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Cautious Dual-Self Expected Utility and Weak Uncertainty Aversion

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  • Kensei Nakamura
  • Shohei Yanagita

Abstract

Uncertainty aversion introduced by Gilboa and Schmeidler (1989) has played a central role in decision theory, but at the same time, many incompatible behaviors have been observed in the real world. In this paper, we consider an axiom that postulates only a minimal degree of uncertainty aversion, and examine its implications in the preferences with the basic structure, called the invariant biseparable preferences. We provide three representation theorems for these preferences. Our main result shows that a decision maker with such a preference evaluates each act by considering two "dual" scenarios and then adopting the worse one as its evaluation in a cautious manner. The other two representations share a structure similar to the main result, which clarifies the key implication of weak uncertainty aversion. Furthermore, we offer another foundation for the main representation in the objective/subjective rationality model and characterizations of extensions of the main representation.

Suggested Citation

  • Kensei Nakamura & Shohei Yanagita, 2025. "Cautious Dual-Self Expected Utility and Weak Uncertainty Aversion," Papers 2501.13410, arXiv.org, revised Apr 2025.
    • Handle: RePEc:arx:papers:2501.13410
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    References listed on IDEAS

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    1. Tomasz Strzalecki, 2011. "Axiomatic Foundations of Multiplier Preferences," Econometrica, Econometric Society, vol. 79(1), pages 47-73, January.
    2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, March.
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