Weighting votes in the Council: towards a ‘Warsaw compromise’?

Daniel Gros, Mika Widgrén, Sebastian Kurpas 20 June 2007



One of the key obstacles to a swift agreement on how to reform EU institutions is the belated insistence of Poland to reopen the issue of voting weights in the Council. The system unanimously agreed in the Constitutional Treaty foresaw a double-majority system under which a (qualified) majority requires two elements – at least 55% of the member states accounting for at least 65% of the EU’s population.

In 2004, the then-Polish-government had agreed, under considerable pressure, to this double-majority formula. The new Polish government has for some time now insisted that this issue should be reconsidered. Initially it proposed that instead of the double-majority, the so-called ‘Penrose’ or square root formula should be used, under which only one majority would be required, namely one calculated using the square root of member states’ populations. Recently, however, the Polish government has changed its stance and is now ready to accept the principle of a double-majority approach, but one in which the second majority element would not be based on a majority of the population, but rather on the square root of the population.

What would Poland gain?

It is widely assumed that the insistence of the Polish government on the square root approach is motivated by the desire to increase its voting power. Our figures show, however, that this will not necessarily be the case. Poland is in general unlikely to gain a lot from the square root approach because it is nearly a big member state: 21 member states are smaller than Poland, and only 5 are larger. Any formula that gives more (relative) weight to smaller member countries is thus likely to affect Poland in a similar way as the other large member countries.

It might be that the Polish government is not so much concerned about its voting weight in general, but its weight in relation to the largest member state(s). In particular, the Polish government might assume that, in general, it is more likely to find itself in a coalition with smaller member states. However, this does not seem to be the case in reality. In recent research, Sara Hagemann and Julia De Clerck-Sachsse show that since May 2004, the four countries that were closest in their voting pattern to Poland were Germany, Belgium, Greece and Italy, i.e. two large and two small countries. It is thus difficult to understand the insistence of the Polish government on the square root approach.

The details matter

In discussing voting rules, one has to distinguish clearly between the way votes are weighted relative to each other, for example by using the square root, and the thresholds that define a qualified majority. The former is a zero-sum game among member states, whereas the latter has important implications for the decision-making capacity of the EU. Unfortunately, it is not altogether clear what the Polish government is proposing concerning the threshold for the required majority among member states. Two options, however, are implied by Poland’s proposal: keep the threshold for member states at 55% or lower it to 50%. Our calculations show that the differences between these two variants of the square root approach are minor.

We can thus concentrate on the general question: Would the square root approach actually make a difference? In how many cases would a blocking minority under the Constitution not constitute a blocking minority under the square root formula? There are two ways to approach this question.

A first shot at answering this question can be obtained by assuming (as is done in the calculations for the passage probabilities) that voting is random. One can then take all possible coalitions that would constitute a qualified majority under the Constitution’s rules and check whether they would also have been a qualified majority under the square root formula. Mika Widgren has calculated that a difference arises in somewhat less than 10% of all cases (i.e. a winning majority under one rule would not be a winner under the other rule). Since only about 13% of all possible combinations would yield a qualified majority (this is called the ‘passage probability’), this implies that the square root formula would make a difference in about 1.1% to 1.3% of all cases (i.e. among all random legislative proposals).

Would it have mattered in past votes?

A second way to approach this issue is to look at experience: i.e. in how many cases would the square root formula have made a difference in reality given the actual voting patterns observed since the 2004 enlargement? The data show that the Council in reality rarely votes (less than 25% of all legislation is passed with a proper vote). Moreover, the vast majority of opposing formations that remain in a minority consist of only one to three Council members. The square root formula would make a difference only for coalitions of at least four member states, since the Constitution stipulates that this is the minimum size for a blocking minority.1

The table below shows that there were only 20 cases (5.5% of all legislative action) in the two-and-a-half-year period following enlargement in which a contesting group of countries was overruled, although opposing minority comprised four member countries or more. It appears that in only a handful of cases would the outcome have been different if the Constitution or the square root formula had been applied, and this over a period of more than two years.


Table 1. Overview of opposing minorities to adopted legislation,
May 2004-December 2006
Size of opposing minority Number of cases % of contested cases % of total legislative action
1 31 30.7 8.6
2 38 37.6 10.6
3 12 11.9 3.3
4 9 8.9 2.5
5 7 6.9 1.9
6 1 1.0 0.3
7 3 3.0 0.8

Source: Hagemann, Sara and Julia De Clerck-Sachsse (2007), Old Rules, New Game: Decision-making in the Council of Ministers after the 2004 Enlargement, CEPS Special Report, March (available for free).


A possible compromise

Our research suggests that the results of the square root approach (in both variants) would not in reality be that different from the Constitution. A simple compromise might thus be the following. The new Treaty adopts the double majority with the 55/65 thresholds agreed in the Constitution. But on top of this, the new Treaty would also contain a clause that permitted any member state to request a recalculation of the votes according to the square root formula. If the results were different, the proposal would not be adopted immediately. The Council might have to re-convene after some time and confirm the decision a second time. This back-up clause would be temporary, however and would expire if it had been invoked only rarely in the course of a specified number of years.

We suggest that this double-majority rule with a square-root ‘handbrake’ might be the winning compromise. The efficiency and transparency of the decision-making process would thus be preserved, and the Polish government could claim victory.



1 Hagemann & De Clerck-Sachsse (2007) also show that one cannot detect a trend since enlargement towards more open contestations (voting), but the frequency of another form of opposition, namely the issuing of ‘formal statements’ has increased.




Topics:  EU institutions

Tags:  EU Constitution, EU Council, Poland

Director of the Centre for European Policy Studies, Brussels

Professor of Economics at Turku School of Economics, Finland and CEPR Research Fellow

Research Fellow at Centre for European Policy Studies


CEPR Policy Research