Truth-Ratios, Evidential Fit, and Deferring to Informants with Low Error Probabilities

Abstract

Suppose that an informant (test, expert, device, perceptual system, etc.) is unlikely to err when pronouncing on a particular subject matter. When this is so, it might be tempting to defer to that informant when forming beliefs about that subject matter. How is such an inferential process expected to fare in terms of truth (leading to true beliefs) and evidential fit (leading to beliefs that fit one’s total evidence)? Using a medical diagnostic test as an example, we set out a formal framework to investigate this question. We establish seven results and make one conjecture. The first four results show that when the test’s error probabilities are low, the process of deferring to the test can score well in terms of (i) both truth and evidential fit, (ii) truth but not evidential fit, (iii) evidential fit but not truth, or (iv) neither truth nor evidential fit. Anything is possible. The remaining results and conjecture generalize these results in certain ways. These results are interesting in themselves—especially given that the diagnostic test is not sensitive to the target disease’s base rate—but also have broader implications for the more general process of deferring to an informant. Additionally, our framework and diagnostic example can be used to create test cases for various reliabilist theories of inferential justification. We show, for example, that they can be used to motivate evidentialist process reliabilism over process reliabilism.