Median expected behavior is simple which makes it easy to calculate.
As an electrical engineer when I design circuits I start off by assuming that all my parts behave exactly as rated. If a resistor says it’s 220+10% Ohms then I use 220 for my initial calculations. Assuming median behavior works wonderfully in telling me what my circuit probably will do.
In fact that’s good enough info for me to base my design decision on for a lot of purposes (given a quick verification of functionality, of course).
This is the exact opposite of what you’re proposing! I look for the cases where everything is off by the greatest amount possible and in the way that combines to form the worst possible outcome. If my circuit has 2 220+10% ohm resistors I’ll consider the cases where both are 242ohms, both are 198ohms and even the bizarre cases where one is 198ohms and the other 242ohms. I do that because if I know my circuit will function under those circumstances, then only when the resistors are out of tolerance (and I can blame someone else) there’s a problem.
In my view, average expected utility is the true metric. But there are circumstances where it’s easier and cheaper to ignore the utility of anything other than the median case, and there are circumstances where it’s easier and cheaper to ignore the utility of anything other than the worst cases.
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.
Median expected behavior is simple which makes it easy to calculate.
As an electrical engineer when I design circuits I start off by assuming that all my parts behave exactly as rated. If a resistor says it’s 220+10% Ohms then I use 220 for my initial calculations. Assuming median behavior works wonderfully in telling me what my circuit probably will do.
In fact that’s good enough info for me to base my design decision on for a lot of purposes (given a quick verification of functionality, of course).
But what about that 10%? What if it might matter? One thing I do is called worst case analysis https://en.wikipedia.org/wiki/Tolerance_analysis#Worst-case
This is the exact opposite of what you’re proposing! I look for the cases where everything is off by the greatest amount possible and in the way that combines to form the worst possible outcome. If my circuit has 2 220+10% ohm resistors I’ll consider the cases where both are 242ohms, both are 198ohms and even the bizarre cases where one is 198ohms and the other 242ohms. I do that because if I know my circuit will function under those circumstances, then only when the resistors are out of tolerance (and I can blame someone else) there’s a problem.
In my view, average expected utility is the true metric. But there are circumstances where it’s easier and cheaper to ignore the utility of anything other than the median case, and there are circumstances where it’s easier and cheaper to ignore the utility of anything other than the worst cases.
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.