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Houshalter comments on Median utility rather than mean? - Less Wrong Discussion
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It's perfectly consistent in the sense that it's not money pumpable, and always makes the same decisions given the same information. It will make different decisions in different situations, given different information. But that is not inconsistent by an reasonable definition of "inconsistent".
It makes a huge difference. If you want to get the best median future, then you can't make decisions in isolation. You need to consider every possible decision you will have to make, and their probability. And choose a decision policy that selects the best median outcome.
As in my previous example (sorry about it being difficult to follow, though I'm not sure yet what I could say to clarify things), it is inconsistent in the sense that it can lead you to pay for probability distributions over outcomes that you could have achieved for free.
Right. As I just said, "you can... consider them sequentially and use your beliefs about what your choices will be in the future to compute the expected utilities of the possible decisions available to you now." (edited to fix grammar). This reduces iterated decisions to isolated decisions: you have certain beliefs about what you'll do in the future, and now you just have to make a decision on the issue facing you now.