eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-01-06
3:1
3:25
10.4230/LIPIcs.ITCS.2020.3
article
Approximately Strategyproof Tournament Rules: On Large Manipulating Sets and Cover-Consistence
Schvartzman, Ariel
1
Weinberg, S. Matthew
1
Zlatin, Eitan
1
Zuo, Albert
2
Department of Computer Science, Princeton University, NJ, USA
Computer Science Department, Stanford University, CA, USA
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).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol151-itcs2020/LIPIcs.ITCS.2020.3/LIPIcs.ITCS.2020.3.pdf
Tournament design
Non-manipulability
Cover-consistence
Strategyproofness