Doctors sometimes resist prescribing costly diagnostic procedures, saying that the result of the test would be unlikely to affect the course of treatment. But what we know about placebo effects for medicine should have implications also for the value of information, even when it leads to no objective health benefits.
I have a theory of how placebos work. The idea is that our bodies, either through conscious choices that we make or simply through physiological changes, must make an investment in order to get healthy. Being sick is like being, perhaps temporarily, below the threshold where the body senses that the necessary investment is worth it. A placebo tricks the body into thinking that we are going to get at least marginally more healthy and that pushes above the threshold triggering the investment which makes us healthy.
The same idea can justify providing information that has no instrumental value. Suppose you have an injury and are considering having an MRI to determine how serious it is. Your doctor says that surgery is rarely worthwhile and so even if the MRI shows a serious injury it won’t affect how you are treated.
But you want to know. For one thing the information can affect how you personally manage the injury. That’s instrumental value that your doctor doesn’t take into account.
But even if there were nothing you could consciously do based on the test result, there may be a valuable placebo reason to have the MRI. If you find out that the injury is mild, the psychological effect of knowing that you are healthy (or at least healthier than you previously thought) can be self-reinforcing.
The downside of course is that when you find out that the injury is serious you get an anti-placebo effect. So the question is whether you are better off on average when you become better informed about your true health status.
If the placebo effect works because the belief triggers a biological response then this is formally equivalent to a standard model of decision-making under uncertainty. Whenever a decision-maker will optimally condition his decision on the realization of information, then the expected value of learning that information is positive.