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Weak Independence and Social Semi-Orders

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  • Susumu Cato

Abstract

type="main"> This paper provides variants of Arrow's impossibility theorem, which states that there exists no non-dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi-order properties of semi-transitivity and the interval-order property. We prove that there exists a vetoer when the number of alternatives is greater than or equal to six.

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  • Susumu Cato, 2015. "Weak Independence and Social Semi-Orders," The Japanese Economic Review, Japanese Economic Association, vol. 66(3), pages 311-321, September.
    • Handle: RePEc:bla:jecrev:v:66:y:2015:i:3:p:311-321
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    File URL: http://hdl.handle.net/10.1111/jere.12051
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    References listed on IDEAS

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    1. Gibbard, Allan F., 2014. "Social Choice And The Arrow Conditions," Economics and Philosophy, Cambridge University Press, vol. 30(3), pages 269-284, November.
    2. Blau, Julian H., 1979. "Semiorders and collective choice," Journal of Economic Theory, Elsevier, vol. 21(1), pages 195-206, August.
    3. 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.
    4. Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 39(2), pages 185-192.
    5. Campbell, Donald E. & Kelly, Jerry S., 2000. "Weak independence and veto power," Economics Letters, Elsevier, vol. 66(2), pages 183-189, February.
    6. Fishburn, Peter C, 1975. "Semiorders and Choice Functions," Econometrica, Econometric Society, vol. 43(5-6), pages 975-977, Sept.-Nov.
    7. Blair, Douglas H. & Pollak, Robert A., 1979. "Collective rationality and dictatorship: The scope of the arrow theorem," Journal of Economic Theory, Elsevier, vol. 21(1), pages 186-194, August.
    8. Susumu Cato, 2016. "Weak independence and the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 295-314, August.
    9. Jamison, Dean T & Lau, Lawrence J, 1973. "Semiorders and the Theory of Choice," Econometrica, Econometric Society, vol. 41(5), pages 901-912, September.
    10. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    11. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
    12. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    13. Robert Powers, 2005. "Positional information and preference aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 575-583, June.
    14. Antonio Quesada, 2003. "Positional independence in preference aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 363-370, June.
    15. Susumu Cato, 2012. "Social choice without the Pareto principle: a comprehensive analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 869-889, October.
    16. Gensemer, Susan H., 1987. "Continuous semiorder representations," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 275-289, June.
    17. Sen, Amartya, 1995. "Rationality and Social Choice," American Economic Review, American Economic Association, vol. 85(1), pages 1-24, March.
    18. Bengt Hansson, 1976. "The existence of group preference functions," Public Choice, Springer, vol. 28(1), pages 89-98, December.
    19. Guha, Ashok, 1972. "Neutrality, Monotonicity, and the Right of Veto," Econometrica, Econometric Society, vol. 40(5), pages 821-826, September.
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    1. Susumu Cato, 2016. "Weak independence and the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 295-314, August.

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