Optimising the decision threshold in a weighted voting system: The case of the IMF's Board of Governors
This provides a practical insight for international organizations like the IMF to improve fairness in decision-making by adjusting the threshold rather than reallocating weights.
The study analyzes how changing the decision threshold in the IMF's weighted voting system affects the alignment between voting weights (quotas) and actual voting power (Banzhaf indices). It finds that a threshold of 58% or 59% minimizes the discrepancy between quotas and voting power.
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%.