This paper determines conditions under which the relation that an estimator is posterior Pitman closer than another, is transitive, for estimating one-dimensional and multi-dimensional parameters. Posterior Pitman closeness is a Bayesian version of the Pitman closeness criterion for pairwise comparison of estimators. Estimators are compared on the basis of the posterior probability of being closer to the parameters of interest. If transitivity is obtained, then if one estimator is better than another, it is also better than all the estimators that the second one is better than. We show that one-dimensional transitivity obtains when the posterior has unique median. In several dimensions one needs uniqueness of the posterior medians of all linear combinations of the parameters and the existence of a posterior 'multivariate median'. A 'multivariate median' of the distribution of the ~"-valued random vector Y is a point m e N" such that for any a s N", the (real) random variable a'Y has (univariate) median a'm. Thus, transitivity of the posterior Pitman closeness criterion in several dimensions is closely related to the existence of a 'best' estimator under the criterion. We provide an example that can arise from a multinomial density and Dirichlet prior where the criterion is not transitive,