Coherent probability from incoherent judgment

People often have knowledge about the chances of events but are unable to e xpress their knowledge in the form of coherent probabilities. This study pr oposed to correct incoherent judgment via an optimization procedure that se eks the (coherent) probability distribution nearest to a judge's estimates of chance. This method was applied to the chances of simple and complex met eorological events, as estimated by college undergraduates. No judge respon ded coherently, but the optimization method found close (coherent) approxim ations to their estimates. Moreover, the approximations were reliably more accurate than the original estimates, as measured by the quadratic scoring rule. Methods for correcting incoherence facilitate the analysis of expecte d utility and allow human judgment to be more easily exploited in the const ruction of expert systems.