A simpler version of the original post is this. Let there be a single, consistent utility function shared by all copies of the agent (X and all Xi). It assigns these utility values:

1. X chooses "sim", and then N instances of Xi choose "sim" and 1000-N instances choose "don't sim" -> 1.0 + 0.2N + 0.1(1000-N)
2. X chooses "don't sim", no Xi gets created -> 0.9

Of course, the post's premise is that the only actually possible universe in category 1 is that where all 1000 Xi instances choose "sim" (because they can't tell if they're in the simulation or not), so the total utility is then 1 + 0.2*1000 = 201.

This is a simple demonstration of TDT giving the right answer which maximizes the utility ("sim") while CDT doesn't (I think?)

What didn't make sense to me was saying X and Xi somehow have "different" utility functions. Maybe this was just confusion generated by imprecise use of words, and not any real difference.

The post then says:

For every agent it is true that she does not gain anything from the utility of another agent despite the fact she and the other agents are identical!

I'm not sure if this is intended to change the situation. Once you have a utility function that gives out actual numbers, you don't care how it works on the inside and whether it takes into accounts another agent's utility or anything else.