Efficient Scoring of Multiple-Choice Tests

This paper studies the optimal scoring of multiple choice tests in which the marks for wrong selection and omission jointly minimize the mean square difference between score and examinees' ability. I find that it is efficient to incentivize the lowest able to omit, except when the test has a very large number of items. The mark for omission is positive in the first case and negative in the second case. The model sheds lights on the statistical properties of two widely used scoring methods, Number right scoring and Formula scoring