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Odlyzko, A. M.
- Unique Subjective Probability on Finite Sets
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1 AT&T Bell Laboratories Murray Hill, NJ 07974q, US
1 AT&T Bell Laboratories Murray Hill, NJ 07974q, US
Source
Journal of the Ramanujan Mathematical Society, Vol 4, No 1 (1989), Pagination: 1-23Abstract
Let An be the family of all subsets of {1,2,..,n} n and p a probability measure on An. We say that p uniquely agrees with a comparative probability relation > on A if, for all A and B in An, 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 An 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.