236 research outputs found
Manipulating Tournaments in Cup and Round Robin Competitions
In sports competitions, teams can manipulate the result by, for instance,
throwing games. We show that we can decide how to manipulate round robin and
cup competitions, two of the most popular types of sporting competitions in
polynomial time. In addition, we show that finding the minimal number of games
that need to be thrown to manipulate the result can also be determined in
polynomial time. Finally, we show that there are several different variations
of standard cup competitions where manipulation remains polynomial.Comment: Proceedings of Algorithmic Decision Theory, First International
Conference, ADT 2009, Venice, Italy, October 20-23, 200
Condorcet-Consistent and Approximately Strategyproof Tournament Rules
We consider the manipulability of tournament rules for round-robin
tournaments of competitors. Specifically, competitors are competing for
a prize, and a tournament rule maps the result of all
pairwise matches (called a tournament, ) to a distribution over winners.
Rule is Condorcet-consistent if whenever wins all of her matches,
selects with probability .
We consider strategic manipulation of tournaments where player might
throw their match to player in order to increase the likelihood that one of
them wins the tournament. Regardless of the reason why chooses to do this,
the potential for manipulation exists as long as increases by
more than decreases. Unfortunately, it is known that every
Condorcet-consistent rule is manipulable (Altman and Kleinberg). In this work,
we address the question of how manipulable Condorcet-consistent rules must
necessarily be - by trying to minimize the difference between the increase in
and decrease in for any potential manipulating
pair.
We show that every Condorcet-consistent rule is in fact -manipulable,
and that selecting a winner according to a random single elimination bracket is
not -manipulable for any . We also show that many
previously studied tournament formats are all -manipulable, and the
popular class of Copeland rules (any rule that selects a player with the most
wins) are all in fact -manipulable, the worst possible. Finally, we consider
extensions to match-fixing among sets of more than two players.Comment: 20 page
A paradox of tournament seeding
A mathematical model of seeding is analysed for sports tournaments where the
qualification is based on round-robin contests. The conditions of
strategyproofness are found to be quite restrictive: if each team takes its own
coefficient (a measure of its past performance), only one or all of them should
qualify from every round-robin contest. Thus the standard draw system creates
incentives for tanking in order to be assigned to a stronger pot as each team
prefers to qualify with teams having a lower coefficient. Major soccer
competitions are shown to suffer from this weakness. Strategyproofness can be
guaranteed by giving to each team the highest coefficient of all teams that are
ranked lower in its round-robin contest. The proposal is illustrated by the
2020/21 UEFA Champions League.Comment: 23 pages, 3 table
Who Can Win a Single-Elimination Tournament?
A single-elimination (SE) tournament is a popular way to select a winner in
both sports competitions and in elections. A natural and well-studied question
is the tournament fixing problem (TFP): given the set of all pairwise match
outcomes, can a tournament organizer rig an SE tournament by adjusting the
initial seeding so that their favorite player wins? We prove new sufficient
conditions on the pairwise match outcome information and the favorite player,
under which there is guaranteed to be a seeding where the player wins the
tournament. Our results greatly generalize previous results. We also
investigate the relationship between the set of players that can win an SE
tournament under some seeding (so called SE winners) and other traditional
tournament solutions. In addition, we generalize and strengthen prior work on
probabilistic models for generating tournaments. For instance, we show that
\emph{every} player in an player tournament generated by the Condorcet
Random Model will be an SE winner even when the noise is as small as possible,
; prior work only had such results for . We also establish new results for significantly more
general generative models.Comment: A preliminary version appeared in Proceedings of the 30th AAAI
Conference on Artificial Intelligence (AAAI), 201
Can strategizing in round-robin subtournaments be avoided?
This paper develops a mathematical model of strategic manipulation in complex sports competition formats such as the soccer world cup or the Olympic games. Strategic manipulation refers here to the possibility that a team may lose a match on purpose in order to increase its prospects of winning the competition. In particular, the paper looks at round-robin tournaments where both first- and second-ranked players proceed to the next round. This standard format used in many sports gives rise to the possibility of strategic manipulation, as exhibited recently in the 2012 Olympic games. An impossibility theorem is proved which demonstrates that under a number of reasonable side-constraints, strategy-proofness is impossible to obtain
Approximately Strategyproof Tournament Rules in the Probabilistic Setting
We consider the manipulability of tournament rules which map the results of
pairwise matches and select a winner. Prior work designs simple
tournament rules such that no pair of teams can manipulate the outcome of their
match to improve their probability of winning by more than , and this is
the best possible among any Condorcet-consistent tournament rule (which selects
an undefeated team whenever one exists) [Schneider et al., 2017, Schvartzman et
al., 2020]. These lower bounds require the manipulators to know precisely the
outcome of all future matches.
We take a beyond worst-case view and instead consider tournaments which are
"close to uniform": the outcome of all matches are independent, and no team is
believed to win any match with probability exceeding . We show
that Randomized Single Elimination Bracket [Schneider et al., 2017] and a new
tournament rule we term Randomized Death Match have the property that no pair
of teams can manipulate the outcome of their match to improve their probability
of winning by more than , for all
, and this is the best possible among any Condorcet-consistent
tournament rule.
Our main technical contribution is a recursive framework to analyze the
manipulability of certain forms of tournament rules. In addition to our main
results, this view helps streamline previous analysis of Randomized Single
Elimination Bracket, and may be of independent interest.Comment: 18 pages, 0 figures, ITCS 202
European qualifiers to the 2018 FIFA World Cup can be manipulated
Tournament organizers supposedly design rules such that a team cannot be better off by exerting a lower effort.
It is shown that the European qualifiers to the 2018 FIFA World Cup are not strategy-proof in this sense: a team might be eliminated if it wins its last match in the group stage, while it advances to play-offs by playing a draw, provided that all other results remain the same. The scenario could have happened in October 2017, after four-fifth of all matches have already been played.
We present a theoretical model and identify nine incentive incompatible qualifiers to recent UEFA European Championships and FIFA World Cups.
A mechanism is suggested in order to seal the way of manipulation in similar group-based qualification systems
the Robin Hood ballads and the appropriation of aristocratic and clerical justice
Robin Hood and the Monk, Robin Hood and the Potter, A Gest of Robyn Hode, and Robin Hood and the Guy of Guisborne. I argue the Robin Hood texts critique common medieval conceptions of justice by creating new ones through the appropriation of recognizable literary vocabularies related to the first and second estates. Instead of presenting a fully developed portrait of identity, the Robin Hood corpus displays ambivalence, which is further evidence that identity for the yeoman, and its operating system of justice, is still being worked out in the text itself. The yeoman is celebrated due to his ability to manipulate and appropriate cultural practices in order to gain wealth and social prestige. This parallels a broad historical trend of middle strata economic and social mobility in the late Middle Ages and the Early Modern period.Includes bibliographical references (pages 217-225)
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