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Party-list proportional representation

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Poster for the European Parliament election 2004 in Italy, showing party lists

Party-list proportional representation (list-PR) is a system ofproportional representation based on preregisteredpolitical parties, with each party beingallocated a certain number of seatsroughly proportional to their share of the vote.[1]

In these systems, parties provide lists of candidates to be elected, or candidates may declare their affiliation with a political party (in some open-list systems). Seats are distributed by election authorities to each party, in proportion to the number of votes the party receives. Voters may cast votes for parties, as inSpain,Turkey, andIsrael (closed lists); or for candidates whose vote totals are pooled together to determine the share of representation of their respective parties, as inFinland,Brazil, and theNetherlands (mixed single vote orpanachage).[2][3]

Voting

[edit]

In most party list systems, a voter will only support one party (achoose-one ballot).Open list systems may allow voters to support more than one candidatewithin a party list. Some open-list systems allow voters to support different candidates across multiple lists, which is calledpanachage.

Selection of party candidates

[edit]

The order in which a party's list candidates get elected may be pre-determined by some method internal to the party or the candidates (aclosed list system) or it may be determined by the voters at large (anopen list system) or by districts (alocal list system).

Closed list

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Main article:Closed list

In a closed list system, each political party has pre-decided who will receive the seats allocated to that party in the elections, so that the candidates positioned highest on this list will always get a seat in the parliament while the candidates positioned very low on the closed list will not. Voters vote only for the party, not for individual candidates.

Open list

[edit]
Main article:Open list

An open list describes any variant of a party-list where voters have at least some influence on the order in which a party's candidates are elected. Open lists can be anywhere fromrelatively closed, where a candidate can move up a predetermined list only with a certain number of votes, tocompletely open, where the order of the list completely depends on the number of votes each individual candidate gets.[4]

Apportionment of party seats

[edit]

Within party-list PR systems, there are a variety of different methods that can be used to determine how many seats are allocated to each party for a given vote breakdown. The method used to allocate seats within party-list proportional representation vary. Someapportionment methods may favor small parties; others may favor large parties:[5]

D'Hondt method

[edit]

TheD'Hondt method is a highest averages method that allocates seats by dividing each party's total votes by a series of divisors (1, 2, 3, ...).[8]

  • Example (5 seats):
PartyVotes
A1000
B800
C400
RoundA quotientB quotientC quotientSeat to
11000800400A
2500800400B
3500400400A
4333.33400400B
5333.33266.67400C
  • Result: A = 2, B = 2, C = 1

Sainte-Laguë method

[edit]

TheSainte-Laguë (Webster) method is a highest averages method using odd-numbered divisors (1, 3, 5, ...) to promote more equal distribution.

  • Same vote totals as above.
RoundA quotientB quotientC quotientSeat to
11000800400A
2333.33800400B
3333.33266.67400C
4333.33266.67133.33A
5200266.67133.33B
  • Result: A = 2, B = 2, C = 1

Modified Sainte-Laguë method

[edit]

Same as Sainte-Laguë but first divisor is 1.4 to favour larger parties.[8]

  • Divisors: 1.4, 3, 5, ...
RoundA quotientB quotientC quotientSeat to
1714.29571.43285.71A
2333.33571.43285.71B
3333.33266.67285.71A
4200266.67285.71C
5200266.67133.33B
  • Result: A = 2, B = 2, C = 1

Hare quota (largest remainder)

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TheHare quota uses a quota to allocate seats, then gives remaining seats to the parties with the largest remainders.

  • Quota = Total votes / Seats = 2200 / 5 = 440
PartyVotesInitial seatsRemainder
A10002120
B8001360
C4000400
  • Remaining 2 seats to C and B (highest remainders)
  • Result: A = 2, B = 2, C = 1

Imperiali quota (largest remainder)

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TheImperiali quota is rarely used; favors large parties more.

  • Quota = Total votes / (seats + 2) = 2200 / 7 = ~314.29
PartyVotesInitial seatsRemainder
A1000357.14
B8002171.42
C400185.71
  • 1 leftover seat to B
  • Result: A = 3, B = 2, C = 1

Huntington–Hill method

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TheHuntington–Hill method is used for US congressional apportionment, based on geometric mean. Too specialized for vote quotas, usually used with population.

The apportionment methods can be classified into two categories:

While the allocation formula is important, equally important is the district magnitude (number of seats in a constituency). The higher the district magnitude, the more proportional an electoral system becomes, with the most proportional results being when there is no division into constituencies at all and the entire country is treated as a single constituency.[citation needed] In some countries the electoral system works on two levels:at-large for parties, and in constituencies for candidates, with local party-lists seen as fractions of general, national lists. In this case, magnitude of local constituencies is irrelevant, seat apportionment being calculated at national level.

List proportional representation may also be combined with other apportionment methods in various mixed systems, using eitheradditional member systems orparallel voting.

Example

[edit]

Below it can be seen how different apportionment methods yield different results when apportioning 100 seats.

Webster's method yields the same result (though this is not always the case). Otherwise, all other methods give a different number of seats to the parties.

Notice how the D'Hondt method breaks thequota rule (shown in red text) and favors the largest party by "rounding" an ideal apportionment of 35.91 up to 37.

Adams' method greatly favors smaller parties, giving 2 seats to the smallest party, and would give at least 1 seat to every party receiving at least one vote.

PartyVotesEntitlementLargest remaindersHighest averages
HareDroop quotaD'Hondt (Jefferson)Sainte-Laguë (Webster)Huntington-HillAdams
votesseats{\displaystyle {\frac {\text{votes}}{\text{seats}}}}votesseats+1{\displaystyle {\frac {\text{votes}}{{\text{seats}}+1}}}votesseats+1{\displaystyle {\frac {\text{votes}}{{\text{seats}}+1}}}votesseats+0.5{\displaystyle {\frac {\text{votes}}{{\text{seats}}+0.5}}}votesseats(seats+1){\displaystyle {\frac {\text{votes}}{\sqrt {{\text{seats}}({\text{seats}}+1)}}}}votesseats{\displaystyle {\frac {\text{votes}}{\text{seats}}}}
A101735.91363637363635
B100035.31353636353534
C38313.52141313141314
D32711.55121211121212
E632.22222223
F421.48111122
Total2832100 seats100100100100100100

Electoral threshold

[edit]
Main article:Electoral threshold

List of countries using party-list proportional representation

[edit]
  Countries with party-list proportional representation (closed list)

  Countries with party-list proportional representation (open list)

  Countries with party-list proportional representation (partially open list)

  Countries withPanachage, a form of open-list party-list proportional representation

The table below lists countries that use a proportional electoral system to fill a nationally elected legislative body. Detailed information on electoral systems applying to the first chamber of the legislature is maintained by theACE Electoral Knowledge Network.[9][10] Countries using PR as part of aparallel voting (mixed-member majoritarian) or othermixed system (e.g.MMP) are not included.

CountryLegislative bodyList typeVariation ofopen lists

(if applicable)

Apportionment methodElectoral thresholdConstituenciesGovernmental systemNotes
AlbaniaParliament (Kuvendi)Open listd'Hondt method4% nationally or 2.5% in a districtCountiesParliamentary republic
AlgeriaPeople's National AssemblyOpen listHare quota5% of votes in respective district.[11]Semi-presidential republic
AngolaNational AssemblyClosed list
d'Hondt method[citation needed]5 member districts and nationwideParliamentary republic with an executive presidencyDouble simultaneous vote use to elect the President and the National Assembly at the same election.
ArgentinaChamber of DeputiesClosed list
d'Hondt method3% of registered voters in the constituencyProvincesPresidential republic
ArmeniaNational AssemblyOpen listD'Hondt method5% (parties), 7% (blocs)Parliamentary republicParty lists run-off, but only if necessary to ensure stable majority of 54% if it is not achieved either immediately (one party) or through building a coalition.[12][13] If a party would win more than 2/3 seats, at least 1/3 seats are distributed to the other parties.
Closed list
ArubaParliamentOpen listD'Hondt method
AustriaNational CouncilOpen listMore open:
14% on the district level (among votes for the candidates party)
Hare quota4% nationallySingle-member districts within federal states (Länder)Semi-presidential republic
Open listMore open:

10% on the regional (state) level (among votes for the candidates party)

Hare quotaFederal states (Länder)
Open listMore open: 7% of the on the federal level (among votes for the candidates party)d'Hondt methodSingle federal (nationwide) constituency
BelgiumChamber of RepresentativeOpen listD'Hondt method5%ConstituenciesConstitutional monarchy
BéninNational AssemblyClosed list
Largest remainder method10%ConstituenciesPresidential republic
BoliviaChamber of SenatorsClosed list
d'Hondt methodDepartmentsPresidential republicBallots use thedouble simultaneous vote: voters cast a single vote for a presidential candidate and their party's list and local candidates at the same time (vote splitting is not possible/allowed)
Bosnia and HerzegovinaHouse of RepresentativeOpen listSainte-Laguë methodParliamentarydirectorial republic
BrazilChamber of DeputiesOpen listD'Hondt method2% distributed in at least 9 Federation Units with at least 1% of the valid votes in each one of themStates and Federal DistrictPresidential republic
BulgariaNational AssemblyOpen listHare quota4%ConstituenciesParliamentary republic
Cape VerdeClosed list
ChileNational CongressOpen listD'Hondt methodNode jure thresholdConstituenciesPresidential republic
ColombiaChamber of RepresentativesClosed list
Unitarypresidential republic
SenateClosed list
Costa RicaClosed list
CroatiaOpen list5%Parliamentary republic
CyprusOpen listPresidential republic
Czech RepublicChamber of DeputiesOpen listRelatively open:
5% on the district level (among votes for the candidates party)
Imperiali quota (with negative seats with smallest remainders if needed) with national remnant in the first scrutiny5% nationally for single party lists, 7% for coalitions of two, 11% for coalitions of more than 2.Regions and capitalParliamentary republic
Hagenbach-Bischoff quota + largest remaindersNational remnant seats redistributed to districts
DenmarkOpen list2%
Dominican RepublicClosed list
Presidential republic
EcuadorNational CongressClosed list
Sainte-Laguë method
El SalvadorLegislative AssemblyOpen listD'Hondt method
EstoniaOpen list5%Parliamentary republic
Faroe Islands
FijiOpen list5%
FinlandOpen listElectoral districtsParliamentary republic
GermanyBundestagLocalized listSeparate vote for candidatesOnly first place candidate may win seat (but not guaranteed to)5% or 3 constituencies, first place for independents (only in constituencies)Constituencies (single-member)Federalparliamentary republicThe system was recently modified to an essentially (non-mixed) closed list proportional system with a local constituency vote to eliminate the need for overhang seats. In the new system, the number of seats a party can win is capped, if they "won" more seats by plurality, not all of their winners will be elected.[14]
Closed list
Sainte-Laguë methodFederal states (Länder)
GreenlandOpen list
GuatemalaClosed list
GuyanaNational AssemblyClosed list
Hare quota + largest remaindersNode jure threshold[citation needed]Regional constituenciesThe president is elected by afirst-past-the-postdouble simultaneous vote system, whereby each list nominates a presidential candidate and the presidential election itself is won by the candidate of the list having a plurality.
National constituency
HondurasOpen list
IcelandOpen listParliamentary republic
IndonesiaHouse of RepresentativeOpen listSainte-Laguë method4%3 to 10 membersconstituenciesPresidential system
IsraelClosed list
3.25%
KosovoOpen listSainte-Laguë method
LatviaOpen listSainte-Laguë method5%Parliamentary republic
LebanonOpen list
LiechtensteinOpen list8%
LuxembourgChamber of DeputiesOpen listPanachage (number of votes equal to the number of members elected)d'Hondt methodNode jure thresholdFour multi-member constituencies, ranging from 7 to 23 membersParliamentary system
MacedoniaClosed list
MoldovaParliamentClosed list
d'Hondt method5% (party), 7% (electoral block), 2% (independent)[15]None
(single nationwide constituency)
Unitary parliamentary republic
MontenegroClosed list
3%
NamibiaClosed list
NetherlandsHouse of RepresentativesOpen listMore open
(25% of the quota to override the default party-list)
d'Hondt methodNode jure threshold, but an effective threshold of 0.67% (1/150) for a seatNone
(single nationwide constituency)
Parliamentary system
NorwayParliament (Storting)Closed list
modifiedSainte-Laguë methodNode jure threshold19 multi-member constituenciesParliamentary systemFirst divisor is 1,4 instead of 1.
4% forleveling seatsOne seat in each constituency is used for nationwide leveling
ParaguayClosed list
PeruClosed list
5%
PolandSejmOpen listMost opend'Hondt method5% (parties) or 8% (coalitions) nationally,[16]no threshold for national minority organisations41 multi-memberconstituencies, ranging from 7 to 20 membersSemi-presidential republic
PortugalAssembly of the RepublicClosed list
d'Hondt methodNode jure thresholdSemi-presidential republic
RomaniaClosed list
San MarinoOpen list3.5%If needed to ensure a stable majority, the two best-placed parties participate in a run-off vote to receive amajority bonus.
São Tomé and PríncipeClosed list
SerbiaClosed list
3%Parliamentary republic
Sierra Leone
Sint MaartenOpen list
SlovakiaOpen list5%Parliamentary republic
SloveniaOpen listLargest remainder (Droop quota)4%Parliamentary republic
d'Hondt method4%
South AfricaNational Assembly of South AfricaClosed list
Node jure thresholdProvinces of South AfricaParliamentary republic with an executive president
SpainCongress of DeputiesClosed list
d'Hondt method3%Provinces of SpainParliamentary system
Sri LankaParliamentOpen list
(for 196/225 seats)
Panachage
(up to 3 preference votes)[17]
d'Hondt method5%
(per constituency)
ConstituenciesSemi-presidential system
Closed list
(for 29/225 seats)
?Node jure thresholdNone
(single nationwide constituency)
SurinameNational AssemblyOpen listMost opend'Hondt methodNode jure thresholdDistricts of SurinameAssembly-independent republic
SwedenRiksdagOpen listMore open
(5% of the party vote to override the default party-list)[18]
Sainte-Laguë method (leveling seats)4% nationally or 12%
in a given constituency
Counties of Sweden
(some counties are further subdivided)
Parliamentary system
SwitzerlandNational CouncilOpen listPanachageHagenbach-Bischoff systemNode jure thresholdCantons of SwitzerlandSemi-direct democracy under anassembly-independent[19][20]directorialrepublic
Timor-LesteOpen list
TunisiaAssembly of the Representatives of the PeopleClosed list
Largest remainder methodNode jure thresholdConstituenciesSemi-presidential system
TurkeyGrand National AssemblyClosed list
d'Hondt method7%. No threshold for independent candidates.Provinces of Turkey
(some provinces are further subdivided)
Presidential system
UruguayChamber of RepresentativesClosed list
d'Hondt methodNode jure thresholdDepartments of UruguayPresidential systemBallots use thedouble simultaneous vote, the same ballot is used for electing the president (first round) and the two chambers
Chamber of SenatorsNone
(single nationwide constituency)
WalesSeneddClosed list
d'Hondt methodNode jure thresholdSenedd Constituencies

Authoritarian regimes

[edit]
CountryLegislative bodyList typeApportionment methodElectoral thresholdConstituenciesGovernmental systemNotes
Burkina FasoNational AssemblyClosed listConstituenciesSemi-presidential republic
BurundiNational AssemblyClosed listD'Hondt method2%ConstituenciesPresidential republic
CambodiaNational AssemblyClosed listD'Hondt methodConstituenciesConstitutional monarchy
Equatorial GuineaChamber of DeputiesClosed list10%ConstituenciesPresidential republic
SenateClosed listConstituencies
Guinea-BissauNational People's AssemblyClosed listSemi-presidential republic
MozambiqueClosed list
RwandaClosed list
TogoNational AssemblyClosed listHighest averages methodNo thresholdConstituenciesPresidential system

See also

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References

[edit]
  1. ^"Proportional Representation Systems".mtholyoke.edu. Archived fromthe original on 2001-01-24. Retrieved2014-12-24.
  2. ^"Proportional Representation Open List Electoral Systems in Europe"(PDF). International Foundation for Electoral Systems. Archived fromthe original(PDF) on 2014-12-24.
  3. ^"Système électoral du Grand-Duché de Luxembourg" (in French). elections.public.lu.
  4. ^Smrek, Michal. "Mavericks or Loyalists? Popular Ballot Jumpers and Party Discipline in the Flexible-List PR Context".Political Research Quarterly.76 (1):323–336.doi:10.1177/10659129221087961.
  5. ^Benoit, Kenneth."Which Electoral Formula Is the Most Proportional? A New Look with New Evidence"(PDF). Archived fromthe original(PDF) on 2010-06-24.
  6. ^Wilson, Helen J."The D'Hondt Method Explained"(PDF).
  7. ^abBalinski, Young (2001).Fair Representation. Brookings Institution Press.ISBN 0-8157-0090-3.
  8. ^ab"Proportional representation | Benefits, Types & Examples | Britannica".www.britannica.com. 2025-05-09. Retrieved2025-05-23.
  9. ^ACE Project: The Electoral Knowledge Network."Electoral Systems Comparative Data, World Map". Retrieved24 October 2017.
  10. ^ACE Project: The Electoral Knowledge Network."Electoral Systems Comparative Data, Table by Country". Retrieved24 October 2017.
  11. ^"Final Report on Algeria's Legislative Elections"(pdf).ACE Project. National Democratic Institute. 10 May 2012. Retrieved10 January 2015.
  12. ^"Armenia, Parliamentary Elections, 2 April 2017: Needs Assessment Mission Report".osce.org. Retrieved2022-05-30.
  13. ^"DocumentView".www.arlis.am.
  14. ^Schorkopf, Frank (2023-03-24)."Abschied von Adenauer oder weshalb die Wahlrechtsreform ein Verfassungsrechtsproblem ist".Verfassungsblog (in German).doi:10.17176/20230324-185228-0.
  15. ^CODUL ELECTORAL [Electoral Code] (94) (in Romanian). Parliament Republic of Moldova. 21 November 1997.
  16. ^May be lowered to 3% and 5% respectively, if only one or none of the lists surpass the standard thresholds.
  17. ^"Sri Lanka electors can vote for one party, three preferences in 2020 general elections: polls chief".EconomyNext. August 4, 2020.
  18. ^Swedish Election Authority:Elections in Sweden: The way its doneArchived 2009-02-25 at theWayback Machine (page 16)
  19. ^Shugart, Matthew Søberg (December 2005)."Semi-Presidential Systems: Dual Executive And Mixed Authority Patterns".French Politics.3 (3):323–351.doi:10.1057/palgrave.fp.8200087.S2CID 73642272.
  20. ^Elgie, Robert (2016). "Government Systems, Party Politics, and Institutional Engineering in the Round".Insight Turkey.18 (4):79–92.ISSN 1302-177X.JSTOR 26300453.

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