Ranking Countries by Medal Priorities Won in the 2014 Sochi Winter Olympics

Abstract

The total number of gold, silver and bronze medals won by each country in the Olympics is often regarded as an indicator of that country’s winning rank. However, the values of the medals differ according to the order in which they are won in each event. One reason why it is done this way is that there has not been a scientific way to assign an appropriate priority for each type of medal which so far has been treated as an intangible. Sometimes people have used the ordinal numbers 3, 2, 1 to rank the medals, but adding ordinals has no arithmetic legitimacy because ordinals cannot be added or multiplied. Here we use the mathematical theory, the analytic hierarchy process, for the measurement of intangibles to quantify the priorities of different games according to environmental and people factors and also quantify the priorities of gold, silver and bronze medals, and then use these priorities to compute the total scores of all three types of medals won by each country in order to determine the ranking of the countries which won medals in the 22nd Winter Olympics held February 07–23, 2014, in Sochi, Russia.