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buybuydandavis comments on Knowledge value = knowledge quality × domain importance - Less Wrong
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You test for the effect of a sham treatment (placebo) by comparing it with no treatment at all.
So you've partitioned the treatments between (placebo + other unknown) versus (other unknown). The effect of the placebo is the difference between the two treatments, just as the effect of a "real drug" is the difference between the (real treatment + unknown effects) and (sham treatment + unknown effects).
It's very difficult to arrange an experimental setup for "no treatment at all", because even enrolling people in a study can be considered a "treatment" - it's an expectation-inducing intervention with perforce no control group.
I agree that it's the partition you want, and I'm not saying it's impossible, but - can you come up with a specific way of running such an experiment?