(EDIT: Chris Meacham came up with a similar example here. I missed that comment before writing this one.)
On the Addendum, here’s an example with three options, with four individuals x1,x2,x3,x4 with welfares 1 through 4 split across the first two worlds.
x1:1,x4:4
x2:2,x3:3
No extra people exist.
In world 1, x4 will be at their peak under any counterpart relation, and x1 will not be at their peak under any counterpart relation since their counterpart will have higher welfare 2 or 3 > 1 in world 2. In world 2, x2 and x3 can’t both be at their peaks simultaneously, since one will have a counterpart with higher welfare 4 > 2, 3 in world 2. Therefore, both world 1 and world 2 cause harm, while world 3 is harmless, so only world 3 is permissible.
(EDIT: the following would also work, by the same argument:
x1:1,x2:3
x3:2,x4:2
No extra people exist.)
The same conclusion follows with any identity constraints, since this just rules out some mappings.
In this way, I see the view as very perfectionist. The view is after all essentially that anything less than a maximally good life is bad (counts against that life), with some specification of how exactly we should maximize. This is similar to minimizing total DALYs, but DALYs use a common reference for peak welfare for everyone, 80-90 years at perfect health (and age discounting?).
(EDIT: Chris Meacham came up with a similar example here. I missed that comment before writing this one.)
On the Addendum, here’s an example with three options, with four individuals x1,x2,x3,x4 with welfares 1 through 4 split across the first two worlds.
x1:1,x4:4
x2:2,x3:3
No extra people exist.
In world 1, x4 will be at their peak under any counterpart relation, and x1 will not be at their peak under any counterpart relation since their counterpart will have higher welfare 2 or 3 > 1 in world 2. In world 2, x2 and x3 can’t both be at their peaks simultaneously, since one will have a counterpart with higher welfare 4 > 2, 3 in world 2. Therefore, both world 1 and world 2 cause harm, while world 3 is harmless, so only world 3 is permissible.
(EDIT: the following would also work, by the same argument:
x1:1,x2:3
x3:2,x4:2
No extra people exist.)
The same conclusion follows with any identity constraints, since this just rules out some mappings.
In this way, I see the view as very perfectionist. The view is after all essentially that anything less than a maximally good life is bad (counts against that life), with some specification of how exactly we should maximize. This is similar to minimizing total DALYs, but DALYs use a common reference for peak welfare for everyone, 80-90 years at perfect health (and age discounting?).