Suppose that the right way to combine epistemic utilities across people is averaging: the overall epistemic utility of the human race is the average of the individual epistemic utilities. Suppose, further, that each individual epistemic utility is strictly proper, and you’re a “humanitarian” agent who wants to optimize overall epistemic utility.
Suppose you’re now thinking about two hypotheses about how many people exist: the two possible numbers are m and n, which are not equal. All things considered, you have credence 0 < p0 < 1 in the hypothesis Hm that there are m people and 1 − p0 in the hypothesis Hn that there are n people. You now want to optimize overall epistemic utility. On an averaging view, if Hm is true, if your credence is p1, your contribution to overall epistemic utility will be:
- (1/m)T(p1)
and if Hm is false, your contribution will be:
- (1/n)F(p1),
where your strictly proper scoring rule is given by T, P. Since your credence is p1, by your lights the expected value after your changing your credence to p0 will be:
- p0(1/m)T(p1) + (1−p0)(1/n)F(p1) + Q(p0)
where Q(p0) is the contribution of other people’s credences, which I assume you do not affect with your choice of p1. If m ≠ n and T, F is strictly proper, the expected value will be maximized at
- p1 = (p0/m)/(p0/m+(1−p0)/n) = np0/(np0+m(1−p0)).
If m > n, then p1 < p0 and if m < n, then p1 > p0. In other words, as long as n ≠ m, if you’re an epistemic humanitarian aiming to improve overall epistemic utility, any credence strictly between 0 and 1 will be unstable: you will need to change it. And indeed your credence will converge to 0 if m > n and to 1 if m < n. This is absurd.
I conclude that we shouldn’t combine epistemic utilities across people by averaging the utilities.
Idea: What about combining them by computing the epistemic utilities of the average credences, and then applying a strictly proper scoring rule, in effect imagining that humanity is one big committee and that a committee’s credence is the average of the individual credences?
This is even worse, because it leads to problems even without considering hypotheses on which the number of people varies. Suppose that you’ve just counted some large number nobody cares about, such as the number of cars crossing some intersection in New York City during a specific day. The number you got is even, but because the number is big, you might well have made a mistake, and so your credence that the number is even is still fairly low, say 0.7. The billions of other people on earth all have credence 0.5, and because nobody cares about your count, you won’t be able to inform them of your “study”, and their credences won’t change.
If combined epistemic utility is given by applying a proper scoring rule to the average credence, then by your lights the expected value of the combined epistemic utility will increase the bigger you can budge the average credence, as long as you don’t get it above your credence. Since you can really only affect your own credence, as an epistemic humanitarian your best bet is to set your credence to 1, thereby increasing overall human credence from 0.5 to around 0.5000000001, and making a tiny improvement in the expected value of the combined epistemic utility of humankind. In doing so, you sacrifice your own epistemic good for the epistemic good of the whole. This is absurd!
I think the idea of averaging to produce overall epistemic utilities is just wrong.
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