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PrimIntelekt comments on The True Prisoner's Dilemma - Less Wrong

56 Post author: Eliezer_Yudkowsky 03 September 2008 09:34PM

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Comment author: PrimIntelekt 04 February 2010 08:17:43PM *  2 points [-]

Important point.

Let's assume that your utility function (which is identical to theirs) simply weights and adds your payoff and theirs; that is, if you get X and they get Y, your function is U(X,Y) = aX+bY. In that case, working backwards from the utilities in the table, and subject to the constraint that a+b=1, here are the payoffs:

a/b=2: (you care twice as much about yourself)
(3,3) (-5,10)
(10,-5) (1,1)

a/b=3:
(3,3) (-2.5,7.5)
(7.5,-2.5) (1,1)

a=b:
Impossible. With both people being unselfish utilitarians, the utilities can never differ based on the same outcome.

b=0: (selfish)
The table as given in the post

I think the most important result is the case a=b: the dilemma makes no sense at all if the players weight both payoffs equally, because you can never produce asymmetrical utilities.

EDIT: My newbishness is showing. How do I format this better? Is it HTML?

Comment author: wnoise 04 February 2010 08:24:35PM 3 points [-]

It's not HTML, but "markdown" which gets turned into HTML.

http://wiki.lesswrong.com/wiki/Comment_formatting

Comment author: PrimIntelekt 05 February 2010 04:16:53AM 1 point [-]

Thank you!