In this paper, we formulate the problem of selecting a set of individuals from a candidate population as a utilitymaximisation 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 .
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 .
R
In this paper, we formulate
We consider
R
as a utilitymaximisation problem. From the decision maker's perspective, it is equivalent to finding a selection policy that maximises expected utility
in order to maximise utility
R
Our framework leads to
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
R
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
contributions of individuals and analyse its links to
A
underlying optimisation problem, our notion of meritocracy, and other notions of fairness such as the
R
EMC also generalises the fair selection properties of Shapley value for general selection policies. We
We also
A
on the utility and meritocracy
R
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
including constraints on statistical parity