License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.13
URN: urn:nbn:de:0030-drops-112283
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11228/
Go to the corresponding LIPIcs Volume Portal

Hulett, Reyna

Single-Elimination Brackets Fail to Approximate Copeland Winner

pdf-format:
LIPIcs-APPROX-RANDOM-2019-13.pdf (0.5 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{hulett:LIPIcs:2019:11228,
  author =	{Reyna Hulett},
  title =	{{Single-Elimination Brackets Fail to Approximate Copeland Winner}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11228},
  URN =		{urn:nbn:de:0030-drops-112283},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.13},
  annote =	{Keywords: Voting theory, mechanism design, query complexity, approximation}
}

Keywords: Voting theory, mechanism design, query complexity, approximation
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
Issue Date: 2019
Date of publication: 17.09.2019

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI