That would mean a large value would be added when going from “guess” to “almost guess”, which would mean that it would be beneficial for a student to lie and claim to almost guess when he’s really completely guessing.
Suppose the student thinks that there is a 10% chance that he is right, and the reward structure is +5/-1 for confidence interval 1.
In fact, make the reward structure:(right/wrong) 1⁄0, 6/-1, 10/-3, 13/-6, 15/-10, 16/-15
That puts the breakpoints at roughly even intervals, keeps the math easy, and with a little bit of clarifying exactly where the breakpoints are, doesn’t reward someone who accurately determines their accuracy and then lies about it.
I sat down late last night trying to prove that this couldn’t work and instead proved that it could. If I did this correctly, in order for it to work, with the confidences increasing from 0 to 1,
left side confidence ⇐ (difference in Y)/(difference in X + difference in Y)
right side confidence >= (difference in Y)/(difference in X + difference in Y).
Differences in X are 5, 4, 3, 2, 1 and differences in Y are 1, 2, 3, 4, 5 leading to values of 1⁄6 through 5⁄6; as 0 < 1⁄6 < 1⁄5 < 2⁄6 < 2⁄5 < 3⁄6 < 3⁄5 < 4⁄6 < 4⁄5 < 5⁄6 < 1 this is immune to lying within a single interval (and also turns out to be so for multiple intervals).
So, what are the downsides of making this a grading standard? The biggest one I see is that it would be unfair except in classes that have as prerequisites an outstanding score in a class that covers credence calibration.
The largest value would be added for the first confidence interval, which would also add the smallest cost to being wrong with that confidence.
That would mean a large value would be added when going from “guess” to “almost guess”, which would mean that it would be beneficial for a student to lie and claim to almost guess when he’s really completely guessing.
Suppose the student thinks that there is a 10% chance that he is right, and the reward structure is +5/-1 for confidence interval 1.
In fact, make the reward structure:(right/wrong) 1⁄0, 6/-1, 10/-3, 13/-6, 15/-10, 16/-15
That puts the breakpoints at roughly even intervals, keeps the math easy, and with a little bit of clarifying exactly where the breakpoints are, doesn’t reward someone who accurately determines their accuracy and then lies about it.
I sat down late last night trying to prove that this couldn’t work and instead proved that it could. If I did this correctly, in order for it to work, with the confidences increasing from 0 to 1,
left side confidence ⇐ (difference in Y)/(difference in X + difference in Y)
right side confidence >= (difference in Y)/(difference in X + difference in Y).
Differences in X are 5, 4, 3, 2, 1 and differences in Y are 1, 2, 3, 4, 5 leading to values of 1⁄6 through 5⁄6; as 0 < 1⁄6 < 1⁄5 < 2⁄6 < 2⁄5 < 3⁄6 < 3⁄5 < 4⁄6 < 4⁄5 < 5⁄6 < 1 this is immune to lying within a single interval (and also turns out to be so for multiple intervals).
So, what are the downsides of making this a grading standard? The biggest one I see is that it would be unfair except in classes that have as prerequisites an outstanding score in a class that covers credence calibration.