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 …

In the late 19th century, Swedish mathematician Edvard Phragmén proposed a load-
balancing approach for selecting committees based on approval ballots. We consider three …

Algorithmic decision-making has become ubiquitous in our societal and economic lives.
With more and more decisions being delegated to algorithms, we have also encountered …

Multiwinner voting rules can be used to select a fixed-size committee from a larger set of
candidates. We consider approval-based committee rules, which allow voters to approve or …

In the apportionment problem, a fixed number of seats must be distributed among parties in
proportion to the number of voters supporting each party. We study a generalization of this …

Committee scoring voting rules are multiwinner analogues of positional scoring rules, which
constitute an important subclass of single-winner voting rules. We identify several natural …

Voting in multi-issue domains allows for compromise outcomes that satisfy all voters to some
extent. Such fairness considerations, however, open the possibility of a special form of …

Proportional representation (PR) is often discussed in voting settings as a major
desideratum. For the past century or so, it is common both in practice and in the academic …

The single transferable vote (STV) voting method is used to elect multiple candidates in
ranked-choice elections. One weakness of STV is that it fails multiple fairness criteria related …

To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on
the context, it varies widely what constitutes the choice of an “optimal” subset of alternatives …