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compute. But the underlying efficiency argument is correspondingly
, because the worst-
case bounds are taken with respect to a coarser coarse-graining of possibilities. So it is, after all, a
judgment call whether to go for the stronger justification and a weaker output that is harder to
compute, or for a weaker justification for a stronger output that is easier to compute.
Some causal search algorithms implement only a greedy version of Ockham’s razor, in the
sense that they find a minimal theory compatible with the data and stop (Chickering and Meek
2002). The greedy strategy is optimal with respect to cycles, as long as one does not leave
simplicity gaps, which greedy strategies never do, because they never produce vertical
disjunctions. Of course, such strategies are not reversal optimal, either with respect to the order on
theories or with respect to the ranking by number of causal connections, since that requires that
the method occasionally produce horizontal disjunctions of causal theories.
The literature on causal inference from non-experimental data is just the tip of the iceberg
concerning the relationship between accurate counterfactual predictions and theoretical truth. It is
more the rule, rather than the exception, that scientific theories are intended causally and are meant
to apply in novel situations. When non-experimental data are relied on to infer theories that govern
unobserved situations, the problem of induction arises, and novel policies can have disastrous
consequences if one gets the theory wrong. For example, on Ptolemy’s earth-centered planetary
theory, space travel was inconceivable: space ships would bounce off the crystalline sphere that
governs the moon and we would have no idea how much fuel it would take to get to any other
planet, since the stationary Earth provides no baseline for measuring the distances.
Copernicus’s sun-centered view, the crystalline spheres no longer make sense (we would be
embedded in such a sphere ourselves) and we know the distances to all the planets, so
interplanetary travel becomes a feasible policy goal. Yet all that separated the two theories, prior
to the invention of the telescope, was Ockham’s razor―Copernicus’s theory saves five epicycles
posited by Ptolemy’s theory to account for the apparent retrograde motion of the planets against
the fixed stars. The motivation for applying Ockham’s razor cannot have been to find the truth in
the short run. There is this justification, however. It is the unique strategy that keeps us from going
round and round and following needlessly crooked paths to the truth.
This work was supported by John Templeton Foundation grant 24145. We are indebted to Hanti
Lin and to Oliver Schulte for recent discussions concerning simplicity, cycles and reversals of