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Caspian comments on Causal Diagrams and Causal Models - Less Wrong
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What about Milton Friedman's thermostat?
Good point. And here's a made-up parallel example to that about weight/exercise:
Suppose level of exercise can influence weight (E -> W), and that being underfed reduces weight (U->W) directly but will also reduce the amount of exercise people do (U->E) by an amount where the effect of the reduced exercise on weight exactly cancels out the direct weight reduction.
Suppose also there is no random variation in amount of exercise, so it's purely a function of being underfed.
If we look at data generated in that situation, we would find no correlation between exercise and weight. Examining only those two variables we might assume no causal relation.
Adding in the third variable, would find a perfect correlation between (lack of) exercise and underfeeding. Implications of finding this perfect correlation: you can't tell if the causal relation between them should be E->U or U->E. And even if you somehow know the graph is (E->W), (U->E) and (E->W), there is no data on what happens to W for an underfed person who exercise, or a well-fed person who doesn't exercise, so you can't predict the effect of modifying E.
It's unlikely that two effects will randomly cancel out unless the situation is the result of some optimizing process. This is the case in Milton Friedman's thermostat but doesn't appear to be the case in your example.
It wouldn't be random. It would be an optimising process, tuned by evolution (another well known optimising process). If you have less food than needed to maintain your current weight, expend less energy (on activities other than trying to find more food). For most of our evolution, losing weight was a personal existential risk.
I had meant to suggest some sort of unintelligent feedback system. Not coincidence, but also not an intelligent optimisation, so still not an exact parallel to his thermostat.
The thermostat was created by an intelligent human.
I never said the optimizing process had to be that intelligent, i.e., the blind-idiot-god counts.