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Decision theory and the "almost implies near" phenomenon

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  • Christopher P Chambers
  • Federico Echenique

Abstract

This paper explores relaxing behavioral axioms in decision theory. We demonstrate that when a preference approximately satisfies a key axiom (like independence or stationarity) its utility representation is close to a standard model. The degree of the axiom's violation quantitatively determines this proximity. Interestingly, we show that in some cases, a relaxed axiom, when combined with another property like homotheticity, still implies an exact representation. We establish these ``almost implies near'' results for choice under risk, uncertainty, and intertemporal choice, connecting axiomatic deviations to the notion of approximate optimization.

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  • Christopher P Chambers & Federico Echenique, 2025. "Decision theory and the "almost implies near" phenomenon," Papers 2502.07126, arXiv.org, revised Jul 2025.
    • Handle: RePEc:arx:papers:2502.07126
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    References listed on IDEAS

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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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    Cited by:

    1. Pierre Bardier, 2025. "The probability of satisfying axioms: a non-binary perspective on economic design," Papers 2502.13850, arXiv.org.

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