Average rank correlation statistics in the presence of ties

The problem of n judges ranking r objects is considered in the situation where ties are permitted. Asymtotic distributions under the null hypothesis of complete randomness in the rankings are derived for the test statistics of average rank correlations between all pairs of ranking where the rank correlations are measured either by Spearman rho or Kendall tau. The relative efficeincies of these average rank correlatins are derived using approximate Bahadur slope and limiting pitman efficiency, and in both cases the Kendall statistic is shown to be more efficient. Some interpretatins of these and related results are also given.