Application-oriented collective decision making: experimental toolbox and dynamic environments

Abstract

Collective decision making problems capture situations where the preferences of agents need to be aggregated into a compromise solution. This thesis focuses on two such problems: voting, where "voters" express preferences over "candidates" and a "winning" candidate needs to be identified, and stable matching, where "agents" have preferences over each other and a "stable" matching of the agents needs to be found. The overarching goal of this thesis is to promote and empower application-oriented theoretical and experimental research on collective decision making problems. Contributing to this goal, in Parts I and II, we extend the toolbox for computational experiments. Such experiments could for instance be used to evaluate the running time of an algorithm, the similarity between two mechanisms, or the quality of a heuristic, and can thus complement, check, and guide theoretical research with practical insights. Concretely, in Chapter 2, after formulating challenges one faces when conducting such experiments, we introduce a map of elections for planning and evaluating experiments. Next, in Chapter 3, we present a large collection of multi-source real-world preference data, which we subsequently classify, analyze, and use to address some classic questions from social choice. In Chapter 4, we turn to synthetic data sources and take a closer look at the popular Mallows model. In the first part of that chapter, we challenge classic ways of using the Mallows model and provide a new parameterization that behaves in line with real-world evidence. In the second part, we propose a new method for "preference learning", and demonstrate how to use it to fit (mixtures of) Mallows models to our previously collected data to obtain a better understanding of it. Subsequently, in Chapter 5, we construct a map of stable matching instances to visualize the relation between instances and experimental results. This involves the introduction and analysis of a distance measure and the development of multiple new synthetic data sources. For application-oriented research aiming at practically relevant insights, it is not just important to conduct computational experiments, but also to design realistic models in the first place. Addressing a so-far often neglected aspect of reality, in Parts III and IV, we contribute to popularizing the study of collective decision making problems that take into account that such problems often take place in a dynamic and changing environment, e.g., where agents change their preferences over time. In Chapter 6, we study a new method to evaluate the robustness of election winners to random noise, and identify (different types of) extremely non-robust winners in real-world elections that cannot be identified using classic worst-case approaches. Lastly, in Chapters 7 and 8, we analyze problems related to minimally adapting a stable matching to reestablish stability in case of changing external requirements or agents' preferences from an algorithmic and experimental perspective.