# Extending choice assessments to choice functions: An algorithm for computing the natural extension

arXiv: https://arxiv.org/abs/2407.21164 · HTML: https://mlsanity.com/paper/2407.21164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 25 references that are in the map.
- First posted on arXiv 30 Jul 2024.

## Builds on (most cited first, 2 of 2)

- [Archimedean Choice Functions: an Axiomatic Foundation for Imprecise Decision Making](https://mlsanity.com/paper/2002.05196/) (2020)
- [Improved linear programming methods for checking avoiding sure loss](https://mlsanity.com/paper/1808.03076/) (2018)

## Abstract (arXiv)

We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natural (most conservative) extension of a given choice assessment to a coherent choice function -- whenever possible -- and use this natural extension to make new choices. We provide a practical algorithm for computing this natural extension and various ways to improve scalability. Finally, we test these algorithms for different types of choice assessments.