Party-list proportional representation

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 free list or 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 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.

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 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.

Apportionment of party seats

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:

• D'Hondt method (biased towards large parties)
• Sainte-Laguë method (generally considered unbiased)
• Huntington–Hill method (biased towards small parties, automatically gives every party at least one seat)
• 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)

D'Hondt method

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, ...).

• Example (5 seats):

• Result: A = 2, B = 2, C = 1

Sainte-Laguë method

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.

• Result: A = 2, B = 2, C = 1

Modified Sainte-Laguë method

Same as Sainte-Laguë but first divisor is 1.4 to favour larger parties.

• Divisors: 1.4, 3, 5, ...

• Result: A = 2, B = 2, C = 1

Hare quota (largest remainder)

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

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

• Result: A = 2, B = 2, C = 1

Imperiali quota (largest remainder)

The Imperiali 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

Huntington–Hill method

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. 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.

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.

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 other mixed system (e.g. MMP) are not included.

Authoritarian regimes

References

References

1. "Proportional Representation Systems". mtholyoke.edu.
2. "Proportional Representation Open List Electoral Systems in Europe". International Foundation for Electoral Systems.
3. "Système électoral du Grand-Duché de Luxembourg". elections.public.lu.
4. Smrek, Michal. "Mavericks or Loyalists? Popular Ballot Jumpers and Party Discipline in the Flexible-List PR Context". [[Political Research Quarterly]].
5. Benoit, Kenneth. "Which Electoral Formula Is the Most Proportional? A New Look with New Evidence".
6. Wilson, Helen J.. "The D'Hondt Method Explained".
7. Balinski, Young. (2001). "Fair Representation". Brookings Institution Press.
8. (2025-05-09). "Proportional representation {{!}} Benefits, Types & Examples {{!}} Britannica".
9. "Electoral Systems Comparative Data, World Map".
10. "Electoral Systems Comparative Data, Table by Country".
11. (10 May 2012). "Final Report on Algeria's Legislative Elections". National Democratic Institute.
12. "Armenia, Parliamentary Elections, 2 April 2017: Needs Assessment Mission Report".
13. "DocumentView".
14. Schorkopf, Frank. (2023-03-24). "Abschied von Adenauer oder weshalb die Wahlrechtsreform ein Verfassungsrechtsproblem ist". Verfassungsblog.
15. (21 November 1997). "CODUL ELECTORAL".
16. May be lowered to 3% and 5% respectively, if only one or none of the lists surpass the standard thresholds.
17. (August 4, 2020). "Sri Lanka electors can vote for one party, three preferences in 2020 general elections: polls chief".
18. Swedish Election Authority: [http://www.val.se/pdf/electionsinsweden_webb.pdf Elections in Sweden: The way its done] {{webarchive. link. (2009-02-25 (page 16))
19. (December 2005). "Semi-Presidential Systems: Dual Executive And Mixed Authority Patterns". French Politics.
20. Elgie, Robert. (2016). "Government Systems, Party Politics, and Institutional Engineering in the Round". Insight Turkey.