yes, your entire example of doctors is simply due to irrationality
So first you say this.
But then you start to backtrack
in the trivial sense that for a poor measure the posterior of a true positive remains far smaller than it being a false positive and may not motivate a decision, shrinking the VoI towards zero, which will frequently be so small as to not justify the cost of testing
And further admit
It is definitely the case that many tests cost too much for too little information and should not be run because the VoI is often zero (for a rational decision maker) and the test is simply a loss as it will not change any decisions.
But then you try to defend the initial claim, that the doctors are being irrational
Nevertheless, the value of free information is always greater than or equal to zero, and if free information makes you worse off, that implies somewhere there is an irrationality.
But we’ve already established that the tests are not free in the world we live in.
If you’re going to prove the doctors are being irrational in the world we live in, then you can’t change a core part of the problem statement. The tests do have costs—in time, in money, in available machines, in false positives that may result in surgeries or other actions with non-zero risk, and in a dozen other ways, some of which were alluded to by Dynomight, like the possibility of lawsuits.
My whole argument, which you said is “generally wrong”, is predicated on the fact that this information is not free. I don’t accept the notion that people are being irrational because they are making decisions based on the reality of the world where information is not free just because we can hypothesize about worlds where that information is free.
So first you say this.
But then you start to backtrack
And further admit
But then you try to defend the initial claim, that the doctors are being irrational
But we’ve already established that the tests are not free in the world we live in.
If you’re going to prove the doctors are being irrational in the world we live in, then you can’t change a core part of the problem statement. The tests do have costs—in time, in money, in available machines, in false positives that may result in surgeries or other actions with non-zero risk, and in a dozen other ways, some of which were alluded to by Dynomight, like the possibility of lawsuits.
My whole argument, which you said is “generally wrong”, is predicated on the fact that this information is not free. I don’t accept the notion that people are being irrational because they are making decisions based on the reality of the world where information is not free just because we can hypothesize about worlds where that information is free.
Do you still disagree?