Some rankings for the Athens Olympic Games using DEA models with a constant input

There is no official method to establish a final ranking for the Olympic games. The usual ranking is based on the Lexicographic Multicriteria Method, the main drawback of which is to overvalue gold medals. Furthermore it does not take in account that the various sports may be of different importance. This work proposes a ranking model to eliminate those drawbacks. First we use a modified cross evaluation DEA (Data Envelopment Analysis) model with weighted restrictions for each sport. The outputs are the number of gold, silver and bronze medals and the input is a unitary constant for all countries. After obtaining a rank for each and every sport we build a general ranking using a weighted sum. The weights are calculated taking in account the number of countries that participated in each sport. We use our model with the results of the Athens Olympic Games.