## LESSWRONGLW

Open thread, Mar. 2 - Mar. 8, 2015

In Pascal's Mugging, the problem seems to be using expected values, which is highly distorted by even a single outlier.

The post led to a huge number of proposed solutions. They all seem pretty bad, and none of them even address the problem itself, just the specific thought experiment. And others, like bounding the utility function, are ok, but not really elegant. We don't really want to disregard high utility futures, we just don't want them to highly distort our decision process. But if we make decisions based on expected utility, they inevitably do.

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Why not "median expected utility"?

This might sound silly, but it's deeper than it looks: the reason why we use the expected value of utility (i.e. means) to determine the best of a set of gambles is because utility is defined as the thing that you maximize the expected value of.

The thing that's nice about VNM utility is that it's mathematically consistent. That means we can't come up with a scenario where VNM utility generates silly outputs with sensible inputs. Of course we can give VNM silly inputs and get silly outputs back--scenarios like ... (read more)

0[anonymous]5yIt seems one problem with using median is that the result depends on how coarsely you model the possible outcomes. E.g. suppose I am considering a bus trip: the bus may be on time, arrive early, or arrive late; and it may be late because it drove over a cliff killing all the passengers, or because it caught fire horribly maiming the passengers, or because it was stuck for hours in a snowstorm, or because it was briefly caught in traffic. With expected utility it doesn't matter how you group them: the expected value of the trip is the weighted sum of the expected value of being late/on-time/early. But the median of [late, on time, early] is different from the median of [cliff, fire, snowstorm, traffic, on time, early]
2Lumifer5yThis is a common problem which is handled by robust statistics [http://en.wikipedia.org/wiki/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 [http://en.wikipedia.org/wiki/M-estimator] (M is for Maximum Likelihood).

# 4

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters: