Impact of Brexit on voting power in Council of the European Union

Abstract The United Kingdom has left the European Union on 31 January 2020. Discussions that preceded such a move were conducted in three dimensions: they pertained a post-Brexit relationship between the UK and EU, future conduct within the UK and the one within the EU. Whilst public discourse has been dominated by the first two, this paper approaches the third one – on how Brexit has affected relationships between remaining 27 EU Member States. Stemming from the calculation of Banzhaf indices, it assesses the impact of Brexit on the voting power of remaining Member States in the Council of the EU – arguably the most important body within the EU institutional architecture – and identifies which countries are going to record the most significant gains and losses in this respect.


Introduction
On 29 March 2017, the Government of the United Kingdom (UK) invoked the Article 50 of the Treaty on European Union (TEU) to withdraw the country from the European Union (EU). This has formally kicked off the negotiations between the UK and the EU over the arrangement of withdrawal. In March 2017, very few people would have predicted almost three long years of political turmoil, which have resulted in the official departure of the UK from the EU on 31 January 2020.
Prior to this date, long and complicated negotiations were conducted on the subject of the post-Brexit relationship between the UK and the EU, and future conduct within the UK and relationships between the EU Member States. As far as public discourse has been dominated by the first and second dimension, this paper approaches the third one -on how Brexit may affect the relationships between the Member States of the Union.
The paper analyses the impact of the UK leaving the EU on the voting power of the remaining Member States in the Council of the EU, one of the two main decision-making bodies of the Union under ordinary legislative procedure which covers the vast majority of areas of EU action. It assesses how voting power in this institution has been redistributed: or in other words, which Member States have recorded the most significant gains, and most remarkable losses.
It is structured as follows: the first chapter explains the relevance of the topic and describes the decision-making procedure within the Council. The second chapter outlines the methodological framework of papers, while the third one presents the results of analysis. The last part of the paper discusses these results and impact of Brexit on the decision-making of the Council of the EU.

Council of the EU
The Council of the EU is a part of Union's institutional framework established in 1958 in order to provide a platform for the exchange of positions of Member States' representatives on Union's policy-making. Today, it is one of the two most important and most powerful institutions of the Union, as the adoption of legislative proposals within ordinary *Corresponding author: Jakub Gábor, Faculty of Social and Economic Sciences, Comenius University in Bratislava, E-mail: gabor.jakub@gmail.com legislative process of the EU (covering the vast majority of areas of Union action) requires its joint adoption by two equal EU legislators -the Council of the EU and European Parliament.
The reason why, out of these two institutions, the Council deserves special attention is that while within the Parliament, all actors -Members of Parliament -have the same voting weight, so the calculations of voting power are rather simple and straightforward, within the Council, Members States differ in terms of their voting weight (and consequently voting power) due to the specific setting of voting procedure. The specifics of decision-making on the soil of the Council of the EU are described further below.
Since the 1950s, the rules for the functioning of Council have been laid down in Union's primary law. From Roma to Lisbon, every modification of the Union's legal ground has introduced different rules of conduct in the Council of the EU -including different rules of voting procedure in this institution.
Depending on the agenda, the Council of the EU adopts decisions by (1) simple majority, (2) qualified majority or (3) consensus. This paper will approach the procedure of qualified majority voting, through which approximately 80% of the EU legislative acts is adopted. [1] This voting method has been modified over time. In 1958, voting weights were defined for all Member States -roughly reflecting the size of population of every Member State of the Union: the weight of votes and the sum of votes required for the adoption of decision in the Council of the EU was explicitly re-defined following every single enlargement by accession treaties with the newcomers.
However, a notable change occurred in 2001 with the adoption of the Treaty of Nice, which introduced a populationdependent qualified majority voting procedure for the Council of the EU. Although the original system of weighted voting remained in order -a simple majority of Member States (15 of 27 before the accession of Croatia, 16 out of 28 after the accession of Croatia) was required to cast a qualified majority of votes (255 of 345 before the accession of Croatia, 260 out of 352 after the accession of Croatia) -any Member State may have asked for the official confirmation that the votes in favour represented at least 62% of the total population of the Union -once this was not the case, the decision was not adopted by the Council of the EU. [2] Another significant change occurred in 2007 with the adoption of the Treaty of Lisbon, which bound Member States to abandon this "triple majority" voting system and introduce the "double majority" voting system from 1 November 2014. The provisions of this Treaty amending the TEU and the Treaty on the Functioning of the EU (TFEU) stated that "as from 1 November 2014, a qualified majority shall be defined as at least 55% of the members of the Council, comprising at least fifteen of them and representing Member States comprising at least 65% of the population of the Union." (Art.

16(4), [3])
This remains valid as long as the Council of the EU deals with a proposal of the European Commission or the High Representative of the Union for Foreign Affairs and Security Policy. Otherwise, the constitution of qualified majority requires at least 72% of the members of the Council, representing Member States comprising at least 65% of the population of the Union. (Art. 238(2), [5]) As the vast majority of the Council of the EU agenda is based upon the proposals of the Commission or the High Representative, this paper approaches the qualified majority as defined in Art. 16(4), [2].
Although there was a transitional period between 1 November 2014 and 31 March 2017, when any Member State of the Union may have requested the use of the "triple majority" voting system established by the Treaty of Nice, only the "double majority" voting system established by the Treaty of Lisbon has been applied since 1 April 2017. (Art. 3(2), Protocol on transitional provisions annexed to the TEU, TFEU and the Treaty establishing the European Atomic Energy In sum, voting in the Council of the EU is based on two criteria today -(1) the number of Member States voting in favour, and (2) the population of Member States voting in favour. However, as long as the voting procedure in the Council of the EU has become more practical to be conducted, it has become more difficult to be evaluated.
Until the rules laid down in the Treaty of Lisbon came into force, the only relevant variable necessary for the calculation of voting power of any Member State in the Council of the EU was the weight of its vote. In spite of the fact there was a population criterion included in the Treaty of Nice, Moberg (2007) points out that almost all coalitions of Member States that fulfilled the minimum-weight-of-votes requirement also fulfilled the minimum-population requirement for voting in the Council [6].
On the other hand, the analysis of the distribution of voting power under the provisions of the Treaty of Lisbon -in other words, under two different dimensions of the qualified majority voting procedure, where votes are not divided equally among 28 Member States -requires the use of advanced statistical methods that go far beyond the simple calculation of the percentage share of the number of states or the size of population of states in the total number of states or the total size of population of states.
Such calculations may be useful for evaluating the correctness of distribution of voting power in the Council of the EU (i.e. evaluating if the design of voting procedure does not give disproportional advantage to some Member State over others).
This makes voting on the soil of the Council of the EU an alluring object of research. Most of the previous studies of this topic have been conducted with regard to the modifications of primary law of the EU, within the "journeys" from Amsterdam to Nice, and Nice to Lisbon in the first decade of current millennium. They pointed to the shortages of models proposed by the EU, and that some of them were used in the official materials of EU Member States. Poland and Spain, for example, did use such studies as the basis of their official argumentation when opposing the distribution of voting power established by Lisbon Treaty and proposing a so-called "Jagiellonian compromise" [7].
However, a decade later, and with a big change in the composition of Union after the departure of UK, the question of correctness of distribution of voting power in the Council of the EU regains its relevance, and some Member States of the EU may -sooner or later -turn to calculations, such as the one presented in this paper, in order to raise point about the distribution of voting power once again.

Methods
In order to analyse the pre-Brexit and post-Brexit voting power of Member States in a qualified majority voting system, one can rely upon several indices. Most commonly, two of them are used: the Shapley-Shubik index or the Penrose-Banzhaf index (often referred to just as the Banzhaf index in literature). While the former is used when voting is taken sequentially (votes are casted one by one), the latter is applied when voting is taken simultaneously [8]. This is the case of voting in the Council of the EU, where votes are cast all at once: this was the main reason why this paper used the Banzhaf index to formulate main arguments and conclusions.
The Banzhaf index is a measure of power formulated by L. S. Penrose and J. F. Banzhaf to quantify the strength of actors whose voting rights are unequal -which is also the case in thevoting procedure in the Council of the EU. The Banzhaf index is based on the concept of a critical voter -a voter who, if they change their vote, he or she also changes the overall outcome of vote. It is possible that there is only one critical voter or that there are multiple critical voters in the group [8].
Nevertheless, there is a notable distinction between the absolute and normalized Banzhaf index. The absolute Banzhaf index is a ratio of (a) times one voter is critical (dividend) and (b) all possible voting outcomes (divisor). The normalized Banzhaf index is a ratio of (a) times one voter is critical (dividend) and (b) times all voters are critical (divisor) [8].
For the purposes of this paper, the normalized Banzhaf index, which provided a more appropriate basis for the comparison of particular actors, was used as it quantified the percentage share of times that a critical voter (Member State) can change the overall outcome of the voting in the Council of the EU from "approved" to "rejected" (and vice versa) by the change of its very own vote from "in favour" to "against" (and vice versa) -and therefore quantified the percentage share of voting power of any Member State [9].
The voting power of any of 28 Member States of the Union participating in voting process under the roof of the Council of the EU could be calculated with the following formula: Despite the fact the Banzhaf index is built on a simple mechanism as described previously it is quite difficult to quantify the voting power of actors within the Council of the EU manually. With 28 Member States, there are literally millions of coalitions of actors (approximately 268 million), which makes it impossible to do the calculation without advanced algorithms [10].
Due to this, the paper quantifies the voting power of Member States (and its change after Brexit) through the computer algorithm for voting power analysis on different coalition models published and maintained by Professor Dennis Leech of the University of Warwick along with Professor Robert Leech of the Imperial College London [11].
While the author is aware of the fact decision-making in the Council of the EU follows both formal and informal rules, and it is often subject to more or less significant variations from what is prescribed (due to, for example, bilateral/ multilateral agreements prior to voting), the in-depth analysis of formal rules regarding voting process and voting power is important to understand the behaviour of actors. In the end, it was the Banzhaf index which was used as one of the main arguments in the talks over the setting of voting procedure in the Council of the EU ten years ago.
In line with the provisions laid down by the Treaty of Lisbon, the analysis used two input variables to the calculations of the Banzhaf index: (1) number of Member States and (2) population of Member States voting in the Council of the EU necessary to pass the thresholds defined in the TEU.
The former is set directly and explicitly in the TEU (the requirement of at least 16 of 28 with the UK or at least 15 of 27 without the UK Member States to vote in favour of a proposal to constitute the qualified majority). The latter required additional data on the size of population. For every Member State and the Union as a whole, these numbers have been retrieved from Eurostat [12], which records the number of persons having usual residence in a country on 1 January of the year.

Results
The Council of the EU has seen a significant change in the distribution of voting power of Member States of the EU when the rules from the Treaty of Lisbon replaced the ones from the Treaty of Nice. The abolition of weighted voting and the establishment of a "double-majority rule" has improved the position of most-populated Member States (who benefited from the size-of-population condition) along with least-populated Member States (who benefited from the number-ofstates condition). This led to the further empowerment of Germany, France and United Kingdom, as well as smaller Member States such as Malta, Luxembourg or Cyprus [13]. Nevertheless, as upcoming paragraphs show, this has not been the case with Brexit.
The results of analysis presented in Table 1 suggest that after Brexit, the strongest have become stronger, and the weakest have become weaker. In absolute terms, the most significant gains of voting power have been recorded by Germany (1,762 points), France (1,552), Spain (1,417), Poland (1,397) and Italy (1,304). In fact, approximately 90% of voting power of the United Kingdom in the Council of the EU has been distributed among these five countries.
The calculations point out that there is a strong (yet not perfect) correlation between the size of population and recorded gains/losses in terms of voting process. In other words, the negotiating power of most-populated countries has increased most, and, at the same time, the negotiating power of the least-populated countries has decreased most.

Discussion
Brexit has had a significant impact on the relationships between the UK and EU, the ones within the UK, as well as the ones within the EU. It has raised several issues worth of elaboration and this paper has approached only one of them: the impact of Brexit on voting in the Council of the EU.
Using a special quantitative method rooted in the theory of probability -the calculation of the Banzhaf indices -it has provided a brief analysis of how voting power of individual EU Member States has changed after the departure of the United Kingdom from the European Union.
The results of this analysis presented in the previous chapter have suggested the voting power of the UK has been distributed rather unequally: that the negotiating power of the strongest, most populated countries has increased, while the negotiating power of the weakest, least populated countries has decreased.
This indeed constitutes a challenge for the EU, as it is likely to have both functional and symbolic implications. "I cannot conceive of the Community without total parity," Konrad Adenauer said to Jean Monnet during the preparations leading up to the signing of the Treaty Establishing the European Coal and Steel Community in April 1951, emphasizing that the EU has been set up on the idea of parity and equality of its Member States: or the idea of getting the Member States from all corners of Europe closer to each other, emphasizing the fact all of them can play a vital role in determining the future of continent. All voting systems in the institutions of the EU (be it Council of the EU or any other institution) have been based on a compromise between two principles: the principle of equality of Member States and that of equality of citizens.
The voting mechanism for the Council of the EU established by the Lisbon Treaty -the so called "double-majority rule" -has been designed to reflect both of them: equality of Member States through the criterion of minimum percentage of members of the Council voting in favour of proposal and that of equality of citizens through the condition of the minimum percentage of population of Member States voting in favour of proposal.
However, since the Lisbon Treaty was adopted and ratified at the end of the first decade of new millennium, the EU has changed in terms of its composition (accession of Croatia, departure of the United Kingdom), as well as relations between and among its Member States. Yet the voting procedure in the Council of the EU, one of the most important -if not the most important -institutions of the EU, has remained unchanged.
While in the post-Brexit voting procedure, the principle of equality of citizens is still reflected very well thanks to the population criterion, the application of that of equality of Member States is likely to miss its initial purpose. As the analysis presented in this paper shows, the current setting of voting rules is likely to tend to attribute disproportionally more weight to the criterion of the population of Member States over the criterion of the number of Member States. This, naturally, tends to favour the most populated countries at stake of the medium-and small-sized ones in terms of population.
For a long period of time, the representatives of the EU have been declaring efforts on achieving the opposite: the ultimate goal of the Community was to bring the Continent together under the promise of parity and equality. Now that the Member States are getting further away from each other in these terms, it will be very interesting to watch the reaction of the Union (and also its Member States) to such a challenge.