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Arrow’s (im)possibility theorem

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  • Pierre Bernhard

    (BIOCORE - Biological control of artificial ecosystems - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - INRA - Institut National de la Recherche Agronomique - LOV - Laboratoire d'océanographie de Villefranche - INSU - CNRS - Institut national des sciences de l'Univers - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - IMEV - Institut de la Mer de Villefranche - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

  • Marc Deschamps

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

Abstract

Arrow's (im)possibility theorem is one of the most famous and important contri- butions in economics. It concerns the difficulty to aggregate a set of individual preferences, given as rankings of a set of available alternatives, into a unique social preferences ranking via a social welfare function, or into a unique social choice. Arrow proves that in a specific framework, it is impossible to find a social welfare function which simultaneously satisfies four conditions: universal domain, weak Pareto principle, independence of irrelevant alternatives, and no dictator. Our no- tice presents this theorem, one of its proofs, and, we hope, invites the reader to discover social choice theory

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  • Pierre Bernhard & Marc Deschamps, 2018. "Arrow’s (im)possibility theorem," Post-Print hal-01941037, HAL.
    • Handle: RePEc:hal:journl:hal-01941037
    Note: View the original document on HAL open archive server: https://inria.hal.science/hal-01941037v1
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    References listed on IDEAS

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    1. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
    2. Patrick Suppes, 2005. "The pre-history of Kenneth Arrow's social choice and individual values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 319-326, December.
    3. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
    4. 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.
    5. repec:bla:econom:v:44:y:1977:i:173:p:81-88 is not listed on IDEAS
    6. Kenneth J. Arrow, 1987. "Arrow on Arrow: an Interview," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy, chapter 23, pages 637-657, Palgrave Macmillan.
    7. Barbera, Salvador, 1980. "Pivotal voters : A new proof of arrow's theorem," Economics Letters, Elsevier, vol. 6(1), pages 13-16.
    8. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    9. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    10. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    11. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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