Comment by lokar
2 hours ago
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
2 hours ago
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)