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[[Voting theorists]] frequently debate which systems can be called "proportional representation", and consider the levels of proportionality achieved by various systems from "low proportional" to "high proportional". The concept of "proportional representation" can be quantified as a measure of the outcome of an election where there are multiple parties and multiple members are elected, and the representatives are demographically similar to the voting population. It is one of many [[types of representation]] in a [[W:Representative government|representative government]].
OneThe [[Partisan system|partisan]] definition for "proportional representation" is that the candidates are partitioned into disjoint parties, and each voter approves all candidates in a single party. For example,<ref>{{Cite book|last=Piotr Faliszewski, Piotr Skowron, Arkadii Slinko, Nimrod Talmon|chapter-url=https://books.google.com/books?id=0qY8DwAAQBAJ&q=multiwinner++voting+a+new+challenge&pg=PA27|title=Trends in Computational Social Choice|date=2017-10-26|publisher=Lulu.com|isbn=978-1-326-91209-3|editor-last=Endriss|editor-first=Ulle|language=en|chapter=Multiwinner Voting: A New Challenge for Social Choice Theory}}</ref> suppose we need to elect a committee of size 10. Suppose that exactly 50% of the voters approve all candidates in party A, exactly 30% approve all candidates in party B, and exactly 20% approve all candidates in party C. Then, proportional representation requires that the committee contains exactly 5 candidates from party A, exactly 3 candidates from party B, and exactly 2 candidates from party C. If the fractions are not exact, then some rounding method should be used, and this can be done by various [[Apportionment (politics)|apportionment methods]]. However, in approval voting there is a different challenge: the voters' approval sets might not be disjoint. For example, a voter might approve one candidate from party A, two candidates from B, and five from C. This raises the question of how proportional representation should be defined. PeopleThe definingconcepts of "[[justified representation]]" areone tryingapproach to dosolving thatthis problem.
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