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Solving the Social Choice problem under equality constraints

Author

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  • Crespo, Juan A.
  • Sanchez-Gabites, J.J

Abstract

Suppose that a number of equally qualified agents want to choose collectively an element from a set of alternatives defined by equality constraints. Each agent may well prefer a different element, and the social choice problem consists in deciding whether it is possible to design a rule to aggregate all the agents’ preferences into a social choice in an egalitarian way. In this paper we obtain criteria that solve this problem in terms of conditions that are explicitly computable from the constraints. As a theoretical consequence, we show that the only way to avoid running into a social choice paradox consists in designing (if possible) the set of alternatives satisfying certain optimality condition on the constraints, that is, in the natural way from the point of view of economics.

Suggested Citation

  • Crespo, Juan A. & Sanchez-Gabites, J.J, 2016. "Solving the Social Choice problem under equality constraints," MPRA Paper 72757, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:72757
    as

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    References listed on IDEAS

    as
    1. Candeal, Juan Carlos & Indurain, Esteban, 1994. "The Moebius strip and a social choice paradox," Economics Letters, Elsevier, vol. 45(3), pages 407-412.
    2. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
    3. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
    4. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
    5. Fuente,Angel de la, 2000. "Mathematical Methods and Models for Economists," Cambridge Books, Cambridge University Press, number 9780521585293.
    6. Baigent, Nicholas, 2011. "Chapter Eighteen - Topological Theories of Social Choice," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 18, pages 301-334, Elsevier.
    7. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Social choice; optimization; rational design.;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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