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alexflint comments on Shut Up And Guess - Less Wrong
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This reminds me of an infamous chemistry exam that no longer existed at my college by the time I got there but had passed into the student lore. For each question, you would first mark your answer (multiple choice, 4 or 5 choices), and then mark a confidence option. These were "high confidence" (5 points if right, -3 if wrong), "low confidence" (3 points if right, 0 if wrong), and "I don't know, give me a point" (1 point regardless of what answer is marked).
This exam was not popular with the students.
Nice. What happens if you think you're right on the cusp of a grade boundary, as in OP's footnote 1? I think there are cases to be considered for when you're right under a grade boundary and right above a grade boundary, and the value you place on a grade change versus potential increase/decrease in intra-grade marks. All together, fairly mathematically taxing to be rational...