  Many applications in preference learning assume that decisions come from the
maximization of a stable utility function. Yet a large experimental literature
shows that individual choices and judgements can be affected by "irrelevant"
aspects of the context in which they are made. An important class of such
contexts is the composition of the choice set. In this work, our goal is to
discover such choice set effects from raw choice data. We introduce an
extension of the Multinomial Logit (MNL) model, called the context dependent
random utility model (CDM), which allows for a particular class of choice set
effects. We show that the CDM can be thought of as a second-order approximation
to a general choice system, can be inferred optimally using maximum likelihood
and, importantly, is easily interpretable. We apply the CDM to both real and
simulated choice data to perform principled exploratory analyses for the
presence of choice set effects.
