Presents a new rule for proportional committee selection from sampled approvals achieving justified representation with sample complexity Õ(k^4 log(m/δ)), separating it from Chamberlin-Courant which requires Θ(k^5 log(m/δ)), with Ω(k^3) lower bound.
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In the dueling bandit setting, the (1+1) EA selects the Condorcet winner with only constant probability when its advantage is Ω(1/n), while a Max-Min Ant System EDA selects it with probability 1-Θ(p), and repeated duels improve the EA's performance.
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Proportionality from Sampled Approvals
Presents a new rule for proportional committee selection from sampled approvals achieving justified representation with sample complexity Õ(k^4 log(m/δ)), separating it from Chamberlin-Courant which requires Θ(k^5 log(m/δ)), with Ω(k^3) lower bound.
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Analysis of Search Heuristics in the Multi-Armed Bandit Setting
In the dueling bandit setting, the (1+1) EA selects the Condorcet winner with only constant probability when its advantage is Ω(1/n), while a Max-Min Ant System EDA selects it with probability 1-Θ(p), and repeated duels improve the EA's performance.