Terence tao had a blogpost about this for the case of true/false questions, with multiple choice left as an exercise for the reader. https://terrytao.wordpress

Terence tao had a blogpost about this for the case of true/false questions, with multiple choice left as an exercise for the reader. https://terrytao.wordpress.com/2016/06/01/how-to-assign-partial-credit-on-an-exam-of-true-false-questions/ https://terrytao.wordpress.com/2016/06/01/how-to-assign-part... At least with the formulation Tao had, one unfortunate side-effect is that if you answer with 100% confidence and get it wrong, you basically fail the entire course.