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Concept
Justified representation
Summary
Justified representation (JR) is a criterion for evaluating the fairness of electoral systems in multiwinner voting, particularly in multiwinner approval voting. It can be seen as an adaptation of the proportional representation criterion to approval voting.
One 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, 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 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.
Several definitions have been suggested in the literature. To describe the definitions, we use the following notation and terminology:
k is the number of seats (i.e., the required committee size).
n is the number of voters (in the above example, k=10 and n=100).
n/k is the Hare quota - the minimum number of supporters that justifies a single seat. For simplicity, we assume that k divides n, so n/k is an integer.
For every integer L ≥ 1, a group of voters is called:
L-large -- if it contains at least L*n/k voters (at least L quotas);
L-cohesive -- if it is L-large, and in addition, there are some L candidates that all voters in the group approve.
L-unanimous -- if it is L-large, and in addition, all group members approve exactly the same candidates.
Official source
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