Optimising the decision threshold in a weighted voting system: The case of the IMF's Board of Governors

In a weighted majority voting game, the players' weights are determined based on the decision-maker'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 the quotas and voting powers is minimised if the decision threshold is 58% or 60%.