Homogeneous Families of Semiorders and the Theory of Probabilistic Consistency.
This work investigates various conditions making precise the observation that the preferences of an individual or group, although not absolutely consistent, are in a sense "probabilistically consistent." This Memorandum studies conditions of probabilistic consistency on a family of binary relations, which can be interpreted at several individuals' relations of preference or the preference relations of a particular individual obtained at different times. The conditions studied all mean more or less that the family of relations is a homogeneous or consistent family of semiorders. The main result is that almost all of the probabilistic consistency conditions studied are equivalent. The logical relations among all these conditions are described, and findings are compared with some recent work by Tversky and Russo. 42 pp. Ref.