  In this paper, we formulate the problem of selecting a set of individuals
from a candidate population as a utility maximisation problem. From the
decision maker's perspective, it is equivalent to finding a selection policy
that maximises expected utility. Our framework leads to the notion of expected
marginal contribution (EMC) of an individual with respect to a selection policy
as a measure of deviation from meritocracy. In order to solve the maximisation
problem, we propose to use a policy gradient algorithm. For certain policy
structures, the policy gradients are proportional to EMCs of individuals.
Consequently, the policy gradient algorithm leads to a locally optimal solution
that has zero EMC, and satisfies meritocracy. For uniform policies, EMC reduces
to the Shapley value. EMC also generalises the fair selection properties of
Shapley value for general selection policies. We experimentally analyse the
effect of different policy structures in a simulated college admission setting
and compare with ranking and greedy algorithms. Our results verify that
separable linear policies achieve high utility while minimising EMCs. We also
show that we can design utility functions that successfully promote notions of
group fairness, such as diversity.
