Comment by akramachamarei
3 hours ago
Would this be fixed buckets? I.e. would you treat 649-650 more predictive than 648-649? Presumably that wouldn't work. I'm sure there's some algorithm that could do this but it seems subtle.
Obviously, if a school has a cutoff score bucketing is easy, but with excess applicants ordering becomes necessary. I guess this sort of probabilistic score would induce an order for any given student relative to sufficiently superior or inferior applicants.... I'm now kinda curious to figure this problem out. Did not expect an algorithms problem to arise in this thread lol
And you don’t want a 100% cutoff. You need to admit some people just under the threshold since the scores are relative. You need fresh data to keep the model tuned.
Some kind of weighted lottery
Allow me to propose a model for this score-based ordering with fuzziness. (Perhaps we can call this problem probabilistic rasterization.)
The final output of an execution of the system, given a static, complete set of applicants is a particular ordering of applicants. Since lottery is involved, there are multiple acceptable orderings for a given input set. The question is to define a set of criteria to classify acceptable orderings, and a desired probability distribution of orderings, which can be satisfied by an algorithm for a maximal proportion of inputs.
For example, given a set of applicants A with score function F, we notate an ordering relation R(x,y) such that, given a limited number of seats, applicant y will be admitted before applicant x. For shorthand, x < y means R(x,y).
Possible acceptance criteria for an ordering R may include:
(1) Given some d in the codomain of F (presumably a group), FOR ALL x,y in A, if F(x) + d ≤ F(y), then x < y
Possible criteria for the distribution of orderings may include:
(1) FOR ALL x,y in A, if F(x) = F(y) then P(x < y) = P(x > y)