Anti-collusion indices and averages for the evaluation of performances and judges

In subjectively assessed artistic sports, judges sometimes collude. To avoid this, Federations adopt various strategies in their regulations. However, it is evident that these methods are often not sufficient to overcome collusions completely. The problem is especially difficult in cases where the judging panel consists of sub-commissions that deal with particular aspects of each performance and the scores of each sub-commission are summarized as mean values, which, in turn, are combined into a final mark. Therefore, the formulation of anti-collusion indices would be useful to assess judges and take account of such scores, rejecting the less reliable ones. An anti-collusion index and related average, recently introduced, can be applied in fields other than sports. This article presents some useful considerations for the application of such instruments to the field of sport.