This paper propose a new inference mechanism for the Plackett-Luce model based on the preliminary observation that the ML estimate can be seen as the stationary distribution of a certain Markov chain. In fact, two inferences mechanisms are proposed, one is approximate and consistent, the other converges to the ML estimate but is slower. The authors then debate on the application settings (pairwise preferences, partial rankings). Finally, the authors exhibit three sets of experiments. The first one compares the proposed algorithm to other approximate inference mechanisms for the PL model in terms of statistical efficiency. Then on real-world datasets, one experiment compares the empirical performance of the approximate methods and a second the speed of exact methods to reach a certain level of optimality.