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I’m not really following. But if you’re told that one of A, B, or C is true; you learn more by being told A is True than if you learn D is True, no?

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Yes, you learn more than 1 bit in that case. However, if you are told A is false, you still don't know whether B or C is true, so you gain less than 1 bit. Assuming A, B and C all have equal probability, your average/expected information gain is <1 bit.

If you ask the question "which of A, B, or C is true?" then you're not asking a yes/no question, and it's not surprising that you expect to gain more than 1 bit of information.

but that’s all consistent. “Expected” gain is less than 1 for the truth booths and sometimes > 1 for actuals; and is > 1 on expected value of the match ups, which aren’t binary questions.

Sure, and the issue is that the article says "Suppose we have calculated the expected information gained by potential truth booths like below:" and then lists some values >1

edit: just saw that the article fixed this recently, and the values are now <1

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