Shepard's Universal Law of Generalization offered a compelling case for the first physics-like law in cognitive science that should hold for all intelligent agents in the universe. Shepard's account is based on a rational Bayesian model of generalization, providing an answer to the question of why such a law should emerge. Extending this account to explain how humans use multiple examples to make better generalizations requires an additional assumption, called the size principle: hypotheses that pick out fewer objects should make a larger contribution to generalization. The degree to which this principle warrants similarly law-like status is far from conclusive. Typically, evaluating this principle has not been straightforward, requiring additional assumptions. We present a new method for evaluating the size principle that is more direct, and apply this method to a diverse array of datasets. Our results provide support for the broad applicability of the size principle.