Fair resource allocation: Using welfare-based dominance constraints

In this paper we consider the problem of supporting resource allocation decisions affecting multiple beneficiaries. Such problems inherently involve efficiency-fairness trade-offs. We introduce a new approach based on the paradigm of maximizing efficiency subject to constraints to ensure that the decision is acceptably fair. In contrast to existing literature, we incorporate fairness in the form of welfare dominance, ensuring that the resultant distribution of benefits to beneficiaries is at least as good as some reference distribution with respect to a set of social welfare functions that satisfy commonly accepted efficiency and fairness related axioms. We introduce a practical means to parameterize the problem, which allows for excluding welfare functions that are deemed insufficiently or overly sensitive to inequality. This allows for analyzing the impact of changes in inequality aversion on efficiency, thus revealing the trade-off between efficiency and fairness. We develop tractable reformulations for the resulting non-linear multi-level optimization problems. We then extend this approach for cases where resources are allocated to groups of individuals with different sizes. We demonstrate the potential use of the suggested framework on two case studies: a workload allocation problem and a healthcare provisioning problem.