Justified representation: Difference between revisions
Added a definition of Full Justified Representation.
(→Extended Justified Representation: , →Proportional Justified Representation: corrections) |
Marylander (talk | contribs) (Added a definition of Full Justified Representation.) |
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Given a matrix of approval votes A where each column represents a candidate c ∈ C and each row represents a voter v ∈ V. A winner set of candidates, W, of size |W| = k provides '''proportional''' '''justified representation''' for (A, k) if there does not exist a positive integer <math> \ell</math> and a subset of voters N∗ ⊆ N with |N∗| ≥ <math> \ell</math>n/k such that there are at least <math> \ell</math> candidates they all approve and ''fewer than <math> \ell</math> winners any of them approve'' (emphasis to distinguish from extended justified representation).
== Full Justified Representation ==
In approval elections, given a matrix of approval votes A where each column represents a candidate c ∈ C and each row represents a voter v ∈ V. A winner set of candidates, W, of size |W| = k provides '''full justified representation''' for (A, k) if there does not exist a subset of voters N∗ ⊆ N with |N∗| ≥ <math> \ell</math>n/k for a positive integer <math> \ell</math> such that there is a subset T ⊆ C of no more than <math> \ell</math> candidates such that for some '''β''' ≤ <math> \ell</math>, each voter in N∗ approves at least '''β''' candidates in T and they all approve fewer than '''β'''<math> \beta</math> winners.<ref name=":0">https://arxiv.org/abs/1911.11747</ref>
In score elections, "each voter in N∗ approves at least '''β''' candidates in T" is replaced by "each voter in N∗ gives the candidates in T a total of at least '''β''' points (with scores normalized to [0,1])." <ref name=":0" />
Full Justified Representation implies Extended Justified Representation since the requirements are the same for '''β''' = <math> \ell</math>. <ref name=":0" />
==Compliant systems==
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