Justified representation: Difference between revisions

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>