Hmm. If we bring actual thermodynamics into the picture, then I think that energy stored in some very usable way (say, a charged battery) has a small number of possible states, whereas when you expend it, it generally ends up as waste heat that has a lot of possible states. In that case, if someone wants to take a bunch of stored energy and spend it on, say, making a robot rotate a huge die made of rock into a certain orientation, then that actually leads to a larger state space than someone else’s preference to keep the energy where it is, even though we’d probably say that the former is costlier than the latter. We could also imagine a third person who prefers to spend the same amount of energy arranging 1000 smaller dice—same “cost”, but exponentially (in the mathematical sense) different state space shrinkage.
It seems that, no matter how you conceptualize things, it’s fairly easy to construct a set of examples in which state space shrinkage bears little if any correlation to either “expected utility” or “cost”.
Hmm. If we bring actual thermodynamics into the picture, then I think that energy stored in some very usable way (say, a charged battery) has a small number of possible states, whereas when you expend it, it generally ends up as waste heat that has a lot of possible states. In that case, if someone wants to take a bunch of stored energy and spend it on, say, making a robot rotate a huge die made of rock into a certain orientation, then that actually leads to a larger state space than someone else’s preference to keep the energy where it is, even though we’d probably say that the former is costlier than the latter. We could also imagine a third person who prefers to spend the same amount of energy arranging 1000 smaller dice—same “cost”, but exponentially (in the mathematical sense) different state space shrinkage.
It seems that, no matter how you conceptualize things, it’s fairly easy to construct a set of examples in which state space shrinkage bears little if any correlation to either “expected utility” or “cost”.