# On a notion of independence proposed by Teddy Seidenfeld

arXiv: https://arxiv.org/abs/2102.10342 · HTML: https://mlsanity.com/paper/2102.10342/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 20 Feb 2021.

## Builds on (most cited first, 6 of 6)

- [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)
- [Exchangeable choice functions](https://mlsanity.com/paper/1703.01924/) (2017)
- [Lexicographic choice functions](https://mlsanity.com/paper/1707.03069/) (2017)
- [Choice functions based on sets of strict partial orders: an axiomatic characterisation](https://mlsanity.com/paper/2003.11631/) (2020)

## Built on by (most cited first, 2 of 2)

- [A theory of desirable things](https://mlsanity.com/paper/2302.07412/) (2023)
- [The logic behind desirable sets of things, and its filter representation](https://mlsanity.com/paper/2302.08176/) (2023)

## Abstract (arXiv)

Teddy Seidenfeld has been arguing for quite a long time that binary preference models are not powerful enough to deal with a number of crucial aspects of imprecision and indeterminacy in uncertain inference and decision making. It is at his insistence that we initiated our study of so-called sets of desirable option sets, which we have argued elsewhere provides an elegant and powerful approach to dealing with general, binary as well as non-binary, decision-making under uncertainty. We use this approach here to explore an interesting notion of irrelevance (and independence), first suggested by Seidenfeld in an example intended as a criticism of a number of specific decision methodologies based on (convex) binary preferences. We show that the consequences of making such an irrelevance or independence assessment are very strong, and might be used to argue for the use of so-called mixing choice functions, and E-admissibility as the resulting decision scheme.