Researchers on education must have thought about this, so I hope to find some directions here. Suppose that I am grading students on a scale from 1 to 10. If I have *no prior knowledge of the ability* of the students but have obtained their test scores (let's say from 1 to 100).

Suppose these test scores have only ordinal meaning. A student with a higher score can be said to have achieved better mastery of the course but having double the score does not mean that one has achieved double as much as another student. We may also assume that a (statistically speaking) large number of students representative of the student population took the exam.

What should be the optimal grading distribution?

We may also assume that the grading distribution/scale should achieve two goals: a) it should be informative about student's grasp of the material, b) it should incentivize students to study the material.

Regarding a) from an information theory perspective, we may want to maximize the information (entropy) of the grade distribution. Thus, we would choose a scale which yields a uniform distribution. However, in practice most teachers implement distributions which are peaked. What is the motivation behind this?