I suspect if you model it out, and assign varying strength of illness signal and varying noise of diagnosis for different doctors’ ability, you’ll find that this only works when the signals are clear enough that you don’t need a doctor to tell someone they’re ill.
You’ve also forgotten that doctors don’t have to coordinate in detail in order to coordinate on answers. Medical school and diagnostic guides are chock full of coordination mechanisms for measurement->diagnosis. In your scheme, doctors who follow the guides and never use their experience, intuition, and good judgement to think deeper are the ones who get paid. Wilson gets paid, House goes elsewhere. That may be your goal—“prefer a younger doctor” is common advice for a reason. But be aware that you’re optimizing for standards, not truth.
I suspect if you model it out, and assign varying strength of illness signal and varying noise of diagnosis for different doctors’ ability, you’ll find that this only works when the signals are clear enough that you don’t need a doctor to tell someone they’re ill.
You’ve also forgotten that doctors don’t have to coordinate in detail in order to coordinate on answers. Medical school and diagnostic guides are chock full of coordination mechanisms for measurement->diagnosis. In your scheme, doctors who follow the guides and never use their experience, intuition, and good judgement to think deeper are the ones who get paid. Wilson gets paid, House goes elsewhere. That may be your goal—“prefer a younger doctor” is common advice for a reason. But be aware that you’re optimizing for standards, not truth.