Psychohistorian comments on Utilons vs. Hedons - Less Wrong

28 Post author: Psychohistorian 10 August 2009 07:20PM

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Comment author: PhilGoetz 11 August 2009 01:40:56AM 4 points [-]

I have the sense that much of this was written as a response to this paradox in which maximizing expected utility tells you to draw cards until you die.

Psychohistorian wrote:

There's a bigger problem causing that causes our intuition to reject this hypothetical as "just wrong:" it leads to major errors in both utilons and hedons. The mind cannot comprehend unlimited doubling of hedons. I doubt you can imagine being 260 times as happy as you are now; indeed, I doubt it is meaningfully possible to be so happy.

The paradox is stated in utilons, not hedons. But if your hedons were measured properly, your inability to imagine them now is not an argument. This is Omega we're talking about. Perhaps it will augment your mind to help you reach each doubling. Whatever. It's stipulated in the problem that Omega will double whatever the proper metric is. Futurists should never accept "but I can't imagine that" as an argument.

As for utilons, most people assign a much greater value to "not dying," compared with having more hedons. Thus, a hedonic reading of the problem returns an error because repeated doubling feels meaningless, and a utilon reading (may) return an error if we assign a significant enough negative value to death. But if we look at it purely in terms of numbers, we end up very, very happy right up until we end up very, very dead.

We need to look at it purely in terms of numbers if we are rationalists, or let us say "ratio-ists". Is your argument really that numeric analysis is the wrong thing to do?

Changing the value you assign life vs. death doesn't sidestep the paradox. We can rescale the problem by an affine transformation so that your present utility is 1 and the utility of death is 0. That will not change the results of expected utility maximization.

Comment author: Psychohistorian 11 August 2009 06:01:08AM 4 points [-]

Let's try a new card game. Losing isn't death, it's 50 years of torture, followed by death in the most horribly painful way imaginable, for you and everyone you know. We'll say that utility is zero, your current utility is one, and a win doubles your current utility. Do you take the bet?

Or, losing isn't death, it's having to listen to a person scratch a chalkboard for 15 seconds. We'll call that 0, your current situation 1, and a win 2. Do you take the bet?

This is the problem with such scaling. You're defining "double your utility" as "the amount of utility that would make you indifferent to an even-odds bet between X and Y" and then proposing a bet between X and Y where the odds are better than even in your favor. No other definition will consistently yield the results you claim (or at least no other definition type - you could define it the same way but with a different odds threshold). It proves nothing useful.

Comment author: MichaelBishop 15 August 2009 10:49:42PM *  0 points [-]

The example may not prove anything useful, but it did something useful for me. It reminded me that 1) we don't have a single perfect-for-all-situations definition of utility. and 2) our intuition often leads us astray.