DiRe Committee : Diversity and Representation Constraints in Multiwinner Elections

K. Relia
IJCAI 2022
Abstract
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. The models that focus on candidate attributes alone may systematically under-represent smaller voter populations. Hence, we develop a model, DiRe Committee Winner Determination (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 and develop a heuristic 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 also present an empirical analysis of feasibility and utility traded-off.  Moreover, 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.

Experiments:

Election type Culture Candidates Voters Instances Parameters
Approval Real-Life (beyond PrefLib) {81} {193} 1 None
Ordinal Real-Life (beyond PrefLib) {10} {26} None None
Ordinal Mallows {50} {100} 10 {0.5}
Ordinal Mallows {50} {100} 5 [0.1,1] (step 0.1)