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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hatthew a day ago | parent [-]

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.

	▲	jncfhnb 13 hours ago \| parent [-]
		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.