During and at the end of Olympic games, we are always given the number of gold, silver and bronze medals won by each country and often the total number won as an indicator of the surmised winner. The groups that report the medal count in this manner indicate that they believe all medals are the same, regardless of the kind of medal involved. Perhaps one reason it is done this way is because there has not been a scientific way to assign appropriate weights to each type of medal. This paper explores use of the measurement theory, the Analytic Hierarchy Process (AHP), to quantify the values of gold, silver and bronze medals and use these values to compute the total value of the medals won by the leading countries in order to determine which country may be considered the winner of the 21st Winter Olympics held February 12–28, 2010, in Vancouver, Canada.
Top1. Introduction
Ideally, one should not think of countries winning the Olympics but of individuals winning medals. It is an interesting thought experiment in a global competitive world to ask the question anyway: How do we decide which country won the 21st Winter Olympics held February 12–28, 2010, in Vancouver, Canada? This issue has been explored by others in references (Bernard & Busse, 2000; Bialek, 2008; Forsyth, 2009; The World Fact Book).
We studied the same question before though not in as elaborate a way (Saaty, 2008) with regard to the 2008 Summer Olympics Games. In that paper, we only prioritized the medals and did not prioritize the games in which they were won. That we do here only incidentally because of the very subjective nature of what determines the importance of a game that varies from country to country and from competition to another. Because of this lack of general agreement on the importance of a game, perhaps the importance of a game should not be part of an objective evaluation of the overall value of the medals.
The International Olympic Committee (IOC) ranked Canada as No. 1 for the 21st Winter Olympics by virtue of its winning 14 gold medals, more than the number of gold medals won by any other country. The IOC had the following tie breaking procedure. If two or more countries were tied in gold medals, only then would the silver medals play a role in the ranking. If they were tied in both gold and silver medals, then bronze medals became important in breaking a tie in the ranking and, if all were equal, then something else has to be considered. Thus according to the IOC’s ranking procedure, usually the silver and bronze medals have no value in determining the winning country, even though these medals are awarded with much fanfare. To the dismay of the winners of silver and bronze medals, they are ignored in the final IOC ranking.
In contrast to the IOC ranking procedure, the media use the total number of medals won by a country to determine the winner of the medal count. But this ranking system too is an imperfect system in which a country winning ten bronze medals would be ranked ahead of a country whose athletes bring home nine gold medals.
It is widely agreed that neither of these two procedures is a good way to determine the country that is the overall winner of an Olympiad. Other procedures have been proposed and will be described here.
Gold medals themselves may not be equal in value due to the effort required and importance of the games in which they are won. Some gold medals are won for games like Ice Hockey that have a high marquee value and attract a large number of spectators paying premium prices. One method of scoring medals has been proposed for this kind of situation by dividing the games into two types of competition: high profile events to which higher numbers are assigned in the weighting of medals and low profile events which receive smaller numbers. The totals are obtained by weighting the priority assigned to the kind of medal by the game profile number and summed for all medals won by each country to determine the winning country.
By way of concluding this discussion, we note that there are other ways of evaluating the medals in the Olympics and the games in which they are won. Different countries place different emphases on the games depending on those in which they excel. For example, in the Winter Olympics, Canadians prefer winning at Ice Hockey, Norwegians prefer the Giant Slalom and Nordic Skiing events, the French prefer Figure Skating, while Americans prefer Freestyle Skiing and Short Track Skating. In the Summer Olympics, Africans prefer winning the Marathon and other long distance running events.