  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.
