Occam’s razor and un-justified selection arguments

Consider the following (hypothetical) result: People living in green cities have fewer health problems that people living in non-green cities. Could the correlation be spurious? We eliminate other differences between the cities including size, income distribution, industrial composition etc and the correlation persists. Can we draw the conclusion that the correlation is causal? ”No”, a selection-oriented economist could object. ”It could be that healthy people prefer to live in green cities. They self-select themselves to these cities and, thus, the correlation is not causal.”

Is this objection valid? One way to frame this problem is to see it as competition between two theories: ”green areas improve health” and ”healthy people prefer green cities”. Which theory is it rational to select? The answer is that if we have experimental results that show an effect of green areas on health relevant variables such as blood-pressure but no evidence (other that the health/green-city correlation) that support the ”healthy people prefer green cities” theory, then we should select the ”green areas improve health” theory.

Why? Because this theory can explain both the outcome of the experiments, and the correlational results. If we select the ”healthy people prefer green cities” theory it cannot explain the experimental results. Thus, we will need two theories instead of one. And according to Occam’s razor, simple theories should be preferred over more complex theories.

Is then Occam’s razor a valid principle? Yes, according to Kevin T. Kelly at Carnegie-Mellon University it can be shown that Occam’s razor is a principle that yields efficient results. What Kelly has shown is the number of retractions one is forced to do before arriving at the truth can be minimised by sticking to Occam’s razor.  Kevin T. Kelly (2010) "Simplicity, Truth, and Probability", in Handbook on the Philosophy of Statistics, Prasanta Bandyopadhyay and Malcolm Forster, eds., Dordrecht: Elsevier.

My argument does not, of course, maintain that selection arguments are never valid. My point is, instead, that a selection argument, in order to be accepted, must be based on independent corroborative empirical evidence. Or, can only be used effectively against causal claims that themselves are based on limited empirical evidence. Thus, the selection argument is not a simple seminar trick that can be used by anyone against any researcher using non-experimental data. An effective selection argument will require empirical support for why the selection theory should be preferred .

This, as I see it, is good news for us who put much of our energy into exploring non-experimental data. If we design and carry out our research carefully, we do not have to worry about getting into arguments with identification fundamentalist or only-experiments-count researchers. Occam’s razor is sharp and provides us with a tool that can fend of more than a few detractors!