The various Newcombe situations have fairly direct analogues in everyday things like ultimatum situations, or promise keeping. They alter it to reduce the number of variables, so the "certainty of trusting other party" dial gets turned up to 100% of Omega, "expectation of repeat" to 0 etc, in order to evaluate how to think of such problems when we cut out certain factors.
That said, I'm not actually sure what this question has to do with Newcombe's paradox / counterfactual mugging, or what exactly is interesting about it. If it's just asking "what information do you use to calculate the probability you plug into the EU calculation?" and Newcombe's paradox is just being used as one particular example of it, I'd say that the obvious answer is "the probability you believe it is now." After all, that's going to already be informed by your past estimates, and any information you have available (such as that community of rationalists and their estimates). If the question is something specific to Newcombe's paradox, I'm not getting it.
This has been in my drafts folder for ages, but in light of Eliezer's post yesterday, I thought I'd see if I could get some comment on it:
A couple weeks ago, Vladimir Nesov stirred up the biggest hornet's nest I've ever seen on LW by introducing us to the Counterfactual Mugging scenario.
If you didn't read it the first time, please do -- I don't plan to attempt to summarize. Further, if you don't think you would give Omega the $100 in that situation, I'm afraid this article will mean next to nothing to you.
So, those still reading, you would give Omega the $100. You would do so because if someone told you about the problem now, you could do the expected utility calculation 0.5*U(-$100)+0.5*U(+$10000)>0. Ah, but where did the 0.5s come from in your calculation? Well, Omega told you he flipped a fair coin. Until he did, there existed a 0.5 probability of either outcome. Thus, for you, hearing about the problem, there is a 0.5 probability of your encountering the problem as stated, and a 0.5 probability of your encountering the corresponding situation, in which Omega either hands you $10000 or doesn't, based on his prediction. This is all very fine and rational.
So, new problem. Let's leave money out of it, and assume Omega hands you 1000 utilons in one case, and asks for them in the other -- exactly equal utility. What if there is an urn, and it contains either a red or a blue marble, and Omega looks, maybe gives you the utility if the marble is red, and asks for it if the marble is blue? What if you have devoted considerable time to determining whether the marble is red or blue, and your subjective probability has fluctuated over the course of you life? What if, unbeknownst to you, a rationalist community has been tracking evidence of the marble's color (including your own probability estimates), and running a prediction market, and Omega now shows you a plot of the prices over the past few years?
In short, what information do you use to calculate the probability you plug into the EU calculation?