  We compare measures of concordance that arise as Pearson's linear correlation
coefficient between two random variables transformed so that they follow the
so-called concordance-inducing distributions. The class of such transformed
rank correlations includes Spearman's rho, Blomqvist's beta and van der
Waerden's coefficient. When only the standard axioms of measures of concordance
are required, it is not always clear which transformed rank correlation is most
suitable to use. To address this question, we compare measures of concordance
in terms of their best and worst asymptotic variances of some canonical
estimators over a certain set of dependence structures. A simple criterion
derived from this approach is that concordance-inducing distributions with
smaller fourth moment are more preferable. In particular, we show that
Blomqvist's beta is the optimal transformed rank correlation in this sense, and
Spearman's rho outperforms van der Waerden's coefficient. Moreover, we find
that Kendall's tau, although it is not a transformed rank correlation of that
nature, shares a certain optimal structure with Blomqvist's beta.
