Multiwinner approval voting, also called approval-based committee voting, is a multi-winner electoral system that uses approval ballots. Each voter may select ("approve") any number of candidates, and multiple candidates are elected. The number of elected candidates is usually fixed in advance. For example, it can be the number of seats in a country's parliament, or the required number of members in a committee.
Multiwinner approval voting is an adaptation of approval voting to multiwinner elections. In a single-winner approval voting system, it is easy to determine the winner: it is the candidate approved by the largest number of voters. In multiwinner approval voting, there are many different ways to decide which candidates will be elected.
Majoritarian approval voting
In majoritarian approval voting, the candidates with the largest number of approvals are selected. It is a type of multiple non-transferable vote. It does not provide proportional representation, and is subject to the Burr dilemma, among other problems. There are several variants:
In block approval voting (also called unlimited voting), each voter can select an unlimited number of candidates, and the k candidates with the most approval votes win (where k is the predetermined committee size). In limited block approval voting, each voter can select a limited number of candidates, but that limit is more than k. In plurality block voting, each voter has up to as many votes as there are seats to be filled, but no more than one per candidate. Plurality block voting provides majoritarian representation. In limited voting, each voter has less votes than seats to be filled. Limited voting is semi-proportional, as it allows the minority to focus on a small number of candidates and guarantee that at least some of them wins. Voting reform advocates refrain from calling it approval voting, similarly to how first-past-the-post or single-winner limited voting are not considered approval voting.
Example for comparison
Candidates are running in a 3 member district of the 10000 voters. Voters may not cast more than one vote for a single candidate.
Under block approval voting (unlimited voting) voter may vote for any number of candidates. Under limited block approval voting voters may cast 6 votes maximum (twice as many as there are winners). Under (plurality) block voting, voters may cast 3 votes (but do not have to). Under limited (block) voting, voters may cast 2 votes maximum. Under the single non-transferable vote, voters may cast 1 vote.
Party A has about 35% support among the electorate (with one particularly well-like candidate), Party B around 25% (with two well-like candidates) and the remaining voters primarily support independent candidates, but mostly lean towards party B if they have to choose between the two parties. All voters vote sincerely, there is no tactical voting.
Under the single non-transferable vote (not a type of approval voting), the 3 most popular candidates according to voters first preferences are elected, regardless of party affiliation. Under limited voting, it is most likely that the party with a plurality takes 2 seats (the number of votes each voter has), and the minority party receives the remaining seats. Under (plurality) block voting, the party with plurality support most likely wins all seats. Under limited block approval voting voters, voters of independent candidates may use their extra votes to help candidates other than their top3, which may result in the reversal of the plurality block vote result. Under block approval voting, any party-affiliated or independent candidates particularly popular among the population may be elected, but it is possible that about half of the population can elect no representatives.
Proportional approval voting
Proportional approval voting refers to voting methods which aim to guarantee proportional representation in case all supporters of a party approve all candidates of that party. Such methods include Proportional approval voting, Sequential proportional approval voting, Phragmen's voting rules and the Method of Equal Shares. In the general case, proportional representation is replaced by a more general requirement called justified representation.
In these methods, the voters fill out a standard approval-type ballot, but the ballots are counted in a specific way that produces proportional representation. The exact procedure depends on which method is being used.