Party-list proportional representation systems are a family of voting systems emphasizing proportional representation (PR) 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 additional member systems.
In these systems, parties make lists of candidates to be elected, and seats get distributed to each party in proportion to the number of votes the party receives. Voters may vote directly for the party, as in Albania, Argentina, Turkey, and Israel; or for candidates whose vote total will pool to the party, as in Finland, Brazil and the Netherlands; or for a list of candidates, as in Hong Kong. Voters in Luxembourg's multi-seat constituencies can choose between voting for a complete list of candidates of a single party ("list vote") or voting for individual candidates from one or several lists ("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).
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 (or Jefferson's 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 (or Webster's 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:
- Macanese "d'Hondt method" (greatly favors small parties)
- Webster/Sainte-Laguë method, LR-Hare (slightly favors very small parties when unmodified, if there is no election threshold)
- LR-Droop (very slightly favors larger parties)
- D'Hondt method (slightly favors larger parties)
- Huntington-Hill method (greatly 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.
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.