Stuart_Armstrong comments on Post retracted: If you follow expected utility, expect to be money-pumped - Less Wrong

0 Post author: Stuart_Armstrong 29 October 2009 12:06PM

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Comment author: Eliezer_Yudkowsky 29 October 2009 12:22:52PM *  14 points [-]

If you have a consistent utility function over outcomes, you cannot be money-pumped. This is not a utility function over changes in money, it is a utility function over total money.

This actually struck me as a problem with your argument from earlier, though I didn't point it out at that time. I think you plain don't understand expected utility, actually.

In the above, the question is the preference between a mix of (.5(B + 1) + .5(B + 2)) vs. (1(B + 1.49)) and a consistent version of a human (as opposed to an actual human) would prefer the former lottery given at least a hundred bucks in bank B. After that, of course, the amount in B changes. But if you start by putting consistent utilities over the total amount of money, you cannot be money-pumped.

Comment author: Stuart_Armstrong 29 October 2009 09:33:48PM 5 points [-]

You were correct. I think that now I understand expected utility; I was arrogant enough to follow my mathematical intuitions, assuming the details would fix themselves later, rather than working it all through. What I would never have done in a published paper, I did in a blog post.

I apologise. The post has been retracted.

Comment author: Wei_Dai 29 October 2009 10:00:58PM 10 points [-]

Can you please write a post on what your old incorrect understanding of expected utility was, and why it was wrong (before it fades away completely)? I suspect your confusion to be a common one, and writing it down would help others. Think of it as payback for those who tried (unsuccessfully, until Eliezer's attempt) to point out that perhaps you didn't understand expected utility correctly.

Comment author: Stuart_Armstrong 30 October 2009 12:18:05PM 1 point [-]

I've added that to the post now - a sketch of the original, and what went wrong (simple version: I applied financial/arbitrage insights to utility, whithout realising that the mere existence of investors and arbitragers in the world would change the price you put on something).

Think of it as payback for those who tried (unsuccessfully, until Eliezer's attempt) to point out that perhaps you didn't understand expected utility correctly.

Oh, it wasn't Eliezer pointing it out that made me realise it; it was me trying to prove Eliezer wrong that did the trick.