  We show how Bruno de Finetti's fundamental theorem of prevision has
computable applications in statistical problems that involve only partial
information. Specifically, we assess accuracy rates for median decision
procedures used in the radiological diagnosis of asbestosis. Conditional
exchangeability of individual radiologists' diagnoses is recognized as more
appropriate than independence which is commonly presumed. The FTP yields
coherent bounds on probabilities of interest when available information is
insufficient to determine a complete distribution. Further assertions that are
natural to the problem motivate a partial ordering of conditional
probabilities, extending the computation from a linear to a quadratic
programming problem.
