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Michaelos comments on Open Thread: September 2011 - LessWrong
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I keep running into problems with various versions of what I internally refer to as the "placebo paradox", and can't find a solution that doesn't lead to Regret Of Rationality. Simple example follows:
You have an illness from wich you'll either get better, or die. The probability of recovering is exactly half of what you estimate it to be due to the placebo effect/positive thinking. Before learning this you have 80% confidence in your recovery. Since you estimate 80%, your actual chance is 40% so you update to this. Since the estimate is now 40%, the actual chance is 20%, so you update to this. Then it's 10%, so you update to that. etc. Until both your estimated and actual chance of recovery are 0. then you die.
An irrational agent, on the other hand, upon learning this could self delude to 100% certainty of recovery, and have a 50% chance of actually recovering.
This is actually causing me real world problems, such as inability to use techniques based on positive thinking, and a lot of cognitive dissonance.
Another version of this problem features in HP:MoR, in the scene where harry is trying to influence the behaviour of dementors.
And to show this isn't JUST a quirk of human mind design, one can envision Omega setting up an isomorphic problem for any kind of AI.
Speaking of Omega setting up an isomorphic situation, the Newcomb's Box problems do a good job of expressing this.
http://lesswrong.com/lw/nc/newcombs_problem_and_regret_of_rationality/
However, I also though of a side question. Is the person who is caught in a cycle of negative thinking like the placebo effect that you mention, engaging in confirmation bias?
I mean, if that person thinks "I am caught in a loop of updates that will inexorably lead to my certain death." And they are attempting to establish that that is true, they can't simply say "I went from 80%/40% to 40%/20% to 20%/10%, and this will continue. I'm screwed!" as evidence of it's truth, because that's like saying "4,6,8" "6,8,10" "8,10,12" as the guesses for the rule that you know "2,4,6" follows. and then saying "The rule is even numbers, right? Look at all this evidence!"
If a person has a hypothesis that their thoughts are leading them to an inexorable and depressing conclusion, then to test the hypothesis, the rational thing to do is for that person to try proving themselves wrong. By trying "10,8,6" and then getting "No, that is not the case." (Because the real rule is numbers in increasing order.)
I actually haven't confirmed that this idea myself yet. I just thought of it now. But casting it in this light makes me feel a lot better about all the times I perform what appear at the time to be self delusions on my brain when I'm caught in depressive thinking cycles, so I'll throw it out here and see if anyone can contradict it.
Thanks for restating parts of the problem in a much clearer manner!
And yea, that article is why this problem is wreaking such havock on me, and I were thinking of it as I wrote the OP. I'm not sure why I didn't link it.
However, I still can't resolve the paradox. Although I'm finally starting to see how one might start on doing so: formalizing an entire decision theory that solves the entire class of problems, and them swapping half my mindware out in a single operation. Doesn't seem like a very^good solution thou so I'd rather keep looking for third options.
I don't think I understand the middle paragraph with all the examples. Probably because the way I actually think of it is not the way I used in the OP, but rather an equation where expectation must be equal to actual probability to call my belief consistent, and jumping straight there. Like so: P=E/2, E=P, thus E=0.
Hmm, I just got a vague intuition saying roughly "Hey, but wait a moment, probability is in the mind. The multiverse is timeless and in each Everett branch you either do recover or you don't! ", but I'm not sure how to proceed from there.