Party-list proportional representation

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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 determine the share of representation of their respective parties, as in Finland, Brazil, and the Netherlands (mixed single vote or panachage).^{[2] [3]}

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.

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).

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.

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]

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. Some apportionment methods may favor small parties; others may favor large parties:^[5]

• D'Hondt method (biased towards large parties)^[6]
• Sainte-Laguë method (generally considered unbiased)^[7]
• Huntington–Hill method (biased towards small parties, automatically gives every party at least one seat)^[7]
• Adams' method (heavily biased towards small parties, automatically gives every party at least one seat)
• LR-Hare (roughly unbiased, some bias towards smaller parties)
• LR-Droop (slightly biased towards large parties)

The D'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):

Party	Votes
A	1000
B	800
C	400

Round	A quotient	B quotient	C quotient	Seat to
1	1000	800	400	A
2	500	800	400	B
3	500	400	400	A
4	333.33	400	400	B
5	333.33	266.67	400	C

• Result: A = 2, B = 2, C = 1

The Sainte-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.

Round	A quotient	B quotient	C quotient	Seat to
1	1000	800	400	A
2	333.33	800	400	B
3	333.33	266.67	400	C
4	333.33	266.67	133.33	A
5	200	266.67	133.33	B

• Result: A = 2, B = 2, C = 1

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

• Divisors: 1.4, 3, 5, ...

Round	A quotient	B quotient	C quotient	Seat to
1	714.29	571.43	285.71	A
2	333.33	571.43	285.71	B
3	333.33	266.67	285.71	A
4	200	266.67	285.71	C
5	200	266.67	133.33	B

• Result: A = 2, B = 2, C = 1

The Hare 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

Party	Votes	Initial seats	Remainder
A	1000	2	120
B	800	1	360
C	400	0	400

• Remaining 2 seats to C and B (highest remainders)

• Result: A = 2, B = 2, C = 1

The Imperiali quota is rarely used; favors large parties more.

• Quota = Total votes / (seats + 2) = 2200 / 7 = ~314.29

Party	Votes	Initial seats	Remainder
A	1000	3	57.14
B	800	2	171.42
C	400	1	85.71

• 1 leftover seat to B

• Result: A = 3, B = 2, C = 1

The Huntington–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:

• 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.^{[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 either additional member systems or parallel voting.

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 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 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.

Party	Votes	Entitlement	Largest remainders		Highest averages
			Hare	Droop quota	D'Hondt (Jefferson)	Sainte-Laguë (Webster)	Huntington-Hill	Adams
			${\displaystyle {\frac {\text{votes}}{\text{seats}}}}${\displaystyle {\frac {\text{votes}}{\text{seats}}}}	${\displaystyle {\frac {\text{votes}}{{\text{seats}}+1}}}${\displaystyle {\frac {\text{votes}}{{\text{seats}}+1}}}	${\displaystyle {\frac {\text{votes}}{{\text{seats}}+1}}}${\displaystyle {\frac {\text{votes}}{{\text{seats}}+1}}}	${\displaystyle {\frac {\text{votes}}{{\text{seats}}+0.5}}}${\displaystyle {\frac {\text{votes}}{{\text{seats}}+0.5}}}	${\displaystyle {\frac {\text{votes}}{\sqrt {{\text{seats}}({\text{seats}}+1)}}}}${\displaystyle {\frac {\text{votes}}{\sqrt {{\text{seats}}({\text{seats}}+1)}}}}	${\displaystyle {\frac {\text{votes}}{\text{seats}}}}${\displaystyle {\frac {\text{votes}}{\text{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

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.^{[9] [10]} 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.[11]	Semi-presidential republic
Angola	National Assembly	Closed list	—	d'Hondt method	[citation needed ]	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 in the constituency	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.[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					—
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% nationally	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	National Congress	Open list	D'Hondt method	No de jure threshold	Constituencies	Presidential republic
Colombia	Chamber of Representatives	Closed list	—	Unitary presidential republic
	Senate	Closed list	—
Costa Rica	Closed list	—
Croatia	Open list	5%	Parliamentary republic
Cyprus	Open list	Presidential republic
Czech Republic	Chamber of Deputies	Open list	Relatively 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 scrutiny	5% nationally for single party lists, 7% for coalitions of two, 11% for coalitions of more than 2.	Regions and capital	Parliamentary republic
				Hagenbach-Bischoff quota + largest remainders		National remnant seats redistributed to districts
Denmark	Open list	2%
Dominican Republic	Closed list	—	Presidential republic
Ecuador	National Congress	Closed list	—	Sainte-Laguë method
El Salvador	Legislative Assembly	Open list	D'Hondt method
Estonia	Open list	5%	Parliamentary republic
Faroe Islands
Fiji	Open list	5%
Finland	Open list	Electoral districts	Parliamentary republic
Germany	Bundestag	Localized list	Separate vote for candidates	Only first place candidate may win seat (but not guaranteed to)	5% or 3 constituencies, first place for independents (only in constituencies)	Constituencies (single-member)	Federal parliamentary republic	The 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 method		Federal states (Länder)
Greenland	Open list
Guatemala	Closed list	—
Guyana	National Assembly	Closed list	—	Hare quota + largest remainders	No de jure threshold[citation needed ]	Regional constituencies	The president is elected by a first-past-the-post double 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
Honduras	Open list
Iceland	Open list	Parliamentary republic
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%	Parliamentary republic
Lebanon	Open list
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)[15]	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)	Closed list	—	modified Sainte-Laguë method	No de jure threshold	19 multi-member constituencies	Parliamentary system	First divisor is 1,4 instead of 1.
			4% for leveling seats		One seat in each constituency is used for nationwide leveling
Paraguay	Closed list
Peru	Closed list	—	5%
Poland	Sejm	Open list	Most open	d'Hondt method	5% (parties) or 8% (coalitions) nationally,[16] no threshold for national minority organisations	41 multi-member constituencies, ranging from 7 to 20 members	Semi-presidential republic
Portugal	Assembly of the Republic	Closed list	—	d'Hondt method	No de jure 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%	Parliamentary republic
Sierra Leone
Sint Maarten	Open list
Slovakia	Open list	5%	Parliamentary republic
Slovenia	Open list	Largest remainder (Droop quota)	4%	Parliamentary republic
		d'Hondt method	4%
South Africa	National Assembly of South Africa	Closed list	—	No de jure threshold	Provinces of South Africa	Parliamentary republic with an executive president
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)[17]	d'Hondt method	5% (per constituency)	Constituencies	Semi-presidential system
		Closed list (for 29/225 seats)	—	?	No de jure threshold	None (single nationwide constituency)
Suriname	National Assembly	Open list	Most open	d'Hondt method	No de jure threshold	Districts of Suriname	Assembly-independent republic
Sweden	Riksdag	Open list	More 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
Switzerland	National Council	Open list	Panachage	Hagenbach-Bischoff system	No de jure threshold	Cantons of Switzerland	Semi-direct democracy under an assembly-independent [19] [20] directorial republic
Timor-Leste	Open list
Tunisia	Assembly of the Representatives of the People	Closed list	—	Largest remainder method	No de jure 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 de jure 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 de jure threshold	Senedd Constituencies

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

• 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

• 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年04月28日 at the Wayback Machine
• Apportionment, or How to Round Seat Numbers
• Glossary of Electoral Formulas

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