Randomness in Competitions

We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and compare the theoretical results with empirical data. Our model shows that single-elimination tournaments are efficient but unfair: the number of games is proportional to the number of teams N, but the probability that the weakest team wins decays only algebraically with N. In contrast, leagues, where every team plays every other team, are fair but inefficient: the top $\sqrt{N}$ of teams remain in contention for the championship, while the probability that the weakest team becomes champion is exponentially small. We also propose a gradual elimination schedule that consists of a preliminary round and a championship round. Initially, teams play a small number of preliminary games, and subsequently, a few teams qualify for the championship round. This algorithm is fair and efficient: the best team wins with a high probability and the number of games scales as $N^{9/5}$, whereas traditional leagues require N^3 games to fairly determine a champion.Comment: 10 pages, 8 figures, reviews arXiv:physics/0512144, arXiv:physics/0608007, arXiv:cond-mat/0607694, arXiv:physics/061221

Literary Competitions Organised by the Ministry of Culture and Arts in 1949–1950 in the Light of Archive Records

The subject of this paper are these literary competitions organized by Ministry of Culture and Arts in the late 1940s and early 1950s. Analysys of the materials from archivesenabled to tackle the issues: these competitions are one of the many aspect of stalinism offensive. Competitions encouraged writers for moving problems of socialist realism, they enforced artists for submission in accordance with Government of country.In article characterized six competitions. Most curious was “Third competition on mass song”, in which took part important writer Tadeusz Różewicz

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

Should We Redesign Forecasting Competitions?

The M3-Competition continues to improve the design of forecasting competitions: It examines more series than any previous competition, improves error analyses. and includes commercial forecasting programs as competitors. To judge where to go from here, I step back to look at the M-Competitions as a whole. I discuss the advantages of the M- Competitions in hopes that they will be retained, describe how to gain additional benefit from future competitions, and finally, describe a low-cost approach to competitions.forecasting, forecasting competitions,

The generalized sports competition problem

Consider a sports competition among various teams playing against each other in pairs (matches) according to a previously determined schedule. At some stage of the competition one may ask whether a particular team still has a (theoretical) chance to win the competition. The computational complexity of this question depends on the way scores are allocated according to the outcome of a match. For competitions with at most $3$ different outcomes of a match the complexity is already known. In practice there are many competitions in which more than $3$ outcomes are possible. We determine the complexity of the above problem for competitions with an arbitrary number of different outcomes. Our model also includes competitions that are asymmetric in the sense that away playing teams possibly receive other scores than home playing teams. \u

Enterprise Education Competitions: A Theoretically Flawed Intervention?

The demand for including enterprise in the education system, at all levels and for all pupils is now a global phenomenon. Within this context, the use of competitions and competitive learning activities is presented as a popular and effective vehicle for learning. The purpose of this chapter is to illustrate how a realist method of enquiry – which utilises theory as the unit of analysis – can shed new light on the assumed and unintended outcomes of enterprise education competitions. The case developed here is that there are inherent flaws in assuming that competitions will ‘work’ in the ways set out in policy and guidance. Some of the most prevalent stated outcomes – that competitions will motivate and reward young people, that they will enable the development of entrepreneurial skills, and that learners will be inspired by their peers – are challenged by theory from psychology and education. The issue at stake is that the expansion of enterprise education policy into primary and secondary education increases the likelihood that more learners will be sheep dipped in competitions, and competitive activities, without a clear recognition of the potential unintended effects. In this chapter, we employ a realist-informed approach to critically evaluate the theoretical basis that underpins the use of competitions and competitive learning activities in school-based enterprise education. We believe that our findings and subsequent recommendations will provide those who promote and practice the use of competitions with a richer, more sophisticated picture of the potential flaws within such activities.Peer reviewedFinal Published versio

Internal Promotion Competitions in Firms

[Excerpt] Using a sample of skilled workers from a cross section of establishments in four metropolitan areas of the United States, I present evidence suggesting that promotions are determined by relative worker performance. I then estimate a structural model of promotion tournaments (treating as endogenous promotions, worker performance, and the wage spread from promotion) that simultaneously accounts for worker and firm behavior and how the interaction of these behaviors gives rise to promotions. The results are consistent with the predictions of tournament theory that employers set wage spreads to induce optimal performance levels, and that workers are motivated by larger spreads