Laudan versus Bayes: how often does Bayes agree with Laudan given multiple lines of evidence?

Larry Laudan advocated the evaluation of theories based on how many problems they solved minus the problems they failed to solve compared to their competitors. Laudan’s criterion has the advantage of being intuitive. In the Bayesian approach, the likelihood of a theory solving a problem presented by the evidence is expressed as the conditional probability of the evidence given the theory, P(E|T). For the case of multiple forms of evidence, we ask to what extent does Laudan’s criterion agree with the Bayesian solution? A random simulation of conditional probabilities shows that the rate of agreement is about 80%. Thus, the Laudan criterion approximates the Bayesian solution and also gives the latter the appearance of being intuitive. Modifications of the Laudan criterion are tested, such as setting a threshold on the differences between likelihoods or summing those differences across multiple forms of evidence.