There's the problem with naive utilitarianism. The experts want to minimize deaths across the population. I want to minimize the risk to my otherwise healthy children (hypothetically. I don't have children and I am vaccinated). These legitimate desires can and do conflict. Who has precedence is entirely political, not scientific.

And plenty of medical experts get the Monty Hall problem wrong.

> And plenty of medical experts get the Monty Hall problem wrong.

Then they're not experts on prob and stats in medicine, and you shouldn't choose them to guide policy making when prob and stats in medicine are relevant. The alternative is to choose those who aren't experts in prob and stats in medicine, which results in policy bred from ignorance of the relevant math and science.

Choosing people who are ignorant of the relevant math and science over those who are knowledgeable is certainly one way to make policy, and it seems that is what folks want, so I guess we'll see how well that it works out.