A NiceTrap (1)

By Moshé Machover

The most problematic issues that had to be decided by the EU Intergovernmental Conference at Nice concerned the so-called qualified majority voting (QMV) rule, used by the EU Council of Ministers (CM) in the major part of its decision-making.

Under QMV, each member state is assigned a certain number of bloc-votes or weight, and in order for a resolution to pass, the total weight of the votes cast for it must equal or exceed a certain quota. Most matters decided by the CM come under this rule. But certain issues which are deemed to be of paramount importance - such as those concerning the constitution of the EU itself — are decided under the unanimity rule, which gives each member state a veto, allowing it to block a proposed resolution.

The prospective enlargement of the EU made it necessary to extend the scope of QMV, as well as to devise new weights and quota that would apply to QMV in the future enlarged CM.

The decisions reached on both of these issues amount, in effect, to an enormous trap that the EU has set up for itself. And, as in a classical horror movie, the jaws of this trap are moving in slow motion, while the leaders of the EU are apparently unaware that eventually they will be locked in, with little hope of escape.

The enormous obstacle of unanimity

It was clear to most people that, in view of the forthcoming enlargement of the EU, many issues that now come under the unanimity rule will have in future to be decided by QMV. This is because, as the number of members will increase from 15 to 27, unanimity will be much harder to achieve.

But most people, including most leaders of the EU, do not seem to realize how much more difficult unanimity will become. In fact, the difficulty grows exponentially with the number of members.

To put it in simple betting terms, if you throw 15 coins at random, the odds against them coming up all heads are 32767 : 1. But with 27 coins, the odds are not about twice as long, as most people would probably guess; in fact, they are 134217727 : 1.

Of course, voting in the CM is not quite like this: ministers do not vote at random, by flipping a coin. Here is where diplomacy comes in: they haggle and bargain, using arguments, inducements and threats; and they compromise. However, the point is that diplomacy has to work against certain objective a priori mathematical odds. The longer these odds, the more difficult it will be for diplomacy to overcome them. And in a 27-member CM the difficulty will be truly enormous, so we can confidently predict that unanimity will be immeasurably harder to achieve than at present. Issues that come under the unanimity rule will tend to be frozen for a very long time, quite possibly causing frustration and discontent in large parts of the EU, and thus posing a potential threat to the viability of the Union.

In view of this prospect, it was disheartening to see how quickly and easily the Nice Conference agreed to drop certain key issues from the list of those to be transferred from the unanimity rule to QMV. For example, central questions regarding taxation and social security will languish under the unanimity rule. This was demanded by both the UK and Sweden, but for exactly opposite reasons. The UK government, still under the spell of some Thatcherite dogmas and terrified of the viciously right-wing British (but mostly foreign-owned!) press, was determined to ensure that a majority of EU members could not impose on it measures that are designed to achieve a re-distribution of wealth, however moderate. The Swedes, who have the most progressive welfare state in the EU, were afraid of the very opposite danger. The other governments at Nice, some of whom had unanimity "red lines" of their own, easily accepted the demand to leave these matters under the unanimity rule.

Three rules, for two scenarios

It took them much longer to agree on the formula for QMV. This is indeed a very complex issue, in which blunders are often made. (2) A difficult bargaining took place, in which the representatives of Germany, France, Portugal, and other member states pulled in various directions, dictated by narrow political considerations unenlightened by proper understanding of what they were doing. Finally, in the small hours of Monday, 11 December, they came to a decision.

In fact, they produced three different versions of QMV, which address two different scenarios.

First, the treaty contains a modification of QMV for the present 15-member CM, which will come into force on the first day of 2005, if the EU will not have been enlarged by that date. This modification was generally felt to be necessary because the present QMV rule gives too little voting power to the bigger members, and too much to the medium-sized and small ones.(3) In rectifying this distortion, the politicians at Nice were faced with a ticklish diplomatic problem. Germany — which after its unification has a much larger population than the UK, France and Italy — rightly demanded to have greater voting power than these three members. However, the leaders of these three countries — especially the president and prime minister of France, both of whom may stand as candidates in the forthcoming French presidential elections — did not want to seem "soft" and give up their existing parity of voting weights with Germany. This circle was squared in an ingenious way. The 2005 modified weighting gives all four member states equal weights. But a new clause has been added, which stipulates that for a resolution to be adopted it must (in addition to satisfying the weight quota) be supported by members representing at least 62% of the EU's population. This was designed to give Germany, with its larger population, a voting-power advantage without giving it more weight. This device turns out to work fairly well: our calculations show that the new 15-member QMV rule will indeed give Germany more voting power than all the other members (although not quite so much as its population size would justify). This rule is also considerably more equitable than the current rule.(4)

So far, so good. But things begin to go seriously wrong when it comes to the QMV rule devised at Nice for an enlarged 27-member CM. First of all, the text of the treaty is unclear (perhaps deliberately) as to what the quota will be. On page 162 of the (English) text, it is stated that the quota will be 258 (out of a total weight of 345). But three pages later there is a "declaration" that implies that the quota will be 255 rather than 258. So in effect we have two different versions of the 27-member rule.

Second, the 27-member rule also contains the 62% population clause; but in this case it turns out that its effect is negligible: our calculations show that the difference it makes is vanishingly small. In particular, it does not give Germany measurably more voting power than to the UK, France and Italy.(4)

The unnoticed trap of a high QMV quota

But the most worrying aspect of the 27-member rule (in both versions) is its quota, which at 258 or even 255 is much too high.

The whole point of moving a list of issues from unanimity to QMV is to facilitate decision-making and avoid paralysis of the EU. But the newly designed QMV itself is going to be extremely immobilistic.

From the time QMV first went into effect, in 1958, through four successive enlargements of the EU (in 1973, 1981, 1986 and 1995) to its present size of 15 members, the QMV quota — the threshold required in order to pass a resolution — was always kept pegged at about 71% of the total weight. The intention behind this was evidently to keep matters on an even keel; in other words, to keep the difficulty of getting a resolution passed by the CM at a constant level.

What the EU leaders have failed to realize is that if the quota is kept at a fixed level, and if that level is greater than 50% of the total weight, then as the number of members increases, so does the resistance of QMV, the a priori difficulty of achieving the required quota.

With the prospective enlargement from the present 15 members to 27, keeping the quota at the old level of 71% would produce a dangerously sclerotic QMV. In order to get a reasonably efficient decision rule, the quota should have been reduced to something like 60% of the total weight. Instead, the Nice Conference decided to raise the quota to 74.8% or 73.9% (depending on which version of the 27-member rule you believe).

Again, let me put this in plain betting terms. In the present 15-member CM, the a priori odds against achieving the present 71% quota are approximately 12 :1. In the projected 27-member CM, with the new weighting and quota(s) decided at Nice, the odds against achieving the quota are approximately 60 : 1 or 48 : 1. This means that the difficulty of passing a resolution — the obstacle against which diplomacy will have to labour — is going to be very much greater than at present!

A grim prospect

Thus we are faced with the grim prospect of a CM — the main decision-making body of the EU — in which unanimity will be extremely rare if not virtually impossible, and whose QMV will make the odds against passing a resolution at least four times as high as at present.

The politicians who made this calamitous decision at Nice are apparently unaware of its eventual implications. The trouble is that, if the Nice Treaty will indeed be ratified in its present form by the existing 15 members, its dire consequences of sclerotic immobilism will not be felt immediately, but only in a few years time, after enlargement takes place.

But then it will most probably be too late to put matters right, because an alteration of the CM decision rules is a constitutional change, which can only be made if a more reasonable alternative will be agreed unanimously by the 27 members!

The only hope is that the EU leaders will realize the folly of their Nice decision before enlargement takes place, and will change it in time. But this is merely a slight glimmer of hope, because experience in many countries suggests that the top political leaders tend to be headstrong and over-confident in their judgement. They are usually sure they understand the consequences of their actions, even when they plainly do not. And they tend to dismiss scientific advice — especially in matters relating to electoral systems and voting power — as "impractical" or too "academic" or "merely theoretical".

So the EU is most probably heading, in slow motion, into the jaws of a self-constructed trap, from which it will not easily be extricated.


1 I am grateful to Prof Dan Felsenthal of the department of Political Science, University of Haifa, for his invaluable help in writing this article.

2 For a detailed exposition, aimed at non-expert readers,see the booklet by Felsenthal and me, Enlargement of the EU and Weighted Voting in its Council of Ministers, which can be freely downloaded from http://www.lse.ac.uk/Depts/cpnss/projects/vp.html

3 This is indeed true. However, the extent of the present distortion is often grossly over-stated, because most people tend to assume, quite wrongly, that an equitable QMV rule would give each member-state a number of bloc votes strictly proportional to the size of its population. In the booklet mentioned in footnote 2 we refute this widespread fallacy, and explain the reason why it is so seductive. The correct formula for equitability would give to each member state voting power in the CM proportional to the square root of its population.

4 For exact details, see our report The Treaty of Nice and Qualified Majority Voting, which can also be freely downloaded from the web-site mentioned in footnote 2.

Moshé Machover was born in Tel-Aviv, studied at the Hebrew University of Jerusalem and taught mathematics there before coming to London University in 1968. He was at first at Chelsea College, then in the History and Philosophy of Science Department at KCL, joining the Philosophy Department in 1992. He was Reader in Mathematical Logic, and was then appointed Professor of Philosophy. Among his publications are: Lectures on Non-Standard Analysis (with J. Hirschfeld), A Course in Mathematical Logic (with J.L. Bell) and Laws of Chaos: A Probabilistic Approach to Political Economy (with E. Farjoun), Set Theory, Logic and their Limitations, and The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes (with D. Felsenthal). His current interests include nonstandard analysis and voting paradoxes.

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