The Coherent Majority Average for Juries' Evaluation Processes

I propose a method to synthesize the performance scores for artistic sports such as rhythmic gymnastics, figure skating, synchronized swimming, and diving by taking into account inter-judge variability, while maintaining all the reliable scores. This procedure is based on the assumption that the majority of the scores in each event are reliable and they relate well to those scores that are closest to them. The method consists of putting scores in order and considering clusters of m consecutive scores, where m is the number of judges making up the simple majority. For each cluster, the difference between the highest and the lowest score is calculated. In cases where the minimum difference is positive, the arithmetic mean of those scores that belong to clusters where the difference is minimal is computed. In cases where the minimum difference is zero (i.e. if the majority of judges unanimously assign the same score), then the set of the scores to consider within the mean is extended to those scores that are very near to those of the majority of the judges. A comparison between the actual evaluation procedures and the proposed model is provided.