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I seem to remember some medical related multiple choice tests in the UK use a mechanism of +1 for correct , 0 for unanswered , -1 for incorrect.
It would make more sense to just use IRT for grading the responses than trying to add more complexity to the answers themselves.
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-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.