eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-09-17
13:1
13:20
10.4230/LIPIcs.APPROX-RANDOM.2019.13
article
Single-Elimination Brackets Fail to Approximate Copeland Winner
Hulett, Reyna
1
https://orcid.org/0000-0001-8877-1659
Department of Computer Science, Stanford University, CA, USA
Single-elimination (SE) brackets appear commonly in both sports tournaments and the voting theory literature. In certain tournament models, they have been shown to select the unambiguously-strongest competitor with optimum probability. By contrast, we reevaluate SE brackets through the lens of approximation, where the goal is to select a winner who would beat the most other competitors in a round robin (i.e., maximize the Copeland score), and find them lacking. Our primary result establishes the approximation ratio of a randomly-seeded SE bracket is 2^{- Theta(sqrt{log n})}; this is underwhelming considering a 1/2 ratio is achieved by choosing a winner uniformly at random. We also establish that a generalized version of the SE bracket performs nearly as poorly, with an approximation ratio of 2^{- Omega(sqrt[4]{log n})}, addressing a decade-old open question in the voting tree literature.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol145-approx-random2019/LIPIcs.APPROX-RANDOM.2019.13/LIPIcs.APPROX-RANDOM.2019.13.pdf
Voting theory
mechanism design
query complexity
approximation