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]

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 called free list orpanachage.

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).

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 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]

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 (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)

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):

• Result: A = 2, B = 2, C = 1

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.

• 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, ...

• Result: A = 2, B = 2, C = 1

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

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

• Result: A = 2, B = 2, C = 1

TheImperiali quota is rarely used; favors large parties more.

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

• 1 leftover seat to B

• Result: A = 3, B = 2, C = 1

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:

• Thehighest averages method (or divisor method), including theD'Hondt method (Jefferson method) is used inArmenia,Austria,Brazil,Bulgaria,Cambodia,Croatia,Estonia,Finland,Poland, andSpain; and theSainte-Laguë method (Webster method) is used inIndonesia,New Zealand,Norway, andSweden.
• Thelargest 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 eitheradditional member systems orparallel 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 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.

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

• 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 theACE Project
• Open, Closed and Free Lists - from theACE Project
• Handbook of Electoral System ChoiceArchived 2010-04-28 at theWayback Machine
• Apportionment, or How to Round Seat Numbers
• Glossary of Electoral Formulas

• Party-list proportional representation
• Proportional representation electoral systems

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