Fishburn, P. C.; Odlyzko, A. M. Unique subjective probability on finite sets. (English) Zbl 0678.60013 J. Ramanujan Math. Soc. 4, No. 1, 1-23 (1989). Summary: Let \({\mathcal A}_ n\) be the family of all subsets of \(\{\) 1,2,...,n\(\}\) and p a probability measure on \({\mathcal A}_ n\). We say that p uniquely agrees with a comparative probability relation \(>\) on \({\mathcal A}_ n\) if, for all A and B in \({\mathcal A}_ n\), \(A>B\) 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 \({\mathcal A}_ n\) is small for small n but grows rapidly and even for modest n has an amazing number and variety of members. The problem translates naturally into systems of equations that have nonnegative integer solutions, and the derivations of the paper are conducted in this format. Cited in 10 Documents MSC: 60C05 Combinatorial probability 05A05 Permutations, words, matrices 11B99 Sequences and sets Keywords:subjective probability; uniquely agreeing measures; regular measures; diversity of regular measures; comparative probability relation PDFBibTeX XMLCite \textit{P. C. Fishburn} and \textit{A. M. Odlyzko}, J. Ramanujan Math. Soc. 4, No. 1, 1--23 (1989; Zbl 0678.60013)