Draft constitution and the decision-making rule for the Council of Ministers of the EU – Looking for alternative solution
Bela Plechanovová
European Integration online Papers (EIoP) Vol. 8 (2004) N° 12;
Date of Publication in EIoP: 23.9.2004
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Introduction to contents list

Failure of the Intergovernmental Conference of the EU last December on the Draft Treaty establishing a Constitution for Europe brought home that the misgivings about the decision-making rule proposed in the treaty, which were pronounced during the second half of last year had a sound basis and wanted to bring attention to an important fact. No matter how ambitious and symbolic the attempt to propose a European Constitution was and how much political pressure was exerted both on member and candidate states that were expressing their discontent with the proposed institutional setting, the decision-making procedure for the Council remained the most contentious issue, which broke the negotiations in Brussels last December. The reason was – as ever – that the Council is a decision-making body where the member states of the EU are represented and which has the critical position in the decision-making process. No wonder, all the member states want to keep their position in this body as strong as possible.

There is a long history of attempts to change the decision-making procedure and the system of representation in the Council dragging on through the 1990s. The problem emerged in early 1990s with the unification of Germany on one hand and with the EFTA enlargement on the other. These processes made more prominent the fact that the decision-making rules for the Council were designed for the original six founding countries of the European Economic Community with the main goal to keep balance between the three large countries – France, Italy and Germany – and the medium and small countries – the Netherlands, Belgium and Luxembourg. This was achieved by preventing the large countries from over-voting the smaller partners by the condition that their combined strength expressed in weighted votes (each of them had 4 votes) was equal to the quota for the qualified majority (12 votes), but was applicable only on decisions based on the proposal of the Commission. On decisions taken without the Commission’s proposal, the large countries had to find one extra ally among the smaller countries.


On the other hand, the medium and small countries (having 2 and 1 vote respectively) could not block the decision taken on the proposal of the Commission of their own; they also had to find an ally among the large countries.

The rules stayed in place principally unchanged for more than four decades. During that time, the EC had grown in membership from the original six to fifteen. All the newcomers were given the same or comparable number of votes as the founding members according to the size of their population. When Denmark and Ireland were joining the EEC, they could not be fitted comfortably into the original scale, as their population was both considerably smaller than that of Belgium and considerably bigger than that of Luxembourg. The solution was found in extending the scale from two votes to ten, but keeping the ratio between the original groups of member states almost the same (from 4:2:1 to 10:5:2) and giving the two new minor members 3 votes each.

Among the new members were only two large countries – the UK and Spain, all the others were medium and small. The overall effect of this character of the process of enlargement was the steady decline of the level of representation of population of the large countries in the main decision-making body of the EC/EU. This process had given the incentive for the demand for reform of the decision-making procedure, particularly for the reweighting of votes in favour of the more populous countries. Two Intergovernmental Conferences were seeking to find a solution during the 1990s but without satisfactory results, even the Treaty of Nice made a step further and brought a change, but it was soon criticised from various angles. The new rule had to provide both for reweighting of votes in favour of the large countries, but brought in also two extra criteria, which were not originally part of the procedure – majority of member states and 62 percent of EU population. The procedure became more complicated and less transparent and understandable to general public. That was one of the reasons why the Convention, among others, reopened also this question and tried to solve this very sensitive problem. Unfortunately, the attempt to come with less complicated and more transparent procedure ended with a result, which is deficient in the most sensitive and most important aspect – in equitability of representation of population of the member states. (Baldwin & Widgrén, 2003; Felsenthal & Machover, 2003; Plechanovová, 2003b).

The aim of this article is to present a design of an alternative decision-making procedure taking into consideration simultaneously the rigorous criteria for evaluation of such procedure and the political acceptability of the solution. The alternative solution will be compared with the decision-making procedures of the Treaty of Nice as applied by the Act of Accession by ten new member states in April 2003, with the solution proposed by the Draft Treaty on the Constitution approved by the Convention in July 2003 and the solution proposed as optimal by Felsenthal and Machover (2003).

I. Criteria of evaluation to contents list

I.I. Quality of decision-making rule

(1) As mentioned above, the main reason why the institutional changes for the Council were looked for was the problem of unequal representation of the population of various member states of the EU in this body. Naturally, the most important criterion will be the level of equitable representation of individual voter in all member states including ten new members. Each individual voter in all member states in the end should have the same capability to influence the final decision made in the Council. But how it can be assessed? We can envisage the decision-making in the Council of the EU as a two-stage voting procedure. In the first stage, the voters in each country vote in their parliamentary elections. As a result, the government representing the majority will of the voters is established. The second stage of the decision-making process takes place in the Council.


Each member country is represented in the Council by the member of its government. No matter how many citizens each country has, a single member in the Council represents it. The question is how many votes or what weight each member of the Council should have to provide for the principal OPOV (one-person-one-vote) to be respected. If the EU would be a single political entity, the best solution would be to have electoral districts of equal size with proportional system of voting. Representative of each district would then have the same weight in the decision-making body of these representatives. But, the EU is an association of states or a federation sui generis, each state being a single electoral district (no matter what kind of electoral rules the member states have within the country). The size of these districts is disparate; Maltese minister in the Council represents around 300 thousand inhabitants, German minister represents around 82 million inhabitants.(1) The ratio between these two remotest values is more than 270; should the German representative then have 270 times more weight than the Maltese should? It might seem so, but it would not be correct. Since each member country is a single political entity with autonomous rights to decide on its political system, it has to be taken as such. When we want to assess the equitable share of weight for each country in the Council, we have to take into consideration that the voting power of individual voter compared among various countries is not equal. Even the size of the Maltese parliament is considerably smaller than of the German one, we still may see clearly that it takes many more German voters to elect a single MP and consequently to establish the government than it takes in Malta. It means that the voting power (the capability to influence the result of the voting) of the German voter is smaller than the voting power of the Maltese voter. This has to be taken into consideration when we speculate about the optimal decision-making procedure for the EU Council.

For measuring the voting power under given decision-making rule, we will use the Penrose measure (or absolute Banzhaf index), which is the probability value of the actor (member state) i being able to influence the outcome of the division by the swing of her/his vote, i.e. the actor being able by withdrawing her/his vote to change the winning coalition into losing one.

Next to it, we will use also the relative Banzhaf index ß , which is a normalized version of the aforementioned measure enabling to compare the relative standing of the actors under the given decision-making rule. Both these tools are particularly suitable for measuring a priori voting power, which the actor gains solely on the basis of the decision-making rule.(2)



The problem is how to translate these differences of voting power of individual voters from various member states into the rules for the decision-making procedure in the Council. Two points are important to mention: (1) it is not the whole population of the country that is represented by the member of the Council, but only the majority of it; (2) the voting power (a probability that the voter would be in a position to decide the outcome of the division) of the individual voters in various countries is different. Additional remark is that the voting power of the member of the Council need not be proportional to the weight allotted to her/him.

The problem of equalizing the differences of indirect voting power in the second stage – in the Council – is solved by the so-called Penrose’s square-root rule, which provides more simple solution to the mathematical formula indicating the indirect voting power of individual voter in the Council.


To equalize the different indirect voting power of voters in various countries, the decision-making procedure in the second stage, in the Council, should be designed to provide for giving each electoral district (member state) a voting power proportional to the square-root of the number of voters in each country.(4)

The tool, which is used for further analysis, is the equitability index . It measures how well the decision-making rule provides for the equitable representation of individual voter (OPOV); the ideal value is 1. To compare several decision-making rules we will use standard deviation as a measure of variance of the effect of the decision-making rule on position of individual actors – the member states. The lower its value, the more equitable solution the decision-making rule represents for the decision-making body as a whole. Additional parameters are maximal and minimal values of deviation, which enable to identify the most favoured and most disfavoured member states and to point to the range of these deviations.



(2) Second criterion for assessment of the democratic qualities of the decision-making rule is the level of majoritarism. Any decision-making rule, which has two stages and particularly the unequal size of primary electoral districts, faces the risk that the final decision need not be backed by majority of individual voters, i.e. citizens of the member states of the EU. The degree of this risk is measured by the majority deficit – the margin by which the majority, which opposes the decision, exceeds the minority that supports it. The mean value of this random variable is mean majority deficit. (Felsenthal & Machover, 2003, p. 11) It may be used for comparison of various decision-making rules for the identical electorate. As a “very good approximation” (Felsenthal & Machover, 1998, p. 54-67) it can be expressed as

The optimal value of MMD is zero in case when majority of voters supports the decision. Values of MMD are comparable only for the rules for identical number of indirect voters (citizens of the EU).

(3) Additional criteria used for evaluation of decision-making procedures will assess the influence of the particular procedure on the ease with which the decision would be taken or inversely – with which the actors would be able – collectively – to block the decision. These may be measured by the degree of compliance of the rule A (the interval of values is 1/2n for unanimity rule and ½ for simple majority rule) and the degree of resistance of the rule R (the interval of values is zero for simple majority and 1 for unanimity). (Felsenthal & Machover, 2003, p. 11-12).


The answer to the question of the optimal value of these two indicators is ambiguous. On one hand, the decision-making rule should allow the decision to be taken, on the other hand, the status quo should be preferred to the change, i.e. it shouldn’t be too easy to accomplish the change. Once the rule requires qualified majority, we cannot expect that the values of A and R should be very close to the values given by the simple majority rule. The precise balance between these two requirements expressed in the “optimal” value of the indicators is then not really clear. We still may compare these values across various solutions for the decision-making rule, including the situation in EU 15 before enlargement, or even earlier for EU 12 (Table 5).

Table 5

I.II. Political criteriato contents list

Next to these rigorous criteria enabling the comparison of the qualities of the decision-making rules we will take into consideration also the political arguments, which were used during the lengthy discussions about this aspect of institutional reform. Several main features may describe the situation:

  1. The main incentive for reform of the decision-making rules in the Council comes from the large member states; their interests and views are behind the reasoning for a change and are important for acceptability of any new solution;
  2. All member states approach their position in the Council not only from the point of view of being able to put a proposal through but also – and even more so – of being able to block the proposal. For that purpose, they follow closely what is the minimal number of allies they need to have on their side to block the decision; e.g. from the beginning of the EEC in late 1950’s Germany never was in a position to be able to block the decision in the Council of her own. She always needed an ally; originally one, after Iberian enlargement two. The idea that Germany would need more allies to block the proposal after the Eastern enlargement and at the same time stay on equal position with other large countries seemed indigestible as may be seen from the solution both from Nice and from the Convention, even these rules have different consequences for Germany’s voting power (see Table 3);
  3. During the development of the EC/EU some member states had gained certain concessions in their position within the Council. After years, under the changing conditions, they still tend to guard their privileges. Spain may be taken as a good example; during the accession negotiations, she had to face major obstacles with the effect of long transition periods in major sectors of fisheries and agriculture when the EC protected its market against Spanish imports. Compensation was found in the institutional sphere; Spain was allotted two Commissioners as the other large countries and eight votes in the Council. When the decision was taken to limit the number of Commissioners nominated from each member state to one, Spain asked for replacement of the old compensation in form of votes in the Council. She gained the replacement in Nice, her 27 votes. She wants to be treated as a large country with institutional position as close to the larger partners as possible.
  4. Recent discussions about the feasible solutions of the reform of the decision-making rule of the Council during the IGC of 2000 brought attention to the fact that most of the proposals, which tried to give more weighted votes to the larger countries, when applied to the enlarged EU, have the effect that the qualified majority need not represent the majority of member states. This was unacceptable particularly to smaller states. They succeeded in Nice to incorporate the criterion of simple majority of members as an extra rule.(5)
  5. Last, but not least, one of the main objectives of the IGC 2000 was to find institutional solutions, which would be transparent and understandable to citizens of the EU. Treaty of Nice in its part on the Council went in the opposite direction; next to reweighting of votes added two extra criteria (majority of members and 62 percent of population of the EU). The Draft Constitution tried to rectify this failure by proposing only two criteria; majority of members and 60 percent of population. Unfortunately, the effect of this particular configuration of thresholds on equitability of the procedure is outstandingly negative (see Table 4).


Table 3

Table 4

II. Construction of the decision-making ruleto contents list

The alternative decision-making rule is designed for 25 current members of the EU. The reason for this particular number is the fact that these member states will have to take decision on eventual changes of the institutional setting (i.e. on the Treaty on Constitution). The steps taken in designing the alternative decision-making rule may be described as follows:

(1) The main criterion for the construction of the rule is the equitable representation of voters; therefore, the square-root rule will lead the basic design. The old established form of weighted votes will be respected. We will assume that the appropriate distribution of the voting powers of the member states is possible to achieve by allotting the weighted votes proportionately to the square root of member state’s population(6); namely, we will

After performing these steps for all member states, we get a distribution of votes slightly reminding of the distribution accepted in Nice (allotted votes are in the interval between 2 and 29 votes; see Table 1).

Table 1

(2) An argument that the qualified majority should include also the majority of member states is accepted as valid since the legitimacy of a decision-making rule not guaranteeing this requirement would be doubtful. Therefore, the proposed procedure will have second criterion – majority of member states ( > 50 percent).

The key question is at what level the quota of both criteria should be set, as this parameter of the solution is as important as the basic design of weighted votes.(7) The quota of the criterion of member states is set on the abovementioned level of > 50 percent, as there is neither reason nor real demand for a higher level. The problem, which stays is the quota of weighted votes.


II.I. Setting the quota of weighted votesto contents list

The method for setting the optimal level of the quota of weighted votes is based on assumption that:

  1. During the lengthy discussions on possible solutions of the problem of reweighting the threshold was looked for in the interval between 60 percent and the current level (app. 71 percent);
  2. The influence of the level of the quota has to be tested by the consecutive computations of the voting power effect of different levels of the quota.

Following these assumptions, the proposed decision-making rule was tested in 15 variants with different levels of quota of weighted votes in the interval between 60 and 70 percent, adding two more votes to the quota of each consecutive variant of solution. The results were analyzed according to the aforementioned criteria and the level of the quota of weighted votes was set on two-thirds majority.

From the fifteen variants which differ only by the level of the quota of weighted votes (60 to 70 percent) the variant with quota 184 votes (of the total 276) was chosen, which is exactly two-thirds majority. The reasons for this choice follow:

  1. Two thirds of weighted votes combined with majority of member states seem to fulfil the requirement for legitimacy for the qualified majority rule. The level is approximately in the middle of the interval between the current level of the quota (71 percent plus of weighted votes) and the level proposed in the Draft Treaty on the Constitution (60 percent of population). The requirement for the majority of member states was practically always present in the decision-making rules for the Council (either implicitly, because it was not possible to assemble the qualified majority of votes without the majority of members being part of it, or by the explicit requirement stated in the rules – Nice Treaty, Draft Constitution)(8);
  2. The two-thirds level of the quota meets the above-mentioned rigorous criteria at satisfactory level. Analysis that is more detailed follows in the next section of the article.
  3. The two-thirds level of the quota provides also for other criteria given by the positions of the member states, namely the aim to keep as much capacity to block the decision as possible. Germany succeeded both under the Nice Treaty and under the Draft Constitution to be in the Council in a position to block a decision if two of the three other largest countries – Britain, France and Italy – were willing to join her. Each of these three has to look for at least three other partners, two of them large, to achieve the same goal. Under the proposed solution, Germany would keep stronger blocking power than the other three largest countries, but would need three large partners. Among them could be also Spain and Poland. Such a solution may be acceptable to Germany – it would keep more blocking power than the other largest three – and at the same time, it may be acceptable to Spain and Poland, as they would be among the large countries in a similar position. (For the effect of changing quota on the position of groups of member states, see Table 2.)

Table 2



This variant is subsequently compared with the decision-making rules as given by the Treaty of Nice and the Draft Treaty on Constitution. In the next step, it is also compared with the proposal presented as optimal by Felsethal and Machover.(9)

III. Results and comparisonto contents list

The qualities of the alternative proposal of the decision-making rule are presented in four figures depicting the effect of the level of quota on the main parameters used for evaluation: standard deviation of the equitability, mean majority deficit, compliance and resistance (Figures 1 to 4). In general, the values of the first two should be small, the smaller the value the better. The compliance and resistance, unlike the prior two parameters, have no predetermined optimal values, the value would fluctuate between the limits given in part I.I (3). The higher the value of A, the easier it would be to get the proposal approved. The value of the reverse indicator, resistance R, grows with the collective ability to block the proposal.

It may be seen that the quota was set at the level, which provides for very low value of standard deviation of e. Even the equitability was the main criterion for setting the quota, the selected threshold does not represent the lowest value of this parameter. The reason is in the application of the three other criteria, as their values are declining – in terms of quality of the rule – with the rising quota (compare Figures 1 with 2 to 4). Next to it, the political criteria described in I.II pointed to the two-thirds level. It provides for satisfactory value of equitability and at the same time for both real (in terms of voting power) and symbolic difference in the position of Germany on one hand, and for the symbolic “near equality” of Spain and Poland with the other large countries on the other hand.

The comparison of the main indicators of all decision-making rules is presented in a synoptic Table 5. In the first step, we will compare the alternative proposal (ALTER) with the rules embodied in the Treaty of Nice and the Draft Constitution. In terms of equitability as a main criterion of the quality of the decision-making rule, the proposed rule is markedly better. Not only is the standard deviation as a measure of overall balance of the rule significantly lower, but also the deviations from the optimal value (e = 1) for individual member states are considerably smaller (Table 4). The value of the mean majority deficit of the alternative proposal finds itself between the rules from Nice Treaty and the Draft Constitution. The main factor influencing the value of this parameter is the level of the quota. Because the ALTER has higher level of the quota of weighted votes/population than the Draft Constitution, it also has higher value of MMD. As to the values of the compliance and resistance of the proposed rule, they also may be found in between the values hit by the other two rules. It should be easier to approve a proposal than under the rule given by the Nice Treaty – often criticized for very high resistance (Baldwin, Berglöf, Giavazzi, Widgrén, 2001; Felsenthal & Machover, 2001) – but it should be considerably more difficult than under the rule proposed by the Draft Constitution. Since there is not an optimal value of these parameters agreed upon, we may resort to comparison with the situation in the EU 15 before enlargement. And here we see that under the proposed ALTER rule the resistance becomes slightly lower with the logical consequence that it should be little bit easier to approve the proposal. This aspect of the comparison seems to be very important, since we hardly find an argument why the decision-making should be considerably easier under the new rules, as they are presented in the Draft Constitution after enlargement by ten new member states, than it was up to now in the EU of 15 members. In this respect, we may consider the values of compliance and resistance as adequate.



And here we may proceed to the comparison of the ALTER with another theoretical rule proposed by Felsenthal and Machover (F&M; Rule B)(10). The basic approach to the construction of the decision-making rule was in both cases similar: the main criterion of the quality of the rule was the equitability as measured on the basis of the Penrose’s square root rule. The further steps were little bit different. F&M designed a distribution of weighted votes allowing very fine differentiation based on the differences of the square roots of the population of member states (see note to Table 1). They dismissed the criterion of majority of member states and set the level of the quota on 60 percent of weighted votes; that makes the main differences of the two compared rules. As a result, the values of most of the parameters used for comparison are quite different. The Rule B reaches almost ideal values of equitability; in this respect are the Rule B and ALTER very close. In all the other parameters, they differ to various degrees. Rule B has lower MMD, very close to Draft Constitution – the reason for that may be seen in the identical level of the quota (60 percent; see the value of MMD for the lowest level of the quota – Figure 2). Rule B has considerably lower level of resistance, higher than the Draft Constitution but fundamentally lower than the rule of Nice. Consequently it has also higher level of compliance compared to ALTER and Nice, but still lower that the Draft Constitution.

Figure 1

Figure 2

Figure 3

Figure 4

The final question is which of these two rules should be recommended as a solution to the most sensitive of the problems that caused the breakdown of the IGC last December? If we would stick to the equitability as the only criterion, then the Rule B should be the choice. But if we take into consideration also the other criteria, there might be arguments put forward advising against it.

  1. Rule B does not provide for the majority of member states being the prerequisite for attaining the QM. Theoretically, only 9 member states would suffice to put the proposal through against the majority of 16 medium, minor and small countries.
  2. The symbolic difference in the position of Germany as the most populous country of the EU as reflected in needing smaller number of partners to block the decision than the other large countries is not guaranteed. Under Rule B Germany would need at least four partners, as many as the other large countries.
  3. The most contentious conclusions relate to the level of compliance/resistance. As we do not have any reasoned opinion on specific optimal level of these parameters applicable to the qualified majority rule, we only may compare the effects of various decision-making rules on the values of A and R. After comparing these values, we may ask: why it should be much easier to put the proposal through in the enlarged EU – as indicated by the values of A and R for the Rule B – than it was up to now in EU 15 or it was in EU 12 ten years ago? (see Table 5) As this question is not being answered in any of the articles of F&M related to their proposal, we should stick to a more conservative position provided by the ALTER proposal for EU after enlargement. It would be little bit easier to approve a proposal than it was before recent enlargement and little bit more difficult than it was ten years ago when the EU had only twelve members.
  4. Last but not least, Rule B allows very fine distinctions of weighted votes based on differences of the square roots of population. On one hand, it guarantees the optimal level of equitability, on the other hand it may induce a need for yearly recalculation of weighted votes, since a shift of hundred thousand (growth or decline) in population numbers results in modification in allotted votes.

To sum up, the ALTER proposal represents a satisfactory solution to the problem of decision-making rule for the Council in all parameters and next to it reflects some major political arguments, which cannot be ignored, should this question have a chance to be solved.

Referencesto contents list

Act concerning the conditions of accession of the Czech Republic, the Republic of Estonia, the Republic of Cyprus, the Republic of Latvia, the Republic of Lithuania, the Republic of Hungary, the Republic of Malta, the Republic of Poland, the Republic of Slovenia and the Slovak Republic and the adjustments of the Treaties on which the Europaen Union is founded, AA2003/ACT, Athens, 16 April 2003

Baldwin, R.E., Berglöf, E., Giavazzi, F., Widgrén, M. (2001), Nice Try: Should the Treaty of Nice be Ratified?, MEI 11(Centre for Economic Policy Research: London)

Baldwin, R.E., Widgrén, M. (2003), Decision Making and the Constitutional Treaty: Will the IGC discard Giscard?, http://hei.unige.ch/%7Ebaldwin/PapersBooks/Decisionmaking_and_theCT.pdf.

Bindseil, U. and Handtke, C. (1997) ‘The power distribution in decision making among EU member states’. European Journal of Political Economy, Vol. 13, pp.171–85.

Draft Treaty establishing the Constitution for Europe, CONV 850/03, Bruxelles, 18 July 2003

Felsenthal, D.S. and Machover, M. (1998) The Measurement of Voting Power. Theory and Practice, Problems and Paradoxes (Edward Elgar: Cheltenham).

Felsenthal, D.S. and Machover, M. (2000) Enlargement of the EU and Weighted Voting in its Council of Ministers, http://www.lse.ac.uk/votingpower.

Felsenthal, D.S. and Machover, M. (2001) The Treaty of Nice and the Qualified Majority Voting, http://www.lse.ac.uk/votingpower.

Felsenthal, D.S. and Machover, M. (2003), Analysis of the QM Rules in the Draft Constitution for Europe Proposed by the European Convention, 2003, http://www.lse.ac.uk/votingpower.

Felsenthal, D.S. and Machover, M. (2004), A Priori Voting Power: What Is It All About? Political Studies Review, Vol. 2, No. 1, p. 1-23

Leech, D., (2001) Fair Reweighting of the Votes in EU Council of Ministers and the Choice of Majority Requirement for Qualified Majority Voting during Successive Enlargements, CSGR Working Paper No 75/01, June 2001.

Leech, D. and Machover, M., (2003) Qualified Majority Voting: The Effect of the Quota, in: Holler, M., Kliemt, H., Schmidtchen, D., Streit, M. (eds.) Jahrbuch für Neue Politishe Oekonomie, Band 22, (Tübingen).

Plechanovová, B., (2003a) The Treaty of Nice and the Distribution of Votes in the Council: Voting Power Consequences for the EU after the Oncoming Enlargement, European Integration online Papers, 2003, Vol. 7, No. 6, http://eiop.or.at/eiop/texte/2003-006a.htm.

Plechanovová, B., (2003b), Voting Power Indices in Analysis of the Political System of the European Union, in: Dvoráková, V., Heroutová, A. (eds.), II. Kongres ceských politologu (Ceská spolecnost pro politické vedy: Praha).

Treaty of Nice amending the Treaty on European Union, the Treaties establishing the European Communities and certain related Acts, SN 1247/1/01 REV 1, Brussels, 14 February 2001

Endnotesto contents list

(1) We may assume that the ratio between the number of inhabitants and the number of voters is very similar in all member countries, so we will use the data on population instead of the number of voters for the purpose of further consideration.

(2) For explanation of reasons of the use of Banzhaf index for the purpose of assessment of constitutional solutions see: Felsenthal & Machover (2004).

(3) For the theorem and proof see Felsenthal & Machover (1998), pp. 55-56, 66-67.

(4) Penrose L.S. (1946) The elementary statistics of majority voting, The Journal of the Royal Statistical Society, 1946, Vol. 109, p. 57, cit. in: Felsenthal & Machover (1998), p. 39. With electoral districts large as the member states of the EU are we may use the number of inhabitants instead.

(5) The distribution of weighted votes together with the level of quota (threshold) guaranteed and until the end of October 2004 still guarantees that the qualified majority always contains also majority of member states. (Exception to this rule was a short period after Greek accession and before Iberian enlargement when QM could be gathered up by just half of member states.)

(6) The Penrose square root rule says that the voting powers should be proportional to the square root of the population rather than the weights, but the allocation of weighted votes according to the square root of population has been used in several proposals with satisfactory results as to the distribution of voting power and equitability, e.g. the Swedish proposal to IGC 2000 analyzed in Plechanovová (2003a), in Felsenthal & Machover (2000), Leech (2002).

(7) On the question of quota see Leech (2001); Leech & Machover (2003). For illustration of the effect on concrete proposals using the same distribution of “weighted votes” but different levels of quota see Plechanovová (2003b), p. 179-183.

(8) For the exemption from this rule see note 5.

(9) First presented in Felsenthal & Machover (2000), repeatedly endorsed in Felsenthal & Machover (2003), (2004).

(10) For the purpose of comparison the design of F&M was applied to the EU of 25 members using the same population data (Eurostat, 2004) as for all the other rules under comparison. F&M have not published their own evaluation of the proposed Rule B with complete data neither for the EU 25 nor for 27, only for EU 28. (Felsenthal & Machover; 2000).

©2004 by Bela Plechanovová
formated and tagged by KH, 31.8.2004