Vladimir_Nesov comments on Counterfactual Calculation and Observational Knowledge - Less Wrong

11 Post author: Vladimir_Nesov 31 January 2011 04:28PM

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Comment author: Vladimir_Nesov 01 February 2011 07:34:01PM 0 points [-]

Even if Omega rewrote the answers of actual copies based on decision of other actual copies (I don't think this follows from the description of the problem), still it would be better to stick with the calculator.

I don't understand this passage. What "actual copies"? What doesn't follow how? What does it mean to "stick with the calculator"? (Which calculator? Who does the "sticking"?)

Comment author: prase 02 February 2011 01:27:27PM *  1 point [-]

Let me try again, then, hopefully more clearly.

Suppose that I am asked to precommit to a strategy before I know the result of the calculation (such assumption removes the potential disagreement with CDT in Counterfactual Mugging). Also, I expect that Omega appears with certainty, no matter what result the calculator gives.

So, I know that I will be given the calculator result, which is 99% correct, and asked by Omega to imagine a counterfactual world where the result was the opposite, and that I am free to determine what should Omega write in that counterfactual world.

The only chance why I should care is when I think that Omega could rewrite my result in the actual world. But I was not sure what algorithm Omega would follow. From the description of the problem it seemed that Omega simply asks the question and "modifies the counterfactual world", which I interpret as "changing Omega's beliefs about the counterfactual world." But anybody can do that, there is no need for Omega's exceptional qualities here, and I am certainly not going to change my beliefs after being asked this question by a janitor in place of Omega.

So Omega must be following some distinct algorithm. He may scan my mind and always rewrite the result depending on how would I respond in the counterfactual world. Hence I have asked whether it rewrites the answers of the actual people, rather than only changing its fantasies about the counterfactual. Probably that interpretation was the natural one when Omega was included, but it didn't occur to me after reading the original post. I continue within this interpretation.

I have four pure strategies: Precommit to tell Omega to write down (in the counterfactual world)

  1. the actual calculator output.
  2. the counterfactual (i.e. opposite) output.
  3. always even.
  4. always odd.

The first one always leads Omega to rewrite my answer to the opposite, which leaves me with 99% chance of losing. The second one wins in 99% of cases. The remaining two are 50% successful. So, answer to your question is "odd".

Is this interpretation correct, or still I am misunderstanding something?

Comment author: Vladimir_Nesov 02 February 2011 02:20:25PM *  1 point [-]

Also, I expect that Omega appears with certainty, no matter what result the calculator gives.

This could work if you give up control over your own test sheet to the counterfactual you mediated by Omega (and have your own decision control the counterfactual test sheet using counterfactual Omega). That's an elegant variant of the problem, with an additional symmetry. (In my thought experiment, the you that observed "odd" doesn't participate in the thought experiment at all, and the test sheet on "even" side is controlled by the you that observed "even".)

Can't parse a significant portion of the rest you wrote, but the strategies you consider and consequences of their use are correct for your variant of the thought experiment.

Comment author: prase 02 February 2011 03:13:22PM 0 points [-]

In my thought experiment, the you that observed "odd" doesn't participate in the thought experiment at all, and the test sheet on "even" side is controlled by the you that observed "even".

So, what does Omega do in your experiment? What algorithm it follows?

(If my question sounds repetitive, it is because not only I am confused, but I don't see a way out from the confusion.)

Comment author: Vladimir_Nesov 02 February 2011 03:20:45PM *  0 points [-]

Omega on the "odd" side predicts what the you on "even" side would command to be done with the test sheet on "odd" side, and does that. That's all Omegas do. You could have a janitor ask you the question on "even" side as easily, we only use "trustworthiness" attribute on "even" side, but need "predictive capability" attribute on "odd" side. An Omega always appears on "even" side to ask the question, and always appears on "odd" side to do the answer-writing.

Comment author: prase 02 February 2011 04:46:03PM *  1 point [-]

Thanks, I have automatically assumed that Omega is parity-symmetric.

Edit: So, the strategies lead to:

  1. If Q is even, I get it right in 99% of cases. If Q is odd, Omega changes my answer, and I get it wrong 99% of the time. Success rate = 0.5.
  2. The same reversed. If Q is even, I write down false answer 99% of the time, but if Q is odd, Omega steps in and changes the answer leading to 99% success. Overall 0.5.
  3. If Q is even, I get it right always, and if Q is odd, the result is wrong always. Success rate = 0.5.
  4. If Q is even, I get it wrong always, but if it is odd, I get it right. Also 0.5.

Can it be lifted above 0.5? The ability to write "even" on the even side leads to Omega putting "even" on the odd side. It even seems that the randomness of the calculator is not needed to create the effect.

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