Proportionality and Fairness in Voting and Ranking Systems

Abstract

Fairness through proportionality has received significant attention in recent social choice research, leading to the development of advanced tools, methods, and algorithms aimed at ensuring fairness in democratic institutions.

Citizen-focused democratic processes where participants deliberate on alternatives and then vote to make the final decision are increasingly popular today. While the computational social choice literature has extensively investigated voting rules, there is limited work that explicitly looks at the interplay of the deliberative process and voting. In this thesis, we build a deliberation model using established models from the opinion-dynamics literature and study the effect of different deliberation mechanisms on voting outcomes achieved when using well-studied voting rules. Our results show that deliberation generally improves welfare and representation guarantees, but the results are sensitive to how the deliberation process is organized. We also show, experimentally, that simple voting rules, such as approval voting, perform as well as more sophisticated rules such as proportional approval voting or method of equal shares if deliberation is properly supported. This has ramifications on the practical use of such voting rules in citizen-focused democratic processes.

Intricately designed proportional voting rules offer robust theoretical and axiomatic fairness guarantees that can prove valuable in similar scenarios beyond the realm of elections. In the second part, we capitalize on these properties and introduce innovative fair-ranking algorithms based on proportional voting methods. Specifically, we define the general task of fair ranking, which involves generating a list of items that is fairly ordered with respect to a given query, as a voting problem. Our findings reveal that proportional voting rules deliver exceptional performance, frequently matching or surpassing the performance of existing benchmarks in terms of aggregate fairness and relevance metrics. These discoveries present exciting avenues for further research and applications, endorsing the widespread adoption of proportional voting rules in domains where fairness is a priority.