On a notion of independence proposed by Teddy Seidenfeld

TL;DR

This paper explores a novel notion of independence in decision-making under uncertainty, based on sets of desirable options, highlighting its strong implications and potential to support mixing choice functions and E-admissibility.

Contribution

It introduces a new interpretation of independence inspired by Seidenfeld, demonstrating its significant impact on decision models and advocating for mixing choice functions.

Findings

Independence assessment leads to strong decision-making implications.

Supports the use of mixing choice functions and E-admissibility.

Provides a new perspective on irrelevance in uncertain inference.

Abstract

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.