Vaniver comments on Einstein's Arrogance - Less Wrong
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It's not an assumption, it's a definition. Whatever is enough to cut your current set of candidates in half is "one bit"- the first bit will eliminate 50,000,000 people, the last bit will eliminate 1. An answer that reduces the set of candidates to .000001 times its original size contains 20 bits of information. (Notice that the question doesn't have bits of information associated with it, since each possible answer reduces the candidate set by a different amount- if they said "no," you acquired only a millionth of a bit of information.)