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Connecting and resolving Sen's and Arrow's theorems

Author

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  • Donald G. Saari

    (Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730, USA)

Abstract

It is shown that the source of Sen's and Arrow's impossibility theorems is that Sen's Liberal condition and Arrow's IIA counter the critical assumption that voters have transitive preferences. But if the procedures are not permitted to treat the transitivity of individual preferences as a valued input, then we cannot expect rational outputs. Once this common cause for these perplexing conclusions is understood, these classical conclusions end up admitting quite benign interpretations where it becomes possible to propose several resolutions.

Suggested Citation

  • Donald G. Saari, 1998. "Connecting and resolving Sen's and Arrow's theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(2), pages 239-261.
    • Handle: RePEc:spr:sochwe:v:15:y:1998:i:2:p:239-261
    Note: Received: 2 April 1996 / Accepted: 15 October 1996
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    Citations

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    Cited by:

    1. Herrade Igersheim, 2005. "Extending Xu's results to Arrow''s Impossibility Theorem," Economics Bulletin, AccessEcon, vol. 4(13), pages 1-6.
    2. Antonio Quesada, 2002. "From social choice functions to dictatorial social welfare functions," Economics Bulletin, AccessEcon, vol. 4(16), pages 1-7.
    3. Antonio Quesada, 2005. "Abstention as an escape from Arrow's theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(1), pages 221-226, October.
    4. Maurice Salles, 2006. "La théorie du choix social : de l'importance des mathématiques," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200617, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    5. Quesada, Antonio, 2007. "Merging discrete evaluations," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 25-34, July.
    6. Herrade Igersheim, 2013. "Invoking a Cartesian product structure on social states," Theory and Decision, Springer, vol. 74(4), pages 463-477, April.
    7. Antonio Quesada, 2002. "Power of Enforcement and Dictatorship," Theory and Decision, Springer, vol. 52(4), pages 381-387, June.
    8. Quesada, Antonio, 2003. "(100-200/m)% veto power," Research in Economics, Elsevier, vol. 57(2), pages 83-92, June.
    9. John W. Patty & Elizabeth Maggie Penn, 2019. "A defense of Arrow’s independence of irrelevant alternatives," Public Choice, Springer, vol. 179(1), pages 145-164, April.
    10. Antonio Quesada, 2009. "Up/Downward Preference Aggregation," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(5), pages 857-873, October.
    11. Denis Bouyssou & Marc Pirlot, 2008. "On some ordinal models for decision making under uncertainty," Annals of Operations Research, Springer, vol. 163(1), pages 19-48, October.

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