Fairness-Efficiency Symbiosis

Manuscript available upon request

Keywords: fairness-efficiency tradeoff, distributive justice, allocation

Ensuring algorithmic decisions induce fair solutions is of critical societal importance. Much has been written about the potential tradeoff between fairness and efficiency in worst case scenarios. Simultaneously, there is growing empirical evidence that the fairness-efficiency tradeoff is often avoidable in practice. This research seeks to understand this apparent divide and provide an understanding for when fairness and efficiency can form a symbiotic relationship, i.e., when both can be improved simultaneously. Based on the distributive justice framework, we distinguish between two fairness perspectives: equity seeks outcomes proportional to recipients’ merit or needs, while equality seeks the same outcomes for all. We provide simple formulas for understanding when (1) fairness will be symbiotic with efficiency, and (2) equity will be more efficient than equality and vice versa. Our analysis reveals that (1) fairness-efficiency symbiosis can occur when moving from a principled (e.g., inefficient, equitable, or equal) initial allocation towards equity or equality, and (2) the relative efficiency of equity compared to equality depends on both the initial allocation and the correlation between equity and efficiency.

Many practical allocation problems are too computationally intensive or time sensitive to iteratively solve and explore the entire Pareto frontier of potential optimal solutions. This does not change the need to consider fairness principles during the algorithmic process. Our theoretical results provide a simple diagnostic tool that can be used to understand the general relationship between fairness and efficiency before incurring the costs of collecting relevant information and without the need to identify the entire Pareto frontier. Overall, these results provide practical guidance about the consequences of embedding different fairness principles into algorithmic decision processes.