Fairly Allocating Utility in Constrained Multiwinner Elections

Abstract: Fairness in multiwinner elections is studied in varying contexts. For instance, diversity of candidates and representation of voters are both separately termed as being fair. A common denominator to ensure fairness across all such contexts is the use of constraints. However, across these contexts, the candidates selected to satisfy the given constraints may systematically lead to unfair outcomes for historically disadvantaged voter populations as the cost of fairness may be borne unequally. Hence, we develop a model to select candidates that satisfy the constraints fairly across voter populations. To do so, the model maps the constrained multiwinner election problem to a problem of fairly allocating indivisible goods. We propose three variants of the model, namely, global, localized, and inter-sectional. Next, we analyze the model's computational complexity, and we present an empirical analysis of the utility traded-off across various settings of our model across the three variants and discuss the impact of Simpson's paradox using synthetic datasets and a dataset of voting at the United Nations. Finally, we discuss the implications of our work for AI and machine learning, especially for studies that use constraints to guarantee fairness.