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The structure of decision schemes with cardinal preferences

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  • Shasikanta Nandeibam

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    Abstract

    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

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    Bibliographic Info

    Article provided by Springer in its journal Review of Economic Design.

    Volume (Year): 17 (2013)
    Issue (Month): 3 (September)
    Pages: 205-238

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    Handle: RePEc:spr:reecde:v:17:y:2013:i:3:p:205-238

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    Related research

    Keywords: Decision scheme; Strategy proofness; Unanimity; Weak dictatorship; Weak random dictatorship; D71; D82; C72;

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    1. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-81, April.
    2. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
    3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    4. James Schummer, 1999. "Strategy-proofness versus efficiency for small domains of preferences over public goods," Economic Theory, Springer, vol. 13(3), pages 709-722.
    5. Laffont, Jean-Jacques & Maskin, Eric, 1980. "A Differential Approach to Dominant Strategy Mechanisms," Econometrica, Econometric Society, vol. 48(6), pages 1507-20, September.
    6. Barbera, Salvador, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 379-89, April.
    7. 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.
    8. 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.
    9. Freixas, Xavier, 1984. "A cardinal approach to straightforward probabilistic mechanisms," Journal of Economic Theory, Elsevier, vol. 34(2), pages 227-251, December.
    10. Barbera, Salvador, 1979. "A Note on Group Strategy-Proof Decision Schemes," Econometrica, Econometric Society, vol. 47(3), pages 637-40, May.
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