An Approximately Reproducing Scoring Scheme That Aligns Random Response and Omission

One formulation of confidence scoring requires the examinee to indicate as a number his personal probability of the correctness of each alternative in a multiple-choice test. For this formulation, a linear transformation of the logarithm of the personal probability of the correct response is maximized if the examinee reports accurately his personal probability. To equate the score assigned to omitted items with the score assigned to chance scores, the transformation can be chosen so that the score is zero if the examinee indicates complete uncertainty. If this is done, the scoring function depends on the number of alternatives. One could also align uncertainty and response omission by granting credit for omitting items, though it is felt this might be hard to explain to examinees.