Perfect representation

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  A winner set W provides perfect representation for a group of n voters and a total seat size k if n = ks for some positive integer s and the voters can be split into k pairwise disjoint groups N1, . . . , Nk of size s each in such a way that there is a one-to-one mapping μ : W → {N1, . . . , Nk} such that for each candidate a ∈ W all voters in μ(a) approve a.

Every winner set that provides perfect representation also provides Proportional Justified Representation [1]. In contrast, Extended Justified Representation may rule out all winner sets that provide perfect representation. [2]