@inproceedings{5b663519508a4db7a32b9dc0faebf17e,

title = "Approximately strategyproof tournament rules: On large manipulating sets and cover-consistence",

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) ≥ 2kk−−11 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).",

keywords = "Cover-consistence, Non-manipulability, Strategyproof-ness, Tournament design",

author = "Ariel Schvartzman and Weinberg, {S. Matthew} and Eitan Zlatin and Albert Zuo",

note = "Funding Information: Funding S. Matthew Weinberg: This work is supported by the National Science Foundation, under grant CNS-0435060, grant CCR-0325197 and grant EN-CS-0329609.; 11th Innovations in Theoretical Computer Science Conference, ITCS 2020 ; Conference date: 12-01-2020 Through 14-01-2020",

year = "2020",

month = jan,

doi = "10.4230/LIPIcs.ITCS.2020.3",

language = "English (US)",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

editor = "Thomas Vidick",

booktitle = "11th Innovations in Theoretical Computer Science Conference, ITCS 2020",

address = "Germany",

}