I develop a simple stochastic model of inference and therapeutic utilization in the presence of placebo effects, when the underlying medical condition may be self-remitting. In the model, expectations generate a “felt” health state which can mimic the medically cured health state even when the treatment in question has no real curing power. This effect may be augmented by self-limitation of the medical condition for which the treatment is utilized. A human agent then applies Bayes’ rule to the felt history as if it were generated pharmacologically. A more sophisticated agent knows of placebo effects but does not know the precise extent to which they contribute to curing. I describe the bias that attends inference and the under – or overutilization of therapies under such a model. A central result of the model is that human placebo learning is generally subject to greater bias in estimating treatment efficacy when diseases are self-limiting. Human agents may commit several types of decision errors under placebo learning. They may continually choose a more costly (expensive, hazardous) treatment when a less costly one would work as well, or they may continually use inferior treatments for life-threatening illnesses. When diseases are self-limiting, both these types of error are more likely when the human agent has high initial beliefs about the treatment. Possible applications of the model include the patent medicine industry, the robustness of markets for herbal and nutritional supplements, and the contemporary stability of counterfeit drug operations.
Of course this applies a lot more broadly than to medicine. It helps explain why people overuse and underuse "treatments" of many different kinds, including education. Here is Dan Carpenter's page on fly fishing.