Finding the Most Probable Ranking of Objects with Probabilistic Pairwise Preferences

This paper discusses the ranking of a set of objects when a possibly inconsistent set of pairwise preferences is given.We consider the task of ranking objects when pairwise preferences not only can contradict each other, but in general are not binary-meaning, for each pair of objects the preference is represented by a pair of non-negative numbers that sum up to one and can be viewed as a confidence in our belief that one object is preferable to the other in the absence of any other information. We propose a probability function on the sequence of objects that includes non-binary preferences and evaluate methods for finding the most probable ranking for this model using it to rank results of a Microsoft on-line handwriting recognizer.