forthcoming)
Duggan J (1996) A geometric proof of Gibbard’s random dictatorship theorem. Econ. Theory 7: 365–369
Dutta B, Peters H, Sen A (2002) Strategy-proof probabilistic mechanisms in economies with pure public goods. J Econ Theory 106: 392–416
Ehlers L, Peters H, Storcken T (2002) Strategy-proof probabilistic decision schemes for one-dimensional single-peaked preferences. J Econ Theory 105: 408–434
Gibbard A (1973) The manipulation of voting schemes: a general result. Econometrica 41: 587–601
Gibbard A (1977) Manipulation of voting schemes that mix voting with chance. Econometrica 45: 665–681
Satterthwaite M (1975) Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10: 187–217
Sen A (2001) Another direct proof of the Gibbard–Satterthwaite theorem. Economics Letters 70: 381–385
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Salvador Barberà is one of the pioneers in probabilistic mechanism design theory. He introduced me to the subject when I visited the Economics Department of the Universitat Autònoma de Barcelona in 1987. My own ideas in this area and on the theory of strategy-proofness in general have been strongly shaped by his work and by numerous discussions I have had with him over the years. It is a particular pleasure to be able to contribute to a volume celebrating his 65th birthday. I would also like to thank Debasis Mishra, Souvik Roy and two anonymous referees of the journal for their comments on the paper.
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Sen, A. The Gibbard random dictatorship theorem: a generalization and a new proof. SERIEs 2, 515–527 (2011). https://doi.org/10.1007/s13209-011-0041-z
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DOI: https://doi.org/10.1007/s13209-011-0041-z