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Social Choice And The Arrow Conditions

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  • Gibbard, Allan F.

Abstract

Arrow’s impossibility result stems chiefly from a combination of two requirements: independence and fixity. Independence says that the social choice is independent of individual preferences involving unavailable alternatives. Fixity says that the social choice is fixed by a social preference relation that is independent of what is available. Arrow found that requiring, further, that this relation be transitive yields impossibility. Here it is shown that allowing intransitive social indifference still permits only a vastly unsatisfactory system, a liberum veto oligarchy. Arrow’s argument for independence, though, undermines any rationale for fixity.

Suggested Citation

  • Gibbard, Allan F., 2014. "Social Choice And The Arrow Conditions," Economics and Philosophy, Cambridge University Press, vol. 30(3), pages 269-284, November.
    • Handle: RePEc:cup:ecnphi:v:30:y:2014:i:03:p:269-284_00
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    Cited by:

    1. Chatterjee, Sidharta, 2022. "Rationalizing Decision Choices: What Influences our Social Decision Making?," MPRA Paper 114985, University Library of Munich, Germany.
    2. John Weymark, 2014. "An introduction to Allan Gibbard’s oligarchy theorem paper," Review of Economic Design, Springer;Society for Economic Design, vol. 18(1), pages 1-2, March.
    3. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    4. Cato, Susumu, 2015. "Weak independent decisiveness and the existence of a unique vetoer," Economics Letters, Elsevier, vol. 131(C), pages 59-61.
    5. Susumu Cato, 2015. "Weak Independence and Social Semi-Orders," The Japanese Economic Review, Japanese Economic Association, vol. 66(3), pages 311-321, September.
    6. John Duggan, 2019. "Weak rationalizability and Arrovian impossibility theorems for responsive social choice," Public Choice, Springer, vol. 179(1), pages 7-40, April.
    7. Cato, Susumu, 2018. "Incomplete decision-making and Arrow’s impossibility theorem," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 58-64.
    8. Duddy, Conal & Piggins, Ashley, 2022. "Collective choice rules with social maximality," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    9. Susumu Cato, 2015. "Conditions on social-preference cycles," Theory and Decision, Springer, vol. 79(1), pages 1-13, July.
    10. Allan Gibbard, 2014. "Intransitive social indifference and the Arrow dilemma," Review of Economic Design, Springer;Society for Economic Design, vol. 18(1), pages 3-10, March.
    11. Duddy, Conal & Piggins, Ashley, 2020. "A foundation for Pareto optimality," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 25-30.

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