It feels to me as if the following things are likely to be true:
If you want your utilities to be real-valued then you can’t value everyone equally in a universe with a countable infinity of people (for reasons analogous to the way you can’t pick one person at random from a universe with a countable infinity of people).
If you allow a more general notion of utilities, you can value everyone equally, but there may be a price to pay (e.g., some pairs of outcomes not being comparable, or not having enough structure for notions like “expected utility” to be defined).
For instance, consider the following construction. We have a countable infinity of possible people (not all necessarily exist). We assume we’ve got a way of assigning utilities to individuals. Now say that a “global utility” means an assignment of a utility to each person (0 for nonexistent people), and put an equivalence relation on global utilities where u~v if you can get from one to the other by changing a finite number of the utilities, by amounts that add up to zero. (Or, maybe better: by changing any number, where {all the changes} is absolutely convergent—i.e., sum of the absolute values is finite—and the sum is zero.)
In this case, you can compute expected utilities “pointwise”, which is nice; swapping two people’s “labels” (or, more generally, permuting finitely many labels) makes no difference to a “global utility”, which is nice; in any world with only finitely many people it’s equivalent to total utilitarianism, which is probably nice; if you increase some utilities and don’t decrease any, you get something strictly better, which is nice; but utilities aren’t always comparable, so in some cases this value system doesn’t know what to do. E.g., if you have disjoint infinite sets A and B of people, { everyone in A gets +1, everyone in B gets −1 } and {everyone in A gets −1, everyone in B gets +1 } are incomparable, which isn’t so nice.
It feels to me as if the following things are likely to be true:
If you want your utilities to be real-valued then you can’t value everyone equally in a universe with a countable infinity of people (for reasons analogous to the way you can’t pick one person at random from a universe with a countable infinity of people).
If you allow a more general notion of utilities, you can value everyone equally, but there may be a price to pay (e.g., some pairs of outcomes not being comparable, or not having enough structure for notions like “expected utility” to be defined).
For instance, consider the following construction. We have a countable infinity of possible people (not all necessarily exist). We assume we’ve got a way of assigning utilities to individuals. Now say that a “global utility” means an assignment of a utility to each person (0 for nonexistent people), and put an equivalence relation on global utilities where u~v if you can get from one to the other by changing a finite number of the utilities, by amounts that add up to zero. (Or, maybe better: by changing any number, where {all the changes} is absolutely convergent—i.e., sum of the absolute values is finite—and the sum is zero.)
In this case, you can compute expected utilities “pointwise”, which is nice; swapping two people’s “labels” (or, more generally, permuting finitely many labels) makes no difference to a “global utility”, which is nice; in any world with only finitely many people it’s equivalent to total utilitarianism, which is probably nice; if you increase some utilities and don’t decrease any, you get something strictly better, which is nice; but utilities aren’t always comparable, so in some cases this value system doesn’t know what to do. E.g., if you have disjoint infinite sets A and B of people, { everyone in A gets +1, everyone in B gets −1 } and {everyone in A gets −1, everyone in B gets +1 } are incomparable, which isn’t so nice.