# A theory of desirable things

arXiv: https://arxiv.org/abs/2302.07412 · HTML: https://mlsanity.com/paper/2302.07412/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 15 Feb 2023.

## Builds on (most cited first, 5 of 5)

- [Archimedean Choice Functions: an Axiomatic Foundation for Imprecise Decision Making](https://mlsanity.com/paper/2002.05196/) (2020)
- [A Desirability-Based Axiomatisation for Coherent Choice Functions](https://mlsanity.com/paper/1806.01044/) (2018)
- [Coherent and Archimedean choice in general Banach spaces](https://mlsanity.com/paper/2002.05461/) (2020)
- [Nonlinear desirability theory](https://mlsanity.com/paper/2209.00686/) (2022)
- [On a notion of independence proposed by Teddy Seidenfeld](https://mlsanity.com/paper/2102.10342/) (2021)

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

- [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)
- [Function-coherent gambles](https://mlsanity.com/paper/2503.01855/) (2025)
- [Function-Coherent Gambles with Non-Additive Sequential Dynamics](https://mlsanity.com/paper/2503.02889/) (2025)
- [Incentive Aware AI Regulations: A Credal Characterisation](https://mlsanity.com/paper/2603.05175/) (2026)

## Abstract (arXiv)

Inspired by the theory of desirable gambles that is used to model uncertainty in the field of imprecise probabilities, I present a theory of desirable things. Its aim is to model a subject's beliefs about which things are desirable. What the things are is not important, nor is what it means for them to be desirable. It can be applied to gambles, calling them desirable if a subject accepts them, but it can just as well be applied to pizzas, calling them desirable if my friend Arthur likes to eat them. Other useful examples of things one might apply this theory to are propositions, horse lotteries, or preferences between any of the above. Regardless of the particular things that are considered, inference rules are imposed by means of an abstract closure operator, and models that adhere to these rules are called coherent. I consider two types of models, each of which can capture a subject's beliefs about which things are desirable: sets of desirable things and sets of desirable sets of things. A crucial result is that the latter type can be represented by a set of the former.