Draft:Approval block voting

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Approval block voting (also called unlimited 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). It does not provide proportional representation.

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 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.

Candidate Party Block approval voting Limited block approval voting Plurality block voting Limited (block) voting Single non-transferable vote
Votes % Elected? Votes % Elected? Votes % Elected? Votes % Elected? Votes % Elected?
Candidate A1 Party A 4200 42% 8. 4000 40% 5. 3555 36% 3. Yes 1800 18% 4. 800 8% 4.
Candidate A2 Party A 4500 45% 5. 4100 40% 4. 3700 37% 1. Yes 3500 35% 1. Yes 1900 19% 1. Yes
Candidate A3 Party A 3900 39% 9. 3800 40% 7. 3600 36% 2. Yes 2000 20% 2. Yes 700 7% 9.
Candidate B1 Party B 5200 52% 1. Yes 4900 49% 1. Yes 2600 26% 4. 1750 18% 5. 900 9% 3. Yes
Candidate B2 Party B 5000 50% 2. Yes 4600 46% 3. Yes 2500 25% 5. 1950 20% 3. Yes 1100 11% 2. Yes
Candidate B3 Party B 4700 47% 4. 4200 42% 2. Yes 2400 24% 6. 1425 14% 7. 400 4% 12.
Candidate I1 Independent 4400 44% 6. 3800 38% 7. 2300 23% 8. 1400 14% 8. 800 8% 4.
Candidate I2 Independent 4900 49% 3. Yes 4000 40% 5. 2395 20% 7. 1500 15% 6. 800 8% 4.
Candidate I3 Independent 4400 44% 6. 3700 37% 9. 1900 19% 9. 1300 13% 9. 700 7% 7.
Candidate I4 Independent 3900 39% 9. 3200 32% 10. 1800 15% 10 1200 12% 10. 700 7% 7.
Candidate I5 Independent 2600 26% 11. 2000 20% 11. 650 7% 11. 625 6% 11. 600 6% 10.
Candidate I6 Independent 2300 23% 12. 1700 17% 12. 600 6% 12. 550 6% 12. 500 5% 11.
TOTAL votes cast 50000 44000 28000 19000 10000
TOTAL possible votes 120000 60000 30000 20000 10000
Voters 10000 100% 10000 100% 10000 100% 10000 100% 10000 100%
  • 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 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.