Ockham Efficiency Theorem for Random Empirical Methods

Ockham’s razor is the principle that, all other things being equal, rational scientists ought to prefer simpler theories to more complex ones. In recent years, philosophers have argued the simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain why and how a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to this problem is the Ockham efficiency theorem (Kelly 2002, 2004, 2007a-d, Kelly and Glymour 2004), which states that scientists who heed Ockham’s razor retract their opinions less often and sooner than do their non-Ockham competitors. The theorem neglects, however, to consider competitors following random (“mixed”) strategies and in many applications random strategies are known to achieve better worst-case bounds than deterministic strategies. In this paper, we describe an extension of the result to a very general class of random, empirical strategies.