On Meritocracy in Optimal Set Selection

TL;DR

This paper explores a fairness concept called Expected Marginal Contribution (EMC) in set selection, showing its alignment with utility maximization and the Shapley value, and analyzing trade-offs in natural policies through experiments.

Contribution

It introduces EMC as a fairness measure in set selection, demonstrating its properties and relationships with utility and existing fairness concepts, and examines policy trade-offs via experiments.

Findings

EMC satisfies an axiomatic fairness definition.

For certain policies, EMC aligns with utility maximization.

Trade-offs exist between meritocracy and utility in natural policies.

Abstract

Typically, merit is defined with respect to some intrinsic measure of worth. We instead consider a setting where an individual's worth is \emph{relative}: when a Decision Maker (DM) selects a set of individuals from a population to maximise expected utility, it is natural to consider the \emph{Expected Marginal Contribution} (EMC) of each person to the utility. We show that this notion satisfies an axiomatic definition of fairness for this setting. We also show that for certain policy structures, this notion of fairness is aligned with maximising expected utility, while for linear utility functions it is identical to the Shapley value. However, for certain natural policies, such as those that select individuals with a specific set of attributes (e.g. high enough test scores for college admissions), there is a trade-off between meritocracy and utility maximisation. We analyse the effect of constraints on the policy on both utility and fairness in extensive experiments based on college admissions and outcomes in Norwegian universities.