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IlyaShpitser comments on Open thread, Mar. 2 - Mar. 8, 2015 - Less Wrong Discussion
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I think I've found the core of our disagreement. I want an algorithm that considers all possible paths through time. It decides on a set of actions, not just for the current time step, but for all possible future time steps. It chooses such that the final probability distribution of possible outcomes, at some point in the future, is optimal according to some metric. I originally thought of median, but it can work with any arbitrary metric.
This is a generalization of expected utility. The VNM axioms require an algorithm to make decisions independently and Just In Time. Whereas this method lets it consider all possible outcomes. It may be less elegant than EU, but I think it's closer to what humans actually want.
Anyway your example is wrong, even without predetermined actions. The algorithm would buy bet A, but then not buy bet B. This is because it doesn't consider bets in isolation like EU, but considers it's entire probability distribution of possible outcomes. Buying bet B would decrease it's expected median utility, so it wouldn't take it.
I am lost, this is just EU in a longitudinal setting? You can average over lots of stuff. Maximizing EU is boring, it's specifying the right distribution that's tricky.
It's not EU, since it can implement arbitrary algorithms to specify the desired probability distribution of outcomes. Averaging utility is only one possibility, another I mentioned was median utility.
So you would take the median utility of all the possible outcomes. And then select the action (or series of actions in this case) that leads to the highest median utility.
No method of specifying utilities would let EU do the same thing, but you can trivially implement EU in it, so it's strictly more general than EU.