Imagine a universe containing infinitely many immortal people, partitioned into two "spheres". In one sphere, all the inhabitants live a blissful existence, whereas the members of the other sphere suffer unbearable agony. Now compare the following two variations:
1) Everyone starts off in the blissful sphere. But each day, one more person gets permanently transferred across to the agony sphere, where they reside for the rest of eternity.
2) Everyone starts off in the agony sphere. But each day, one more person gets permanently transferred across to the blissful sphere, where they reside for the rest of eternity.
Which scenario is better? The answer, paradoxically, appears to be "both". At any moment in time, there will be infinitely many people in the original sphere, and only a finite number who have been transferred across. So option 1 is better.
However, each particular person will spend only a finite amount of time in the first sphere, whereas they will spend an eternity in their post-transfer home. So option 2 is better.
[A clarification is in order. As stated, it remains possible for some people to remain forever in their original sphere. (Suppose we assign each person a natural number. Each day we can transfer across the next even-numbered person. Then the infinitely many odd-numbered people never get transferred at all!) So let us stipulate that no-one is "skipped" in this way, and that every individual will indeed get transferred at some point.]
How are we to evaluate the options without falling into paradox?
(I owe this problem to recent discussion with ANU grad students. I think they in turn got it from Alan Hajek.)