A characterization of Brandenburger–Friedenberg–Keisler’s assumption

Brandenburger et al.’s (2008) preference-based definition of assumption has two requirements: nontriviality and strict determination. We show that a decision maker’s preferences satisfy strict determination (on a given event) if and only if her unconditional preferences are equivalent to a lexicographic evaluation of her conditional preferences. An immediate application of this result yields a characterization of all lexicographic probability systems (LPS’s)—similar to the characterization in Brandenburger et al.(2008) for a strict subset of LPS’s—under which an event is assumed.