Unique subjective probability on finite sets.

Let A sub n be the family of all subsets of {1,2,...,n} and p a probability measure on A sub n. We say that p uniquely agrees with a comparative probability relation > on A sub n if, for all A and B in A sub n, A > B if and only if p (A) > p (B), and p is the only measure with this representation. The set of probability measures that uniquely agree with some > on A sub n is small for small n but grows rapidly and even for modest n has an amazing number and variety of members.