Branching-independent random utility model

Abstract

This paper introduces a subclass of the Random Utility Model (RUM), called branching-independent RUM. In this subclass, the probability distribution over the ordinal rankings of alternatives satisfies the following property: for any k∈{1,…,n−1}, where n denotes the number of alternatives, when fixing the first k and the last n−k alternatives, the relative rankings of the first k and the last n−k alternatives are independent. Branching-independence is motivated by the classical example due to Fishburn (1998), which illustrates the non-uniqueness problem in random utility models. Surprisingly, branching-independent RUM is characterized by the Block-Marschak condition, which also characterizes general RUM. In fact, I show that a construction similar to the one used in Falmagne (1978) generates a branching-independent RUM. In addition, within the class of branching-independent RUMs, the probability distribution over preferences is uniquely determined. Hence, while branching-independent RUM has the same explanatory power as general RUM, it is uniquely identified.