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). 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 allocated to each party in proportion to the number of votes the party receives. Voters may vote directly for the party, as in Israel, for candidates and that vote will pool to the party, as in Turkey and Brazil, or for a list of candidates, as in Hong Kong.
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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).
Many variations on seat allocation within party-list proportional representation exist. The three most common are:
List proportional representation may also be combined in various hybrids, e.g. using the additional member system.
List of main apportionment methods (most proportional to least proportional):
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.