A revenue allocation scheme based on pairwise comparisons

A model of sharing revenues among groups when group members are ranked several times is presented. The methodology is based on pairwise comparison matrices, allows for the use of any weighting method, and makes possible to tune the level of inequality. Our proposal is demonstrated on the example of Formula One prize money allocation among the constructors. We introduce an axiom called scale invariance, which requires the ranking of teams to be independent of the parameter controlling inequality. The eigenvector method is revealed to violate this condition in our dataset, while the row geometric mean method always satisfies it. The revenue allocation is not influenced by the arbitrary valuation given to the race prizes in the official points scoring system of Formula One.