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Impossibility theorems are modified and unified

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  • Uuganbaatar Ninjbat

Abstract

Arrow’s impossibility theorem and the Muller–Satterthwaite theorem are further interconnected by showing that translating one result into the other’s setting leads to similar results. This approach generated more impossibility theorems which are interesting on their own. Moreover, an implication of having these impossibility results on a unifying impossibility theorem in Eliaz (Soc Choice Welf 22:317–330, 2004 ) is also discussed. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • 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.
    • Handle: RePEc:spr:sochwe:v:45:y:2015:i:4:p:849-866
    DOI: 10.1007/s00355-015-0887-2
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    1. Kfir Eliaz, 2004. "Social aggregators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 317-330, April.
    2. Can, Burak & Storcken, Ton, 2012. "Impossibilities with Kemeny updating," Economics Letters, Elsevier, vol. 116(2), pages 229-231.
    3. 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.
    4. Susumu Cato, 2010. "Brief proofs of Arrovian impossibility theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 267-284, July.
    5. Campbell, Donald E. & Kelly, Jerry S., 2000. "Weak independence and veto power," Economics Letters, Elsevier, vol. 66(2), pages 183-189, February.
    6. Hannu Nurmi, 2004. "Monotonicity and its Cognates in the Theory of Choice," Public Choice, Springer, vol. 121(1), pages 25-49, October.
    7. Dan Felsenthal & Nicolaus Tideman, 2013. "Varieties of failure of monotonicity and participation under five voting methods," Theory and Decision, Springer, vol. 75(1), pages 59-77, July.
    8. M. Sanver & William Zwicker, 2012. "Monotonicity properties and their adaptation to irresolute social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 371-398, July.
    9. 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.
    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. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    12. David Schmeidler & Hugo Sonnenschein, 1974. "The Possibility of a Cheatproof Social Choice Function: A Theorem of A. Gibbard and M. Satterthwaite," Discussion Papers 89, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Barbera, Salvador, 1983. "Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 413-417, June.
    14. 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.
    15. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    16. Can, Burak & Storcken, Ton, 2013. "Update monotone preference rules," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 136-149.
    17. Pattanaik, Prasanta K., 2002. "Positional rules of collective decision-making," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 7, pages 361-394, Elsevier.
    18. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    19. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    20. Barbera, Salvador, 1980. "Pivotal voters : A new proof of arrow's theorem," Economics Letters, Elsevier, vol. 6(1), pages 13-16.
    21. Cato, Susumu, 2009. "Another induction proof of the Gibbard-Satterthwaite theorem," Economics Letters, Elsevier, vol. 105(3), pages 239-241, December.
    22. 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.
    23. Suzumura, Kotaro, 1988. "Reduction of Social Choice Problems : A Simple Proof of Arrow’s General Possibility Theorem," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 29(2), pages 219-221, December.
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    Cited by:

    1. Cato, Susumu, 2017. "Unanimity, anonymity, and infinite population," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 28-35.
    2. 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.
    3. Uuganbaatar Ninjbat, 2018. "Impossibility theorems with countably many individuals," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 9(3), pages 333-350, August.

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