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Infinite supermodularity and preferences

Author

Listed:
  • Alain Chateauneuf

    (Paris School of Economics and University of Paris I)

  • Vassili Vergopoulos

    (Paris School of Economics and University of Paris I)

  • Jianbo Zhang

    (University of Kansas)

Abstract

Chambers and Echenique (J Econ Theory 144:1004–1014, 2009) proved that preferences in a wide class cannot disentangle the usual economic assumptions of quasisupermodularity and supermodularity. This paper further studies the ordinal content of the much stronger assumption of infinite supermodularity in the same context. It is shown that weakly increasing binary relations on finite lattices fail to disentangle infinite supermodularity from quasisupermodularity and supermodularity. Moreover, for a complete preorder, the mild requirement of strict increasingness is shown to imply the existence of infinitely supermodular representations.

Suggested Citation

  • Alain Chateauneuf & Vassili Vergopoulos & Jianbo Zhang, 2017. "Infinite supermodularity and preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 99-109, January.
    • Handle: RePEc:spr:joecth:v:63:y:2017:i:1:d:10.1007_s00199-015-0942-3
    DOI: 10.1007/s00199-015-0942-3
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    References listed on IDEAS

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    1. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
    2. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    4. Chambers, Christopher P. & Echenique, Federico, 2008. "Ordinal notions of submodularity," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1243-1245, December.
    5. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    6. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
    7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    Cited by:

    1. Brian Duricy, 2023. "Preferences on Ranked-Choice Ballots," Papers 2301.02697, arXiv.org.

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    More about this item

    Keywords

    Supermodularity; Infinite supermodularity; Lattice;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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