# Archimedean Choice Functions: an Axiomatic Foundation for Imprecise Decision Making

arXiv: https://arxiv.org/abs/2002.05196 · HTML: https://mlsanity.com/paper/2002.05196/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2020.

## Built on by (most cited first, 6 of 6)

- [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)
- [Extending choice assessments to choice functions: An algorithm for computing the natural extension](https://mlsanity.com/paper/2407.21164/) (2024)
- [The AI off-switch problem as a signalling game: bounded rationality and incomparability](https://mlsanity.com/paper/2502.06403/) (2025)

## Abstract (arXiv)

If uncertainty is modelled by a probability measure, decisions are typically made by choosing the option with the highest expected utility. If an imprecise probability model is used instead, this decision rule can be generalised in several ways. We here focus on two such generalisations that apply to sets of probability measures: E-admissibility and maximality. Both of them can be regarded as special instances of so-called choice functions, a very general mathematical framework for decision making. For each of these two decision rules, we provide a set of necessary and sufficient conditions on choice functions that uniquely characterises this rule, thereby providing an axiomatic foundation for imprecise decision making with sets of probabilities. A representation theorem for Archimedean choice functions in terms of coherent lower previsions lies at the basis of both results.