orthonormal comments on Decision Theories, Part 3.75: Hang On, I Think This Works After All - Less Wrong

23 Post author: orthonormal 06 September 2012 04:23PM

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Tags: tdt decision_theory prisoners_dilemma timeless

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Comment author: cousin_it 10 September 2012 01:00:28PM *  2 points [-]

Unless I've misunderstood Masquerade, there seems to be a version of SlowCooperateBot that Masquerade also cooperates with:

def TemptingCooperateBot(X):
- if X(TemptingCooperateBot)=C is provable in PA:
- - return C
- if 2+2=3 is provable in PA+4:
- - return D
- return C

If that's correct, then Wei's comment seems to be a good summary of the reason why your approach works. But maybe I'm still missing something.

Comment author: orthonormal 15 September 2012 09:46:39PM 0 points [-]

Thanks for the reply, and sorry for the delay...

Masquerade correctly defects against TemptingCooperateBot, for the following reasons:

  • PA proves "FB(TCB)=TCB(FB)=C"
  • PA+5 proves "TCB(DB)=C" and of course PA proves "DB(TCB)=D"
  • PA+5 proves "TCB(Masquerade)=C" (though this is actually irrelevant, as Masquerade will defect at this point whether the sanity check succeeds or fails)

It's not that there's anything magical about PA+4 in Masquerade; my mental image is that Masquerade uses a large value for N, so that it has time to find mutual cooperation with all but the very loopiest of opponents. If you delay it until PA+4, then it'll just start from there, more or less.

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