Inequalities for Random Utility Models,with Applications to Ranking and Subset Choice Data

Inequalities on orderings of independent random variables are derived in the context of random utility models for ranking and subset choice data. The inequalities can be used to assess whether ranking or subset choice data are consistent with an independent random utility model. The main technique used for the inequalities is association, with conditions for the sharpness for the inequalities coming from identifying when the association inequality is an equality. Applications to real data sets are given.