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Craig_Heldreth comments on What topics would you like to see more of on LessWrong? - Less Wrong Discussion
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I don't know if it can be reliably measured - my impression is that it's pretty damn hard, and that once you heard about most tests (the kind that are used to show irrationality in the first place, i.e. those already discussed on less wrong), you won't fall for them but that doesn't say much about how less likely you are for thinking right in "real life" situations where your brain isn't primed by "this is a test of rationality".
Some sub-components can be reliably measured - such as calibration. Any others?
Battleground God
I got through unscathed, but I suspect most atheists would. I don't think that test is very good at discerning rationality beyond the "knows about logic" and "doesn't believe in God".
FWIW, I started it with "God Exists" as true and also got through it unscathed. But you're right, it doesn't seem to try very hard presenting atheists with pitfalls and traps. I was at least expecting some kind of foul trickery about the Big Bang.