Review of Economic Design

, Volume 17, Issue 3, pp 205–238 | Cite as

The structure of decision schemes with cardinal preferences

  • Shasikanta Nandeibam
Original Paper


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.


Decision scheme Strategy proofness Unanimity Weak dictatorship Weak random dictatorship 

JEL Classification

D71 D82 C72 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Economics and International DevelopmentUniversity of BathBathUK

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