This is really interesting, thanks, not something I’d thought of.
If the teacher (or whoever set the test) also has a spread of credence over the answers then a Bayesian update would compare the values of P(A), P(B|¬A) and P(C|¬A and ¬B) [1] between the students and teacher. This is my first thought about how I’d create a fair scoring rule for this.
[1] P(D|¬A and ¬B and ¬C) = 1 for all students and teachers so this is screened off by the other answers.
This is really interesting, thanks, not something I’d thought of.
If the teacher (or whoever set the test) also has a spread of credence over the answers then a Bayesian update would compare the values of P(A), P(B|¬A) and P(C|¬A and ¬B) [1] between the students and teacher. This is my first thought about how I’d create a fair scoring rule for this.
[1] P(D|¬A and ¬B and ¬C) = 1 for all students and teachers so this is screened off by the other answers.