From fundamental concepts and results to recent advances in computational social choice, this open access book provides a thorough and in-depth look at multi-winner voting based on approval preferences. The main focus is on axiomatic analysis, algorithmic results and several applications that are relevant in artificial intelligence, computer science and elections of any kind.
What is the best way to select a set of candidates for a shortlist, for an executive committee, or for product recommendations? Multi-winner voting is the process of selecting a fixed-size set of candidates based on the preferences expressed by the voters. A wide variety of decision processes in settings ranging from politics (parliamentary elections) to the design of modern computer applications (collaborative filtering, dynamic Q&A platforms, diversity in search results, etc.) share the problem of identifying a representative subset of alternatives. The study of multi-winner voting provides the principled analysis of this task.

Approval-based committee voting rules (in short: ABC rules) are multi-winner voting rules particularly suitable for practical use. Their usability is founded on the straightforward form in which the voters can express preferences: voters simply have to differentiate between approved and disapproved candidates. Proposals for ABC rules are numerous, some dating back to the late 19th century while others have been introduced only very recently. This book explains and discusses these rules, highlighting their individual strengths and weaknesses. With the help of this book, the reader will be able to choose a suitable ABC voting rule in a principled fashion, participate in, and be up to date with the ongoing research on this topic.

About the Author: Martin Lackner works on artificial intelligence, specifically on computational social choice. His research deals with fundamental questions about fair collective decision making and how algorithms can support such decisions. Currently, he is principal investigator of the project "Algorithms for Sustainable Group Decision Making" at TU Wien. Before that, he was holding a postdoctoral researcher position at the University of Oxford. He obtained his doctoral degree from TU Wien and has published over 50 papers at top artificial intelligence and algorithms venues (and also in economics and philosophy journals).

Piotr Skowron is an Assistant Professor at the University of Warsaw. He obtained his PhD from the University of Warsaw, followed by a postdoc position at the University of Oxford and a Humboldt fellowship for postdoctoral researchers at TU Berlin. His research mainly concerns the topic of computational social choice, specifically committee elections. His work links various ideas from computational social choice, game theory, resource allocation, and approximation algorithms. For his contribution to the literature on committee elections, he won the 2020 IJCAI Computers and Thought Award. He has published more than 70 articles and conference papers in the top venues on algorithmic game theory and artificial intelligence.