  I study dynamic random utility with finite choice sets and exogenous total
menu variation, which I refer to as stochastic utility (SU). First, I
characterize SU when each choice set has three elements. Next, I prove several
mathematical identities for joint, marginal, and conditional Block--Marschak
sums, which I use to obtain two characterizations of SU when each choice set
but the last has three elements. As a corollary under the same cardinality
restrictions, I sharpen an axiom to obtain a characterization of SU with full
support over preference tuples. I conclude by characterizing SU without
cardinality restrictions. All of my results hold over an arbitrary finite
discrete time horizon.
