  We consider a preference learning setting where every participant chooses an
ordered list of $k$ most preferred items among a displayed set of candidates.
(The set can be different for every participant.) We identify a distance-based
ranking model for the population's preferences and their (ranked) choice
behavior. The ranking model resembles the Mallows model but uses a new distance
function called Reverse Major Index (RMJ). We find that despite the need to sum
over all permutations, the RMJ-based ranking distribution aggregates into
(ranked) choice probabilities with simple closed-form expression. We develop
effective methods to estimate the model parameters and showcase their
generalization power using real data, especially when there is a limited
variety of display sets.
