Measuring optimization power in terms of achieved outcome is wrong for the same reason that attributing a highly desired outcome to rationality is wrong. Even if I win the lottery, it was still a negative expected dollars choice to play the lottery. What we really want is something like the minimum utility outcome a process will achieve where the minimum is taken over a given a set of starting states. Or we could have a probability distribution over starting states and get the expected utility of the outcome. ETA: oops, I don’t mean utility of the outcome, I mean measure of the set of outcomes with greater utility than the minimum or expected or whatever.
The problem of the size of the solution space isn’t a problem if we content ourselves with comparing optimization power of different processes (I think...).
Even if I win the lottery, it was still a negative expected dollars choice to play the lottery.
At that point in the post, I hadn’t introduced mixed states. So the only options are to choose among fully deterministic worlds. Obviously if you had the choice between “win the lottery or don’t win the lottery”, then you’d go for the first.
Later when I bring in mixed states you can model such things as “buy a lottery ticket” as the achieved state, which generally has expected disutility.
Measuring optimization power in terms of achieved outcome is wrong for the same reason that attributing a highly desired outcome to rationality is wrong. Even if I win the lottery, it was still a negative expected dollars choice to play the lottery. What we really want is something like the minimum utility outcome a process will achieve where the minimum is taken over a given a set of starting states. Or we could have a probability distribution over starting states and get the expected utility of the outcome. ETA: oops, I don’t mean utility of the outcome, I mean measure of the set of outcomes with greater utility than the minimum or expected or whatever.
The problem of the size of the solution space isn’t a problem if we content ourselves with comparing optimization power of different processes (I think...).
At that point in the post, I hadn’t introduced mixed states. So the only options are to choose among fully deterministic worlds. Obviously if you had the choice between “win the lottery or don’t win the lottery”, then you’d go for the first.
Later when I bring in mixed states you can model such things as “buy a lottery ticket” as the achieved state, which generally has expected disutility.