13,387 research outputs found

    Motivation and Performance, Blog 12

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    Student blog posts from the Great VCU Bike Race Book

    Optimal Data Collection For Informative Rankings Expose Well-Connected Graphs

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    Given a graph where vertices represent alternatives and arcs represent pairwise comparison data, the statistical ranking problem is to find a potential function, defined on the vertices, such that the gradient of the potential function agrees with the pairwise comparisons. Our goal in this paper is to develop a method for collecting data for which the least squares estimator for the ranking problem has maximal Fisher information. Our approach, based on experimental design, is to view data collection as a bi-level optimization problem where the inner problem is the ranking problem and the outer problem is to identify data which maximizes the informativeness of the ranking. Under certain assumptions, the data collection problem decouples, reducing to a problem of finding multigraphs with large algebraic connectivity. This reduction of the data collection problem to graph-theoretic questions is one of the primary contributions of this work. As an application, we study the Yahoo! Movie user rating dataset and demonstrate that the addition of a small number of well-chosen pairwise comparisons can significantly increase the Fisher informativeness of the ranking. As another application, we study the 2011-12 NCAA football schedule and propose schedules with the same number of games which are significantly more informative. Using spectral clustering methods to identify highly-connected communities within the division, we argue that the NCAA could improve its notoriously poor rankings by simply scheduling more out-of-conference games.Comment: 31 pages, 10 figures, 3 table

    The global event? The media, football and the FIFA World Cup

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    An examination of the FIFA World Cup as media mega event and the role played by television in this process

    Who Can Win a Single-Elimination Tournament?

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    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 nn player tournament generated by the Condorcet Random Model will be an SE winner even when the noise is as small as possible, p=Θ(lnn/n)p=\Theta(\ln n/n); prior work only had such results for pΩ(lnn/n)p\geq \Omega(\sqrt{\ln n/n}). 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

    The Menstrual Cycle and Performance Feedback Alter Gender Differences in Competitive Choices

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    Economic experiments have shown that in mixed gender groups women are more reluctant than men to choose tournaments when given the choice between piece rate and winner-take-all tournament style compensation. These gender difference experiments have all relied on a framework where subjects were not informed of their abilities relative to potential competitors. We replicate these findings with math and word tasks, and then show that feedback about relative performance moves high ability females towards more competitive compensation schemes, moves low ability men towards less competitive schemes such as piece rate and group pay, and removes the average gender difference in compensation choices. We also examine between and within-subjects differences in choices for females across the menstrual cycle. We find women's relative reluctance to choose tournaments comes mostly from women in the low hormone phase of their menstrual cycle. Women in the high hormone phase are substantially more willing to compete than women in the low phase, though still somewhat less willing to compete than men. There are no significant differences between the choices of any of these groups after they receive relative performance feedback.competition, tournaments, gender, hormones, menstruation, feedback

    The "No Justice in the Universe" phenomenon: why honesty of effort may not be rewarded in tournaments

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    In 2000 Allen Schwenk, using a well-known mathematical model of matchplay tournaments in which the probability of one player beating another in a single match is fixed for each pair of players, showed that the classical single-elimination, seeded format can be "unfair" in the sense that situations can arise where an indisputibly better (and thus higher seeded) player may have a smaller probability of winning the tournament than a worse one. This in turn implies that, if the players are able to influence their seeding in some preliminary competition, situations can arise where it is in a player's interest to behave "dishonestly", by deliberately trying to lose a match. This motivated us to ask whether it is possible for a tournament to be both honest, meaning that it is impossible for a situation to arise where a rational player throws a match, and "symmetric" - meaning basically that the rules treat everyone the same - yet unfair, in the sense that an objectively better player has a smaller probability of winning than a worse one. After rigorously defining our terms, our main result is that such tournaments exist and we construct explicit examples for any number n >= 3 of players. For n=3, we show (Theorem 3.6) that the collection of win-probability vectors for such tournaments form a 5-vertex convex polygon in R^3, minus some boundary points. We conjecture a similar result for any n >= 4 and prove some partial results towards it.Comment: 26 pages, 2 figure

    Manipulating Tournaments in Cup and Round Robin Competitions

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    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
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