The paper considers random utility models that use a single common vector of random utilities for the computation of best, worst and best–worst choice probabilities, i.e. consistent models. Choice probabilities are derived for two distributions of the random terms: i.i.d. extreme value, i.e. Logit, and multivariate normal, i.e. Probit.The numerical results show, in both Logit and Probit, statistically significant differences between utility coefficients of best and worst models. The estimations based on worst choice data exhibit coefficient attenuation and higher mean values of travel time savings with larger standard errors.