Metric-Distortion Bounds Under Limited Information

In this work we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, consider mechanisms which perform sequence pairwise comparisons between candidates. We show that widely-popular deterministic mechanism employed most knockout phases yields \(\mathcal {O}(\log m)\) while eliciting only \(m-1\) out \(\varTheta (m^2)\) possible comparisons, where m represents number also provide matching lower bound on its distortion. contrast, any performs fewer than has unbounded Moreover, power incomplete rankings. Most notably, when every agent provides her k-top preferences an upper \(6 m/k + 1\) distortion, for \(k \in \{1, 2, \dots , m\}\), substantially improving over previous 12m/k recently established by Kempe [25, 26]. Finally, are concerned with sample complexity required to ensure near-optimal high probability. main random (m/\epsilon ^2)\) voters suffices guarantee \(3 \epsilon \) probability, sufficiently small \(\epsilon > 0\). This result based analyzing sensitivity introduced Gkatzelis, Halpern, and Shah [22].