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Localized or local list systems of party-list proportional representation hold elections in small (local) electoral districts, while still maintaining proportional representation at the national level. Voting takes place in small district, but localized list rules differ from single-member districts in that each district, some or all of the seats are reserved for underrepresented parties, i.e. those that are represented less-than-proportionally in the legislature. These seats are then assigned to parties in districts in which they have received the most votes.
To ensure that each party receives a proportional share of seats relative to its share of the popular vote, the first step in ballot counting is to add up the votes going to each party either overall (at-large) or by multi-member constituencies. The results by party are then used to divide the number of seats proportionately among the different parties. The party list is composed of the candidates running in each district.
Once the number of seats won by a party is known, that party's candidates with the highest percentages of votes in their district are the ones elected, until all the seats corresponding to that party have been filled.
This system affords voters a way of voting for individual candidates. However, the system is designed to ensure proportionality, so the candidate with the highest popular vote in a single local constituency may not be elected (because his or her party-mates in other constituencies may have a higher voter share) and candidates with fewer votes can be elected (because they are the best candidates in their party's list). It is possible for more than one candidate to be elected in a single district, or for no candidate to be elected.
Localized lists are used in Italy for provincial elections and were used for Senatorial elections from 1948 to 2001. They are also used in a Mixed-member proportional representation variant in the Landtag of Baden-Württemberg (the first-place candidate in each district is guaranteed a seat, and each constituency has more seats than it has districts to ensure proportionality)