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DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections

The study of fairness in multiwinner elections focuses on settings where candidates have attributes. However, voters may also be divided into predefined populations under one or more attributes (e.g., "California" and "Illinois" populations under the "state" attribute), which may be same or different from candidate attributes. The models that focus on candidate attributes alone may systematically under-represent smaller voter populations. Hence, we develop a model, DiRe Committee WinnerDetermination (DRCWD), which delineates candidate and voter attributes to select a committee by specifying diversity and representation constraints and a voting rule. We analyze its computational complexity, inapproximability, and parameterized complexity. We develop a heuristic-based algorithm, which finds the winning DiRe committee in under two minutes on 63% of the instances of synthetic datasets and on 100% of instances of real-world datasets. We present an empirical analysis of the running time, feasibility, and utility traded-off. Overall, DRCWD motivates that a study of multiwinner elections should consider both its actors, namely candidates and voters, as candidate-specific models can unknowingly harm voter populations, and vice versa. Additionally, even when the attributes of candidates and voters coincide, it is important to treat them separately as diversity does not imply representation and vice versa. This is to say that having a female candidate on the committee, for example, is different from having a candidate on the committee who is preferred by the female voters, and who themselves may or may not be female.

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