Multiwinner approval voting

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Multiwinner approval voting[1], also called approval-based committee voting,[2] 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[]

Block approval voting (unlimited voting)[]

The straightforward extension of approval balloting to multi-winner elections is called block approval voting is a type of multiple non-transferable vote, where 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). This does not provide proportional representation and is subject to the Burr dilemma, among other problems.

Limited block approval voting[]

Limited block approval voting is the type of multiple non-transferable vote, where the k candidates with the most votes win, where each voter can select an limited number of candidates, but that limit is more than k. This is subject to the same problems as unlimited block approval voting.

Plurality-at-large and limited voting[]

Main articles: Plurality block voting and Limited voting

Plurality-at-large or plurality block voting (BV) and limited voting (LV) are both types of the multiple non-transferable vote category of multi-winner systems. Under 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 and under limited voting, each voter has less votes than seats to be filled. Plurality block voting provides majoritarian representation, while limited voting is semi-proportional. Therefore voting reform advocates refrain from calling it approval voting,[3] similarly to how first-past-the-post or single-winner limited voting are not considered approval voting.

Proportional approval voting[]

Methods such as Proportional approval voting[4][5] or Sequential proportional approval voting have the advantage of guaranteeing proportional representation in case all supporters of a party approve all candidates of that party. 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.[how?]

Party-approval voting[]

Party-approval voting (also called approval-based apportionment)[6] is a method in which each voter can approve one or more parties, rather than approving individual candidates. It is a combination of multiwinner approval voting with party-list voting.

Other methods[]

Other ways of extending Approval voting to multiple winner elections are satisfaction approval voting[7] excess method,[8] and minimax approval.[9] These methods use approval ballots but count them in different ways.

Usage[]

Multiwinner approval voting, while less common than standard approval voting, is used in several places.

Block approval voting[]

  • Korean villages used block approval voting for competitive elections following the surrender of Japan, according to observations made by journalist Anna Louise Strong in 1946: "In one village there were twelve candidates, of whom five were to be chosen for the Village Committee. Each voter was given twelve cards, bearing the names of the candidates. He then cast his chosen ones into the white box and the rejected ones into the black."[10]
  • Several Swiss cantons elect their government using such methods and so do French cities with population below 1000.[11]
  • In 1963, the proportional representation in East Germany was replaced by a procedure in which the candidates had to receive more than 50% of the votes. Had more candidates than seats in this constituency won the majority, the order of the list would determine who would join the Volkskammer.

References[]

  1. ^ Aziz, Haris; Gaspers, Serge; Gudmundsson, Joachim; Mackenzie, Simon; Mattei, Nicholas; Walsh, Toby (2014-07-11). "Computational Aspects of Multi-Winner Approval Voting". arXiv:1407.3247 [cs.GT].
  2. ^ Aziz, Haris; Brill, Markus; Conitzer, Vincent; Elkind, Edith; Freeman, Rupert; Walsh, Toby (2017). "Justified representation in approval-based committee voting". Social Choice and Welfare. 48 (2): 461–485. doi:10.1007/s00355-016-1019-3. S2CID 8564247.
  3. ^ "Voting Systems Confused with Approval Voting". The Center for Election Science. Retrieved March 12, 2020.
  4. ^ http://www2.math.uu.se/~svante/papers/sjV9.pdf
  5. ^ Brill, Markus; Laslier, Jean-François; Skowron, Piotr (2016). "Multiwinner Approval Rules as Apportionment Methods". arXiv:1611.08691 [cs.GT].
  6. ^ Brill, Markus; Gölz, Paul; Peters, Dominik; Schmidt-Kraepelin, Ulrike; Wilker, Kai (2020-04-03). "Approval-Based Apportionment". Proceedings of the AAAI Conference on Artificial Intelligence. 34 (2): 1854–1861. arXiv:1911.08365. doi:10.1609/aaai.v34i02.5553. ISSN 2374-3468. S2CID 208158445.
  7. ^ Plaza, Enric. Technologies for political representation and accountability (PDF). CiteSeerX 10.1.1.74.3284. Retrieved 2011-06-17.
  8. ^ https://as.nyu.edu/content/dam/nyu-as/faculty/documents/Excess%20Method%20(final).pdf
  9. ^ LeGrand, Rob; Markakis, Evangelos; Mehta, Aranyak (2007). Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems - AAMAS '07 (PDF). p. 1. doi:10.1145/1329125.1329365. ISBN 9788190426275. S2CID 13870664. Retrieved 2011-06-17.
  10. ^ Strong, Anna. "In North Korea: First Eye-Witness Report". Marxists Internet Archive. Retrieved May 14, 2019.
  11. ^ Vander Straeten, Karine; Lachat, Romain; Laslier, Jean-François (2018). "Chapter 9: Strategic voting in multi-winner elections with approval balloting: An application to the 2011 regional government election in Zurich". In Stephenson, Laura B.; Aldrich, John H.; Blais, André (eds.). The Many Faces of Strategic Voting. Tactical Behavior in Electoral Systems Around the World. Ann Arbor, Michigan: The University of Michigan Press. pp. 178–202.
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