A Ranking for the Vancouver 2010 Winter Olympic Games Based on a Hyerarchcical Copeland Method

IntroductionMany studies have been carried out to evaluate the results of the Olympic Games.Some of them are based on how these events can bring benefits to the host cities [Glynn (2008); Cheng (2008); Xiaoduo and Jianxin (2008)] and others are interested in social studies [Bernstein (2000), Farrell (1989), Levine (1974) and Ball (1972)].Besides these studies, we can find researches in the environmental and health areas [Hadjichristodoulou, Mouchtouri and Vaitsi (2006); Allen et al (2006); Weiler, Layton and Hunt (1998); Streets et al (2007)], some about tourism industry and others that evaluate mathematics and economics aspects of the Games [Heazlewood (2006), Bernard and Busse (2004), Lins et al (2003) and Li et al (2008)].In this work we are interested in studying the results of the Winter Olympic Games, held in Vancouver in 2010, in order to propose a new ranking to the countries that took part in the Games.Traditionally, as discussed in Soares de Mello et al (2009), the International Olympic Committee (IOC) shows the results of both Summer and Winter Olympic Games in a table that rank the nations by the number of gold medals won.This is a Lexicographic method.Although this is not an official ranking, to the media and people in general, this is a summary of the participation of the nations, i.e., their production in the games.In the literature we can find other studies that suggest alternative rankings for the Olympic Games.As an alternative to rankings based on Lexicographic Methods, some studies as Lozano et al (2002) use Data Envelopment Analysis models with population and GNP as inputs and the number of gold, silver and bronze medals as outputs, to rank the nations.Others authors as Lins et al (2003) improved that model by adding a new constraint that defined as a constant the total number of medals (Zero Sum Gains DEA model (ZSG-DEA).As an extension of these studies some authors use others social and economics variables to build their models such as Churilov and Flitman (2006).These results found in Lozano et al (2002) were followed by the proposal of using GDP per capita and not only GDP as an input and creating weight restriction to the DMUs as done by Li et al (2008).In almost a sequence many researchers have been published new approaches to the same problem [Wu et al www.intechopen.com

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