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.ITCS.2020.3
URN: urn:nbn:de:0030-drops-116881
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11688/
Schvartzman, Ariel ;
Weinberg, S. Matthew ;
Zlatin, Eitan ;
Zuo, Albert
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 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).
BibTeX - Entry
@InProceedings{schvartzman_et_al:LIPIcs:2020:11688,
author = {Ariel Schvartzman and S. Matthew Weinberg and Eitan Zlatin and Albert Zuo},
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 = {Thomas Vidick},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/11688},
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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Keywords: |
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Tournament design, Non-manipulability, Cover-consistence, Strategyproofness |
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Collection: |
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11th Innovations in Theoretical Computer Science Conference (ITCS 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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06.01.2020 |
