Party-list proportional representation explained

Party-list proportional representation (list-PR) is a system of proportional representation based on preregistered political parties, with each party being allocated a certain number of seats roughly 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 in Spain, Turkey, and Israel (closed lists); or for candidates whose vote totals are pooled together to parties, as in Finland, Brazil, and the Netherlands (mixed single vote or panachage).^{[2] [3]}

Voting

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

Selection of party candidates

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 (a closed list system) or it may be determined by the voters at large (an open list system) or by districts (a local list system).

Closed list

See main article: Closed list. In a closed list systems, 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

See 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 from relatively closed, where a candidate can move up a predetermined list only with a certain number of votes, to completely open, where the order of the list completely depends on the number of votes each individual candidate gets.^[4]

Apportionment of party seats

Many variations on seat allocation within party-list proportional representation exist. Different apportionment methods may favor smaller or larger parties:^[5]

• D'Hondt method (biased towards large parties)^[6]
• Sainte-Laguë method (roughly unbiased)
• Huntington–Hill method (roughly unbiased)
• Adams method (biased towards small parties)
• LR-Hare (roughly unbiased)
• LR-Droop (biased towards large parties)

The apportionment methods can be classified into two categories:

• The highest averages method (or divisor method), including the D'Hondt method (Jefferson method) is used in Armenia, Austria, Brazil, Bulgaria, Cambodia, Croatia, Estonia, Finland, Poland, and Spain; and the Sainte-Laguë method (Webster method) is used in Indonesia, New Zealand, Norway, and Sweden.
• The largest remainder (LR) methods, including the Hamilton (Hare) method and Droop method.

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. 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 either additional member systems or parallel voting.

Example

Below it can be seen how different apportionment methods yield different results when apportioning 100 seats. Here, parties B and A are

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 the quota rule (shown in red text) and favors the largest party by "rounding" an ideal apportionment of 35.91 up to 37.

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

Party! rowspan="3"

Votes	Entitlement	Largest remainders		Highest averages
Hare		Droop quota	D'Hondt (Jefferson)	Sainte-Laguë (Webster)	Huntington-Hill	Adams
(votes)/(seats)		(votes)/(seats +1)	(votes)/(seats +1)	(votes)/(seats +0 . 5)	(votes)/(\sqrt{ seats ( seats +1 )) }	(votes)/(seats)
A	1017	35.91	36	36	37	36	36	35
B	1000	35.31	35	36	36	35	35	34
C	383	13.52	14	13	13	14	13	14
D	327	11.55	12	12	11	12	12	12
E	63	2.22	2	2	2	2	2	3
F	42	1.48	1	1	1	1	2	2
Total	2832	100 seats	100	100	100	100	100	100

Electoral threshold

See main article: Electoral threshold.

List of countries using 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 the ACE Electoral Knowledge Network.^{[7] [8]} Countries using PR as part of a parallel voting (mixed-member majoritarian) or other mixed system (e.g. MMP) are not included.

Country	Legislative body	List type	Variation of open lists(if applicable)	Apportionment method	Electoral threshold	Constituencies	Governmental system	Notes
Albania	Parliament (Kuvendi)	Open list		d'Hondt method	4% nationally or 2.5% in a district	Counties	Parliamentary republic
Algeria	People's National Assembly	Open list		Hare quota	5% of votes in respective district.^[9]		Semi-presidential republic
Angola	National Assembly	Closed list	—	d'Hondt method		5 member districts and nationwide	Parliamentary republic with an executive presidency	Double simultaneous vote use to elect the President and the National Assembly at the same election.
Argentina	Chamber of Deputies	Closed list	—	d'Hondt method	3% of registered voters	Provinces	Presidential republic
Armenia	National Assembly	Open list		D'Hondt method	5% (parties), 7% (blocs)		Parliamentary republic	Party 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.^[10] ^[11] If a party would win more than 2/3 seats, at least 1/3 seats are distributed to the other parties.
		Closed list	—
Aruba	Parliament	Open list		D'Hondt method
Austria	National Council	Open list	More open 14% on the district level (among votes for the candidates party)	Hare quota	4%	Single-member districts within federal states (Länder)	Semi-presidential republic
		Open list	More open 10% on the regional (state) level (among votes for the candidates party)	Hare quota		Federal states (Länder)
		Open list	More open 7% of the on the federal level (among votes for the candidates party)	d'Hondt method		Single federal (nationwide) constituency
Belgium	Chamber of Representative	Open list		D'Hondt method	5%	Constituencies	Constitutional monarchy
Bénin	National Assembly	Closed list	—	Largest remainder method	10%	Constituencies	Presidential republic
Bolivia	Chamber of Senators	Closed list	—	d'Hondt method		Departments	Presidential republic	Ballots use the double 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 Herzegovina	House of Representative	Open list		Sainte-Laguë method			Parliamentary directorial republic
Brazil	Chamber of Deputies	Open list		D'Hondt method	2% distributed in at least 9 Federation Units with at least 1% of the valid votes in each one of them	States and Federal District	Presidential republic
Bulgaria	National Assembly	Open list		Hare quota	4%	Constituencies	Parliamentary republic
Cape Verde		Closed list	—
Chile		Open list
Colombia	Chamber of Representatives	Closed list	—				Unitary presidential republic
	Senate	Closed list	—
Costa Rica		Closed list	—
Croatia		Open list			5%
Cyprus		Open list
Czech Republic		Open list			5%
Denmark		Open list			2%
Dominican Republic		Closed list	—
East Timor		Open list
Ecuador	National Congress	Closed list	—	Sainte-Laguë method
El Salvador	Legislative Assembly	Open list		D'Hondt method
Estonia		Open list			5%
Faroe Islands
Fiji		Open list			5%
Finland		Open list
Greenland		Open list
Guatemala		Closed list	—
Guyana		Closed list	—
Honduras		Open list
Iceland		Open list
Indonesia	House of Representative	Open list		Sainte-Laguë method	4%	3 to 10 members constituencies	Presidential system
Israel		Closed list	—		3.25%
Kosovo		Open list		Sainte-Laguë method
Latvia		Open list		Sainte-Laguë method	5%
Lebanon
Liechtenstein		Open list			8%
Luxembourg	Chamber of Deputies	Open list	Panachage (number of votes equal to the number of members elected)	d'Hondt method	No de jure threshold	Four multi-member constituencies, ranging from 7 to 23 members	Parliamentary system
Macedonia		Closed list
Moldova	Parliament	Closed list	—	d'Hondt method	5% (party), 7% (electoral block), 2% (independent)^[12]	None (single nationwide constituency)	Unitary parliamentary republic
Montenegro		Closed list	—		3%
Namibia		Closed list	—
Netherlands	House of Representatives	Open list	More open (25% of the quota to override the default party-list)	d'Hondt method	No de jure threshold, but an effective threshold of 0.67% (1/150) for a seat	None (single nationwide constituency)	Parliamentary system
Norway	Parliament (Storting)	Open list	De facto Closed list (50% of votes to override)	Sainte-Laguë method	4%
Paraguay		Closed list
Peru		Closed list	—		5%
Poland	Sejm	Open list			5% threshold or more for single parties, 8% or more for coalitions or 0% or more for minorities	41 multi-member constituencies, ranging from 7 to 20 members	Parliamentary republic
Portugal	Assembly of the Republic	Closed list	—	d'Hondt method	No threshold		Semi-presidential republic
Romania		Closed list	—
San Marino		Open list			3.5%			If needed to ensure a stable majority, the two best-placed parties participate in a run-off vote to receive a majority bonus.
São Tomé and Príncipe		Closed list	—
Serbia		Closed list	—		3%
Sierra Leone
Sint Maarten		Open list
Slovakia		Open list			5%
Slovenia		Open list		Largest remainder (Droop quota)	4%
				d'Hondt method	4%
South Africa		Closed list	—
Spain	Congress of Deputies	Closed list	—	d'Hondt method	3%	Provinces of Spain	Parliamentary system
Sri Lanka	Parliament	Open list (for 196/225 seats)	Panachage (up to 3 preference votes)^[13]	d'Hondt method	5% (per constituency)	Constituencies	Semi-presidential system
		Closed list (for 29/225 seats)	—	?	No threshold	None (single nationwide constituency)
Suriname	National Assembly	Open list	Most open	d'Hondt method	No threshold	Districts of Suriname	Assembly-independent republic
Sweden	Riksdag	Open list	More open (5% of the party vote to override the default party-list)^[14]	Sainte-Laguë method (leveling seats)	4% nationally or 12% in a given constituency	Counties of Sweden (some counties are further subdivided)	Parliamentary system
Switzerland	National Council	Open list	Panachage	Hagenbach-Bischoff system	No threshold	Cantons of Switzerland	Semi-direct democracy under an assembly-independent^[15] ^[16] directorial republic
Tunisia	Assembly of the Representatives of the People	Closed list	—	Largest remainder method	No threshold	Constituencies	Semi-presidential system
Turkey	Grand National Assembly	Closed list	—	d'Hondt method	7%. No threshold for independent candidates.	Provinces of Turkey (some provinces are further subdivided)	Presidential system
Uruguay	Chamber of Representatives	Closed list	—	d'Hondt method	No threshold	Departments of Uruguay	Presidential system	Ballots use the double simultaneous vote, the same ballot is used for electing the president (first round) and the two chambers
	Chamber of Senators					None (single nationwide constituency)
Wales	Senedd	Closed list	—	d'Hondt method	No threshold

Authoritarian regimes

Country	Legislative body	List type	Apportionment method	Electoral threshold	Constituencies	Governmental system	Notes
Burkina Faso	National Assembly	Closed list			Constituencies	Semi-presidential republic
Burundi	National Assembly	Closed list	D'Hondt method	2%	Constituencies	Presidential republic
Cambodia	National Assembly	Closed list	D'Hondt method		Constituencies	Constitutional monarchy
Equatorial Guinea	Chamber of Deputies	Closed list		10%	Constituencies	Presidential republic
	Senate	Closed list			Constituencies
Guinea-Bissau	National People's Assembly	Closed list				Semi-presidential republic
Mozambique		Closed list
Rwanda		Closed list
Togo	National Assembly	Closed list	Highest averages method	No threshold	Constituencies	Presidential system

See also

• Comparison of the Hare and Droop quotas
• General ticket (party block voting), a term usually given to less or non proportional equivalents
• Mixed-member proportional representation, a kind of party-list proportional representation
• Leveling seats
• List MP
• Ley de Lemas
• Sectoral representation in the House of Representatives of the Philippines
• Outline of democracy

External links

• Advantages and disadvantages of List PR - from the ACE Project
• Open, Closed and Free Lists - from the ACE Project
• Handbook of Electoral System Choice
• Apportionment, or How to Round Seat Numbers
• Glossary of Electoral Formulas

Notes and References

1. Web site: Proportional Representation Systems . mtholyoke.edu.
2. Web site: Proportional Representation Open List Electoral Systems in Europe . dead . https://web.archive.org/web/20141224074108/http://www.ifes.org/~/media/Files/Publications/White%20PaperReport/2009/Proportional_Representation_Open_List_Electoral_Systems_Europe.pdf . 2014-12-24 . International Foundation for Electoral Systems.
3. Web site: Système électoral du Grand-Duché de Luxembourg(fr) . elections.public.lu.
4. Smrek . Michal . Mavericks or Loyalists? Popular Ballot Jumpers and Party Discipline in the Flexible-List PR Context . . 76 . 1 . 323-336 . 10.1177/10659129221087961.
5. Web site: Benoit . Kenneth . Which Electoral Formula Is the Most Proportional? A New Look with New Evidence . dead . https://web.archive.org/web/20100624102008/http://polmeth.wustl.edu/analysis/vol/8/PA84-381-388.pdf . 2010-06-24.
6. Web site: Wilson . Helen J. . The D'Hondt Method Explained .
7. Web site: ACE Project: The Electoral Knowledge Network. Electoral Systems Comparative Data, World Map. 24 October 2017.
8. Web site: ACE Project: The Electoral Knowledge Network. Electoral Systems Comparative Data, Table by Country. 24 October 2017.
9. Web site: 10 May 2012 . Final Report on Algeria's Legislative Elections . 10 January 2015 . ACE Project . National Democratic Institute . pdf.
10. Web site: Armenia, Parliamentary Elections, 2 April 2017: Needs Assessment Mission Report . 2022-05-30 . . en.
11. Web site: DocumentView . www.arlis.am.
12. 21 November 1997 . 94 . Parliament Republic of Moldova . CODUL ELECTORAL . Electoral Code. Romanian.
13. Web site: Sri Lanka electors can vote for one party, three preferences in 2020 general elections: polls chief. August 4, 2020. EconomyNext.
14. Swedish Election Authority: Elections in Sweden: The way its done (page 16)
15. Shugart . Matthew Søberg . Semi-Presidential Systems: Dual Executive And Mixed Authority Patterns . French Politics . December 2005 . 3 . 3 . 323–351 . 10.1057/palgrave.fp.8200087 . 73642272. free .
16. Elgie . Robert . Government Systems, Party Politics, and Institutional Engineering in the Round . Insight Turkey . 2016 . 18 . 4 . 79–92 . 26300453 . 1302-177X.