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Ordinal aggregation results via Karlin's variation diminishing property

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  • Choi, Michael
  • Smith, Lones

Abstract

When is the weighted sum of quasi-concave functions quasi-concave? We answer this, extending an analogous preservation of the single-crossing property in QS: Quah and Strulovici (2012). Our approach develops a general preservation of n-crossing properties, applying the variation diminishing property in Karlin (1956). The QS premise is equivalent to Karlin's total positivity of order two, while our premise uses total positivity of order three: The weighted sum of quasi-concave functions is quasi-concave if each has an increasing portion more risk averse than any decreasing portion.

Suggested Citation

  • Choi, Michael & Smith, Lones, 2017. "Ordinal aggregation results via Karlin's variation diminishing property," Journal of Economic Theory, Elsevier, vol. 168(C), pages 1-11.
    • Handle: RePEc:eee:jetheo:v:168:y:2017:i:c:p:1-11
    DOI: 10.1016/j.jet.2016.12.001
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    References listed on IDEAS

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    1. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    3. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
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    Cited by:

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    2. Barthel, Anne-Christine & Hoffmann, Eric & Sabarwal, Tarun, 2022. "Characterizing robust solutions in monotone games," Games and Economic Behavior, Elsevier, vol. 135(C), pages 201-219.
    3. Shuo Liu & Harry Pei, 2017. "Monotone equilibria in signalling games," ECON - Working Papers 252, Department of Economics - University of Zurich.
    4. Anton Kolotilin & Roberto Corrao & Alexander Wolitzky, 2022. "Persuasion with Non-Linear Preferences," Papers 2206.09164, arXiv.org, revised Aug 2022.
    5. Hector Chade & Jeroen Swinkels, 2021. "Screening in Vertical Oligopolies," Econometrica, Econometric Society, vol. 89(3), pages 1265-1311, May.
    6. Liu, Shuo & Pei, Harry, 2020. "Monotone equilibria in signaling games," European Economic Review, Elsevier, vol. 124(C).
    7. Anne-Christine Barthel & Eric Hoffmann & Tarun Sabarwal, 2021. "A Unified Approach to p-Dominance and its Generalizations in Games with Strategic Complements and Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202109, University of Kansas, Department of Economics.
    8. Marilyn Pease & Mark Whitmeyer, 2024. "How to Make an Action Attractive," Papers 2408.09294, arXiv.org, revised Apr 2026.

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    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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