Modifying Olympics Medal Table via a Stochastic Multicriteria Acceptability Analysis

摘要

This paper addresses the issue of developing a widely accepted Olympics ranking scheme based upon the Olympic Game medal table published by the International Olympic Committee, since the existing lexicographic ranking and sum ranking systems are both criticized as biases. More specifically, the lexicographic ranking system is deemed as overvaluing gold medals, while the sum ranking system fails to reveal the real value of gold medals and fails to discriminate National Olympic Committees that won equal number of medals. To start, we employ a sophisticated mathematical method based upon the incenter of a convex cone to aggregate the lexicographic ranking system. Then, we consider the fact that the preferences between the lexicographic and the sum ranking systems may not be consistent across National Olympic Committees and develop a well-designed mathematical transformation to obtain interval assessment results under typical preference. The formulation of intervals is inspired by the observation that it is extremely difficult to achieve a group consensus on the exact value of weights with respect to each ranking system, since different weight elicitation methods may produce different weight schemes. Finally, regarding the derived decision making problem involving interval-valued data, this paper utilizes the Stochastic Multicriteria Acceptability Analysis to obtain a comprehensive ranking of all National Olympic Committees. Instead of determining precise weights, this work probes the weight space to guarantee each alternative getting the most preferred one. The proposed method is illustrated by presenting a new ranking of 12 National Olympic Committees participating in the London 2012 Summer Olympic Games.