This isn't about your decision controlling them. It's about the information gained by knowing you're the nth person. The fact that you might not be a person doesn't really matter, since you have to be a person for any of the possibilities mentioned.

the sum could be far below 1, if you are in fact neither of these people

P(U=m|T=n)∝1/n

That should be

a = number of nonhuman sentients.

P(U=m|T=n)∝1/(a+n)

which approaches a constant as a increases without limit.

Oops. I've checked this several times, and hadn't seen that.

Let this be a lesson. When quadrillions of lives are counting on it, make sure someone double-checks your math.

I'm going to consider the ramifications of this for a while. This argument might still apply significantly. It might not.