On Meritocracy in Optimal Set Selection

We consider the problem of selecting a set of individuals from a candidate population in order to maximise utility. When the utility function is defined over sets, this raises the question of how to define meritocracy. We define and analyse an appropriate notion of meritocracy derived from the utility function. We introduce the notion of expected marginal contributions of individuals and analyse its links to the underlying optimisation problem, our notion of meritocracy, and other notions of fairness such as the Shapley value. We also experimentally analyse the effect of different policy structures on the utility and meritocracy in a simulated college admission setting including constraints on statistical parity.