Perfect representation: Difference between revisions
Added a clarification of the definition and a possible criticism.
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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''.
In other words, in a multi-winner approval-voting election, for a given set of ballots cast, if there is a possible election result where candidates could each be assigned an equal number of voters where each voter has approved their assigned candidate and no voter is left without a candidate, then for a method to pass the perfect representation criterion, such a result must be the actual result.
Every winner set that provides perfect representation also provides [[Justified representation | Proportional Justified Representation ]] <ref> https://www.researchgate.net/publication/308022665_Some_Notes_on_Justified_Representation </ref>. In contrast, [[Justified representation | Extended Justified Representation ]] may rule out all winner sets that provide perfect representation. <ref>https://arxiv.org/abs/1407.8269</ref>▼
Consider the following election with two winners, where A, B, C and D are candidates, and the number of voters approving each candidate are as follows:
100 voters: A, B, C
100 voters: A, B, D
1 voter: C
1 voter: D
A method passing the perfect representation criterion must elect candidates C and D despite near universal support for candidates A and B. This could be seen as an argument against perfect representation as a useful criterion.
▲Every winner set that provides perfect representation also provides [[Justified representation | Proportional Justified Representation
[[Category:Types of representation]]
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