It can’t, because utility functions are defined over a single world, not over the set of all possible worlds. If your utility function were defined over all possible worlds, you would just say “maximize utility” instead of “maximize expected utility”.
This doesn’t sound right to me. Assuming “world” means “world at time t”, a utility function at the very least has type (World → Utilons). It maps a single world to a single utility measure, but it’s still defined over all worlds, the same way that (+3) is defined over all integers. If it was only defined for a single world it wouldn’t really be much of a function, it’d be a constant.
We use expected utility due to uncertainty. If we had perfect information, we could maximize utility by searching over all action sequences, computing utility for each resulting world, and returning the sequence with the highest total utility.
If you maximize expected utility, that means that an action that results in utility 101 for one future you in one possible world, and utility 0 for 9 future yous in 9 equally-likely possible worlds
I think this illustrates the problem with your definition. The utility you’re maximizing is not the same as the “utility 101 for one future you”. You first have to map future you’s utility to just plain utility for any of this to make sense.
It maps a single world to a single utility measure, but it’s still defined over all worlds,
I meant “the domain of a utility function is a single world.”
However, it turns out that the standard terminology includes both utility functions over a single world (“outcome”), and a big utility function over all possible worlds (“lottery”).
My question/observation is still the same as it was, but my misuse of the terminology has mangled this whole thread.
This doesn’t sound right to me. Assuming “world” means “world at time t”, a utility function at the very least has type (World → Utilons). It maps a single world to a single utility measure, but it’s still defined over all worlds, the same way that (+3) is defined over all integers. If it was only defined for a single world it wouldn’t really be much of a function, it’d be a constant.
We use expected utility due to uncertainty. If we had perfect information, we could maximize utility by searching over all action sequences, computing utility for each resulting world, and returning the sequence with the highest total utility.
I think this illustrates the problem with your definition. The utility you’re maximizing is not the same as the “utility 101 for one future you”. You first have to map future you’s utility to just plain utility for any of this to make sense.
I meant “the domain of a utility function is a single world.”
However, it turns out that the standard terminology includes both utility functions over a single world (“outcome”), and a big utility function over all possible worlds (“lottery”).
My question/observation is still the same as it was, but my misuse of the terminology has mangled this whole thread.