  Paired comparison data considered in this paper originate from the comparison
of a large number N of individuals in couples. The dataset is a collection of
results of contests between two individuals when each of them has faced n
opponents, where n is much larger than N. Individual are represented by
independent and identically distributed random parameters characterizing their
abilities.The paper studies the maximum likelihood estimator of the parameters
distribution. The analysis relies on the construction of a graphical model
encoding conditional dependencies of the observations which are the outcomes of
the first n contests each individual is involved in. This graphical model
allows to prove geometric loss of memory properties and deduce the asymptotic
behavior of the likelihood function. This paper sets the focus on graphical
models obtained from round-robin scheduling of these contests.Following a
classical construction in learning theory, the asymptotic likelihood is used to
measure performance of the maximum likelihood estimator. Risk bounds for this
estimator are finally obtained by sub-Gaussian deviation results for Markov
chains applied to the graphical model.
