Related to this, there is a paper I once read, but have no way of locating again, that considered the following model situation (to the best of my recall).
Suppose that there is a disease for which there are two treatments, A and B, that may differ in efficacy. There are many doctors, each of whom comes across this disease from time to time and will prescribe A or B. Each doctor knows the results they have had with the cases they have seen, and based on that can form a preference for A or B. Each doctor also knows all the other doctors’ recommendations — A or B — but nothing about the other doctors’ cases. How much should each doctor weigh the other doctors’ recommendations, given that they know that everyone’s recommendation is a factor in everyone else’s?
It turns out that no matter how many other doctors there are, the weight that each doctor should attach to them should be no more than if there were just a single other doctor.
Related to this, there is a paper I once read, but have no way of locating again, that considered the following model situation (to the best of my recall).
Suppose that there is a disease for which there are two treatments, A and B, that may differ in efficacy. There are many doctors, each of whom comes across this disease from time to time and will prescribe A or B. Each doctor knows the results they have had with the cases they have seen, and based on that can form a preference for A or B. Each doctor also knows all the other doctors’ recommendations — A or B — but nothing about the other doctors’ cases. How much should each doctor weigh the other doctors’ recommendations, given that they know that everyone’s recommendation is a factor in everyone else’s?
It turns out that no matter how many other doctors there are, the weight that each doctor should attach to them should be no more than if there were just a single other doctor.