sistawendy | Nun solves grade inflation.

Almost two years ago I took a stab at solving the grade inflation problem. Basically, my earlier scheme boils down to a ranking system, but it's missing a couple of things: slack for teachers, and a guarantee that how teachers use that slack won't screw students. Here goes.

Let n_k be the number of students in class k where k is in [1..c], and let there be ranks i in [1..m_k] with b_i,k students in each, where higher i means the student has done better, such that for all i and k b_i,k > 0, and

Sum[i=1..m](b_i,k) = n_k
Administrators can impose constraints like for all i and k, m_k >= 3 and max(b_i,k / m_k) <= 0.7.

Here's where it gets interesting. Define

w_k = Sum[i=1..m_k](ib_i,k)
Let r_j,k where j is in [1..n_k] be the rank to which student j belongs. The score s(j,k) for a student in rank r_j,k is

s(j,k) = 2^(r_j,k/w_k) - 1
giving you a score strictly between 0 and 1 and guaranteeing that for all k

Product[j=1..n_k](s(j,k)+1) = 2

Student j's cumulative score across all classes is then

S(j)=[Product[k=1..c](s(j,k))]^(1/c)
which will also be strictly between 0 and 1. The higher S(j) is, the better a student j has been, say his teachers. Assign letters to specific, non-overlapping ranges between 0 and 1 if you must, but never, ever change them.

Teachers, especially those who aren't numerically inclined, may squawk, but I could write an Excel spreadsheet to compute s(j,k) and check at least some of the constraints.

Please forgive my bastard notation. Next: a closed-form solution to the Arab-Israeli conflict.

ETA: The underscore is to indicate a subscript.

ETAA: b_i,k is b with two subscripts, i and k. Curse you,