Descriptive and Substantive Representation in Approval-Based Committee Voting
Kirti Singh

Abstract:
Approval-based committee voting (ABC voting) is a form of multi-winner voting in which all voters admit a set of candidates they approve of as their ballot. After all ballots are collected, a winning committee of size k is chosen. An important class of axioms in this context are the proportionality axioms. These capture the idea that the support of a candidate should be proportional to their presence in the winning committee. Investigating this class of axioms is part of the larger project of investigating fairness in multi-winner voting. This thesis can be regarded to be a part of this larger project as well.
In the context of political elections, representing voters based on their preferences for certain candidates is seen as a kind of substantive representation. This form is contrasted with descriptive representation. The latter emphasizes the demographic similarity of the representer to the representee, whereas the former emphasizes that the representer should work according to their voters’ interests. The beginning of this thesis contains an argument for the pursuit of descriptive representation in many multi-winner voting contexts. After this, it will be argued that the kinds of proportionality and fairness that have been studied in the ABC context are preference-based, that is, substantive. This paves the way for the main contribution of this thesis: a formalisation and study of descriptive representation in the context of ABC voting by proposing an extended version of the ABC model.
The middle sections contain the definition of two classes of voting rules and their axiomatic analysis. For this, established ABC axioms are generalised to the ABCC setting and the two rules are compared on the basis of their performance with respect to these axioms and their computational properties. One of the conclusions is that both rules perform poorly with respect to proportionality axioms, suggesting incompatibility of extreme forms of descriptive and substantive representation. Furthermore, determining the winning committees for both classes of rules is intractable. In the final section, I try to understand this incompatibility by considering domain restrictions for which the rules are well-behaved. I finish by proposing an alternative class of voting rules with the aim of balancing substantive and descriptive representation.