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Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence

Authors: Ariel Schvartzman, S. Matthew Weinberg, Eitan Zlatin, and Albert Zuo

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)


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 binom{n}{2} matches. Prior work defines a tournament rule to be k-SNM-α if no set of ≤ k teams can fix the ≤ binom{k}{2} 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) ≥ (k-1)/(2k-1) for all k, and [Jon Schneider et al., 2017] 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 [Jon Schneider et al., 2017], 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).

Cite as

Ariel Schvartzman, S. Matthew Weinberg, Eitan Zlatin, and Albert Zuo. Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 3:1-3:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{schvartzman_et_al:LIPIcs.ITCS.2020.3,
  author =	{Schvartzman, Ariel and Weinberg, S. Matthew and Zlatin, Eitan and Zuo, Albert},
  title =	{{Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{3:1--3:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.3},
  URN =		{urn:nbn:de:0030-drops-116881},
  doi =		{10.4230/LIPIcs.ITCS.2020.3},
  annote =	{Keywords: Tournament design, Non-manipulability, Cover-consistence, Strategyproofness}
}
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