Editing Proportional representation (section)

=== How mixed-member proportional representation (MMP) works ===
{{Main|Mixed-member proportional representation}}

Mixed-member proportional representation combines election of district members with election of additional members as compensatory top-up. Often MMP systems use single-member districts (SMDs) to elect district members. (Denmark, Iceland and Sweden use multi-member districts in their MMP systems.) MMP with SMDs is described here.

The mixed-member proportional system combines first-past-the-post voting with party-list PR in a way that the overall result of the election is supposed to be proportional. The voter may vote for a district candidate as well as a party. The main idea behind MMP is ''compensation'', meaning that the list-PR seat allocation is not independent of the results of the district level voting. First-past-the-post is a single winner system and cannot be proportional (winner-takes-all), so these disproportionalities are compensated by the party-list component.

A simple, yet common version of MMP has as many list-PR seats as there are single-member districts. In the example it can be seen, as is often the case in reality, that the results of the district elections are highly disproportional: large parties typically win more seats than they should proportionally, but there is also randomness{{snd}}a party that receives more votes than another party might not win more seats than the other. Any such dis-proportionality produced by the district elections is addressed, where possible, by the allocation of the compensatory additional members.
{| class="wikitable sortable"
|+Results under mixed-member proportional representation
! colspan="4" |
|[[File:Mixed compensatory example fptp.svg|frameless|upright=0.75]]
|[[File:Mixed-compensatory-example compensatory seats.svg|frameless|upright=0.75]]
|[[File:Mixed-compensatory-example total seats.svg|frameless|upright=0.75]]
| colspan="2" |[[File:Party list pr-example total seats.svg|center|frameless|upright=0.75]]
|-
! colspan="3" |Party
!Popular vote
!FPTP seats<br>(Number of districts won)
!Compensatory seats<br>(party-list PR seats)
! colspan="2" |Total number of seats
!Seats %
|-
| style="background:#D10000" |
| style="background:#ff2c2c" |
|Party A
|43.91%
|64
|24
| colspan="2" |88
|44%
|-
| style="background:#0008A5" |
| style="background:#000cff" |
|Party B
|39.94%
|33
|47
| colspan="2" |80
|40%
|-
| style="background:#03AA00" |
| style="background:#05ff00" |
|Party C
|9.98%
|0
|20
| colspan="2" |20
|10%
|-
| style="background:#820084" |
| style="background:#fb00ff" |
|Party D
|6.03%
|3
|9
| colspan="2" |12
|6%
|-
| colspan="3" |''TOTAL''
|''100%''
|''100''
|''100''
| colspan="2" |''200''
|''100%''
|}
MMP gives only as many compensatory seats to a party as they need to have the number of seats of each party be proportional. Another way to say this is that MMP focuses on making the outcome proportional.

==== Differences from mixed-member majoritarian system ====
Compare the MMP example to a [[Mixed-member majoritarian representation|mixed-member majoritarian]] system, where the party-list PR seat allocation is independent of the district results (this is also called [[parallel voting]]). Under a mixed-member majoritarian system, there is no compensation (no regard to how the district seats were filled) when allocating party-list seats so as to produce a proportional allocation of seats overall. The popular vote, the number of district seats won by each party, and the number of district and party-list PR seats are the same as in the MMP example above, yet the parties' seat tallies are different.{{Original research inline|date=May 2025}}

'''Parallel voting (using non-compensatory party seats)'''
{| class="wikitable"
|+Results under parallel voting
! colspan="4" |
|[[File:Mixed compensatory example fptp.svg|frameless|upright=0.75]]
|[[File:Mixed compensatory example non compensatory parallel seats.svg|frameless|upright=0.75]]
|[[File:Mixed compensatory example non compensatory total seats.svg|frameless|upright=0.75]]
| colspan="2" |[[File:Parallel voting mmm-example total seats.svg|center|frameless|upright=0.75]]
|-
! colspan="3" |Party
!Popular vote
!FPTP seats<br>(Number of districts won)
!Party-list PR seats
! colspan="2" |Total number of seats
!Seats %
|-
| style="background:#D10000" |
| style="background:#ff2c2c" |
|Party A
|43.91%
|64
|44
| colspan="2" |108
|54.0%
|-
| style="background:#0008A5" |
| style="background:#000cff" |
|Party B
|39.94%
|33
|40
| colspan="2" |73
|36.5%
|-
| style="background:#03AA00" |
| style="background:#05ff00" |
|Party C
|9.98%
|0
|10
| colspan="2" |10
|5.0%
|-
| style="background:#820084" |
| style="background:#fb00ff" |
|Party D
|6.03%
|3
|6
| colspan="2" |9
|4.5%
|-
| colspan="3" |''TOTAL''
|''100%''
|''100''
|''100''
| colspan="2" |''200''
|''100%''
|}
The overall results are not proportional, although they are more balanced and fair than most single-winner first-past-the-post elections. Parallel voting is mostly [[Semi-proportional representation|semi-proportional]]. [[Mixed electoral system|Mixed system]]s are the most proportional if the additional members are allocated in a compensatory way.

There are many versions of MMP in use. Some use only a [[Mixed single vote|single vote]]; in some, voters cast two votes, one for a local candidate and one for a party. Some allocate compensatory seats to best losers; others allocate according to party lists. Some use levelling seats to compensate for potential [[overhang seat]]s; others don't. Most impose an electoral threshold in order for a party to be eligible for any additional seats; some allow parties that elect one or more district seats to be eligible for additional seats even if its party share is below the threshold. Any barrier to access to the additional seats may produce wasted votes and dis-proportionality in the final result.{{Original research inline|date=May 2025}}

As well, there is [[single non-transferable vote]], which is also semi-proportional. It has the advantage that parties play no direct role in elections and voters do not need to mark ranked votes. Each voter casts one vote for a candidate and as many candidates win by plurality as the number of seats in the district. Due to each voter casting just one vote, as in STV, and each district electing multiple members, as in STV, mixed representation is produced in each district and overall rough proportionality more or less. Without transferable votes, more votes are wasted than under STV.{{Original research inline|date=May 2025}}