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Lumifer comments on Robert Aumann on Judaism - Less Wrong Discussion
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It's not a bias, but an expected-value calculation. Most falsehoods are utterly useless to believe, along the lines of "The moon is made of green cheese." Merely affecting a belief-in-belief can be useful for the vast majority of other cases without actually spoiling your own reasoning abilities by swallowing a poison pill of deliberate falsehood in the name of utility.
The issue is that without possessing complete information about your environment, you can't actually tell, a priori, which false beliefs are harmless and which ones will lose and lose badly.
When you have a sophisticated meta-level argument for object-level wrongness, you're losing.
I am not sure what is the point that you are making. Without "possessing complete information about your environment" you actually can't tell which of your beliefs are true and which are false. Humans make do with estimates and approximations, as always.
That if you start deliberately believing false things, it's not actually useful, it's harmful. Expected regret almost always goes up from deliberately believing something you know to to be wrong.