Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e.g. elections to parliament), emphasizing proportional representation. 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, like in Israel, or they may vote for candidates and that vote will pool to the party, like in Turkey. The order in which the party's list candidates get elected may be pre-determined by some method internal to the party (a closed list system) or they may be determined by the voters at large (an open list system).
There are many variations on seat allocation within party-list proportional representation. The three most common are: the d'Hondt method used in Israel and Austria, among other places, the Sainte-Laguë method, used in many Scandinavian countries, New Zealand, and the German Federal State Bremen, and the largest remainder method. List PR may also be combined in various hybrids (e.g. using the Additional member system).
The Sainte-Laguë method and the LR-Hare method rank as the most proportional followed by LR-Droop; single transferable vote; modified Sainte-Laguë, d'Hondt and largest remainder Imperiali. 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.
