# Party-list proportional representation

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.
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 parties, as in Finland, Brazil, and the Netherlands (mixed single vote or panachage).

## 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 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

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

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

Many variations on seat allocation within party-list proportional representation exist. Different apportionment methods may favor smaller or larger parties:
* D'Hondt method (biased towards large parties)
* Sainte-Laguë method (roughly unbiased)
* Huntington–Hill method (roughly unbiased)
* Adams method (biased towards small parties)
* LR-Hare (roughly unbiased)
* LR-Droop (biased towards large parties)
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. Here, parties B and A are
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 | Largest remainders | Highest averages | Highest averages | Highest averages | Highest averages |
| Party | Votes | Entitlement | Hare | Droop quota | D'Hondt (Jefferson) | Sainte-Laguë (Webster) | Huntington-Hill | Adams |
| Party | Votes | Entitlement | ${\frac {\text{votes}}{\text{seats}}}$ | ${\frac {\text{votes}}{{\text{seats}}+1}}$ | ${\frac {\text{votes}}{{\text{seats}}+1}}$ | ${\frac {\text{votes}}{{\text{seats}}+0.5}}$ | ${\frac {\text{votes}}{\sqrt {{\text{seats}}({\text{seats}}+1)}}}$ | ${\frac {\text{votes}}{\text{seats}}}$ |
| 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 |

### 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.
| 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. | | Semi-presidential republic | |
| Angola | National Assembly | Closed list | — | d'Hondt method | | 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 | 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. If a party would win more than 2/3 seats, at least 1/3 seats are distributed to the other parties. |
| Armenia | National Assembly | Closed 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. If a party would win more than 2/3 seats, at least 1/3 seats are distributed to the other parties. |
| 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% | Single-member districts within federal states (Länder) | Semi-presidential republic | |
| Austria | National Council | Open list | More open: 10% on the regional (state) level (among votes for the candidates party) | Hare quota | 4% | Federal states (Länder) | Semi-presidential republic | |
| Austria | National Council | Open list | More open: 7% of the on the federal level (among votes for the candidates party) | d'Hondt method | 4% | Single federal (nationwide) constituency | Semi-presidential republic | |
| 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 | | Open list | | | | | | |
| Colombia | Chamber of Representatives | Closed list | — | | | | Unitary presidential republic | |
| Colombia | Senate | Closed list | — | | | | Unitary presidential republic | |
| Costa Rica | | Closed list | — | | | | | |
| Croatia | | Open list | | | 5% | | | |
| Cyprus | | Open list | | | | | | |
| Czech Republic | | Open list | | | 5% | | | |
| Denmark | | Open list | | | 2% | | | |
| Dominican Republic | | Closed list | — | | | | | |
| Ecuador | National Congress | Closed list | — | Sainte-Laguë method | | | | |
| El Salvador | Legislative Assembly | Open list | | D'Hondt method | | | | |
| Estonia | | Open list | | | 5% | | | |
| Faroe Islands | | | | | | | | |
| Fiji | | Open list | | | 5% | | | |
| Finland | | Open list | | | | | | |
| 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. |
| Germany | Bundestag | Closed list | — | Sainte-Laguë method | 5% or 3 constituencies, first place for independents (only in constituencies) | Federal states (Länder) | 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. |
| Greenland | | Open list | | | | | | |
| Guatemala | | Closed list | — | | | | | |
| Guyana | | Closed list | — | | | | | |
| Honduras | | Open list | | | | | | |
| Iceland | | Open list | | | | | | |
| 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% | | | |
| 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) | 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) | Open list | De facto Closed list (50% of votes to override) | Sainte-Laguë method | 4% | | | |
| Paraguay | | Closed list | | | | | | |
| Peru | | Closed list | — | | 5% | | | |
| Poland | Sejm | Open list | | d'Hondt method | 5% threshold or more for single parties, 8% or more for coalitions or 0% or more for minorities | 41 multi-member constituencies, ranging from 7 to 20 members | Semi-presidential republic| |
| Portugal | Assembly of the Republic | Closed list | — | d'Hondt method | No 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% | | | |
| Sierra Leone | | | | | | | | |
| Sint Maarten | | Open list | | | | | | |
| Slovakia | | Open list | | | 5% | | | |
| Slovenia | | Open list | | Largest remainder (Droop quota) | 4% | | | |
| Slovenia | | Open list | | d'Hondt method | 4% | | | |
| South Africa | | Closed list | — | | | | | |
| 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) | d'Hondt method | 5% (per constituency) | Constituencies | Semi-presidential system | |
| Sri Lanka | Parliament | Closed list (for 29/225 seats) | — | ? | No threshold | None (single nationwide constituency) | Semi-presidential system | |
| Suriname | National Assembly | Open list | Most open | 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) | 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 threshold | Cantons of Switzerland | Semi-direct democracy under an assembly-independent directorial republic | |
| Timor-Leste | | Open list | | | | | | |
| 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 | — | 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 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 |
| Uruguay | Chamber of Senators | Closed list | — | d'Hondt method | No threshold | None (single nationwide constituency) | Presidential system | Ballots use the double simultaneous vote, the same ballot is used for electing the president (first round) and the two chambers |
| Wales | Senedd | Closed list | — | d'Hondt method | No threshold | | | |

### Authoritarian regimes

| Country | Legislative body | List type | Apportionment method | Electoral threshold | Constituencies | Governmental system |
| 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 |
| Equatorial Guinea | Senate | Closed list | | | Constituencies | Presidential republic |
| 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 |