Multiwinner Voting: A New Challenge for Social Choice Theory

In this paper, the authors explore a new challenge in social choice theory known as "affordable committees." They examine three rules that play an important role in constructing fair and representative committees: Method of Equal Shares, Greedy Justified Candidate Rule, and Greedy EJR. These rules are designed to ensure that the total voting weight of a committee is equal to 1, allowing for a diverse selection of candidates.
The authors highlight the importance of capturing the diversity of a committee through its coverage, or the number of voters represented by it. They also discuss the Chamberlin-Courant rule, which selects committees maximizing coverage, but often falls short of selecting the desired number of candidates. To address this issue, the authors propose a completion method to output a full committee.
The authors use everyday language and engaging metaphors to demystify complex concepts. For instance, they compare the voting process to a candy store, where each voter has a "voting weight" of k/n, similar to the number of candies they can buy. They also explain that the completion method is like a "sugar-topping machine" that fills in any remaining gaps in the committee selection.
In summary, this paper tackles the challenge of constructing fair and representative committees through the lens of affordability, diversity, and coverage. By using simple language and engaging metaphors, the authors make complex concepts more accessible to a wider audience, while still capturing the essence of the article without oversimplifying.