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A Study on Linear Inequality Representation of Social Welfare Functions

Author

Listed:
  • Keisuke Sato

    (University of Tsukuba, Japan)

  • Yoshitsugu Yamamoto

    (University of Tsukuba, Japan)

Abstract

This paper presents a study on the recently proposed linear inequality representation of Arrovian Social Welfare Functions (ASWFs). We first give an alternative proof of the ASWF integer linear inequality representation theorem, and then show several sufficient conditions on preference domains for the linear inequalities of the representation to form integral polytopes. We also show that a given probabilistic ASWF induces a real vector satisfying the inequalities.

Suggested Citation

  • Keisuke Sato & Yoshitsugu Yamamoto, 2006. "A Study on Linear Inequality Representation of Social Welfare Functions," Tinbergen Institute Discussion Papers 06-022/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20060022
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    File URL: https://papers.tinbergen.nl/06022.pdf
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    References listed on IDEAS

    as
    1. Barbera, Salvador & Sonnenschein, Hugo, 1978. "Preference aggregation with randomized social orderings," Journal of Economic Theory, Elsevier, vol. 18(2), pages 244-254, August.
    2. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    3. Kalai, Ehud & Muller, Eitan, 1977. "Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures," Journal of Economic Theory, Elsevier, vol. 16(2), pages 457-469, December.
    4. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    5. McLennan, Andrew, 1980. "Randomized preference aggregation: Additivity of power and strategy proofness," Journal of Economic Theory, Elsevier, vol. 22(1), pages 1-11, February.
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    Cited by:

    1. Ehlers, Lars & Storcken, Ton, 2008. "Arrow's Possibility Theorem for one-dimensional single-peaked preferences," Games and Economic Behavior, Elsevier, vol. 64(2), pages 533-547, November.

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    More about this item

    Keywords

    Social welfare function; Linear inequality representation; Extreme points; Probabilistic social welfare function; Integral polytope;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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