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A Unifying Impossibility Theorem

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Abstract

This paper considers social choice correspondences assigning a choice set to each non-empty subset of social alternatives. We impose three requirements on these correspondences: unanimity, independence of preferences over infeasible alternatives and choice consistency with respect to choices out of all possible alternatives. With more than three social alternatives and the universal preference domain, any social choice correspondence that satisfies our requirements is serially dictatorial. A number of known impossibility theorems — including Arrow’s Impossibility Theorem, the Muller-Satterthwaite Theorem and the impossibility theorem under strategic candidacy — follow as corollaries. Our new proof highlights the common logical underpinnings behind these theorems.

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  • Priscilla Man & Shino Takayama, 2012. "A Unifying Impossibility Theorem," Discussion Papers Series 448, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uq2004:448
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    File URL: https://economics.uq.edu.au/files/44932/448.pdf
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    References listed on IDEAS

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    Cited by:

    1. Muto, Nozomu & Sato, Shin, 2016. "Bounded response of aggregated preferences," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 1-15.
    2. Paul Frijters & Benno Torgler & Brendan Markey-Towler, 2016. "On the Problem of Constructing Rational Preferences," The Economic Record, The Economic Society of Australia, vol. 92, pages 68-82, June.
    3. Matías Núñez, 2014. "The strategic sincerity of Approval voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 157-189, May.
    4. Priscilla Man & Shino Takayama, 2013. "A Unifying Impossibility Theorem for Compact Metricsocial Alternatives Space," Discussion Papers Series 477, School of Economics, University of Queensland, Australia.
    5. Uuganbaatar Ninjbat, 2015. "Impossibility theorems are modified and unified," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 849-866, December.
    6. Bossert, Walter & Cato, Susumu, 2021. "Superset-robust collective choice rules," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 126-136.
    7. Susumu Cato, 2019. "The possibility of Paretian anonymous decision-making with an infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 587-601, December.
    8. Louis Anthony (Tony) Cox, 2015. "Overcoming Learning Aversion in Evaluating and Managing Uncertain Risks," Risk Analysis, John Wiley & Sons, vol. 35(10), pages 1892-1910, October.
    9. 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.
    10. Ning Yu, 2015. "A quest for fundamental theorems of social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 533-548, March.
    11. Cato, Susumu, 2017. "Unanimity, anonymity, and infinite population," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 28-35.
    12. Brendan Markey-Towler, 2016. "Economics cannot isolate itself from political theory: a mathematical demonstration," Papers 1701.06410, arXiv.org.
    13. Dougherty, Keith L. & Heckelman, Jac C., 2020. "The probability of violating Arrow’s conditions," European Journal of Political Economy, Elsevier, vol. 65(C).
    14. Nanyang Bu, 2016. "Joint misrepresentation with bribes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 115-125, January.
    15. Shino Takayama & Akira Yokotani, 2014. "Serial Dictatorship with Infinitely Many Agents," Discussion Papers Series 503, School of Economics, University of Queensland, Australia.

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    JEL classification:

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

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