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"Convex preferences": a new definition

Author

Listed:
  • Richter, Michael

    (Department of Economics, Royal Holloway, University of London)

  • Rubinstein, Ariel

    (School of Economics, Tel Aviv Univeristy and Department of Eocnomics, New York University)

Abstract

We suggest a concept of convexity of preferences that does not rely on any algebraic structure. A decision maker has in mind a set of orderings interpreted as evaluation criteria. A preference relation is defined to be convex when it satisfies the following: if for each criterion there is an element that is both inferior to b by the criterion and superior to a by the preference relation, then b is preferred to a. This definition generalizes the standard Euclidean definition of convex preferences. It is shown that under general conditions, any strict convex preference relation is represented by a maxmin of utility representations of the criteria. Some economic examples are provided.

Suggested Citation

  • Richter, Michael & Rubinstein, Ariel, 2019. ""Convex preferences": a new definition," Theoretical Economics, Econometric Society, vol. 14(4), November.
    • Handle: RePEc:the:publsh:3286
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    References listed on IDEAS

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    5. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, December.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
    8. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
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    Cited by:

    1. Chambers, Christopher P. & Miller, Alan D. & Yenmez, M. Bumin, 2020. "Closure and preferences," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 161-166.
    2. Takashi Kunimoto & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Working Papers 2020-15, Brown University, Department of Economics.
    3. Aguiar, Victor H. & Hjertstrand, Per & Serrano, Roberto, 2020. "A Rationalization of the Weak Axiom of Revealed Preference," Working Paper Series 1321, Research Institute of Industrial Economics.

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    More about this item

    Keywords

    Convex preferences; abstract convexity; maxmin utility;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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