  We provide an axiomatic system modeling conditional preference orders which
is based on conditional set theory. Conditional numerical representations are
introduced, and a conditional version of the theorems of Debreu on the
existence of numerical representations is proved. The conditionally continuous
representations follow from a conditional version of Debreu's Gap Lemma the
proof of which relies on a conditional version of the axiom of choice, free of
any measurable selection argument. We give a conditional version of the von
Neumann and Morgenstern representation as well as automatic conditional
continuity results, and illustrate them by examples.
