Ockham Efficiency Theorem for Stochastic Empirical Methods |
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Authors: | Kevin T Kelly Conor Mayo-Wilson |
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Institution: | (1) University of Hamburg, 30 Vogt-Kolln-Str. 30, 22527 Hamburg, Germany;; |
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Abstract: | Ockham’s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent
years, philosophers have argued that 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 how and why
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 that problem is
the Ockham efficiency theorem (Kelly 2002, Minds Mach 14:485–505, 2004, Philos Sci 74:561–573, 2007a, b, Theor Comp Sci 383:270–289, c, 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 loss than deterministic strategies. In this paper, we describe two
ways to extend the result to a very general class of random, empirical strategies. The first extension concerns expected retractions,
retraction times, and errors and the second extension concerns retractions in chance, times of retractions in chance, and
chances of errors. |
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