Why spend only half on U1? Spend (1 - epsilon). And write a lottery ticket giving the U2-oriented decision maker the power with probability epsilon. Since epsilon infinity = infinity, you still get infinite expected* utility (according to U2). And you also get pretty close to the max possible according to U1.
Infinity has uses even beyond allocating hotel rooms. (HT to A. Hajek)
Of course, Hajek’s reasoning also makes it difficult to locate exactly what it is that U2 “says you should do”.
In general, it should be impossible to allocate 0 to U2 in this sense. What’s the probability that an angel comes down and magically forces you to do the U2 decision? Around epsilon, i’d say.
U2 then becomes totally meaningless, and we are back with a bounded utility function.
Why spend only half on U1? Spend (1 - epsilon). And write a lottery ticket giving the U2-oriented decision maker the power with probability epsilon. Since epsilon infinity = infinity, you still get infinite expected* utility (according to U2). And you also get pretty close to the max possible according to U1.
Infinity has uses even beyond allocating hotel rooms. (HT to A. Hajek)
Of course, Hajek’s reasoning also makes it difficult to locate exactly what it is that U2 “says you should do”.
In general, it should be impossible to allocate 0 to U2 in this sense. What’s the probability that an angel comes down and magically forces you to do the U2 decision? Around epsilon, i’d say.
U2 then becomes totally meaningless, and we are back with a bounded utility function.