On proportionality in complex domains

The many real-world collective decision-making scenarios have provided plenty of examples for computational social choice researchers to study. The field of computational social choice takes the computer-science perspective in studying the methods used to aggregate group opinions into a single collective outcome. The classical example sees an electorate voting in some election to choose a single winning candidate. However, this thesis goes beyond this and studies scenarios with multiple winning candidates. Real-world applications of this include the distribution of parliamentary seats to political parties or forming a shortlist of candidates. Plenty of focus from researchers in this area has been dedicated to studying aggregation methods that capture the notion of proportional representation. The thesis will investigate the extent to which proportionality can be developed for certain complex domains. What are these complex domains? Take, as a foundation, the scenario where we are to elect multiple candidates to a committee. What if the seats on the committee are valued differently by the voters? Or there is a constraint that prohibits electing both candidate A and candidate B? We identify such scenarios as complex domains and the thesis' main objective is to determine, when in such domains, how to produce proportionally representative collective outcomes.
In the end, the thesis provides an exploration of aggregation methods that aim to choose many winners. And for the most part, this exploration is done through investigating to what extent one can lift proportionality notions from standard multiwinner voting settings to some of their more complex counterparts.