Optimism
Eliezer Yudkowsky, in his Intuitive Explanation of Bayesian Reasoning, argues that it is irrational to justify the belief that if a biological war will break out it won't wipe out humanity by pointing out that one is an optimist:
p(you are currently an optimist | biological war occurs within ten years and wipes out humanity) =
p(you are currently an optimist | biological war occurs within ten years and does not wipe out humanity)Since the two probabilities for p(X|A) and p(X|~A) are equal, Bayes' Theorem says that p(A|X) = p(A); as we have earlier seen, when the two conditional probabilities are equal, the revised probability equals the prior probability. If X and A are unconnected - statistically independent - then finding that X is true cannot be evidence that A is true; observing X does not update our probability for A; saying "X" is not an argument for A.
But this seems to be a somewhat nasty interpretation of the optimist's justification. The optimist presumably doesn't believe that her being an optimist is what justifies her optimistic expectation. Rather, by pointing out that she is an optimist, she points out that she makes certain assumptions about the world, and it's those assumptions that support her expectation. The assumptions in question say that the world is not too bad. And since
p(the world is not too bad | biological war occurs within ten years and wipes out humanity) !=
p(the world is not too bad | biological war occurs within ten years and does not wipe out humanity)
the justification is perfectly ok.
Well, it is unless the optimistic assumption itself is unjustified. Is it? Or are there any reasons to believe that the world is not too bad?
I think there are. I'm not sure how to estimate the badness of an entire world, but anyway it's better to take the optimistic assumption to concern the centered world of the subject in question, i.e. its individual alternatives. Some of my alternatives are better off than me, and some are worse off. But my evidence suggests to me that I'm closer to those who are better off: I would pay far less for trading places with a particularly lucky alternative than I would to avoid trading places with a particularly unlucky one.
So oddly it might not be irrational if Democrats and Republicans come to very different expectations concerning the outcome of the November election based on the same empirical data, as I recently saw in a poll somewhere.