A symmetric difference metric topology on the collection of binary relations on a countably infinite set provides a new setting for the study of properties of preferences and, as an illustration, is used to lend credence and meaning to some simple intuitions about properties of binary relations....

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...