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Nisan comments on Open Thread: March 2010, part 3 - Less Wrong
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Can't answer until I know the laws of time travel.
No, seriously. Is the resulting universe randomly selected from all possible self-consistent ones? By what weighting? Does the resulting universe look like the result of iteration until a stable point is reached? And what about quantum branching?
Considering that all I know of causality and reality calls for non-circular causal graphs, I do feel a bit of justification in refusing to just hand out an answer.
I could tell you that time travel works by exploiting closed time-like curves in general relativity, and that quantum effects haven't been tested yet. But yes, that wouldn't be telling you how to handle probabilities.
So, it looks like this is a situation where the prior you were born with is as good as any other.