thumb|Poster for the European Parliament election 2004 in Italy, showing party lists
Party-list proportional representation systems are a family of voting systems emphasizing proportional representation in elections in which multiple candidates are elected (e.g., elections to parliament) through allocations to 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: Luxembourg's ("panachage") and ("list vote").
Apportionment of party seats
Many variations on seat allocation within party-list proportional representation exist.
The two most common are:
The highest average method, including the D'Hondt method used in Albania, Argentina, Armenia, Austria, Brazil, Bulgaria, Croatia,  Cambodia, Estonia, Finland, Israel, Poland, Spain and many other countries; and the Sainte-Laguë method used in Norway, Sweden, New Zealand, the German Bundestag, and in six German states (e.g., North Rhine-Westphalia and Bremen).
The largest remainder (LR) methods, including the Hamilton method.
List proportional representation may also be combined in various hybrids, e.g., using the additional member system.
List of main apportionment methods:
modified d'Hondt method (favours smaller parties)
Huntington-Hill method (slightly favors small parties)
Webster/Sainte-Laguë method, LR-Hare (slightly favors very small parties when unmodified, if there is no electoral threshold)
LR-Droop (very slightly favors larger parties)
D'Hondt method (slightly favors larger parties)
LR-Imperiali (greatly favors 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.
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 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
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.
This system of open list is known as panachage.
See also
Comparison of the Hare and Droop quotas
Outline of democracy
List MP
Leveling seats
Ley de Lemas
Sectoral representation in the House of Representatives of the Philippines
General ticket, a term usually given to less or non proportional equivalents
Mixed-member proportional representation, a system similar to Party-list proportional representation.
References
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
Apportionment, or How to Round Seat Numbers
Glossary of Electoral Formulas
