Related papers: Function-coherent gambles

Function-coherent gambles

URL: http://arxiv.org/abs/2503.01855v2
Date: Fri, 25 Apr 2025 06:57:11 GMT
Title: Function-coherent gambles
Authors: Gregory Wheeler,
Abstract summary: This paper introduces function-coherent gambles, a generalization that accommodates non-linear utility.<n>We prove a representation theorem that characterizes acceptable gambles through continuous linear functionals.<n>We demonstrate how these alternatives to constant-rate exponential discounting can be integrated within the function-coherent framework.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates non-linear utility while preserving essential rationality properties. We establish core axioms for function-coherence and prove a representation theorem that characterizes acceptable gambles through continuous linear functionals. The framework is then applied to analyze various forms of discounting in intertemporal choice, including hyperbolic, quasi-hyperbolic, scale-dependent, and state-dependent discounting. We demonstrate how these alternatives to constant-rate exponential discounting can be integrated within the function-coherent framework. This unified treatment provides theoretical foundations for modeling sophisticated patterns of time preference within the desirability paradigm, bridging a gap between normative theory and observed behavior in intertemporal decision-making under genuine uncertainty.

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