Plurality block voting (BV)

In a block voting election, all candidates compete for m positions, often referred to as the district magnitude. Each voter selects up to m candidates on the ballot.^[2] The m candidates with the most votes, but not necessarily a majority, are elected and fill the positions.^[3]

Majority-at-large voting / Two-round block voting

The majority-at-large voting is a variation of plurality-at-large voting, but where no candidate receives a majority, the field of candidates is thinned out before a second round.

General ticket / Party block voting (PBV)

Party block voting (PBV) or the general ticket is the party-list version of block voting. In contrast to the classic block vote, where candidates may stand as non-partisan and some minority nominations can theoretically succeed, PBV associates each candidate with a party list voted on by electors, often leading to a landslide outcome. The Parliament of Singapore uses this system for most of its elections.

Block approval voting

Block approval voting permits every voter to vote for any number of candidates, provided that they do not vote more than once for the same candidate. Block voting, specifically plurality block voting, is compared with preferential block voting as both often produce landslide victories for similar candidates. Instead of checkboxes, preferential block voting utilizes a preferential ballot, making it a multiple transferable vote rather than a multiple non-transferable vote. Under both systems, a slate of the top preferred candidate and their clones typically secures every available seat.

Limited voting (LV) / Partial block voting

Partial block voting, also known as limited voting, operates similarly to plurality-at-large voting. However, in partial block voting, each voter casts fewer votes than the number of candidates to be elected. This process enables reasonably sized minorities to achieve some representation, preventing a simple plurality from sweeping every seat. Partial bloc voting is employed in elections to the Gibraltar Parliament, allowing each voter ten votes for seventeen open seats. The typical outcome sees the most popular party winning ten seats and forming the ruling administration. In contrast, the second-most popular party secures seven seats to form the opposition. The Spanish Senate also adopts partial block voting, offering four seats per constituency, with each voter casting three votes. Historically, three- and four-member constituencies in the United Kingdom used partial block voting until the abolition of multimember constituencies.

With fewer votes per voter, the threshold to win decreases under partial block voting, making the results more akin to proportional representation, provided voters and candidates use effective strategies.^[4] Extreme cases, where each voter casts only one vote, equate to the single non-transferable vote. However, such scenarios may result in wasted votes and unfair outcomes due to vote-splitting (albeit likely more balanced than elections under Block Voting). Consequently, the proportion of votes necessary to win a seat under SNTV may be notably small. Single transferable voting (STV) is more systematic, resulting in fewer wasted votes. With STV, the Droop quota typically guarantees victory, although one or two contestants may be elected with less than that quota.^{[5][circular reference]}

Plurality block voting and majority block voting

Consider a scenario with 12 candidates in a 3-member district among 10,000 voters. Both plurality block voting and majority block voting allow voters to cast three votes (although they need not use all three) but restrict voting to one vote per candidate.

Party A garners roughly 35% support among the electorate, Party B secures around 25%, and the remaining voters mainly support independent candidates but lean toward Party B if compelled to choose between the two parties. Assuming all voters cast their votes sincerely and avoid tactical voting, the following tabulation elucidates the outcomes:

In the second round, voters of independent candidates can vote for candidates of party B. As even fewer voters cast all their 3 votes, even in the second round, some winners do technically win with a majority, but only a plurality in fact (similar to differences between turnout levels in two-round voting).

Block voting and approval block voting

A 3-member district with 10,000 voters features 12 candidates. Block voting allows each voter to cast only one vote for a single candidate.

• Under unlimited block approval voting, voters can select any number of candidates.
• Under limited block approval voting, voters can cast up to six votes, twice the number of winners.
• Under plurality block voting, voters can cast up to three votes, though it's not mandatory.
• Under limited (block) voting, voters can cast a maximum of two votes.
• Under the single non-transferable vote (which is not block voting), voters can cast only one vote.

Party A has an approximate 35% electorate support, notably due to one well-received candidate. Party B holds around 25% backing, comprising two popular candidates. The remaining voters primarily favor independent candidates, but tend to lean towards Party B if pressed to choose between the two main parties. All voters engage in sincere voting with no tactical influence.

• Under the single non-transferable vote, the three most popular candidates based on voters' initial preferences are elected, irrespective of party affiliation.
• In limited voting, it is probable that the party with a plurality secures two seats (reflecting the number of votes each voter has), while the minority party gains the remaining seats.
• Plurality block voting generally results in the party with the most support winning all available seats.
• Limited block approval voting allows independent candidates' supporters to use their additional votes to assist candidates other than their top three choices, possibly leading to a reversal of the outcome observed in plurality block voting.
• Block approval voting permits any popular party-affiliated or independent candidates to be elected, but it's plausible that nearly half of the population might not have a representative elected.