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A quest for fundamental theorems of social choice

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  • Ning Yu

Abstract

We explore the frontier between possibility and impossibility results by analyzing different combinations of “pro-socialness” and “consistency” conditions. This exercise delivers stronger versions of four classical impossibility theorems, and offers a thorough understanding of connections among them. We also characterize social choice functions that are “independent of irrelevant alternatives,” which makes evident that the fundamental difficulty of social choice lies in “pairwise” consistency requirements. We also introduce a concise pedagogical approach to classical impossibility theorems. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • 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.
    • Handle: RePEc:spr:sochwe:v:44:y:2015:i:3:p:533-548
    DOI: 10.1007/s00355-014-0846-3
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    1. Priscilla Man & Shino Takayama, 2013. "A unifying impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 249-271, October.
    2. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 211-215, July.
    3. David M. Grether & Charles R. Plott, 1982. "Nonbinary Social Choice: An Impossibility Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(1), pages 143-149.
    4. Ning Yu, 2012. "A one-shot proof of Arrow’s impossibility theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 523-525, June.
    5. David M. Kreps, 2012. "Microeconomic Foundations I: Choice and Competitive Markets," Economics Books, Princeton University Press, edition 1, volume 1, number 9890.
    6. Campbell, Donald E, 1992. "Implementation of Social Welfare Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 525-533, August.
    7. Sen, Amartya, 1993. "Internal Consistency of Choice," Econometrica, Econometric Society, vol. 61(3), pages 495-521, May.
    8. Samuelson, Larry, 1985. "On the independence from irrelevant alternatives in probabilistic choice models," Journal of Economic Theory, Elsevier, vol. 35(2), pages 376-389, August.
    9. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    10. 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.
    11. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58, pages 328-328.
    12. Matthew O. Jackson & Sanjay Srivastava, 1996. "A Characterization of Game-Theoretic Solutions Which Lead to Impossibility Theorems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 23-38.
    13. 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.
    14. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    15. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-1037, July.
    16. 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.
    17. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, December.
    18. Campbell, Donald E, 1992. "Transitive Social Choice in Economic Environments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 341-352, May.
    19. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    20. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    21. Barbera, Salvador, 1980. "Pivotal voters : A new proof of arrow's theorem," Economics Letters, Elsevier, vol. 6(1), pages 13-16.
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