Resumé

There is no foundation for the view that the balance between small and large member countries has changed through the successive enlargements of the EU. In most cases, the share of votes of the large countries is about 75 percent of what it would have been if the votes had been distributed in proportion to their population, and this figure has changed very little over the years. The great exception is Germany, which is due to the reunification. The effects of the enlargements and of a greater share of small and overrepresented countries have been borne to the same extent by all member countries. The relationship between the over/underrepresentation of small and large countries has not changed since 1958. The share of the total population needed for a decision by qualified majority has, however, fallen, particularly with the accession of Spain and Portugal and the German reunification, and the majority has in a way become "less qualified." This will continue with the coming enlargements, but the widespread belief that the small countries could outvote countries with a majority of the population is erroneous. This article examines the changes in the system that were suggested during the 1996 Intergovernmental Conference. A change of the same magnitude as these could be achieved through a simple formula based on objective criteria and would also eliminate the inconsistencies of the present system and the need for new negotiations at each enlargement.

The Problem

The central task of the 1996 Intergovernmental Conference of the European Union was to solve the institutional issues facing the Union with the coming enlargement. One important element in that context was the large member countries' demand for a reform of the voting system in the Council. Similar proposals have been made on earlier occasions, in particular in connection with the successive enlargements, but the matter has not earlier been brought as far as it was at this conference.

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* Axel Moberg, Karl Nordströms väg 16, S-168 51 Bromma, Sweden. E-mail: ulla.axel@stockholm.mail.telia.com

Several member countries linked this issue with increased use of qualified majority decisions and with a change in the composition of the Commission. The conference did not reach an agreement on all these matters. It was, however, decided that the large member countries, which now nominate two members of the Commission, should give up one of them on the next enlargement of the Union, provided that there had been an agreement to change the voting rules, either through a reweighting of votes or through a double majority system. Qualified majority voting was introduced in a number of new areas.

The discussions on the voting system at the conference raises a number of interesting points. Several aspects have already been discussed, e.g., by Hosli in her article on coalition making in the Union (Hosli 1996), and by Widgrén (1995), Stålvant (1993) and Hamilton (1991). These authors have concentrated on the voting power of individual countries in a game theory context with a particular focus on whether one country can make a coalition win a vote by joining it, or make it lose by defecting. That is, of course, of great interest, but these studies do not deal in depth with the relationship between the relative voting power of the countries and their share of the population, i.e., the representativity of the voting system, nor with the effects of the forthcoming enlargements to East and Central European countries.

The purpose of this article is to look at these two aspects. After some general remarks, it looks into the motives and concerns of the different groups of countries, discusses the evolution of the voting system in the European Union and finally comments on the effects of the various models that have been discussed at the conference, or informally during the conference, and adds a few new models.

The article is mainly based on the author's own calculations of figures for the population and the actual votes. Only limited reference is made to the discussions at the conference, which were rather superficial. It is natural that member states were hesitant to show their hand in the negotiations, but there was also very little common analysis of the situation and the effects of various models.

The article focuses mainly on the effects for individual countries and, unlike the articles mentioned above, it does so without making use of Banzhafs or Shapley-Shubik's indices. Several interesting conclusions can still be made with less sophisticated methods. Another point is that the indices, while being the correct measure of a country's voting power in a game theory context, are based on the assumption that all coalitions are equally probable and that any given country could be sitting on the critical votes. However, the actual political landscape hardly looks like that. Individual countries with a firm view on a given issue are unlikely to find themselves in a pivotal position. The likelihood is greater for countries in a

middle position or countries with a greater interest in trade-offs between
different issues.

It should be noted that this article only discusses one aspect of the institutional matters at the conference, the balance between small and large countries, and only one element of this aspect, i.e., the voting system in cases where decisions are made by qualified majority. It does not deal with other elements, such as the composition of the Commission, or other aspects, such as the balance between supranationalism and intergovernmental cooperation or the balance between the institutions of the Union.

The latter aspects could be of interest. It could be argued that the voting rules should depend on the substance of the matter. However, the basic features of decision making in the Council were decided already in the 1950s when the EEC was founded. Some matters should be decided by unanimity, some by qualified majority and the small unspecified rest by simple majority. There have been changes in this mix over the years, so that, quantitatively, qualified majority is the rule in well over three fourths of all decisions. The links to the weighting that were made at the conference were, however, basically of a bargaining nature. Some countries could accept more decisions by qualified majority on the condition that their weight in the voting increased, but there were hardly any links between the substance of the decisions and the weighting.²

It should also be borne in mind that the antagonism between small and large countries, which the discussion of the voting system at the conference seems to imply, is artificial. In the daily work of the Union, the dividing line is rarely between small and large countries, but rather between groups of countries with different political priorities.

Furthermore, it should be noted that a formal vote is rarely taken in the decision making process of the Union. Rather, the Presidency interprets the discussion in the Council and subordinate bodies in terms of whether there is a qualified majority or not. This should not lead to the false conclusion that the voting power of the countries is unimportant. On the contrary, it is constantly in the minds of all participants and influences the alliances they try to form in the negotiations. Member states are aware that they can be outvoted, and this probably tends to stimulate consensus decisions.

The Present System

The present system can, of course, only be explained in its historic context. It was originally conceived for the Community of six in the 1950s and was only slightly modified at the first enlargement in 1973. At each subsequent enlargement, the new member countries have been slotted into the existing classes of countries of roughly the same size, or into new classes between

them. The number of classes has increased from three to six. No total
restructuring has taken place. The percentage of votes required for a qualified
majority has remained at about 71 percent over the years.

The present system is, intentionally, a degressively proportional system, where the small members are somewhat overrepresented, as a rule the more the smaller the country is, and the larger countries somewhat underrepresented. This can be seen as a compromise between the principle "one man, one vote" and the traditional intergovernmental principle "one country, one vote," reflecting the fact that both federalist and intergovernmental elements exist in the Union. This principle has basically not been questioned in the discussions (nor is it the author's intention to do so). Instead, the question has been how far this degressive principle should go.

The division into classes by size is rather crude and lumps together member countries of rather different sizes. The differences within each group have increased over the years. The most conspicuous case is that, after the reunification, Germany has not asked for and has not been given more votes. Thus, there is now a significant difference in size between the countries that have 10 votes each. The Netherlands with approx. 15 million inhabitants are in the same group as Greece, Belgium and Portugal with approx. 10 million inhabitants, each with five votes. Another group with Sweden and Austria, only slightly smaller than the latter countries with approx. nine and eight million inhabitants respectively, have been given one vote less. With these inconsistencies, there is hardly any point in trying to find a mathematical formula that describes the present distribution of votes. As a matter of curiosity, however, the formula that seems to come closest is one vote per country and the rest distributed in proportion to the square root of the population.

Motives for Change

The large countries base their demands on the allegation that the balance has changed in favor of the small countries with the successive enlargements, and particularly with the latest enlargement to Austria, Finland and Sweden. They have often pointed at the difference in number of votes per inhabitant, particularly in the two extreme countries Germany and Luxembourg, and they have often warned against a situation where decisions could be made by a minority of the total population.

However, since the concept of "balance" has never been defined, it is impossible to find an exact answer to what the large countries were trying to get at the conference. Conclusions will have to be based on their arguments and proposals. Their motives were probably mixed: In some cases, they probably concerned the real power of a group of member countries, such as

the Mediterranean countries. In other cases, the motives were probably less rational, concerning prestige and national pride. To some extent, there seems to exist a notion that the "large" countries and former great powers should be seen as a group with a special status and somehow qualitatively different from the small countries, or even that the votes should reflect the "political weight" of a country rather than the size of the population. It has, in fact, been suggested that the large countries should be compensated as a group for the loss of influence they are said to have suffered.

One conclusion is that the large countries do not seem to be primarily concerned about the fact that they are underrepresented in the present system. None of them has taken the trouble to show any figures about it, and no proposals about a fully proportional system have been made.

Nor does it seem likely that the large countries are aiming at a system where they can get a qualified majority by their combined votes, even against the will of small countries. Ideas about a directorate of the large countries have existed (e.g., confidential proposals by General de Gaulle made in connection with the first enlargement), but very few statements at or in connection with the conference can be interpreted in such a way. The proposals that the large countries made at the conference would not give those effects.

What the large countries seem to have been particularly preoccupied with at this conference is rather keeping the present (or restoring past) possibilities for a few of them of blocking a decision. This is important, since decision making in the EU operates largely through blocking minorities. The discussions of weighting of votes during the latest enlargement negotiations and the loannina compromise were about just that.

In the EEC6, one large country could block a decision with the support of one small country. In EC9 and ECIO, one large and two medium-sized countries were necessary to block a decision. After the accession of Spain and Portugal, at least two large and one medium-sized country were necessary. Now, two large and two medium-sized countries, or three large countries, are required for a blocking minority. The possibilities of the large countries to block a decision will continue to diminish in the same way with future enlargements.

Another line of argument that was used to some extent, is that the percentage of the population that the countries forming a qualified majority represent has decreased. This will be examined in the section on the effects of the enlargements.

The Present Balance

The over or underrepresentation of each country can easily be calculated as

the ratio between its share of the votes and its share of the population. It shows the difference between the present situation and the share that the country would have had if the votes had been distributed in proportion to the population. If the ratio is below one, the country is underrepresented. If it is over one, the country is overrepresented. The figures for individual member countries, including EU26, based on one of the extrapolations made at the conference, can be seen in Table 1. Another measure for the same relationship, which has often been used in the public debate, is to calculate the number of inhabitants each country needs for one vote. The practical disadvantage of that measure is that it is necessary to compare the figures to the average in order to see which countries are over or underrepresented.

The table shows that most of the large countries have about 75 percent of the votes they would have had if the system had been fully proportional to the population. The most important exception is Germany. Spain, one of the countries that insist most on an increased weight in the voting, is closest to a proportional representation with about 10 percent of the votes and 10 percent of the population. If its share of the votes were increased substantially, it could become overrepresented.

The överrepresentation of the medium-sized and small countries is greater, but the point here is that this does not lead to such a great underrepresentation of the large countries, precisely because these countries have a small weight in the comparison.

As a rule, the överrepresentation is greater the smaller the country is. The only exceptions are Sweden and Austria that have slightly fewer votes per inhabitant than the slightly larger countries Greece, Belgium and Portugal. This is the only case where, contrary to the basic rule, larger countries are favored in relation to smaller countries. The most overrepresented country in relative terms is, of course, Luxembourg.

In absolute terms (actual votes compared to the votes each country would have if the 87 votes were distributed in proportion to its population), the picture is slightly different. The most underrepresented country is still Germany with about nine votes less than the proportional distribution. The other large countries have about 3.5 votes less, Spain 1.28 less, Netherlands 1.4 more, and most of the smaller countries have 1.8-2.2 votes more. The most overrepresented countries are Portugal, Belgium and Greece with 2.6-2.7 votes more.

Effects of the Enlargements

Small Changes in Representativity

It is obvious that the share of the votes of each old member must diminish as new members join. The shares of the individual founder countries have fallen to about half of what it was at the beginning. The combined shares of the largest countries have fallen from almost 90 percent to less than 70 in population terms, and somewhat more in terms of votes. Hosli's articles (1995; 1996) discuss the absolute change in voting power at the successive enlargements. However, the change should also be studied in relation to the change in the country's share of the population, i.e., the ratio above.

As can be seen from Table 2, the ratio for all member countries has changed very little since 1958, or since they joined the union. The ratio for most of the large countries has fallen from an average of 0.8 to 0.73-0.75. The original ratio for France was somewhat higher, because France was smaller than the other large countries in 1958, but this difference has now disappeared.

The great exception is Germany, whose ratio has fallen
considerably, but this is mainly attributable to the reunification.

Proportional Changes for Large and Small Countries

The proportion between the ratios for small and large countries has not changed. All member countries have given up the same proportion of their share of the votes to the new member countries. Also the effects of an increased share of small and overrepresented member countries have been borne to the same extent by all member countries. The large countries have become somewhat more underrepresented, but the small countries have also become proportionally less overrepresented. It also affects the ratio of the new member countries.

The effects of the increased share of small and overrepresented countries become obvious if one makes the mental experiment of enlarging the Union with a few large countries, such as Russia, Ukraine and Turkey. In that case, the ratio increases and large old member countries become less underrepresented and the small countries more overrepresented.

In fact, this phenomenon has already occurred with the accession of countries that were larger than the average, such as the UK and Spain. Another example is that before the German reunification, the ratios for most of the large countries were close to the present figures. After the reunification,

the ratio for Germany fell sharply, but the ratio for all other countries,
including the large ones, increased. Then, at the latest enlargement, the ratios
for all countries decreased somewhat.

"Less Qualified" Majority

Another effect of the enlargements is that the theoretically smallest percentage of the population required to reach a qualified majority diminishes. The last row in Table 2 shows that the greatest change took place with the accession of Spain and Portugal when it became possible to outvote two of the largest countries. The second largest change was the German reunification. These changes will continue with coming enlargements. The widespread belief that a number of small countries have enough votes to outvote countries with a majority of the population is erroneous. Nor will it be true if the present system were continued in an enlarged Union. Even in an EU of 26 or 27, a majority, if tiny, of the population will be required for a qualified majority of the votes. It should be noted that the percentage is highly dependent on the number of votes given to the new member countries that fall outside the present groupings. If Latvia, Slovenia, and Estonia were given three votes each, as in Table 1, the majority would only be 50.3 percent. If they were given two votes, the minimum majority would be 55.2 percent, and even fewer votes have been suggested. In any case, the minimum percentage of the population does diminish and the qualified majority becomes less qualified. This is a valid argument for changing the voting system.

One way of addressing these problems is to change the threshold for qualified majority rather than the weighting of the votes, an idea that did not receive much support at the conference. On the contrary, there is wide support for the idea that the threshold should be maintained so that the decision making at least does not become more cumbersome.

Effects for "Coalitions"

It is easy to appreciate the difficulties in identifying consistent coalitions. The position of a country is not a simple dichotomy, such as free trade/ protectionism, but rather a question about the priority each country gives to different interests. A country may take a more free trade oriented position in one matter, and less so in another matter. A country may have common interests with another country on one issue, but with a third country on other issues. The positions of countries change over time. Even so, a number of factors, such as sector interests, administrative and political traditions, domestic political climate and agenda give the individual countries a profile that is not likely to change radically in the short run. The priority given by

some countries to, for example, free tråde, environmental matters, Mediterranean agriculture or transparency will probably not change drastically after each election, even if changes do occur. This gives some possibilities to identify reasonably stable interest groupings, which Hosli does at the end of her article (Hosli 1996).

The calculations of over/underrepresentation can, of course, also be applied to groups of countries, or possible coalitions. It should be noted that, for dichotomous groups, an increasing underrepresentation of one group means an increasing överrepresentation of the other. If one group gets more "underrepresented," the opposite group become more "overrepresented." (This was not the case for individual member states above). Any classification of countries as belonging to one group or the other is, of course, subjective and should be used with care. The conclusions depend highly on the composition of the group.

Table 3 shows how the ratios for selected groups have developed since EEC6. It is, of course, not quite realistic, since the political agenda and the profiles of all countries have changed in these 40 years, but it may indicate some trends. If one departs, just as an illustration, from Hamilton's classification of countries as most free trade oriented³ or environmentally minded, it can be seen that both groups have become less overrepresented over most of the successive enlargements and will become underrepresented in EU26. If one chooses less generous definitions,⁴ the free trade group becomes increasingly underrepresented, and the environmentalist group will also become underrepresented in EU26, and more so if the United Kingdom were included in that group. The underrepresentation of these groups, where several countries are overrepresented, is of course due to the great weight of Germany and the United Kingdom. The pattern seems to be largely the same for the group of present "net contributors" to the EU budget, but the composition of that group can change rapidly. This could give some clue to the possible policy effects of a change in the weighting. The figures do support Hosli's view that the last enlargement meant some reinforcement of the "Northern" flank of the Union, but it could also be argued that this was a correction of the earlier underrepresentation of some of these groups.

Any forecast of the effects of coming enlargements will, of course, have to be based on speculation. It may be assumed that none of the present candidate countries will join the more environmentally oriented group and maybe not the free trade group. Whether some of them will be in favor of a CAP reform or become net contributors will depend largely on the outcome of the accession negotiations and the development of EU policies. It can, however, be noted that the present members of the free trade and environmental groups (at least in a strict sense), would lose their present blocking minority, if the present distribution of votes were continued into EU26. It could be restored through a reform of the system.

Different Proposals: Reweighting of Votes

The proposals for a change in the weighting of votes that have been advanced more or less formally are all about an increase in votes for the four largest countries, and in some cases Spain and The Netherlands. Hardly any specific reasons have been given for the rather arbitrary changes that have been suggested. The proposals should, above all, be seen the in light of the possible blocking minorities.

In some cases, it has been proposed to increase the number of votes for all countries, but with a greater increase for the largest. One example is the final proposal from the Dutch Presidency, which is the only one that has been published. The proposal was that the votes of the five largest countries should increase to 25 (2.5 times), those of The Netherlands to 12 (2.4 times), those of the other countries should double and those of Luxembourg should increase 1.5 times. A few other proposals were based on the idea that the number of votes should be decreased by the same absolute figure, which would mean a greater relative reduction for the medium-sized and small countries.

The Dutch proposal would mean that a qualified majority would require the support of countries with at least 61 percent of the population in the present Union, and that a blocking minority would require at least two of the largest countries and one country the size of Sweden or Austria. In EU26 the threshold would be 56.7 percent of the population for a qualified majority and at least three of the largest countries and one country of Sweden/Austria size for a blocking minority. Several of the proposals advanced by other countries were of approximately the same magnitude. Proposals of this kind would to some extent increase or restore the blocking possibilities of the large countries.

The small countries have been hesitant to accept these changes for a number of reasons. Basically, it would diminish their weight in the decision making, and it would be difficult to explain to the public. A number of other objections can also be made. The changes are quite arbitrary. If the idea is to

give greater weight to population, the faet that Germany is given the same number of votes as the other large countries is hardly logical. The disadvantage for Sweden and Austria remains or even increases in some proposals, and furthermore, the proposals do not give a clear answer to what the voting weight should be of the candidate countries that fall outside the present classes. (Is Latvia a small Ireland or a big Luxembourg, is Romania a big Netherlands or a small Spain?) This would make new negotiations necessary, which increases the risk that the small countries would have to make further concessions at a later stage of the enlargement.

Percentage of the Population as a Benchmark

One of the proposals at the conference was that member states should first decide the minimum percentage of the population required for decisions by qualified majority and then decide whether that percentage should be attained through a reweighting of votes or through a system with double majority. There are several problems with this idea.

First, the method conventionally used for calculating the percentage of the population behind a qualified majority is unreliable. The method is to find the combination of small and large countries with the lowest percentage of the population that can reach a qualified majority (or the largest minority that can be outvoted). Both groups will consist of an unpredictable mix of small and large countries, and small changes in the percentage can lead to great changes in the composition and the number of votes.

Second, since the voting system is not proportional, a reweighting intended to give a minimum majority of say 60 percent of the population and a double majority system at the same level do not give the same results. This is particularly the case with Germany's position. Furthermore, a reweighting of that size can be made in any number of ways. How the distribution is made is, of course, of great interest to member countries.

Third, and most important, a reweighting based on a certain required percentage of the population for a qualified majority could lead to more drastic increases in the votes of the large countries than other proposals and in some cases absurd consequences. One reason is that some of the large countries must belong to the group that is outvoted, and the number of votes increases also for those countries. This can push the required increase in votes for the large countries upwards disproportionately.

The Dutch proposal of 25 votes for the large countries (which corresponds to 12.5 since the votes of practically all countries were at least doubled) gave a minimum percentage of the population of 56.7 in EU26. Clearly, a population threshold of 60 percent in EU26 would require an even greater increase in votes for the largest countries. Table 4 shows the number of votes

that the large countries needed to be given to ensure that a qualified majority of the votes cannot be reached unless it is supported by approx. 70 percent of the population or, more important, that countries with more than the opposite percentage can always block a decision. This example is only meant as an illustration of the difficulties with this approach. The result depends largely on the assumptions that are made for the intermediate countries. In this example, the large countries are given the same number of votes, Spain is given 80 percent of that figure, Romania and The Netherlands a number in proportion to that, and all other countries remain unchanged.

The examples in Table 4 (where the figure for only one country in each group is given) show that if 65 percent of the population were required for a qualified majority of the votes, some of the large or medium-sized countries could become overrepresented and several small countries underrepresented. It should also be noted that as long as the distribution of votes is not proportional to the population, a coalition with the necessary percentage of the population cannot always reach a qualified majority. Vice versa, a group of countries may be able to block a decision, even if it does not reach the required percentage of the population.

Double Majority: Votes and Population

The idea of a double majority consisting of the qualified majority of votes in the present system and a certain percentage of the population, which has often been advocated by Germany, has attracted considerable attention. One of the elegant points about the model is that it gives Germany greater voting power

than the other large countries without demonstrating this as clearly as a
reweighting model.

The actual effects of the two components can only be compared to each other and to reweighting models by the share that a country would hold of the blocking minority in each respect. (This is because the threshold for a qualified majority and for a blocking minority is not the same percentage for the votes and for the population criterion). The effects of a double majority system depend on the level of the population criterion. Table 5 shows that the only effect in the present Union, at the levels that have been discussed most, would be that Germany got greater blocking power, greater than it would get with any of the reweighting proposals. At 60 percent in the present Union, Germany alone would have 55 percent of a blocking minority by the population against 38 percent by votes in the present system. The other large countries would hardly gain anything in EUIS, but they would get increased blocking power when the Union has been enlarged with several new countries or if the population criterion were set higher. It is interesting to note that in the present system, the support of countries with at least 58.2 percent of the population is necessary for a qualified majority. If the level of 58.5 percent were maintained also in EU26, the three largest countries would still have a blocking minority. If the threshold were set higher, other blocking minorities of three countries or less would become possible. In order to give any advantage to the small countries, the criterion would have to be set extremely high (85-90 percent).

The increased blocking possibilities for the large countries and the more complicated decision making procedure have been the most important points in the criticism of the system. Another point is that this model is in a way based on two population criteria, i.e., votes partly based on population and

one explicit population criterion. However, some of the small countries have shown sympathy for the idea, because it could be presented to the public opinion more easily than a reweighting. It could be argued that the old weighted votes remain unchanged, but that a population criterion has been added as an extra safety catch. The question is how realistic that view is. Simple logic says that if you introduce a new leg in the decision making procedure, it is unlikely that you will put the same weight on the old leg as before. There could even be a risk that the weight is shifted over to the new leg, so that population would become the main criterion and that the old weighted votes are relegated to a secondary role as a safety catch.

Double Majority: Countries and Population

This proposal is about a double majority, consisting of a (simple) majority of the population and a (normally two thirds) majority of the number of countries. It dispenses completely with the weighted votes. This is the model that Hosli was mainly discussing in a previous article (Hosli 1995), but it only received limited attention at the conference. The effects of the population criterion in this model would be the same as in the previous one, but it does not contain double population criteria.

The special problems are connected with the share of the countries that should be required for a qualified majority. A criterion of 2/3 of the countries would mean that in EU26 a decision can be blocked by a minority of one third of the countries representing 5-6 percent of the population against at least 12 percent today. A lower share, for example a simple majority, would avoid that problem, but the combined effects of both criteria would then make the majority "less qualified" than in the present system.

However, this model is the only one that takes care of one special problem. If the present system were continued into a Union of 26, half the number of member states would be sufficient to reach a qualified majority of the votes. In an EU27 (including Malta) it would be possible for the large and a handful of the medium-sized countries to reach a qualified majority of the votes against a majority of the number of countries. If the votes are reweighted, this would happen at an earlier stage. This aspect was hardly discussed at the conference.

Possible Solutions?

If there is a political will, it is certainly possible to find a generally acceptable formula for reweighting the votes. It should remain a compromise between a proportional system and equal representation of all states, a degressive proportionality that gives some överrepresentation to the small countries. It

would help if it were based on objective and coherent criteria, so that the matter could be settled once and for all, and no new negotiations would be necessary at future enlargements. It would also help if the absolute figures for the votes were higher than in the present system, because the figures for individual countries would in that case not be so strongly affected by how they are rounded off. For one of the small countries, the way the figures are rounded off can mean a difference of 25-50 percent in positive or negative terms and can thus have greater effects than the choice of system. Any voting model could be supplemented by a provision that a decision must be backed by at least half the number of member countries. Överrepresentation of the small countries can basically be achieved in two ways.

One way is to give each country a number of votes which is the sum of two elements: a number of votes, regardless of the size of the country (e.g., the two votes Luxembourg has now), and then some additional votes in proportion to each country's share of the population. The balance between large and small countries in such a model will be decided by the relationship between the total number of "basic" votes and the total number of "proportional votes." If the share of "proportional" votes is low, the winners will be the small states and possibly Germany. The proportions of 1 basic to 1.1 proportional votes (with the same number of votes for Germany and the other three) would come closest to the present weighting in an ordinary least

square calculation of the shares of the votes. If the share of "proportional" votes is high, the winners will be the large states. The number of proportional votes alone would decide the division of the countries into classes. About 75 proportional votes would give a division into "natural clusters" with a substantial difference in size between the groups that are given different numbers of votes. This figure would correspond to one vote for each increment rounded off to approx. 5 million inhabitants. The problem with this model is that it creates an opportunity for endless and repeated negotiations about the components.

The other possibility is some kind of bent curve. One very simple and practical model could be based on a number of votes corresponding to the square root of the population of the country in millions, which would give a consistent degressive proportionality. One million inhabitants would give one vote, four million two votes, nine million three votes, etc. up to eight votes for the largest countries, or possibly nine for Germany. This would give the large countries almost the same increase and roughly the same distribution as the Dutch proposal, eliminate the inconsistencies of the present system and give a division into natural clusters. This model could also be of interest to the small and medium-sized countries, because the principle it is based on gives some certainty that the voting system will remain unchanged. This is because the system would be difficult to change in order to increase the voting power of one group or another. It is, of course, possible to make optical changes to the

number of votes or to fine-tune the model by multiplying the square root or the population by a constant factor, but the proportions between the votes of different countries will remain the same (apart from effects from rounding off the figures). The only way of changing the balance is by adding or subtracting votes to/from the figures that the formula gives. The effects of the various models are summarized in Table 6.

Conclusions

The main conclusion of this article is that there is no foundation for the view that the balance between small and large countries has changed with the successive enlargements, at least not in terms of representativity. But it is a fact that the minimum percentage of the total population, which the countries

behind a qualified majority decision must represent, has diminished and will continue to do so with future enlargements. That is one valid argument for a change in the voting system. How far this change should go is a purely political matter. It concerns both which distribution of the actual voting power the countries can accept and how a change can be presented in the public debate. No mathematical formula can say what is reasonable. However, most of the suggestions made at the conference were of about the same magnitude as the proposal of the Dutch Presidency. If that magnitude is acceptable, the formulas above can make the system less arbitrary than the present system or the various proposals. Especially the formula based on the square root of the population would give the small countries some guarantee against repeated revisions where they might have to make concessions several times at future enlargements.

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NOTES

1. The article is basedon the author's work as Deputy Director in the Swedish Ministry for Foreign Affairs during the Intergovernmental Conference. The findings are entirely the author's own and do not necessarily reflect the views of the Swedish Government.

2. There was some discussion about a "super-qualified majority" in a different context, how to develop the Common Foreign and Security policy.

3. Free trade: The Nordic countries, UK, Germany, Austria, Benelux countries. Environment: Nordic countries, Germany, Austria, Benelux countries.

4. Free trade: Germany, UK, Netherlands, the Nordic countries. Environment: Germany, Netherlands, Austria, Nordic countries.

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Power in the European Union," International Studies Quarterly 39, 351-70.

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