Party-list proportional representation

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.

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; or a choice between the last two ways stated: panachage.

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:

• 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 method.

Different apportionment formulas may favour smaller or larger parties:

• D'Hondt method (slightly favours larger parties)
• Adams' method (greatly favours very small parties)
• Webster/Sainte-Laguë method
• Macanese d'Hondt method (greatly favours smaller parties)
• Huntington–Hill method (slightly favours small parties)
• Hamilton method
• Imperiali method (greatly disfavours very small parties, not strictly proportional)
• LR-Hare (slightly favours very small parties when unmodified, if there is no electoral threshold)
• LR-Droop (very slightly favours larger parties)
• LR-Hagenbach-Bischoff (slightly favours larger parties)
• LR-Imperiali (greatly favours larger parties)

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. 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 $\textstyle {\frac {V}{2^{s}}}$, 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
				${\frac {\text{votes}}{\text{seats}}}$	$\textstyle \operatorname {Integer} \left({\frac {\text{votes}}{{\text{seats}}+1}}\right)+1$	${\frac {\text{votes}}{{\text{seats}}+1}}$	${\frac {\text{votes}}{{\text{seats}}+2}}$	${\frac {\text{votes}}{{\text{seats}}+1}}$	${\frac {\text{votes}}{\text{seats}}}$	${\frac {\text{votes}}{{\text{seats}}+0.5}}$	${\frac {\text{votes}}{\sqrt {{\text{seats}}({\text{seats}}+1)}}}$	${\frac {\text{votes}}{{\text{seats}}+2}}$	${\frac {\text{votes}}{2^{\text{seats}}}}$
	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. 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.
Angola	National Assembly	Closed list	—	Highest averages method(D'Hondt method)		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. 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
El Salvador
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. In 2020 parliament voted to return to the majority bonus two elections thereafter.
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)	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					5% or less
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)	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)	Highest averages method (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	Highest averages method (D'Hondt method: Hagenbach-Bischoff system)	No threshold	Cantons of Switzerland	Semi-direct democracy under an assembly-independent 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)

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 system similar to 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 Archived 2010-04-28 at the Wayback Machine
• Apportionment, or How to Round Seat Numbers
• Glossary of Electoral Formulas