Decision and Choice: Random Utility Models of Choice and Response Time

Abstract

‘Horse race’ random utility models of choice and response time account for the stochastic variability underlying choices of a single ‘best’ opation from some available, potentially infinite set of options, and the variability of the times to choose. It is demonstrated that given certain regularity conditions any set of choice probabilities and response times can be represented by a set of independent random variables satisfying the horse race property, i.e., the option chosen is the one which happens to be associated with the minimum choice (or decision) time with respect to all options in the available set. The result is related to concepts from the theory of competing risks. Moreover, it is shown that the proportional hazard rate condition is equivalent to assuming independence between the time of choice and the identity of the element chosen. Adding the independent horse race assumption then implies Luce's choice model. Any horse race model generated by a generalized stable survival function satisfies independence between time of choice and the element chosen. The general feature model is one possible process interpretation of the horse race random utility model. The results are generalized to subset choices and structures of transition probabilities.