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Incompleteness, Independence, and Negative Dominance

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  • Harvey Lederman

Abstract

This paper introduces the axiom of Negative Dominance, stating that if a lottery $f$ is strictly preferred to a lottery $g$, then some outcome in the support of $f$ is strictly preferred to some outcome in the support of $g$. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent.

Suggested Citation

  • Harvey Lederman, 2023. "Incompleteness, Independence, and Negative Dominance," Papers 2311.08471, arXiv.org.
  • Handle: RePEc:arx:papers:2311.08471
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    References listed on IDEAS

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    1. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    2. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2015. "Harsanyi's Aggregation Theorem with Incomplete Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 61-69, February.
    3. Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
    4. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2021. "Expected utility theory on mixture spaces without the completeness axiom," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    5. Pejsachowicz, Leonardo & Toussaert, Séverine, 2017. "Choice deferral, indecisiveness and preference for flexibility," Journal of Economic Theory, Elsevier, vol. 170(C), pages 417-425.
    6. Gorno, Leandro, 2017. "A strict expected multi-utility theorem," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 92-95.
    7. Paola Manzini & Marco Mariotti, 2008. "On the Representation of Incomplete Preferences Over Risky Alternatives," Theory and Decision, Springer, vol. 65(4), pages 303-323, December.
    8. Mandler, Michael, 2009. "Indifference and incompleteness distinguished by rational trade," Games and Economic Behavior, Elsevier, vol. 67(1), pages 300-314, September.
    9. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    10. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
    11. Mongin, Ph., 1991. "Harsanyi's aggregation theorem: multi-profile version and unsettled questions," LIDAM Discussion Papers CORE 1991036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    13. Manzini Paola & Mariotti Marco, 2004. "A Theory of Vague Expected Utility," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-17, December.
    14. Pejsachowicz, Leonardo & Toussaert, Séverine, 2017. "Choice deferral, indecisiveness and preference for flexibility," LSE Research Online Documents on Economics 83566, London School of Economics and Political Science, LSE Library.
    15. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
    16. Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
    17. Michael Mandler, 2004. "Status quo maintenance reconsidered: changing or incomplete preferences?," Economic Journal, Royal Economic Society, vol. 114(499), pages 518-535, November.
    18. Gil Riella, 2015. "On the representation of incomplete preferences under uncertainty with indecisiveness in tastes and beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(3), pages 571-600, April.
    19. Leonardo Pejsachowicz & Séverine Toussaert, 2017. "Choice deferral, indecisiveness and preference for flexibility," Post-Print hal-02862199, HAL.
    20. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    21. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    22. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, July.
    23. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
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    Cited by:

    1. Christian Tarsney & Harvey Lederman & Dean Spears, 2024. "Share the Sugar," Papers 2403.17641, arXiv.org.

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