  Many applications, e.g. in content recommendation, sports, or recruitment,
leverage the comparisons of alternatives to score those alternatives. The
classical Bradley-Terry model and its variants have been widely used to do so.
The historical model considers binary comparisons (victory or defeat) between
alternatives, while more recent developments allow finer comparisons to be
taken into account. In this article, we introduce a probabilistic model
encompassing a broad variety of paired comparisons that can take discrete or
continuous values. We do so by considering a well-behaved subset of the
exponential family, which we call the family of generalized Bradley-Terry (GBT)
models, as it includes the classical Bradley-Terry model and many of its
variants. Remarkably, we prove that all GBT models are guaranteed to yield a
strictly convex negative log-likelihood. Moreover, assuming a Gaussian prior on
alternatives' scores, we prove that the maximum a posteriori (MAP) of GBT
models, whose existence, uniqueness and fast computation are thus guaranteed,
varies monotonically with respect to comparisons (the more A beats B, the
better the score of A) and is Lipschitz-resilient with respect to each new
comparison (a single new comparison can only have a bounded effect on all the
estimated scores). These desirable properties make GBT models appealing for
practical use. We illustrate some features of GBT models on simulations.
