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The structure of decision schemes with cardinal preferences


Reference:

Nandeibam, S., 2013. The structure of decision schemes with cardinal preferences. Review of Economic Design, 17 (3), pp. 205-238.

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http://dx.doi.org/10.1007/s10058-012-0130-x

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Abstract

This paper replaces Gibbard'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.

Details

Item Type Articles
CreatorsNandeibam, S.
DOI10.1007/s10058-012-0130-x
Related URLs
URLURL Type
http://www.scopus.com/inward/record.url?eid=2-s2.0-84863968691&partnerID=8YFLogxKUNSPECIFIED
DepartmentsFaculty of Humanities & Social Sciences > Economics
RefereedYes
StatusPublished
ID Code30891

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