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The two faces of independence: betweenness and homotheticity

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  • Daniel R. Burghart

    (California State University Sacramento)

Abstract

This paper shows that expected utility belongs to the intersection of models satisfying betweenness and a homotheticity condition for risky choice. Betweenness models can accommodate variable risk attitudes, originally highlighted by the Allais paradox, by restricting indifference curves to be linear while allowing non-parallelism. Homotheticity, in contrast, restricts indifference curves to be parallel while permitting non-linearities, such as those highlighted by inverse-S probability weighting. Data from an experiment indicate that approximately 2/3s of participants satisfied homotheticity. Of this group, about half satisfied the expected utility hypothesis. The other half violated expected utility and therefore betweenness. These results indicate that homothetic preferences, and in particular those violating betweenness, can be empirically relevant for decision making under risk.

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  • Daniel R. Burghart, 2020. "The two faces of independence: betweenness and homotheticity," Theory and Decision, Springer, vol. 88(4), pages 567-593, May.
    • Handle: RePEc:kap:theord:v:88:y:2020:i:4:d:10.1007_s11238-019-09735-2
    DOI: 10.1007/s11238-019-09735-2
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    Cited by:

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    3. Daniel R. Burghart & Thomas Epper & Ernst Fehr, 2020. "The uncertainty triangle – Uncovering heterogeneity in attitudes towards uncertainty," Journal of Risk and Uncertainty, Springer, vol. 60(2), pages 125-156, April.

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    More about this item

    Keywords

    Risk preferences; Expected utility; Independence axiom; Betweenness; Homotheticity; Revealed preferences;
    All these keywords.

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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