RobinZ comments on Newcomb's Problem and Regret of Rationality - Less Wrong

64 Post author: Eliezer_Yudkowsky 31 January 2008 07:36PM

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Comment author: RobinZ 26 July 2010 09:00:46PM *  3 points [-]

Wait - we can't assume that the probability of being correct is the same for two-boxing and one-boxing. Suppose Omega has a probability X of predicting one when you choose one and Y of predicting one when you choose two.

E1 = E($1 000 000) * X E2 = E($1 000) + E($1 000 000) * Y

The special case you list corresponds to Y = 1 - X, but in the general case, we can derive that E1 > E2 implies

X > Y + E($1 000) / E($1 000 000)

If we assume linear utility in wealth, this corresponds to a difference of 0.001. If, alternately, we choose a median net wealth of $93 100 (the U.S. figure) and use log-wealth as the measure of utility, the required difference increases to 0.004 or so. Either way, unless you're dead broke (e.g. net wealth $1), you had better be extremely confident that you can fool the interrogator before you two-box.