The P2 ratio is not only significantly small with respect to random partitions but also with respect to random perturbations of the original partition. Thus, when you randomly replace k Rabbis on the first list with k Rabbis on the second list the probabilities of getting the P2-ratio of WRR or a smaller ratio are for k=1,2,3,4,5 respectively: 0.035906, 0.022370 ,0.017372, 0.015322, 0.014150.