A classical method for ranking n potential events as sources of error is Bayes' theorem. However, a ranking based on Bayes' theorem lacks a fundamental symmetry: the ranking in terms of blame for error will not be the reverse of the ranking in terms of credit for lack of error. While this is not a flaw in Bayes' theorem, it does lead one to inquire whether there are related methods which have such symmetry. Related methods explored here include the logical version of Bayes' theorem based on probabilities of conditionals, probabilities of biconditionals, and ratios or differences of credit to blame. We find that of all the methods described, probabilities of biconditionals and logical correlation coefficients provide a particularly attractive method for ranking blame for error and credit for lack of error which have the symmetry property we are interested in.
Greene, Nataniel, "Methods of Assessing and Ranking Probable Sources of Error" (2008). CUNY Academic Works.