Worst case isn’t a great metric either. E.g. you are required to pay the mugger, because it’s the worst possible case. Average case doesn’t solve it either, because the utility the mugger is promising is even greater than improbability he’s right. Rare outliers can throw off the average case by a lot.
We need to invent some kind of policy to decide what actions to prefer, given a set of the utilities and probabilities of each possible outcome. Expected utility isn’t good enough. Median utility isn’t either. But there might be some compromise between them that gets what we want. Or a totally different algorithm altogether.
Worst case isn’t a great metric either. E.g. you are required to pay the mugger, because it’s the worst possible case. Average case doesn’t solve it either, because the utility the mugger is promising is even greater than improbability he’s right. Rare outliers can throw off the average case by a lot.
We need to invent some kind of policy to decide what actions to prefer, given a set of the utilities and probabilities of each possible outcome. Expected utility isn’t good enough. Median utility isn’t either. But there might be some compromise between them that gets what we want. Or a totally different algorithm altogether.
That’s why I find it interesting that mean and median converge in many cases of repeated choices.