`Fuzzy' Multiple-Choice Quizzes and How to Grade Them

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Traditional multiple-choice quizzes do not tell us how confident the students are in their answers. To provide this additional information, researchers have proposed “fuzzy” multiple-choice quizzes, in which a student explicitly describes his/her degree of confidence in each possible answer. The idea is reasonable, but, as we show, the current grading scheme for such quizzes discourages students from providing the correct degrees of confidence. In this paper, we show that there is only one grading scheme which encourages students to provide the correct degrees: when the number of points is proportional to the logarithm of the degree. Somewhat surprisingly, this scheme turns out to be related to the notion of entropy.