Revenue allocation in Formula One: a pairwise comparison approach

TL;DR

This paper introduces a pairwise comparison model for allocating Formula One prize money, emphasizing fairness and tunable inequality, and compares different weighting methods to ensure consistent team rankings.

Contribution

It presents a novel revenue allocation method based on pairwise comparisons that satisfies scale invariance and accounts for preference intensity, improving fairness in prize distribution.

Findings

Eigenvector method violates scale invariance in dataset

Row geometric mean method satisfies scale invariance

Allocation is unaffected by arbitrary race prize valuations

Abstract

A model is proposed to allocate Formula One World Championship prize money among the constructors. 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. We introduce an axiom called scale invariance, which requires the ranking of the 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 and takes the intensity of pairwise preferences into account, contrary to the standard Condorcet method. Our approach can be used to share revenues among groups when group members are ranked several times.