Function-coherent gambles
This provides a theoretical foundation for modeling sophisticated time preferences in decision-making under uncertainty, bridging normative theory and observed behavior, but it is incremental as it extends an existing framework.
The paper tackles the limitation of the desirable gambles framework to linear utility by introducing function-coherent gambles, a generalization that accommodates non-linear utility while preserving rationality properties, and applies it to unify various forms of discounting in intertemporal choice.
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.