An Automatic Ockham’s Razor for Bayesians?
Received: 26 July 2017 / Accepted: 30 April 2018
Ó Springer Science+Business Media B.V., part of Springer Nature 2018
Abstract It is sometimes claimed that the Bayesian framework automatically
implements Ockham’s razor—that conditionalizing on data consistent with both a
simple theory and a complex theory more or less inevitably favours the simpler
theory. It is shown here that the automatic razor doesn’t in fact cut it for certain
mundane curve-ﬁtting problems.
It is sometimes alleged that, across an array of interesting cases, the Bayesian
framework automatically implements Ockham’s razor: conditionalizing on data
accounted for equally well by both a simple theory and a complex theory more or
less inevitably favours the simpler theory.
Roughly speaking, the idea is as follows. Suppose that we are able to account for
the data seen so far using members of a smaller family of hypotheses (with fewer
adjustable parameters) as well as members of a larger family of hypotheses (with
more adjustable parameters). Within the smaller family we expect that the live
hypotheses are fairly similar to one another compared to how similar the live
hypotheses are to one another in the larger family—that is just an expected
byproduct of the difference in the number of adjustable parameters. But this is to say
that the smaller family in effect makes sharper predictions about what future data
& Gordon Belot
Department of Philosophy, University of Michigan, Ann Arbor, USA
See, e.g., Rosenkrantz (1983, p. 82), Jefferys and Berger (1992), McKay (2003, ch. 28), White (2005),
and Henderson et al. (2010, §4). It will be assumed throughout that Bayesian priors are probability
measures—and in particular that they are both normalized and countably additive.