Abstract
This paper develops a generalization of Fishburn's SSB utility theory. Let P be a set of probability measures. A new representational form yields a bilinear functional u on P× P for which u( p, q)> 0 if and only if p is preferred to q, where u( p, p)≤0, and u( q, p)<0 whenever u( p, q)> 0. Since u is not necessarily skew-symmetric, i.e., u( p, q)≠− u( q,), it provides imprecise preference discriminability. It is also discussed that u is related to SSB utility with a threshold structure.
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