The demiurge flipped a fair coin. If it landed heads, he created 100 people, of whom 10 had a birthmark on their back. If it landed tails, he created 10 people, of whom 9 had a birthmark on their back. You’re one of the created people and the demiurge has just apprised you of the above facts.
What should your credence be that you have a birthmark on your back?
This seems a plausible answer:
- Answer A: (1/2)(10/100)+(1/2)(9/10)=1/2
Let’s think a bit about Brier scores, considered as measures of epistemic disutility. If everybody goes for Answer A, then the expected total epistemic disutility will be:
- TD(A) = (1/2)(100)(1/2)2 + (1/2)(10)(1/2)2 = 13.75
That’s not the best one we can do. It turns out that the strategy that minimizes the expected total epistemic disutility will be:
- Answer B: 19/110
which yields the expected total disutility:
- TD(B) = 7.9.
The same 19/110 answer will be optimal with any other proper scoring rule. Moreover, what holds for proper scoring rules also holds for betting scenarios, and so the strategy of going for 19/110, if universally adopted, will make for better total utility in betting scenarios. In other words, we have both an epistemic utility and a pragmatic utility argument for the strategy of adopting 19/110.
On the other hand, the 1/2 answer will optimize the expected average epistemic and pragmatic utilities in the population. But do we want to do that? After all, we know from Parfit that optimizing average pragmatic utilities can be a very bad idea (as it leads to killing off of those who are below average in happiness).
Yet the 1/2 answer has an intuitive pull.