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.
