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Min, Max, and Sum

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  • Segal, Uzi
  • Sobel, Joel

Abstract

This paper provides characterization theorems for preferences that can be represented by the minimum, the maximum, and the sum of components, or combinations of these forms. It contains a discussion of applications to social choice.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Segal, Uzi & Sobel, Joel, 2002. "Min, Max, and Sum," Journal of Economic Theory, Elsevier, vol. 106(1), pages 126-150, September.
    • Handle: RePEc:eee:jetheo:v:106:y:2002:i:1:p:126-150
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    References listed on IDEAS

    as
    1. Kevin W. S. Roberts, 1980. "Interpersonal Comparability and Social Choice Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 421-439.
    2. Peter A. Diamond, 1967. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility: Comment," Journal of Political Economy, University of Chicago Press, vol. 75(5), pages 765-765.
    3. Bliss, C. J., 1975. "Capital Theory and the Distribution of Income," Elsevier Monographs, Elsevier, edition 1, number 9780720436044 edited by Bliss, C. J..
    4. Segal, Uzi, 1992. "Additively separable representations on non-convex sets," Journal of Economic Theory, Elsevier, vol. 56(1), pages 89-99, February.
    5. Edi Karni, 1998. "Impartiality: Definition and Representation," Econometrica, Econometric Society, vol. 66(6), pages 1405-1416, November.
    6. W. M. Gorman, 1968. "The Structure of Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 367-390.
    7. Ben-Porath, Elchanan & Gilboa, Itzhak & Schmeidler, David, 1997. "On the Measurement of Inequality under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 194-204, July.
    8. Yaari, Menahem E., 1981. "Rawls, edgeworth, shapley, nash: Theories of distributive justice re-examined," Journal of Economic Theory, Elsevier, vol. 24(1), pages 1-39, February.
    9. John C. Harsanyi, 1953. "Cardinal Utility in Welfare Economics and in the Theory of Risk-taking," Journal of Political Economy, University of Chicago Press, vol. 61(5), pages 434-434.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
    12. Mak, King-Tim, 1984. "Notes on separable preferences," Journal of Economic Theory, Elsevier, vol. 33(2), pages 309-321, August.
    13. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    14. Blackorby, Charles & Donaldson, David, 1982. "Ratio-Scale and Translation-Scale Full Interpersonal Comparability without Domain Restrictions: Admissible Social-Evaluation Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 249-268, June.
    15. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
    16. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
    17. Uzi Segal, 2000. "Let's Agree That All Dictatorships Are Equally Bad," Journal of Political Economy, University of Chicago Press, vol. 108(3), pages 569-589, June.
    18. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
    19. Eric Maskin, 1978. "A Theorem on Utilitarianism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(1), pages 93-96.
    20. Fare, Rolf & Primont, Daniel, 1981. "Separability vs strict separability: A further result," Journal of Economic Theory, Elsevier, vol. 25(3), pages 455-460, December.
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    Cited by:

    1. Marcello D’Agostino & Valentino Dardanoni, 2009. "What’s so special about Euclidean distance?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 211-233, August.
    2. De Castro, Luciano & Yannelis, Nicholas C., 2018. "Uncertainty, efficiency and incentive compatibility: Ambiguity solves the conflict between efficiency and incentive compatibility," Journal of Economic Theory, Elsevier, vol. 177(C), pages 678-707.
    3. Aniruddha Ghosh & M. Ali Khan & Metin Uyanık, 2023. "Continuity postulates and solvability axioms in economic theory and in mathematical psychology: a consolidation of the theory of individual choice," Theory and Decision, Springer, vol. 94(2), pages 189-210, February.
    4. Kamaga, Kohei, 2018. "When do utilitarianism and egalitarianism agree on evaluation? An intersection approach," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 41-48.
    5. Kaname Miyagishima & Kristof Bosmans & Erwin Ooghe, 2014. "A characterization of maximin: corrigendum," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 219-220, October.
    6. Mitra, Manipushpak & Sen, Debapriya, 2014. "Subsistence induced and complementarity induced irrelevance in preferences," MPRA Paper 59474, University Library of Munich, Germany.
    7. Tapan Mitra & Kemal Ozbek, 2021. "Ranking by weighted sum," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 511-532, September.
    8. Luciano De Castro & Nicholas C. Yannelis, 2011. "Ambiguity aversion solves the conflict between efficiency and incentive compatibility," Economics Discussion Paper Series 1106, Economics, The University of Manchester.
    9. Hougaard, Jens Leth & Keiding, Hans, 2005. "Rawlsian maximin, Dutch books, and non-additive expected utility," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 239-251, November.
    10. Jensen, Martin Kaae & Kozlovskaya, Maria, 2016. "A representation theorem for guilt aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 148-161.
    11. Mark Voorneveld, 2014. "From preferences to Leontief utility," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 197-204, October.
    12. Nabil I. Al-Najjar & Luciano De Castro, 2010. "Uncertainty, Efficiency and Incentive Compatibility," Discussion Papers 1532, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Kuntal Banerjee, 2014. "On the representation of preference orders on sequence spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 497-506, August.

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    More about this item

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • D1 - Microeconomics - - Household Behavior
    • D6 - Microeconomics - - Welfare Economics

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