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Houshalter comments on Causal Diagrams and Causal Models - Less Wrong
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After reading this post I was stunned. Now I think the central conclusion is wrong, though I still think it is a great post, and I will go back to being stunned if you convince me the conclusion is correct.
You've shown how to identify the correct graph structure from the data. But you've erred in assuming that the directed edges of the graph imply causality.
Imagine you did the same analysis, except instead of using O="overweight" you use W="wears size 44 or higher pants". The data would look almost the same. So you would reach an analogous conclusion: that wearing large pants causes one not to exercise. This seems obviously false unless your notion of causality is very different from mine.
In general, I think the following principle holds: inferring causality requires an intervention; it cannot be discovered from observational data alone. A researcher who hypothesized that W causes not-E could round up a bunch of people, have half of them wear big pants, observe the effect of this intervention on exercise rates, and then conclude that there is no causal effect.
He addressed that in the third footnote.
The model assumes that those are the only relevant variables. Given that assumption, we can prove that weight causes exercise. And that it can't be the other way around.
If there are unobserved variables, it's possible that they can cause weight and cause exercise. However that wasn't one of the hypotheses anyone believed beforehand; they were arguing whether weight causes exercise or if exercise causes weight.
Second, even if there is an unobserved variable, it still suggests that exercising more will not improve your weight. Otherwise internet use would correlate with weight. Because internet use affects exercise. If exercise affected weight at all, then internet use would indirectly cause weight gain, and therefore correlate with it.
The whole point of the article is about this trick. Where taking a weird and unrelated variable like internet use, lets us discover the direction of causation. Which according to common knowledge about statistics, shouldn't be possible. Not without randomized controlled experiments.