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Emile comments on Request: Interesting Invertible Facts - Less Wrong
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Venting when angry leads to less happiness after the initial catharsis.
In romantic relationships, similar personalities attract, rather than opposites.
The blog Barking up the Wrong Tree also collects psychology experiments of this kind. The posts are often based on single studies, so I don't know how well-established they are, but it's often possible to reverse the result and invent a plausible explanation. Some examples:
Spending money on other people makes you happier than spending it on yourself
Heavy TV-watchers are less happy when given more channel options (which itself is an example of the general finding that having a large number of choices reduces happiness)
Chronically ill patients may be less happier if they hope for a cure
I don't think these are exactly what Eliezer is looking for - these are statements that go against our natural inclinations, whereas I think Eliezer is looking like things that are (as someone said) "obviously correct in both directions", i.e. stuff we could rationalize as true either way upon encountering it.
I know what you mean, and I worried about that when I posted those examples. The problem is that I can't tell if I'm suffering from the hindsight bias when I'm trying to evaluate "Could I believe both this statement and its inverse, regardless of which one was presented as the truth?" In these cases, I can come up with fake rationalisations for both (even though one is more counter-intuitive), which makes me think that they might be invertible. They would need to be tested on people in experiments like the ones in the article by Meyers.