Block approval voting

Block approval 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. It does not provide proportional representation.

Example with 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 voter may vote for any number of candidates.
Under limited block approval voting voters may cast 6 votes maximum.
Under block voting, voters may cast 3 votes.
Under the single non-transferable vote, voters may cast 1 vote.

Party A has about 35% support among the electorate, Party B around 25% 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, the 3 most popular candidates according to voters first preferences are elected, regardless of party affiliation.
Under 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.