Distance Based Ranking Models

SUMMARY A class of ranking models is proposed for which the probability of a ranking decreases with increasing distance from a modal ranking. Some special distances, namely those associated with Kendall and Cayley, decompose into a sum of independent components under the uniform distribution. These distances lead to multiparameter generalizations whose parameters may be interpreted as information at various stages in a ranking process. Estimation of model parameters is described, and the results are applied to an example of word associations. A censoring argument motivates simple extensions of these models to include partial rankings. The generalized Cayley distance model is illustrated for random arrangements arising from mechanisms other than ranking.