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Axiomatization of a Preference for Most Probable Winner

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  • Pavlo Blavatskyy

Abstract

In binary choice between discrete outcome lotteries, an individual may prefer lottery L 1 to lottery L 2 when the probability that L 1 delivers a better outcome than L 2 is higher than the probability that L 2 delivers a better outcome than L 1 . Such a preference can be rationalized by three standard axioms (solvability, convexity and symmetry) and one less standard axiom (a fanning-in). A preference for the most probable winner can be represented by a skew-symmetric bilinear utility function. Such a utility function has the structure of a regret theory when lottery outcomes are perceived as ordinal and the assumption of regret aversion is replaced with a preference for a win. The empirical evidence supporting the proposed system of axioms is discussed. Copyright Springer 2006

Suggested Citation

  • Pavlo Blavatskyy, 2006. "Axiomatization of a Preference for Most Probable Winner," Theory and Decision, Springer, vol. 60(1), pages 17-33, February.
    • Handle: RePEc:kap:theord:v:60:y:2006:i:1:p:17-33
    DOI: 10.1007/s11238-005-4753-z
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    References listed on IDEAS

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    1. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
    2. Pavlo R. Blavatskyy, "undated". "Axiomatization of a Preference for Most Probable Winner," IEW - Working Papers 230, Institute for Empirical Research in Economics - University of Zurich.
    3. Pavlo Blavatskyy, 2004. "Axiomatization of a Preference for Most Probably Winner," CERGE-EI Working Papers wp226, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
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    1. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    2. Arjan Verschoor & Ben D’Exelle, 2022. "Probability weighting for losses and for gains among smallholder farmers in Uganda," Theory and Decision, Springer, vol. 92(1), pages 223-258, February.
    3. Aziz, Haris & Brandl, Florian & Brandt, Felix, 2015. "Universal Pareto dominance and welfare for plausible utility functions," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 123-133.
    4. Krzysztof Kontek, 2018. "Boundary effects in the Marschak-Machina triangle," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(6), pages 587-606, November.
    5. Denis Bouyssou & Marc Pirlot, 2008. "On some ordinal models for decision making under uncertainty," Annals of Operations Research, Springer, vol. 163(1), pages 19-48, October.
    6. Brandl, Florian & Brandt, Felix & Hofbauer, Johannes, 2019. "Welfare maximization entices participation," Games and Economic Behavior, Elsevier, vol. 114(C), pages 308-314.
    7. Michael Birnbaum & Ulrich Schmidt, 2008. "An experimental investigation of violations of transitivity in choice under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 37(1), pages 77-91, August.
    8. Felix Brandt & Patrick Lederer & Warut Suksompong, 2022. "Incentives in Social Decision Schemes with Pairwise Comparison Preferences," Papers 2204.12436, arXiv.org, revised Nov 2022.
    9. repec:cup:judgdm:v:15:y:2020:i:6:p:1052-1053 is not listed on IDEAS
    10. repec:cup:judgdm:v:13:y:2018:i:6:p:587-606 is not listed on IDEAS
    11. Florian Brandl & Felix Brandt, 2020. "Arrovian Aggregation of Convex Preferences," Econometrica, Econometric Society, vol. 88(2), pages 799-844, March.
    12. Sudeep Bhatia & Graham Loomes & Daniel Read, 2021. "Establishing the laws of preferential choice behavior," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(6), pages 1324-1369, November.
    13. David J. Butler & Ganna Pogrebna, 2018. "Predictably intransitive preferences," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(3), pages 217-236, May.
    14. Enrico Diecidue & Haim Levy & Moshe Levy, 2020. "Probability Dominance," The Review of Economics and Statistics, MIT Press, vol. 102(5), pages 1006-1020, December.
    15. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    16. Pištěk, Miroslav, 2019. "SSB representation of preferences: Weakening of convexity assumptions," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 84-88.
    17. Michael Birnbaum & Ulrich Schmidt, 2010. "Testing transitivity in choice under risk," Theory and Decision, Springer, vol. 69(4), pages 599-614, October.
    18. Pištěk, Miroslav, 2018. "Continuous SSB representation of preferences," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 59-65.
    19. David Butler, 2020. "Intransitive preferences or choice errors? A reply to Birnbaum," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 15(6), pages 1052-1053, November.
    20. Kontek, Krzysztof, 2015. "Fanning-Out or Fanning-In? Continuous or Discontinuous? Estimating Indifference Curves Inside the Marschak-Machina Triangle using Certainty Equivalents," MPRA Paper 63965, University Library of Munich, Germany.
    21. repec:cup:judgdm:v:13:y:2018:i:3:p:217-236 is not listed on IDEAS

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    More about this item

    Keywords

    expected utility theory; axiomatization; betweenness; fanning-in; skew-symmetric bilinear utility; regret theory; C91; D81;
    All these keywords.

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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