On a notion of independence proposed by Teddy Seidenfeld
This work addresses foundational issues in decision theory for researchers dealing with uncertainty, but it appears incremental as it builds on existing frameworks like sets of desirable option sets.
The paper tackles the problem of imprecision and indeterminacy in uncertain inference and decision-making by exploring a notion of irrelevance and independence proposed by Seidenfeld, showing that its consequences are very strong and might support the use of mixing choice functions and E-admissibility as decision schemes.
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.