Lexicographic probability, conditional probability, and nonstandard probability

The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS’s are equivalent; without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS’s are equivalent to NPS’s. However, if the state space is infinite, NPS’s are shown to be more general than LPS’s. JEL classification numbers: C70; D80; D81;