Approximately strategyproof tournament rules: On large manipulating sets and cover-consistence

Ariel Schvartzman, S. Matthew Weinberg, Eitan Zlatin, Albert Zuo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the manipulability of tournament rules, in which n teams play a round robin tournament and a winner is (possibly randomly) selected based on the outcome of all n2 matches. Prior work defines a tournament rule to be k-SNM-α if no set of ≤ k teams can fix the ≤ k2 matches among them to increase their probability of winning by > α and asks: for each k, what is the minimum α(k) such that a Condorcet-consistent (i.e. always selects a Condorcet winner when one exists) k-SNM-α(k) tournament rule exists? A simple example witnesses that α(k) ≥ 2kk11 for all k, and [22] conjectures that this is tight (and prove it is tight for k = 2). Our first result refutes this conjecture: there exists a sufficiently large k such that no Condorcet-consistent tournament rule is k-SNM-1/2. Our second result leverages similar machinery to design a new tournament rule which is k-SNM-2/3 for all k (and this is the first tournament rule which is k-SNM-(< 1) for all k). Our final result extends prior work, which proves that single-elimination bracket with random seeding is 2-SNM-1/3 [22], in a different direction by seeking a stronger notion of fairness than Condorcet-consistence. We design a new tournament rule, which we call Randomized-King-of-the-Hill, which is 2-SNM-1/3 and cover-consistent (the winner is an uncovered team with probability 1).

Original languageEnglish (US)
Title of host publication11th Innovations in Theoretical Computer Science Conference, ITCS 2020
EditorsThomas Vidick
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771344
DOIs
StatePublished - Jan 2020
Event11th Innovations in Theoretical Computer Science Conference, ITCS 2020 - Seattle, United States
Duration: Jan 12 2020Jan 14 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume151
ISSN (Print)1868-8969

Conference

Conference11th Innovations in Theoretical Computer Science Conference, ITCS 2020
CountryUnited States
CitySeattle
Period1/12/201/14/20

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • Cover-consistence
  • Non-manipulability
  • Strategyproof-ness
  • Tournament design

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  • Cite this

    Schvartzman, A., Weinberg, S. M., Zlatin, E., & Zuo, A. (2020). Approximately strategyproof tournament rules: On large manipulating sets and cover-consistence. In T. Vidick (Ed.), 11th Innovations in Theoretical Computer Science Conference, ITCS 2020 [3] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 151). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ITCS.2020.3