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Davorak 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?
I would expect it to be extremely hard. I do not limit the scope of these tests to simple paper question and answer. I would be ok if an MRI was needed, for the teste not to know the test was about rationality, if it required a group of well trained actors to fool the teste, or a virtual simulation(within todays technology). Of course tests that can be used/verified immediately by users are preferable.
In the end the techniques required may be prohibitive, but at least it would make known what techniques/technologies to watch/promote for the future.