Invariably Suboptimal - An attempt to improve the voting rules of Treaties of Nice and Lisbon

TL;DR

This paper examines whether adjusting quotas in EU voting systems under Nice and Lisbon treaties can better align voting power with the square root law, but finds they remain significantly suboptimal even with optimal quotas.

Contribution

It analyzes the potential for quota adjustments to improve the EU voting systems' adherence to the square root law, revealing persistent deviations.

Findings

Even with optimal quotas, systems deviate from the ideal distribution.

Current systems are significantly suboptimal.

Quota adjustments alone cannot fully correct the deviation.

Abstract

We investigate the voting rules in the Council of the European Union. It is known that the current system, according to the Treaty of Nice, and the voting system proposed in the Lisbon treaty both strongly deviate from the square root law by Penrose. This is known to be the ideal voting rule under certain assumptions. In 2004 Slomczynski and Zyczkowski designed a voting system, now known as the Jagiellonian Compromise. It satisfies the square root law with very high accuracy. Each member state in this system obtains a voting weight proportional to the square root of the population. Additionally the quota is fixed in such a way that the voting power of each country is also proportional to the square root of the population. In this paper we investigate to which extent a change of the quota in the Treaty of Nice and the Treaty of Lisbon may bring the voting power closer to the ideal square root distribution. Our computations show that even with optimal quota both systems are way off the ideal power distribution.