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

Author(s): Schvartzman, Ariel; Weinberg, S Matthew; Zlatin, Eitan; Zuo, Albert

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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).
Publication Date: 2020
Citation: Schvartzman, Ariel, 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): 3:1-3:25. doi:10.4230/LIPIcs.ITCS.2020.3
DOI: 10.4230/LIPIcs.ITCS.2020.3
ISSN: 1868-8969
Pages: 3:1 - 3:25
Type of Material: Conference Article
Journal/Proceeding Title: 11th Innovations in Theoretical Computer Science Conference (ITCS)
Version: Final published version. This is an open access article.

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