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Independence of irrelevant alternatives revisited

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  • Susumu Cato

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Abstract

This paper aims to reexamine the axiom of the independence of irrelevant alternatives in the theory of social choice. A generalized notion of independence is introduced to clarify an informational requirement of binary independence which is usually imposed in the Arrovian framework. We characterize the implication of binary independence. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Susumu Cato, 2014. "Independence of irrelevant alternatives revisited," Theory and Decision, Springer, vol. 76(4), pages 511-527, April.
  • Handle: RePEc:kap:theord:v:76:y:2014:i:4:p:511-527
    DOI: 10.1007/s11238-013-9384-1
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    References listed on IDEAS

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    1. 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.
    2. Andreu Mas-Colell & Hugo Sonnenschein, 1972. "General Possibility Theorems for Group Decisions," Review of Economic Studies, Oxford University Press, vol. 39(2), pages 185-192.
    3. Campbell, Donald E. & Kelly, Jerry S., 2000. "Weak independence and veto power," Economics Letters, Elsevier, vol. 66(2), pages 183-189, February.
    4. Fishburn, Peter C., 1970. "Arrow's impossibility theorem: Concise proof and infinite voters," Journal of Economic Theory, Elsevier, vol. 2(1), pages 103-106, March.
    5. Fleurbaey, Marc & Suzumura, Kotaro & Tadenuma, Koichi, 2005. "Arrovian aggregation in economic environments: how much should we know about indifference surfaces?," Journal of Economic Theory, Elsevier, vol. 124(1), pages 22-44, September.
    6. Donald J. Brown, 1975. "Aggregation of Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 89(3), pages 456-469.
    7. Blau, Julian H, 1971. "Arrow's Theorem with Weak Independence," Economica, London School of Economics and Political Science, vol. 38(152), pages 413-420, November.
    8. 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.
    9. Donald Campbell & Jerry Kelly, 2007. "Social welfare functions that satisfy Pareto, anonymity, and neutrality, but not independence of irrelevant alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 69-82, July.
    10. Marc Fleurbaey & Kotaro Suzumura & Koichi Tadenuma, 2005. "The informational basis of the theory of fair allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(2), pages 311-341, April.
    11. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163, October.
    12. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    13. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.
    14. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    15. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046, October.
    16. Ray, Paramesh, 1973. "Independence of Irrelevant Alternatives," Econometrica, Econometric Society, vol. 41(5), pages 987-991, September.
    17. 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.
    18. Blair, Douglas H & Pollak, Robert A, 1982. "Acyclic Collective Choice Rules," Econometrica, Econometric Society, vol. 50(4), pages 931-943, July.
    19. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    20. Sen, Amartya, 1993. "Internal Consistency of Choice," Econometrica, Econometric Society, vol. 61(3), pages 495-521, May.
    21. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
    22. Guha, Ashok, 1972. "Neutrality, Monotonicity, and the Right of Veto," Econometrica, Econometric Society, vol. 40(5), pages 821-826, September.
    23. Susumu Cato, 2011. "Pareto principles, positive responsiveness, and majority decisions," Theory and Decision, Springer, vol. 71(4), pages 503-518, October.
    24. McLean, Iain, 1995. "Independence of irrelevant alternatives before Arrow," Mathematical Social Sciences, Elsevier, vol. 30(2), pages 107-126, October.
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    Citations

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    Cited by:

    1. Susumu Cato, 2014. "Common preference, non-consequential features, and collective decision making," Review of Economic Design, Springer;Society for Economic Design, vol. 18(4), pages 265-287, December.
    2. Dan Qin, 2015. "On $$\mathcal {S}$$ S -independence and Hansson’s external independence," Theory and Decision, Springer, vol. 79(2), pages 359-371, September.

    More about this item

    Keywords

    Arrow’s impossibility theorem; Independence of irrelevant alternatives; Binary independence; Collective choice rule; D71;

    JEL classification:

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

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