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

Party-list proportional representation (list-PR) is a subset of proportional representation electoral systems in which multiple candidates are elected (e.g., elections to parliament) through their position on an electoral list. They can also be used as part of mixed-member electoral systems.[1]

In these systems, parties make lists of candidates to be elected, and seats are distributed by elections authorities to each party in proportion to the number of votes the party receives. Voters may vote for the party, as in Albania, Argentina, Turkey, and Israel; or for candidates whose vote total will pool to the party/parties, as in Finland, Brazil and the Netherlands;[2] or a choice between the last two ways stated: panachage.[3]

## Voting

In most party list systems, a voter may only vote for one party (single choice ballot) with their list vote, although ranked ballots may also be used (spare vote). Open list systems may allow more than one preference votes within a party list (votes for candidates are called preference votes - not to be confused with the other meaning of preferential voting as in ranked-choice voting). Some systems allow for voters to vote for candidates on multiple lists, this 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

 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 tend to 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

 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 list 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.

In France, party lists in proportional elections must include as many candidates (and twice as many substitutes for the departmental elections) as there are seats to be allocated, whereas in other countries "incomplete" lists are allowed, which is not a problem under a panachage system.

## Apportionment of party seats

Many variations on seat allocation within party-list proportional representation exist. The two most common types are:

Different apportionment formulas may favour smaller or larger parties:[4]

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 - the most proportional being when there is no division into constituencies at all and the entire country is treated as a single constituency.[citation needed] More, 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 (most commonly majoritarian) in various mixed systems, e.g., using the additional member system.

### Example

Below it can be seen how different apportionment methods yield different results with the same number of seats and votes (100 and 2832 in this example).

As there are 100 seats, the percentage values for every party's share of the vote is equal to the party's vote count divided by the Hare quota (which is the ratio of vote and seat totals), and in this case the share of seats under the largest remainder method using this quota happens to be the same as the percentage values rounded to the nearest integer (because exactly 3 party's results has to be rounded up, same as there are 3 seats to assign with the largest remainder method after 97 seats are assigned based on the integer part of the vote share divided by the Hare quota). The Webster/Sainte-Laguë method yields the same result (but this is not always the case), otherwise all other methods give a different number of seats to the parties.

Notable is how the D'Hondt method breaks the quota rule (shown in red text) and favours the largest party with 37% of seats, even though it only got 35,91% of the vote (the quota rule would allow either 35 or 36 seats in this case = rounding up or rounding down, but no jump to 34 or 37). Also, the Adams and Huntington-Hill methods, which (without a threshold) greatly favour smaller parties gave 2 seats to the smallest party and would have both given at least 1 seat to every party if it got even just 1 vote from 2832. Of the highest average methods, modified versions of the formulas may not be strictly proportional. For example, the Imperiali method (not to be confused with the Imperiali quota) can be seen as a modified version of the D'Hondt (or Adams) method, and it is technically not proportional (e.g., if a party received 500/1000 votes, and there were 100 seats to be apportioned, it may sometimes not only get 50 - the clearly proportional number of seats - but could also get 51). The Macanese modification of the d'Hondt method, whose quotients are based on the formula ${\displaystyle \textstyle {\frac {V}{2^{s))))$, is clearly disproportional; the great variations between the parties' vote shares are effectively reduced, and each party has a roughly equal number of seats.

Party Votes % Largest remainder method Highest averages method
Hare quota Droop quota Hagenbach-Bischoff quota Imperiali quota D'Hondt (Jefferson) Adams Sainte-Laguë (Webster) Huntington-Hill Imperiali Macanese D'Hondt
${\displaystyle {\frac {\text{votes)){\text{seats))))$ ${\displaystyle \textstyle \operatorname {Integer} \left({\frac {\text{votes))((\text{seats))+1))\right)+1}$ ${\displaystyle {\frac {\text{votes))((\text{seats))+1))}$ ${\displaystyle {\frac {\text{votes))((\text{seats))+2))}$ ${\displaystyle {\frac {\text{votes))((\text{seats))+1))}$ ${\displaystyle {\frac {\text{votes)){\text{seats))))$ ${\displaystyle {\frac {\text{votes))((\text{seats))+0.5))}$ ${\displaystyle {\frac {\text{votes)){\sqrt ((\text{seats))({\text{seats))+1)))))$ ${\displaystyle {\frac {\text{votes))((\text{seats))+2))}$ ${\displaystyle {\frac {\text{votes)){2^{\text{seats))))}$
A 1017 35,91% 36 35 36 36 37 35 36 36 38 19
B 1000 35,31% 35 35 36 36 36 34 35 35 37 18
C 383 13,52% 14 14 13 14 13 14 14 13 13 17
D 327 11,55% 12 12 12 11 11 12 12 12 11 17
E 63 2,22% 2 2 2 2 2 3 2 2 1 15
F 42 1,48% 1 2 1 1 1 2 1 2 0 14
Total 2832 100 100 100 100 100 100 100 100 100 100 100

### Electoral threshold

 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.[6][7] Countries using PR as part of a parallel voting (mixed-member majoritarian) or another mixed system (e.g. MMP) are not included.

Country Legislative body List type Variation of open lists

(if applicable)

Allocating formula Electoral threshold Constituencies Governmental system Notes
Albania Parliament (Kuvendi) Open list Highest averages method(D'Hondt method) 4% nationally or 2.5% in a district Counties
Algeria People's National Assembly Open list Largest remainder method(Hare quota) 5% of votes in respective district.[8]
Angola National Assembly Closed list
Highest averages method(D'Hondt method) [citation needed] 5 member districts and nationwide Double simultaneous vote use to elect the President and the National Assembly at the same election.
Argentina Chamber of Deputies Closed list
Highest averages method(D'Hondt method) 3% of registered voters
Armenia National Assembly Open list Largest remainder method (? quota) 5% (parties), 7% (blocs) 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.[9][10] If a party would win more than 2/3 seats, at least 1/3 seats are distributed to the other parties.
Closed list
Largest remainder method (? quota)
Aruba Parliament Open list
Austria National Council Open list More open:
14% on the district level (among votes for the candidates party)
Largest remainder method (Hare quota) 4% Single-member districts within federal states (Länder) Parliamentary republic
Open list More open:

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

Largest remainder method(Hare quota) Federal states (Länder)
Open list More open: 7% of the on the federal level (among votes for the candidates party) Highest averages method(D'Hondt method) Single federal (nationwide) constituency
Belgium Chamber of Representatives Open list 5%
Bénin National Assembly Closed list
Bolivia Chamber of Senators Closed list D'Hondt method 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 Representatives Open list
Brazil Chamber of Deputies Open list Highest averages method (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 4%
Burkina Faso National Assembly Closed list
Burundi 2%
Cambodia
Cape Verde
Chile
Colombia
Costa Rica
Croatia 5%
Cyprus
Czech Republic 5%
Denmark 2%
Dominican Republic
East Timor
Equatorial Guinea
Estonia 5%
Faroe Islands
Fiji 5%
Finland
Greece 3% Nationwide closed lists and open lists in multi-member districts. The winning party used to receive a majority bonus of 50 seats (out of 300), but this system will be abolished two elections after 2016.[11] In 2020 parliament voted to return to the majority bonus two elections thereafter.[12]
Greenland
Guatemala
Guinea-Bissau
Guyana
Honduras
Iceland
Indonesia 4%
Israel 3.25%
Kazakhstan 7%
Kosovo
Latvia 5%
Lebanon
Liechtenstein 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
Moldova Parliament Closed list
Highest averages method(D'Hondt method) 5% (party), 7% (electoral block), 2% (independent)[13] None
(single nationwide constituency)
Unitary parliamentary republic
Montenegro 3%
Mozambique
Namibia
Netherlands House of Representatives Open list More open
(25% of the quota to override the default party-list)
Highest averages method
(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) 4%
Paraguay
Peru 5%
Poland 5% threshold or more for single parties, 8% or more for coalitions or 0% or more for minorities
Portugal
Romania
Rwanda
San Marino 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
Serbia 3%
Sint Maarten
Slovakia 5%
Slovenia 4%
South Africa
Spain Congress of Deputies Closed list
Highest averages method
(D'Hondt method)
3% Provinces of Spain Parliamentary system
Sri Lanka Parliament Open list
(for 196/225 seats)
Panachage
(up to 3 preference votes)[14]
Highest averages method
(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 Highest averages method
(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)[15]
Highest averages method
(Sainte-Laguë method)
4% nationally or 12%
in a given constituency
Counties of Sweden
(some counties are further subdivided)
Parliamentary system
Switzerland National Council Open list Panachage Highest averages method
(D'Hondt method: Hagenbach-Bischoff system)
No threshold Cantons of Switzerland Semi-direct democracy under an assembly-independent[16][17] directorial republic
Togo National Assembly Closed list
Highest averages method No threshold Constituencies Presidential system
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
Highest averages method
(D'Hondt method)
7% for multi-party alliances. No threshold for independent candidates. Provinces of Turkey
(some provinces are further subdivided)
Presidential system
Uruguay Chamber of Representatives Closed list
Highest averages method
(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)

## References

1. ^ "Proportional Representation Systems". mtholyoke.edu.
2. ^ "Proportional Representation Open List Electoral Systems in Europe" (PDF). International Foundation for Electoral Systems. Archived from the original (PDF) on 2014-12-24.
3. ^ "Système électoral du Grand-Duché de Luxembourg(fr)". elections.public.lu.
4. ^ Benoit, Kenneth. "Which Electoral Formula Is the MostProportional? A New Lookwith New Evidence" (PDF). Archived from the original (PDF) on 2010-06-24.
5. ^ Wilson, Helen J. "The D'Hondt Method Explained" (PDF).
6. ^ ACE Project: The Electoral Knowledge Network. "Electoral Systems Comparative Data, World Map". Retrieved 24 October 2017.
7. ^ ACE Project: The Electoral Knowledge Network. "Electoral Systems Comparative Data, Table by Country". Retrieved 24 October 2017.
8. ^ "FINAL REPORT ON ALGERIA'S LEGISLATIVE ELECTIONS" (pdf). ACE Project. National Democratic Institute. 10 May 2012. Retrieved 10 January 2015.
9. ^ "Armenia, Parliamentary Elections, 2 April 2017: Needs Assessment Mission Report". www.osce.org. Retrieved 2022-05-30.
10. ^ "DocumentView". www.arlis.am.
11. ^ "Greek MPs approve end to bonus seats, lower voting age". Reuters. 2016-07-21. Retrieved 2019-06-22.
12. ^ "Parliament votes to change election law | Kathimerini". www.ekathimerini.com. Retrieved 2020-01-25.
13. ^ "CODUL ELECTORAL" [Electoral Code]. Article 94, Act of 21 November 1997 (in Romanian). Parliament Republic of Moldova.
14. ^ "Sri Lanka electors can vote for one party, three preferences in 2020 general elections: polls chief". EconomyNext. August 4, 2020.
15. ^ Swedish Election Authority: Elections in Sweden: The way its done Archived 2009-02-25 at the Wayback Machine (page 16)
16. ^ 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.
17. ^ Elgie, Robert (2016). "Government Systems, Party Politics, and Institutional Engineering in the Round". Insight Turkey. 18 (4): 79–92. ISSN 1302-177X. JSTOR 26300453.