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Decision theory and the "almost implies near" phenomenon

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  • Christopher P Chambers
  • Federico Echenique

Abstract

We propose to relax traditional axioms in decision theory by incorporating a measurement, or degree, of satisfaction. For example, if the independence axiom of expected utility theory is violated, we can measure the size of the violation. This measure allows us to derive an approximation guarantee for a utility representation that aligns with the unmodified version of the axiom. Almost satisfying the axiom implies, then, a utility that is near a utility representation. We develop specific examples drawn from expected utility theory under risk and uncertainty.

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  • Christopher P Chambers & Federico Echenique, 2025. "Decision theory and the "almost implies near" phenomenon," Papers 2502.07126, arXiv.org.
    • Handle: RePEc:arx:papers:2502.07126
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    1. Christina McGranaghan & Kirby Nielsen & Ted O'Donoghue & Jason Somerville & Charles D. Sprenger, 2024. "Distinguishing Common Ratio Preferences from Common Ratio Effects Using Paired Valuation Tasks," American Economic Review, American Economic Association, vol. 114(2), pages 307-347, February.
    2. Ok, Efe A. & Masatlioglu, Yusufcan, 2007. "A theory of (relative) discounting," Journal of Economic Theory, Elsevier, vol. 137(1), pages 214-245, November.
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