The problem of $n$ rankings is considered and the asymptotic distributions of measures of concordance based on rank correlations are derived under the null model of complete randomness. The Bahadur efficiencies of the measures are computed. A matrix analysis then reveals the asymptotic distribution and superior efficiency of average Kendall tau. Some interpretation of the results is also made.
"Asymptotic Theory for Measures of Concordance with Special Reference to Average Kendall Tau." Ann. Statist. 10 (4) 1269 - 1276, December, 1982. https://doi.org/10.1214/aos/1176345992