Just compare the cardinality of the number of days to the cardinality of the number of people.
If |days| < |people| then start them in the heaven sphere.
If |days| = |people| then it doesn’t matter (by symmetry the first are last, and the last first, so to speak).
If |days| > |people| then start them in the hell sphere.
My first impression was the same as yours, but then I realized there was no guarantee about any of the cardinality, even for the set of days. The post assumes the reals, but comparing the cardinality should work for any sets (although if they’re bigger than the reals can we really compare “utility” at all?)
Just compare the cardinality of the number of days to the cardinality of the number of people. If |days| < |people| then start them in the heaven sphere. If |days| = |people| then it doesn’t matter (by symmetry the first are last, and the last first, so to speak). If |days| > |people| then start them in the hell sphere.
My first impression was the same as yours, but then I realized there was no guarantee about any of the cardinality, even for the set of days. The post assumes the reals, but comparing the cardinality should work for any sets (although if they’re bigger than the reals can we really compare “utility” at all?)
I think that’s a better statement of what I tried to say.