Ok, so we seem to be in agreement regarding everything except my attempt to capture the rules with the (admittedly meaningless if taken literally) slogan "subjective probabilities cannot flow backward in time".
It is interesting that neither of us sees any practical difference between necessary facts (the true value of Q) and contingent facts (whether the calculator made a mistake) in this exercise. The reason apparently being that we can only construct counterfactuals on contingent facts (for example, observations). We can't directly go counterfactual on necessary facts - only on observations that provide evidence regarding necessary facts. But it is impossible for observations to provide so much evidence regarding a necessary fact that we are justified in telling Omega that his counterfactual is impossible.
But that apparently means that dragging Omega into this problem didn't change anything - his presence just confused people. (I notice that Shokwave - the one person who you claimed had understood the problem - is now saying that the value of Q is different in the counterfactual worlds). I am becoming ever more convinced that allowing Omega into a decision-theory example is as harmful as allowing a GoTo statement into a computer program. But then, as my analogy reveals, I am from a completely different generation.
We can't directly go counterfactual on necessary facts - only on observations that provide evidence regarding necessary facts.
Yes we can. Omega could offer you to control worlds where Q is actually odd.
I notice that Shokwave - the one person who you claimed had understood the problem - is now saying that the value of Q is different in the counterfactual worlds
Link? The value of Q is uncertain, and this holds in considering either possible observation.
Consider the following thought experiment ("Counterfactual Calculation"):
Should you write "even" on the counterfactual test sheet, given that you're 99% sure that the answer is "even"?
This thought experiment contrasts "logical knowledge" (the usual kind) and "observational knowledge" (what you get when you look at a calculator display). The kind of knowledge you obtain by observing things is not like the kind of knowledge you obtain by thinking yourself. What is the difference (if there actually is a difference)? Why does observational knowledge work in your own possible worlds, but not in counterfactuals? How much of logical knowledge is like observational knowledge, and what are the conditions of its applicability? Can things that we consider "logical knowledge" fail to apply to some counterfactuals?
(Updateless analysis would say "observational knowledge is not knowledge" or that it's knowledge only in the sense that you should bet a certain way. This doesn't analyze the intuition of knowing the result after looking at a calculator display. There is a very salient sense in which the result becomes known, and the purpose of this thought experiment is to explore some of counterintuitive properties of such knowledge.)