Block approval voting (also called unlimited voting, in reference to limited voting) is a winner-take-all system where each voter either approves or disapproves of each candidate, and the k candidates with the most approval votes win (where k is the predetermined committee size).[1][2] It does not provide proportional representation.[2]

Example with comparison

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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 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.

Candidate Party Block approval voting Plurality block voting Single non-transferable vote
Votes % Elected? Votes % Elected? Votes % Elected?
Candidate A1 Party A 4200 42% 8. 3555 36% 3.  Y 800 8% 4.
Candidate A2 Party A 4500 45% 5. 3700 37% 1.  Y 1900 19% 1.  Y
Candidate A3 Party A 3900 39% 9. 3600 36% 2.  Y 700 7% 9.
Candidate B1 Party B 5200 52% 1.  Y 2600 26% 4. 900 9% 3.  Y
Candidate B2 Party B 5000 50% 2.  Y 2500 25% 5. 1100 11% 2.  Y
Candidate B3 Party B 4700 47% 4. 2400 24% 6. 400 4% 12.
Candidate I1 Independent 4400 44% 6. 2300 23% 8. 800 8% 4.
Candidate I2 Independent 4900 49% 3.  Y 2395 20% 7. 800 8% 4.
Candidate I3 Independent 4400 44% 6. 1900 19% 9. 700 7% 7.
Candidate I4 Independent 3900 39% 9. 1800 15% 10 700 7% 7.
Candidate I5 Independent 2600 26% 11. 650 7% 11. 600 6% 10.
Candidate I6 Independent 2300 23% 12. 600 6% 12. 500 5% 11.
  • 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 (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 top 3, 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.

References

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  1. ^ Fishburn, Peter C.; Little, John D. C. (May 1988). "An Experiment in Approval Voting". Management Science. 34 (5): 555–568. doi:10.1287/mnsc.34.5.555. hdl:1721.1/47581. ISSN 0025-1909.
  2. ^ a b Lackner, Martin; Skowron, Piotr (2023). Multi-Winner Voting with Approval Preferences. Springer Nature. ISBN 978-3-031-09016-5.