Editing Block voting (section)

== Examples of voting systems ==

=== 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:

{| class="wikitable"
! rowspan="3" |Candidate
! colspan="2" rowspan="3" |Party
! colspan="4" rowspan="2" |Plurality block voting
! colspan="8" |Majority block voting / 2 round voting
|-
! colspan="4" |1st round
! colspan="4" |2nd round
|-
!Votes
!%
! colspan="2" |Elected?
!Votes
!%
! colspan="2" |Elected?
!Votes
!%
! colspan="2" |Elected?
|-
|Candidate A1
| style="background:#D10000" |
|Party A
|'''3555'''
|'''36%'''
|'''3.'''
|'''Yes'''
|3555
|36%
|3.
|
|4100
|41%
|5.
|
|-
|Candidate A2
| style="background:#D10000" |
|Party A
|'''3700'''
|'''37%'''
|'''1.'''
|'''Yes'''
|3700
|37%
|1.
|
|4200
|42%
|4.
|
|-
|Candidate A3
| style="background:#D10000" |
|Party A
|'''3600'''
|'''36%'''
|'''2.'''
|'''Yes'''
|3600
|36%
|2.
|
|3900
|39%
|7.
|
|-
|Candidate B1
| style="background:#0008A5" |
|Party B
|2600
|26%
|4.
|
|2600
|26%
|4.
|
|'''5100'''
|'''51%'''
|'''1.'''
|'''Yes'''
|-
|Candidate B2
| style="background:#0008A5" |
|Party B
|2500
|25%
|5.
|
|2500
|25%
|5.
|
|'''4900'''
|'''49%'''
|'''2.'''
|'''Yes'''
|-
|Candidate B3
| style="background:#0008A5" |
|Party B
|2400
|24%
|6.
|
|2400
|24%
|6.
|
|'''4800'''
|'''48%'''
|'''3.'''
|'''Yes'''
|-
|Candidate I1
|
|Independent
|2300
|23%
|8.
|
|2300
|23%
|8.
|''eliminated''
|
|
|
|
|-
|Candidate I2
|
|Independent
|2395
|20%
|7.
|
|2395
|20%
|7.
|''eliminated''
|
|
|
|
|-
|Candidate I3
|
|Independent
|1900
|19%
|9.
|
|1900
|19%
|9.
|''eliminated''
|
|
|
|
|-
|Candidate I4
|
|Independent
|1800
|15%
|10
|
|1800
|15%
|10
|''eliminated''
|
|
|
|
|-
|Candidate I5
|
|Independent
|650
|7%
|11.
|
|650
|7%
|11.
|''eliminated''
|
|
|
|
|-
|Candidate I6
|
|Independent
|600
|6%
|12.
|
|600
|6%
|12.
|''eliminated''
|
|
|
|
|-
| colspan="3" |''TOTAL votes cast''
|28000
|
|
|
|28000
|
|
|
|27000
|
|
|
|-
| colspan="3" |TOTAL possible votes
|30000
|
|
|
|30000
|
|
|
|30000
|
|
|
|-
| colspan="3" |Voters
|10000
|100%
|
|
|10000
|100%
|
|
|10000
|100%
|
|
|}
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 system|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.
{| class="wikitable"
! rowspan="2" |Candidate
! colspan="2" rowspan="2" |Party
! colspan="4" |Block approval voting
! colspan="4" |Limited block approval voting
! colspan="4" |Plurality block voting
! colspan="4" |Limited (block) voting
! colspan="4" |Single non-transferable vote
|-
!Votes
!%
! colspan="2" |Elected?
!Votes
!%
! colspan="2" |Elected?
!Votes
!%
! colspan="2" |Elected?
!Votes
!%
! colspan="2" |Elected?
!Votes
!%
! colspan="2" |Elected?
|-
|Candidate A1
| style="background:#D10000" |
|Party A
|4200
|42%
|8.
|
|4000
|40%
|5.
|
|'''3555'''
|'''36%'''
|'''3.'''
|'''Yes'''
|1800
|18%
|4.
|
|800
|8%
|4.
|
|-
|Candidate A2
| style="background:#D10000" |
|Party A
|4500
|45%
|5.
|
|4100
|40%
|4.
|
|'''3700'''
|'''37%'''
|'''1.'''
|'''Yes'''
|'''3500'''
|'''35%'''
|'''1.'''
|'''Yes'''
|'''1900'''
|'''19%'''
|'''1.'''
|'''Yes'''
|-
|Candidate A3
| style="background:#D10000" |
|Party A
|3900
|39%
|9.
|
|3800
|40%
|7.
|
|'''3600'''
|'''36%'''
|'''2.'''
|'''Yes'''
|'''2000'''
|'''20%'''
|'''2.'''
|'''Yes'''
|700
|7%
|9.
|
|-
|Candidate B1
| style="background:#0008A5" |
|Party B
|'''5200'''
|'''52%'''
|'''1.'''
|'''Yes'''
|'''4900'''
|'''49%'''
|'''1.'''
|'''Yes'''
|2600
|26%
|4.
|
|1750
|18%
|5.
|
|'''900'''
|'''9%'''
|'''3.'''
|'''Yes'''
|-
|Candidate B2
| style="background:#0008A5" |
|Party B
|'''5000'''
|'''50%'''
|'''2.'''
|'''Yes'''
|'''4600'''
|'''46%'''
|'''3.'''
|'''Yes'''
|2500
|25%
|5.
|
|'''1950'''
|'''20%'''
|'''3.'''
|'''Yes'''
|'''1100'''
|'''11%'''
|'''2.'''
|'''Yes'''
|-
|Candidate B3
| style="background:#0008A5" |
|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.
|
|-
| colspan="3" |''TOTAL votes cast''
|50000
|
|
|
|44000
|
|
|
|28000
|
|
|
|19000
|
|
|
|10000
|
|
|
|-
| colspan="3" |TOTAL possible votes
|120000
|
|
|
|60000
|
|
|
|30000
|
|
|
|20000
|
|
|
|10000
|
|
|
|-
| colspan="3" |Voters
|10000
|100%
|
|
|10000
|100%
|
|
|10000
|100%
|
|
|10000
|100%
|
|
|10000
|100%
|
|
|}

* 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.