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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

Suggested Citation

  • Shasikanta Nandeibam, 2013. "The structure of decision schemes with cardinal preferences," Review of Economic Design, Springer;Society for Economic Design, vol. 17(3), pages 205-238, September.
  • Handle: RePEc:spr:reecde:v:17:y:2013:i:3:p:205-238
    DOI: 10.1007/s10058-012-0130-x
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    References listed on IDEAS

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    1. Salvador Barbera, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Oxford University Press, vol. 46(2), pages 379-389.
    2. 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.
    3. Freixas, Xavier, 1984. "A cardinal approach to straightforward probabilistic mechanisms," Journal of Economic Theory, Elsevier, vol. 34(2), pages 227-251, December.
    4. Gibbard, Allan, 1978. "Straightforwardness of Game Forms with Lotteries as Outcomes," Econometrica, Econometric Society, vol. 46(3), pages 595-614, May.
    5. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    6. Barbera, Salvador, 1979. "A Note on Group Strategy-Proof Decision Schemes," Econometrica, Econometric Society, vol. 47(3), pages 637-640, May.
    7. 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.
    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. Laffont, Jean-Jacques & Maskin, Eric, 1980. "A Differential Approach to Dominant Strategy Mechanisms," Econometrica, Econometric Society, vol. 48(6), pages 1507-1520, September.
    10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Citations

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    Cited by:

    1. Yves SPRUMONT, 2016. "Strategy-proof Choice of Acts : A Preliminary Study," Cahiers de recherche 07-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Brandl, Florian & Brandt, Felix & Suksompong, Warut, 2016. "The impossibility of extending random dictatorship to weak preferences," Economics Letters, Elsevier, vol. 141(C), pages 44-47.
    3. BAHEL, Eric & SPRUMONT, Yves, 2017. "Strategyproof choice of acts: beyond dictatorship," Cahiers de recherche 2017-01, Universite de Montreal, Departement de sciences economiques.

    More about this item

    Keywords

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

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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