the problem seems to be using expected values, which is highly distorted by even a single outlier … Why not “median expected utility”?
This is a common problem which is handled by robust statistics. Means, while efficient, are notably not robust. The median is a robust alternative from the class of L-estimators (L is for Linear), but a popular alternative for location estimates nowadays is something from the class of M-estimators (M is for Maximum Likelihood).
Maximum Likelihood doesn’t really lead to desirable behavior when the number of possibilities is very large. E.g. i roll a dice with a 2 and a 3 give you a dollar, and unrelated but horrible things happen on any other number.
Maximum likelihood means taking the outcome with the highest probability relative to everything else, correct? This isn’t really desirable since the outcome with the highest probability, might still have very low absolute probability.
This is a common problem which is handled by robust statistics. Means, while efficient, are notably not robust. The median is a robust alternative from the class of L-estimators (L is for Linear), but a popular alternative for location estimates nowadays is something from the class of M-estimators (M is for Maximum Likelihood).
Maximum Likelihood doesn’t really lead to desirable behavior when the number of possibilities is very large. E.g. i roll a dice with a 2 and a 3 give you a dollar, and unrelated but horrible things happen on any other number.
Huh?
Maximum likelihood means taking the outcome with the highest probability relative to everything else, correct? This isn’t really desirable since the outcome with the highest probability, might still have very low absolute probability.
No, not at all, what you are talking about is called the mode of the distribution.
Why don’t you look at the links in my post?
And the equation.
I don’t see how it’s different than the mode. Even the graphs show it as being the same: 1 2.
Think about a bimodal distribution, for example. But in any case, we’re talking about M-estimates, weren’t we?