Measuring Olympics Achievements via Stochastic Multicriteria Acceptability Analysis

Abstract

The lexicographic and sum ranking systems are two widely-used instruments to measure Olympics achievements. However, the lexicographic ranking system is typically criticized as overvaluing gold medals, while the sum ranking system is particularly criticized as devaluing gold medals and incapable of discriminating National Olympic Committees (NOCs) with identical total number of medals. Meanwhile, there are controversial scoring schemes to assign points to gold, silver and bronze medals. In addition, measuring Olympics achievements in either the Winter or the Summer Olympic Games is unfair to the NOCs who perform significantly different at both Olympics. These issues are addressed in this study by developing a sophisticated mathematical transformation without the exact weights determination to aggregate the lexicographic ranking system in an interval metric. An interval decision matrix is therefore formulated under the simultaneous consideration of the Winter and the Summer Olympics. A Stochastic multicriteria acceptability analysis method is finally utilized to provide a robust measurement with sufficient discriminating power. Spearman’s rank correlation coefficients are calculated to indicate the merits of our method. The proposed method and relative analysis are demonstrated using the date drawn from the Sochi 2014 Winter Olympics and the Rio 2016 Summer Olympics.