TY - JOUR

T1 - The structure of decision schemes with cardinal preferences

AU - Nandeibam, Shashikanta

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84863968691&partnerID=8YFLogxK

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

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84863968691&partnerID=8YFLogxK

U2 - 10.1007/s10058-012-0130-x

DO - 10.1007/s10058-012-0130-x

M3 - Article

VL - 17

SP - 205

EP - 238

JO - Review of Economic Design

JF - Review of Economic Design

SN - 1434-4742

IS - 3

ER -