Given a question, say for a quiz, how can one tell if a question is bad or just difficult? If tested on many people, both kinds of questions have low rates of being answered correctly, however, we wish to eliminate the former but keep the latter (difficult questions are a good way of testing for high skill or ability).
If the question is one of many within a category, we can probabilistically use the answers to other questions to distinguish whether a question-answerer is less knowledgeable and stumped by a difficult question, or highly knowledgeable but fooled by a bad question.
Construct a concrete procedure on this concept. Potentially tricky feedback effect.
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