Ockham Efficiency Theorem for Empirical Methods Conceived as Empirically-Driven, Countable-State Stochastic Processes

Ockham’s razor is the principle that, all other things being equal, it is rational to prefer simpler scientific theories to more complex ones. In a series of a papers, Kelly, Glymour, and Schulte argue that scientists who heed Ockham’s razor make fewer errors and retract their opinions less often than do their complexity preferring counterparts. The centerpiece of their argument is the Ockham Efficiency Theorem, which provides a precise explanation of errors, retractions, and Ockham’s razor within a model of scientific inquiry developed by formal-learning theorists. Kelly, Glymour, and Schulte’s previous arguments, however, were restricted in two important ways: (1) they applied only to deterministic (rather than randomized) methods for choosing scientific theories from data and (2) they failed to successfully model inference from statistical data with error. In this paper, we full address the first issue by extending the Ockham Efficiency Theorem to prove that, amongst any set of randomized strategies, a systematic preference for simpler theories minimizes the number of errors and retractions one commits before converging to the true theory. By incorporating probabilistic elements into the model employed by formal learning theorists, moreover, we take a large step towards addressing the second issue as well.