2 ms·

Take a step back and look at his description of the bet and equation (2). Is says “a simple gamble”. It doesn’t say anything about an infinite series of iterat

by kgwgk 6y ago

Take a step back and look at his description of the bet and equation (2). Is says “a simple gamble”. It doesn’t say anything about an infinite series of iterations of the bet. It’s a single step problem. Do you play once or do you pass? (If the question is “do you want to play twice (or N times)” it’s also effectively a single-period problem. One just has to consider the distribution of outcomes after two (or N) rounds.) The usual EUT resolution is what I just described, which you don’t find problematic. He does find it problematic, because for him calculating an expectation is interacting with a copy of yourself in a parallel universe or something. The reason why he talks about infinite sequences of games is not because the problem is about an infinite sequence of games. To solve the simple problem he has to hypothesize that there is an infinite sequence of them.

mrow84 6y ago
edit: As noted in your other comment, the expectation with a standard utility function is actually negative, thus the premise for part of the below is incorrect, and therefore so are its conclusions. A more faithful reproduction of Peters' argument is that EE recovers the correct solution without requiring the addition of an arbitrary utility function, and corresponding appeals to irrationality. original comment: Yes, you are correct that in the initial framing it is just a single gamble, but of course the point is that an individual's life is made up of many gambles. Expected utility assures us that this bet has a positive expectation, and so naively we might think that iterating it also produces a positive expectation sequence, but it does not, as we saw. We can recover a correct answer by considering the expected utility of the whole sequence, but there is nothing in the problem to suggest that we should do so, unless we acknowledge the cause of the issue, which is that the ergodic hypothesis does not hold. The point of the whole "parallel universe" thing is that even though the expectation in a single step may be positive, an individual never realises that ensemble average - they only ever realise a time average. Thus, the time average is the more useful object of study.

by kgwgk 6y ago

mrow84 6y ago

edit: As noted in your other comment, the expectation with a standard utility function is actually negative, thus the premise for part of the below is incorrect, and therefore so are its conclusions. A more faithful reproduction of Peters' argument is that EE recovers the correct solution without requiring the addition of an arbitrary utility function, and corresponding appeals to irrationality. original comment: Yes, you are correct that in the initial framing it is just a single gamble, but of course the point is that an individual's life is made up of many gambles. Expected utility assures us that this bet has a positive expectation, and so naively we might think that iterating it also produces a positive expectation sequence, but it does not, as we saw. We can recover a correct answer by considering the expected utility of the whole sequence, but there is nothing in the problem to suggest that we should do so, unless we acknowledge the cause of the issue, which is that the ergodic hypothesis does not hold. The point of the whole "parallel universe" thing is that even though the expectation in a single step may be positive, an individual never realises that ensemble average - they only ever realise a time average. Thus, the time average is the more useful object of study.