We consider the estimation of probabilistic ranking models in the context of conjoint experiments. By using approximate rather than exact ranking probabilities, we avoided the computation of high-dimensional integrals. We extended the approximation technique proposed by Henery (1981) in the context of the Thurstone-Mosteller-Daniels model to any independent locally shifted random utility model. In particular, this allowed us to estimate any independent random utility model with common shape (e.g., normal, logistic) and scale. Moreover, our approach also allows for the analysis of any partial ranking. Partial rankings are essential in practical conjoint analysis to collect data efficiently to relieve respondents' task burden. We applied the approach to the reanalysis of the career preference data set described in Maydeu-Olivares and Bockenholt (2005), and to a holiday preferences data set. (Contains 8 tables and 3 figures.)