{"id":{"repo_id":"tu-berlin","oai_identifier":"oai:depositonce.tu-berlin.de:11303/24203"},"canonical_url":"https://search.dev.ndltd.org/etd/tu-berlin/oai:depositonce.tu-berlin.de:11303/24203","repository":{"repo_id":"tu-berlin","name":"Technische Universität Berlin","base_url":"https://api-depositonce.tu-berlin.de/server/oai/request"},"display":{"title":"Facets of proportionality","abstract":"In this thesis, we study proportional representation in three different collective decision-making settings: voting, budgeting, and clustering. In these settings, we develop new axioms and rules to assess and enable outcomes which proportionally reflect the opinions of all agents taking part in the decision-making. In the first part, we examine proportionality in multiwinner voting. In this setting, voters submit preferences over candidates, based on which we must select a subset of these candidates. We strengthen existing proportionality axioms for a general class of preferences to be efficiently verifiable and hard to achieve. In particular, our axioms are applicable to both approval and ordinal preference models, providing a framework to encompass both settings. We also investigate tradeoffs between individual excellence, diversity, and proportional representation and give rules achieving all three desiderata at the same time. In the second part, we study proportionality in participatory budgeting (PB), where we need to select a subset of costly projects subject to a budget constraint. Specifically, we study PB with approval preferences and generalize existing results to a large class of potential utility functions. We establish novel proportionality guarantees for the Method of Equal Shares, which is currently used in real-life PB elections. Then we consider a generalized setting incorporating both divisible and indivisible projects, and define proportional methods for this domain. In the third part, we focus on proportional representation in metric spaces. This setting subsumes facility location, clustering, and data summarization problems. For this setting, we establish novel connections between prominent fairness concepts like proportional fairness and individual fairness. Further, we relate the clustering setting to the proportionality notions we developed in the first part of the thesis and show that algorithms satisfying these notions provide the best known approximation guarantees. Finally, we analyze sortition, the process of randomly selecting representative panels/committees from a population. We model this setting using metric spaces and show that randomly selected panels according to two particular mechanisms make decisions closely aligned with the will of the underlying population.","abstract_html":"In this thesis, we study proportional representation in three different collective decision-making settings: voting, budgeting, and clustering. In these settings, we develop new axioms and rules to assess and enable outcomes which proportionally reflect the opinions of all agents taking part in the decision-making. In the first part, we examine proportionality in multiwinner voting. In this setting, voters submit preferences over candidates, based on which we must select a subset of these candidates. We strengthen existing proportionality axioms for a general class of preferences to be efficiently verifiable and hard to achieve. In particular, our axioms are applicable to both approval and ordinal preference models, providing a framework to encompass both settings. We also investigate tradeoffs between individual excellence, diversity, and proportional representation and give rules achieving all three desiderata at the same time. In the second part, we study proportionality in participatory budgeting (PB), where we need to select a subset of costly projects subject to a budget constraint. Specifically, we study PB with approval preferences and generalize existing results to a large class of potential utility functions. We establish novel proportionality guarantees for the Method of Equal Shares, which is currently used in real-life PB elections. Then we consider a generalized setting incorporating both divisible and indivisible projects, and define proportional methods for this domain. In the third part, we focus on proportional representation in metric spaces. This setting subsumes facility location, clustering, and data summarization problems. For this setting, we establish novel connections between prominent fairness concepts like proportional fairness and individual fairness. Further, we relate the clustering setting to the proportionality notions we developed in the first part of the thesis and show that algorithms satisfying these notions provide the best known approximation guarantees. Finally, we analyze sortition, the process of randomly selecting representative panels/committees from a population. We model this setting using metric spaces and show that randomly selected panels according to two particular mechanisms make decisions closely aligned with the will of the underlying population.","abstract_has_math":false,"creators":["Peters, Jannik"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Brill, Markus"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025","date_published":"2025","updated_at":"2026-07-27T21:28:35Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":["https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.14279/depositonce-23017"],"render_values":[{"text":"https://doi.org/10.14279/depositonce-23017","href":"https://doi.org/10.14279/depositonce-23017","code":true}]}]},"links":{"outbound_url":"https://depositonce.tu-berlin.de/handle/11303/24203","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Brill, Markus"]},{"key":"dc:creator","label":"Author","values":["Peters, Jannik"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-05-06T12:32:20Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-05-06T12:32:20Z"]},{"key":"dc:date.issued","label":"Date","values":["2025"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://depositonce.tu-berlin.de/handle/11303/24203","https://doi.org/10.14279/depositonce-23017"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we study proportional representation in three different collective decision-making settings: voting, budgeting, and clustering. In these settings, we develop new axioms and rules to assess and enable outcomes which proportionally reflect the opinions of all agents taking part in the decision-making. In the first part, we examine proportionality in multiwinner voting. In this setting, voters submit preferences over candidates, based on which we must select a subset of these candidates. We strengthen existing proportionality axioms for a general class of preferences to be efficiently verifiable and hard to achieve. In particular, our axioms are applicable to both approval and ordinal preference models, providing a framework to encompass both settings. We also investigate tradeoffs between individual excellence, diversity, and proportional representation and give rules achieving all three desiderata at the same time. In the second part, we study proportionality in participatory budgeting (PB), where we need to select a subset of costly projects subject to a budget constraint. Specifically, we study PB with approval preferences and generalize existing results to a large class of potential utility functions. We establish novel proportionality guarantees for the Method of Equal Shares, which is currently used in real-life PB elections. Then we consider a generalized setting incorporating both divisible and indivisible projects, and define proportional methods for this domain. In the third part, we focus on proportional representation in metric spaces. This setting subsumes facility location, clustering, and data summarization problems. For this setting, we establish novel connections between prominent fairness concepts like proportional fairness and individual fairness. Further, we relate the clustering setting to the proportionality notions we developed in the first part of the thesis and show that algorithms satisfying these notions provide the best known approximation guarantees. Finally, we analyze sortition, the process of randomly selecting representative panels/committees from a population. We model this setting using metric spaces and show that randomly selected panels according to two particular mechanisms make decisions closely aligned with the will of the underlying population.","In dieser Arbeit untersuchen wir die proportionale Repräsentation in drei verschiedenen kollektiven Entscheidungsfindungskontexten: Wahlen, Budgeting und Clustering. In diesen Kontexten entwickeln wir neue Axiome und Regeln, um Ergebnisse zu bewerten und zu ermöglichen, die die Meinungen aller an der Entscheidungsfindung beteiligten Akteure proportional widerspiegeln. Im ersten Teil untersuchen wir Proportionalität bei Abstimmungen mit mehreren Gewinnern. In diesem Fall geben die Wähler ihre Präferenzen über die Kandidaten ab, auf deren Grundlage wir eine Teilmenge dieser Kandidaten auswählen müssen. Wir verstärken bestehende Proportionalitätsaxiome für eine allgemeine Klasse von Präferenzen, so dass diese effizient überprüfbar und schwieriger zu erreichen sind. Insbesondere sind unsere Axiome sowohl auf Zustimmungs- als auch auf ordinale Präferenzmodelle anwendbar und bieten einen Rahmen, der beide Szenarien umfasst. Wir untersuchen auch Kompromisse zwischen individueller Exzellenz, Vielfalt und proportionaler Repräsentation und geben Regeln an, die alle drei Aspekte gleichzeitig erfüllen. Im zweiten Teil untersuchen wir die Proportionalität bei Bürgerhaushalten, bei denen eine Teilmenge kostspieliger Projekte ausgewählt werden muss, die einer Budgetbeschränkung unterliegen. Insbesondere untersuchen wir den Bürgerhaushalt mit Zustimmungspräferenzen und verallgemeinern bestehende Ergebnisse auf eine große Klasse von möglichen Nutzenfunktionen. Wir stellen neue Proportionalitätsgarantien für die Methode der gleichen Anteile auf, die derzeit bei realen Bürgerhaushaltswahlen verwendet wird. Anschließend betrachten wir ein verallgemeinertes Szenario, das sowohl teilbare als auch unteilbare Projekte umfasst, und definieren proportionale Regeln für dieses Setting. Im dritten Teil konzentrieren wir uns auf die proportionale Repräsentation in metrischen Räumen. Dieser Bereich umfasst die Probleme der Facility Location, des Clusterings und der Datenzusammenfassung. In diesem Zusammenhang stellen wir neue Verbindungen zwischen bekannten Fairnesskonzepten wie proportionaler Fairness und individueller Fairness her. Darüber hinaus stellen wir eine Beziehung zwischen dem Clustering und den Proportionalitätskonzepten her, die wir im ersten Teil der Arbeit entwickelt haben, und zeigen, dass diese Konzepte die besten bekannten Approximationsgarantien implizieren. Schließlich analysieren wir die zufälligen Auswahl repräsentativer Gremien (auch als Bürgerräte oder Sortition bekannt). Wir modellieren diese Situation mit Hilfe metrischer Räume und zeigen, dass für zwei Mechanismen zufällig ausgewählte Gremien Entscheidungen treffen, die eng mit dem Willen der zugrunde liegenden Bevölkerung übereinstimmen."]},{"key":"dc:title","label":"Title","values":["Facets of proportionality"]}]}],"canonical_facts":{"dc:contributor.advisor":["Brill, Markus"],"dc:creator":["Peters, Jannik"],"dc:date.accessioned":["2025-05-06T12:32:20Z"],"dc:date.available":["2025-05-06T12:32:20Z"],"dc:date.issued":["2025"],"dc:description.abstract":["In this thesis, we study proportional representation in three different collective decision-making settings: voting, budgeting, and clustering. In these settings, we develop new axioms and rules to assess and enable outcomes which proportionally reflect the opinions of all agents taking part in the decision-making. In the first part, we examine proportionality in multiwinner voting. In this setting, voters submit preferences over candidates, based on which we must select a subset of these candidates. We strengthen existing proportionality axioms for a general class of preferences to be efficiently verifiable and hard to achieve. In particular, our axioms are applicable to both approval and ordinal preference models, providing a framework to encompass both settings. We also investigate tradeoffs between individual excellence, diversity, and proportional representation and give rules achieving all three desiderata at the same time. In the second part, we study proportionality in participatory budgeting (PB), where we need to select a subset of costly projects subject to a budget constraint. Specifically, we study PB with approval preferences and generalize existing results to a large class of potential utility functions. We establish novel proportionality guarantees for the Method of Equal Shares, which is currently used in real-life PB elections. Then we consider a generalized setting incorporating both divisible and indivisible projects, and define proportional methods for this domain. In the third part, we focus on proportional representation in metric spaces. This setting subsumes facility location, clustering, and data summarization problems. For this setting, we establish novel connections between prominent fairness concepts like proportional fairness and individual fairness. Further, we relate the clustering setting to the proportionality notions we developed in the first part of the thesis and show that algorithms satisfying these notions provide the best known approximation guarantees. Finally, we analyze sortition, the process of randomly selecting representative panels/committees from a population. We model this setting using metric spaces and show that randomly selected panels according to two particular mechanisms make decisions closely aligned with the will of the underlying population.","In dieser Arbeit untersuchen wir die proportionale Repräsentation in drei verschiedenen kollektiven Entscheidungsfindungskontexten: Wahlen, Budgeting und Clustering. In diesen Kontexten entwickeln wir neue Axiome und Regeln, um Ergebnisse zu bewerten und zu ermöglichen, die die Meinungen aller an der Entscheidungsfindung beteiligten Akteure proportional widerspiegeln. Im ersten Teil untersuchen wir Proportionalität bei Abstimmungen mit mehreren Gewinnern. In diesem Fall geben die Wähler ihre Präferenzen über die Kandidaten ab, auf deren Grundlage wir eine Teilmenge dieser Kandidaten auswählen müssen. Wir verstärken bestehende Proportionalitätsaxiome für eine allgemeine Klasse von Präferenzen, so dass diese effizient überprüfbar und schwieriger zu erreichen sind. Insbesondere sind unsere Axiome sowohl auf Zustimmungs- als auch auf ordinale Präferenzmodelle anwendbar und bieten einen Rahmen, der beide Szenarien umfasst. Wir untersuchen auch Kompromisse zwischen individueller Exzellenz, Vielfalt und proportionaler Repräsentation und geben Regeln an, die alle drei Aspekte gleichzeitig erfüllen. Im zweiten Teil untersuchen wir die Proportionalität bei Bürgerhaushalten, bei denen eine Teilmenge kostspieliger Projekte ausgewählt werden muss, die einer Budgetbeschränkung unterliegen. Insbesondere untersuchen wir den Bürgerhaushalt mit Zustimmungspräferenzen und verallgemeinern bestehende Ergebnisse auf eine große Klasse von möglichen Nutzenfunktionen. Wir stellen neue Proportionalitätsgarantien für die Methode der gleichen Anteile auf, die derzeit bei realen Bürgerhaushaltswahlen verwendet wird. Anschließend betrachten wir ein verallgemeinertes Szenario, das sowohl teilbare als auch unteilbare Projekte umfasst, und definieren proportionale Regeln für dieses Setting. Im dritten Teil konzentrieren wir uns auf die proportionale Repräsentation in metrischen Räumen. Dieser Bereich umfasst die Probleme der Facility Location, des Clusterings und der Datenzusammenfassung. In diesem Zusammenhang stellen wir neue Verbindungen zwischen bekannten Fairnesskonzepten wie proportionaler Fairness und individueller Fairness her. Darüber hinaus stellen wir eine Beziehung zwischen dem Clustering und den Proportionalitätskonzepten her, die wir im ersten Teil der Arbeit entwickelt haben, und zeigen, dass diese Konzepte die besten bekannten Approximationsgarantien implizieren. Schließlich analysieren wir die zufälligen Auswahl repräsentativer Gremien (auch als Bürgerräte oder Sortition bekannt). Wir modellieren diese Situation mit Hilfe metrischer Räume und zeigen, dass für zwei Mechanismen zufällig ausgewählte Gremien Entscheidungen treffen, die eng mit dem Willen der zugrunde liegenden Bevölkerung übereinstimmen."],"dc:identifier.uri":["https://depositonce.tu-berlin.de/handle/11303/24203","https://doi.org/10.14279/depositonce-23017"],"dc:language.iso":["en"],"dc:rights.uri":["https://creativecommons.org/licenses/by/4.0/"],"dc:title":["Facets of proportionality"],"dc:type":["Doctoral Thesis"]},"updated_at":"2026-07-27T21:28:35Z"}