We assign a probabilistic evaluation to a firm as a measure, in the form of a probability distribution over [0,1], of the quality of the firm’s products. When two firms compete to develop a new product, a prospective investor can use the two evaluations to determine which firm is likely to...

A preference profile has a one-dimensional Euclidean representation if it can be derived from an arrangement of individuals and alternatives on a line, with each individual preferring the nearer of each pair of alternatives. We provide a polynomial-time algorithm that determines whether a given...

A simple head-to-head voting scheme in which voters hold complete and transitive preferences over alternatives generates all binary relations on finite sets. The minimal number of voters required to generate a binary relation provides a measure of complexity for binary relations. Complexity so...