Expansionism fails to rank worlds where some spatio-temporal locations are infinitely far apart (see Bostrom (2011), p. 13). For example: < 2 , 2, 2, … (infinite distance) … 1 , 1, 1> vs. < 1, 1, 1, … (infinite distance) … 1, 2, 1>. Here, the former world is better at an infinite number of locations, and worse at only one, so it seems intuitively better: but the expansion that starts at the single 2 location in the second world is forever greater in the latter world.
For these cases, you could start expanding from one point in each cluster of locations that are finitely close to each other. If there are finitely many, then you can alternate between them or do one step into each cluster for each step of the sum (or whatever you’re aggregating).
If there’s a countable infinity, then you can use a bijection N2≃N, but that is not very nice, and will give far less weight to the clusters you start on later.
For these cases, you could start expanding from one point in each cluster of locations that are finitely close to each other. If there are finitely many, then you can alternate between them or do one step into each cluster for each step of the sum (or whatever you’re aggregating).
If there’s a countable infinity, then you can use a bijection N2≃N, but that is not very nice, and will give far less weight to the clusters you start on later.