  Multi-winner voting is the process of selecting a fixed-size set of
representative candidates based on voters' preferences. It occurs in
applications ranging from politics (parliamentary elections) to the design of
modern computer applications (collaborative filtering, dynamic Q&A platforms,
diversifying search results). All these applications share the problem of
identifying a representative subset of alternatives -- and the study of
multi-winner voting is the principled analysis of this task.
  This book provides a thorough and in-depth look at multi-winner voting based
on approval preferences. One speaks of approval preferences if voters express
their preferences by providing a set of candidates they approve. Approval
preferences thus separate candidates in approved and disapproved ones, a
simple, binary classification. The corresponding multi-winner voting rules are
called approval-based committee (ABC) rules. Due to the simplicity of approval
preferences, ABC rules are widely suitable for practical use.
  Recent years have seen a rising interest in ABC voting. While multi-winner
voting has been originally a topic studied by economists and political
scientists, a significant share of recent progress has occurred in the field of
computational social choice. This discipline is situated in the intersection of
artificial intelligence, computer science, economics, and (to a lesser degree)
political science, combining insights and methods from these distinct fields.
The goal of this book is to present fundamental concepts and results for ABC
voting and to discuss the recent advances in computational social choice. The
main focus is on axiomatic analysis, algorithmic results, and relevant
applications.
