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casebash comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong
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If the PRA isn't trying to "maximize" an unbounded function, it can't very well get "beaten" by another agent who chooses x+n because they didn't have the same goal. I reject, therefore, that an agent that obeys its stopping function in an unbounded scenario may be called any more or less "rational" based on that reason only than any other agent that does the same, regardless of the utility it may not have collected.
By removing all constraints, you have made comparing results meaningless.
So an agent that chooses only 1 utility could still be a perfectly rational agent in your books?
Might be. Maybe that agent's utility function is actually bounded at 1 (it's not trying to maximize, after all). Perhaps it wants 100 utility, but already has firm plans to get the other 99. Maybe it chose a value at random from the range of all positive real numbers (distributed such that the probability of choosing X grows proportional to X) and pre-committed to the results, thus guaranteeing a stopping condition with unbounded expected return. Since it was missing out on unbounded utility in any case, getting literally any is better than none, but the difference between x and y is not really interesting.
(humorously) Maybe it just has better things to do than measuring its *ahem* stopping function against the other agents.