INDUCED BINARY PROBABILITIES AND THE LINEAR ORDERING POLYTOPE - A STATUS-REPORT

This report summarizes research on the problem of characterizing all systems of binary probabilities on a finite set that are induced by probability distributions over the family of linear orders of the set. We begin with essential definitions, remarks about the two largely separate literatures on the problem, and historical notes. The rest of the paper focuses on systems of inequalities that define the facets of the space of all induced binary probability systems, i.e. facets of the linear ordering polytope.