Dóra Gréta Petróczy

Dóra Gréta Petróczy

In a weighted majority voting game, the players' weights are determined based on the constitutional planner's intentions. The weights are challenging to change in numerous cases, as they represent some desired disparity. However, the voting weights and the actual voting power do not necessarily coincide. Changing a decision threshold would offer some remedy. The International Monetary Fund (IMF) is one of the most important international organisations that uses a weighted voting system to make decisions. The voting weights in its Board of Governors depend on the quotas of the 191 member countries, which reflect their economic strengths to some extent. We analyse the connection between the decision threshold and the a priori voting power of the countries by calculating the Banzhaf indices for each threshold between 50% and 87%. The difference between quotas and voting powers is minimised if the decision threshold is 58% or 59%.

Dóra Gréta Petróczy, László Csató

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.