Let w(1),w(2),..., w(n) be positive weights. Put these weights in an urn and draw them out, without replacement, each time picking the next draw with probability proportional to its weight relative to the remaining weights. Let sigma be the resulting permutation of {1,2,...,n}. This model is widely used in psychology (Luce model),settling poker games (ICM) and in betting on horse races. Basic enumerative questions; pick sigma from this measure, how many fixed points, cycles, inversions, length of longest increasing cycle,... are largely open. In joint work with Jocopo Borgia, Sourav Chatterjee and Gene Kim we have made first steps. We can find the 'permuton limit' and prove a central limit theorem for the number of inversions. There are sweeping generalizations to chambers of a hyperplane arrangement.