  We consider the problem of aggregating pairwise comparisons to obtain a
consensus ranking order over a collection of objects. We use the popular
Bradley-Terry-Luce (BTL) model which allows us to probabilistically describe
pairwise comparisons between objects. In particular, we employ the Bayesian BTL
model which allows for meaningful prior assumptions and to cope with situations
where the number of objects is large and the number of comparisons between some
objects is small or even zero. For the conventional Bayesian BTL model, we
derive information-theoretic lower bounds on the Bayes risk of estimators for
norm-based distortion functions. We compare the information-theoretic lower
bound with the Bayesian Cram\'{e}r-Rao lower bound we derive for the case when
the Bayes risk is the mean squared error. We illustrate the utility of the
bounds through simulations by comparing them with the error performance of an
expectation-maximization based inference algorithm proposed for the Bayesian
BTL model. We draw parallels between pairwise comparisons in the BTL model and
inter-player games represented as edges in a comparison graph and analyze the
effect of various graph structures on the lower bounds. We also extend the
information-theoretic and Bayesian Cram\'{e}r-Rao lower bounds to the more
general Bayesian BTL model which takes into account home-field advantage.
