jimrandomh comments on Omega's subcontracting to Alpha - Less Wrong

7 Post author: Stuart_Armstrong 16 March 2010 06:52PM

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Tags: bayesian decision_theory omega decision

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Comment author: jimrandomh 16 March 2010 07:26:55PM *  0 points [-]

I would translate this scenario into the following world-program:

U(S) =
{
envelopeIsFilled = coinflip()
acceptNote = S()
if (acceptNote == envelopeIsFilled)
CONTRADICTION
else
return (envelopeIsFilled ? 1e6 : 0) + (acceptNote ? 10 : 0)
}

Based on this world-program, it is obvious that you should refuse the note.

Comment author: Vladimir_Nesov 16 March 2010 09:09:05PM 3 points [-]

You didn't take into account that Omega appears conditionally on contents of the envelope and your decision.

Comment author: thomblake 16 March 2010 07:30:13PM 0 points [-]

Heh. I first read "1e6" above as a function determining whether the user-agent is internet explorer 6.

What is "CONTRADICTION" supposed to do in this "program"?

Comment author: jimrandomh 16 March 2010 07:52:15PM 0 points [-]

This program must be embedded in a larger one, since the original problem description didn't say what Omega would do if it couldn't truthfully make the prediction it did. Call that larger program U2(S). The only thing we are told about U2 is that it only calls U if it can do so in a way which guarantees that U won't reach a contradiction. Suppose, for example, that if Omega's prediction couldn't be made truthfully then you wouldn't get any money at all. This corresponds to the world program:

U2(S) =
{
try {
return U(S)
} catch(contradiction) {
return 0
}
}

Note that there are plenty of mathematically equivalent ways to write this - for example, using a would_throw(U,S,RNG) function.

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