  Asymptotics of the normalizing constant is computed for a class of one
parameter exponential families on permutations which includes Mallows model
with Spearmans's Footrule and Spearman's Rank Correlation Statistic. The MLE,
and a computable approximation of the MLE are shown to be consistent. The
pseudo-likelihood estimator of Besag is shown to be $\sqrt{n}$-consistent. An
iterative algorithm (IPFP) is proved to converge to the limiting normalizing
constant. The Mallows model with Kendall's Tau is also analyzed to demonstrate
flexibility of the tools of this paper.
