The structure of decision schemes with cardinal preferences
This paper replacesGibbard’s (Econometrica 45:665-681, 1977 ) assumption of strict ordinal preferences by themore natural assumption of cardinal preferences on the set pure social alternatives and we also admit indifferences among the alternatives. By following a similar line of reasoning to the Gibbard-Satterthwaite theoremin the deterministic framework, we first show that if a decision scheme satisfies strategy proofness and unanimity, then there is an underlying probabilistic neutrality result which generates an additive coalitional power function. This result is then used to prove that a decision scheme which satisfies strategy proofness and unanimity can be represented as a weak random dictatorship. A weak random dictatorship assigns each individual a chance to be a weak dictator. An individual has weak dictatorial power if the support of the social choice lottery is always a subset of his/her maximal utility set. In contrast to Gibbard’s complete characterization of randomdictatorship, we also demonstrate with an example that strategy proofness and unanimity are sufficient but not necessary conditions for a weak random dictatorship. Copyright Springer-Verlag 2013
Volume (Year): 17 (2013)
Issue (Month): 3 (September)
|Contact details of provider:|| Web page: http://www.springer.com|
|Order Information:||Web: http://www.springer.com/economics/journal/10058|
References listed on IDEAS
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.:
- Salvador Barbera, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 379-389.
- Barbera, Salvador & Bogomolnaia, Anna & van der Stel, Hans, 1998.
"Strategy-proof probabilistic rules for expected utility maximizers,"
Mathematical Social Sciences,
Elsevier, vol. 35(2), pages 89-103, March.
- Barbera, S & Bogomolnaia, A & van der Stel, H, 1996. "Strategy-Proof Probabilistic Rules for Expected Utility Maximizers," UFAE and IAE Working Papers 330.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Freixas, Xavier, 1984. "A cardinal approach to straightforward probabilistic mechanisms," Journal of Economic Theory, Elsevier, vol. 34(2), pages 227-251, December.
- Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
- Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
- Barbera, Salvador, 1979. "A Note on Group Strategy-Proof Decision Schemes," Econometrica, Econometric Society, vol. 47(3), pages 637-640, May.
- James Schummer, 1999. "Strategy-proofness versus efficiency for small domains of preferences over public goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 709-722.
- Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
- Laffont, Jean-Jacques & Maskin, Eric, 1980. "A Differential Approach to Dominant Strategy Mechanisms," Econometrica, Econometric Society, vol. 48(6), pages 1507-1520, September.
- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July. Full references (including those not matched with items on IDEAS)