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Never choose the uniquely largest a characterization


In this paper we characterize choice behaviour that picks the second largest element if there is a uniquely largest; otherwise, the largest elements are picked. Having defined our choice function, we offer a complete characterization of the latter in terms of pure choice function conditions. Similarities to and divergences from conventional choice theory are explained. We discuss the motivations underlying our exercise and provide several examples for the axiomatized choice behaviour.

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  1. Arrow, K. J.: Rational choice functions and orderings. Economica26, 121–127 (1959)

    Google Scholar 

  2. Arrow, K. J., Intriligator, M. D.: In: Handbook of mathematical economics, Vol. III. Amsterdam: North-Holland, 1986

    Google Scholar 

  3. Bordes, G.: Consistency, rationality and collective choice. Rev. Econ. Stud.43, 447–457 (1976)

    Google Scholar 

  4. Dasgupta, P.: An inquiry into well-being and destitution. Oxford: Oxford University Press, 1993

    Google Scholar 

  5. Hargreaves Heap, S., Hollis, M., Lyons, B., Sugden, R., Weale, A.: The theory of choice. A critical guide. Oxford: Blackwell, 1992

    Google Scholar 

  6. Kelly, J. S.: Arrow impossibility theorems. New York: Academic Press, 1978

    Google Scholar 

  7. Machina, M. J.: Dynamic consistency and non-expected utility. In: Bacharach, M. and Hurley, S. (eds.) Foundations of decision theory — issues and advances, pp. 39–91. Cambridge, Mass.: Blackwell, 1991

    Google Scholar 

  8. Malishevski, A. V.: Judging the rationality of decisions in the presence of vague alternatives. Working Paper 840, Pasadena, Ca.: California Institute of Technology, 1993

    Google Scholar 

  9. Parks, R. P.: Rationalizations, extensions, and social choice paths. Mimeo, Washington University, St. Louis, 1971

    Google Scholar 

  10. Plott, C. R.: Path independence, rationality, and social choice. Econometrica41, 1075–1091 (1973)

    Google Scholar 

  11. Saari, D. G.: Inner consistency or not inner consistency; a reformulation is the answer. Discussion Paper, Department of Mathematics, Northwestern University, Evanston, Ill., 1992

    Google Scholar 

  12. Sen, A.: Collective choice and social welfare. San Francisco: Holden-Day, 1970

    Google Scholar 

  13. Sen, A.: Social choice theory: a re-examination. Econometrica45, 53–89 (1977)

    Google Scholar 

  14. Sen, A.: Social choice theory. In: Arrow, K. J. and Intriligator, M. D. (eds.) Handbook of Mathematical Economics, Vol. III, pp. 1073–1181. Amsterdam: North-Holland, 1986

    Google Scholar 

  15. Sen, A.: Internal consistency of choice. Econometrica61, 495–521 (1993)

    Google Scholar 

  16. Sugden, R.: Why be consistent? A critical analysis of consistency requirements in choice theory. Economica52, 167–184 (1985)

    Google Scholar 

  17. Suzumura, K.: Rational choice, collective decisions, and social welfare. Cambridge: Cambridge, University Press, 1983

    Google Scholar 

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Helpful discussions with R. Deb, M. R. Johnson, P. K. Pattanaik, A. Sen, Y. Xu, and participants at a seminar on individual and social choice in Osnabrück, November 1993, are gratefully acknowledged. One of the authors wishes to thank the British Council and the University of Osnabrück for financial support. We are also grateful to the Department of Economics at Queen Mary and Westfield College, London, for its hospitality.

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Baigent, N., Gaertner, W. Never choose the uniquely largest a characterization. Econ Theory 8, 239–249 (1996).

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