A characterization of Brandenburger-Friedenberg-Keisler's assumption

- The equivalence of strict determination and lexicographic evaluation of conditional preferences is shown.
- The set of all LPS's under which an event is assumed is characterized.
- Does so in a manner that resembles Brandenburger et al.'s (2008) characterization of assumption for LCPS's.

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.