The Treaty of Lisbon, the latest treaty governing law-making in the European
Union (EU), went fully into effect in 2014.
Since then, the United Kingdom (UK) has petitioned to leave the European
Union, based on a 2016 referendum in the UK (that exit is colloquially
referred to as “Brexit”).
We use two power indices from game theory literature, the normalized
Banzhaf index and the Shapley-Shubik index, to give insight into current
voting power and then to understand redistribution of power when the UK
Analyzing voting power in the Council of Ministers, we leverage generating
functions to help with computation. We assess how equitably power is
distributed with and without the UK by tying our power indices to the Gini
index, originally developed to measure how equitably income is distributed.
We show that the system displays only slightly more equitable distribution
of power despite the departure of such a critical member state.