A method is presented to estimate the accuracy of an automated classification system based only on expert ratings on test cases, where the system may be substantially more accurate than the raters. In this method an estimate of overall rater accuracy is derived from the level of inter-rater agreement, Bayesian updating based on estimated rater accuracy is applied to estimate a ground truth probability for each classification on each test case, and then overall system accuracy is estimated by comparing the relative frequency that the system agrees with the most probable classification at different probability levels. A simulation analysis provides evidence that the method yields reasonable estimates of system accuracy under diverse and predictable conditions.