We are in the world where the calculator displays even, and we are 99% sure it is the world where the calculator has not made an error. This is Even World, Right Calculator. Counterfactual worlds:

• Even World, Wrong Calculator (1% of Even Worlds)
• Odd World, Right Calculator (99% of Odd Worlds)
• Odd World, Wrong Calculator (1% of Odd Worlds)

All Omega told us was that the counterfactual world we are deciding for, the calculator shows Odd. We can therefore eliminate Odd World, Wrong Calculator. Answering the question is, in essence, deciding which world we think we're looking at.

So, in the counterfactual world, we're either looking at Even World, Wrong Calculator or Odd World, Right Calculator. We have an equal prior for the world being Odd or Even - or, we think the number of Odd Worlds is equal to the number of Even Worlds. We know the ratio of Wrong Calculator worlds to Right Calculator worlds (1:99). This is, therefore, 99% evidence for Odd World. The correct decision for the counterfactual you in that world is to decide Odd World. The correct decision for you?

Ignoring Bostrom's book on how to deal with observer selection effects (did Omega go looking for a Wrong Calculator world and report it? Did Omega go looking for an Odd World to report to you? Did Omega pick at random from all possible worlds? Did Omega roll a three-sided die to determine which counterfactual world to report?), I believe the correct decision is to answer Odd World for the counterfactual world, with 99% certainty if you are allowed to specify as such.

I reason that by virtue of it being a counterfactual world, it is contingent on my not having the observation of my factual world; factual world observations are screened off by the word "counterfactual".

The other possibility (which I tentatively think is wrong) is that our 99% confidence of Even World (from our factual world) comes up against our 99% confidence of Odd World (from our counterfactual) and they cancel out, bringing you back to your prior. So you should flip a coin to decide even or odd. I think this is wrong because 1) I think you could reason from 50% in the countefactual world to 50% in the factual world, which is wrong, and 2) this setup is identical to punching in the formula, pressing the button and observing "even", then pressing the button again and observing "odd". I don't think you can treat counterfactual worlds as additional observations in this manner.

edit: It occurs to me that with Omega telling you about the counterfactual world, you are receiving a second observation. For this understanding, you would specify Even World with 99% confidence in the factual world and either Even or Odd World depending on how the coin landed for the counterfactual world.

Nah. See, given that the real calculator says "even", there's a 0.99% chance that it's correct and that, in a repetition of the experiment, it would say incorrectly say "odd". There's also a 0.99% chance that the real calculator is incorrect and that, in a repetition of the experiment, it would correctly say "odd". The counterfactual case is just as likely to be the calculator being correct as the calculator being incorrect.

ETA: The above is wrong. I was confused about the problem because I wasn't thinking updatelessly. It's like Newcomb's problem.

Q is most likely even,

Derived from the likelihood of the calculator being in error

so in the counterfactual the calculator is most likely in error,

You can't conclude this - think about what evidence you have that the calculator is in error!

I'm not sure what to make of the fact that "lake" was the answer that jumped out at me.

My goodness, that bias is quite overcoming, wouldn't you say?

Same applies to 'overcoming' of 'overcoming bias'.

Oh, I see - the ref is to 'Overcoming Bias.com'. For a moment I was confused because overpoweringfalsehood.com doesn't work and I didn't see any URL in your profile and I thought you were talking about you being burned and not all of us.

On the same theme as the previous one:

I've begun worshipping the sun for a number of reasons. First of all, unlike some other gods I could mention, I can see the sun. It's there for me every day. And the things it brings me are quite apparent all the time: heat, light, food, a lovely day. There is no mystery, no one asks for money, I don't have to dress up, and there is no boring pageantry. And interestingly enough, I have found that the prayers I offer to the sun and the prayers I formerly offered to "God" are all answered at about the same 50-percent rate.

George Carlin

If the null hypothesis was true, the probability that we would get 3 heads or less is 0.08

Is the idea that the coin will land heads 90% of the time really something that can be called the "null hypothesis"?

It's a good point, but I stand by what I said.

I've heard anecdotes of disgruntled graduate students attacking their schools because they weren't given their degrees. (The example that comes to mind is of a woman who set explosives in a lab.) I definitely consider that creepy. I would start worrying about safety if an obviously unqualified student kept ranting about how she deserved her degree.

Charles Guiteau, who assassinated James Garfield, was chronically unemployed but convinced that the government owed him a high office (he wanted to be an ambassador.) I would consider his obsession with "deserving" a position far out of his reach was a warning sign for criminal behavior.

So it's not just about sex. "Creepiness" is something I associate with being convinced you deserve something that it's totally unreasonable (socially) for you to be granted. Most unemployed workers are disappointed, sure, but that's not the same thing.