# A Desirability-Based Axiomatisation for Coherent Choice Functions

arXiv: https://arxiv.org/abs/1806.01044 · HTML: https://mlsanity.com/paper/1806.01044/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2018.

## Built on by (most cited first, 5 of 5)

- [A theory of desirable things](https://mlsanity.com/paper/2302.07412/) (2023)
- [On a notion of independence proposed by Teddy Seidenfeld](https://mlsanity.com/paper/2102.10342/) (2021)
- [Decision-making with E-admissibility given a finite assessment of choices](https://mlsanity.com/paper/2204.07428/) (2022)
- [The logic behind desirable sets of things, and its filter representation](https://mlsanity.com/paper/2302.08176/) (2023)
- [Results about sets of desirable gamble sets](https://mlsanity.com/paper/2404.17924/) (2024)

## Abstract (arXiv)

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules to imprecise-probabilistic uncertainty models. We provide them with a clear interpretation in terms of attitudes towards gambling, borrowing ideas from the theory of sets of desirable gambles, and we use this interpretation to derive a set of basic axioms. We show that these axioms lead to a full-fledged theory of coherent choice functions, which includes a representation in terms of sets of desirable gambles, and a conservative inference method.