On the Babington Smith Class of Models for Rankings

In 1950, Babington Smith proposed a general family of probability models for rankings based on a paired comparisons idea. Mallows [9] studied several simple subclasses of the Babington Smith models, but the full class was considered computationaly intractible for practical application at that time. With modern computers, the models are simple to use. With this incentive, we investigate various properties of the Babington Smith models, including their characterization as maximum entropy models, the relationships among different parametrizations of the models, and the conditions under which various forms of stochastic transitivity, unimodality and consensus are obtained. The maximum entropy characterization suggests models that are nested within the Babington Smith models and models that are more general. Computational details for the models are briefly discussed. The models are illustrated with examples where words are ranked in accordance to their perceived degree of association with a target word.