# Function-coherent gambles

arXiv: https://arxiv.org/abs/2503.01855 · HTML: https://mlsanity.com/paper/2503.01855/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 29 references that are in the map.
- First posted on arXiv 22 Feb 2025.

## Builds on (most cited first, 1 of 1)

- [A theory of desirable things](https://mlsanity.com/paper/2302.07412/) (2023)

## Abstract (arXiv)

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.