Voting in the European Union: The square root system of Penrose and a critical point

TL;DR

This paper analyzes voting systems in the EU, proposing a square root law for weights, identifying a critical quota point at 62%, and advocating for a more representative and transparent decision-making process.

Contribution

It introduces a voting weight scheme based on the Penrose law and identifies a critical quota value to improve fairness and transparency in EU voting systems.

Findings

The Penrose square root law provides a fair weighting scheme.

A critical quota of 62% optimizes system effectiveness.

The proposed system is simple, transparent, and unbiased.

Abstract

The notion of the voting power is illustrated by examples of the systems of voting in the European Council according to the Treaty of Nice and the more recent proposition of the European Convent. We show that both systems are not representative, in a sense that citizens of different countries have not the same influence for the decision taken by the Council. We present a compromise solution based on the law of Penrose, which states that the weights for each country should be proportional to the square root of its population. Analysing the behaviour of the voting power as a function of the quota we discover a critical point, which allows us to propose the value of the quota to be 62%. The system proposed is simple (only one criterion), representative, transparent, effective and objective: it is based on a statistical approach and does not favour nor handicap any European country.