Nice European Council
December 2000
Included in the Treaty of Nice
are changes to the following institutional provisions:
- The size and composition of the European Commission.
- The weighting of votes in the Council and the introduction of
voting rules with triple majority.
- The extension of qualified-majority voting.
By applying generating functions, The Seville
Game Theory Group obtain the power of the countries under
the Nice rules, exposed in the Protocol
on the Enlargement of the European Union.
La batalla de Niza por Javier Elorza, El País 21 diciembre de 2000
El abrazo de la Unión por Enrique Barón, El País 29 junio de 2000
The countries in the future European Union Council are:
{Germany, United Kingdom, France, Italy, Spain, Poland, Romania,
The Netherlands, Greece, Czech Republic, Belgium, Hungary, Portugal,
Sweeden, Bulgaria, Austria, Slovak Republic, Denmark, Finland, Ireland,
Lithuania, Latvia, Slovenia, Estonia, Cyprus, Luxembourg, Malta}
The population in millions of the above countries is presented in the ordered set:
{82.038, 59.247, 58.966, 57.612, 39.394, 38.667, 22.489,
15.760, 10.533, 10.290, 10.213, 10.092, 9.980,
8.854, 8.230, 8.082, 5.393, 5.313, 5.160, 3.744,
3.701, 2.439, 1.978, 1.446, 0.752, 0.429, 0.379}
The index of population is given by
{0.170, 0.123, 0.123, 0.120, 0.0819, 0.0804, 0.0467,
0.0328, 0.0219, 0.0214, 0.0212, 0.0210, 0.0207,
0.0184, 0.0171, 0.0168, 0.0112, 0.0110, 0.0107, 0.00778,
0.00769, 0.00507, 0.00411, 0.00301, 0.00156, 0.000892, 0.000788}
The proportional rule gives us the following apportionment
of 345 votes in the 27-EU:
{58,42,42,41,28,28,16,11,7,7,7,7,7,6,6,6,4,4,4,3,3,2,1,1,1,0,0}
The Nice rule of distribution of 345 votes is given by:
{29,29,29,29,27,27,14,13,12,12,12,12,12,10,10,10,7,7,7,7,7,4,4,4,4,4,3}
Proportional and Nice 27-EU Apportionment
The proportional rule gives us the following apportionment of 237 votes in the 15-EU:
{52,38,37,37,25,10,7,6,6,6,5,3,3,2,0}
On 1 January 2005, the Nice rule of distribution of 237 votes in the 15-EU
is given by:
{29,29,29,29,27,13,12,12,12,10,10,7,7,7,4}
Proportional and new 15-EU Apportionment
Proportional and old 15-EU Apportionment
On January 2005 in the 15-EU:
Acts of the Council shall require for their adoption at least 169 votes in favour
cast by at least a majority of the members where this Treaty requires them to be
adopted on a proposal from the Commission.
When a decision is to be adopted by the Council by a qualified majority, a
member of the Council may request verification that the qualified majority
comprises at least 62% of the total population of the Union.
If that condition is shown not to have been met, the decision in question shall
not be adopted.
The Banzhaf Power in the 15-EU with the
majority Nice rule
The distribution of population and Banzhaf power indices, under the
Nice weighting of votes with the quota q = 169, the mayority of the
members and the 62% of the total population is:
People Banzhaf V Banz V+M Banz V+M+P
Germany 0.219 0.119 0.119 0.121
United Kingdom 0.158 0.119 0.119 0.120
France 0.157 0.119 0.119 0.120
Italy 0.153 0.119 0.119 0.120
Spain 0.105 0.111 0.111 0.111
Netherlands 0.0420 0.0554 0.0554 0.0550
Greece 0.0281 0.0521 0.0521 0.0516
Belgium 0.0272 0.0521 0.0521 0.0516
Portugal 0.0266 0.0521 0.0521 0.0516
Sweeden 0.0236 0.0432 0.0432 0.0430
Austria 0.0215 0.0432 0.0432 0.0430
Denmark 0.0142 0.0312 0.0312 0.0309
Finland 0.0137 0.0312 0.0312 0.0309
Ireland 0.00998 0.0312 0.0312 0.0309
Luxembourg 0.00114 0.0203 0.0203 0.0196
The Banzhaf Power in the 15-EU with the
2/3 Nice rule
In other cases, for their adoption acts of the Council in the 15-EU shall require at least
169 votes in favour, cast by at least two thirds of the members.
The distribution of population and Banzhaf power indices, under the
Nice weighting of votes with the quota q = 169, the two thirds of the
members and the 62% of the total population is:
People Banzhaf V Banz V+(2/3) Banz V+(2/3)+P
Germany 0.219 0.119 0.104 0.106
United Kingdom 0.158 0.119 0.104 0.104
France 0.157 0.119 0.104 0.104
Italy 0.153 0.119 0.104 0.104
Spain 0.105 0.111 0.0984 0.0983
Netherlands 0.0420 0.0554 0.0598 0.0594
Greece 0.0281 0.0521 0.0563 0.0558
Belgium 0.0272 0.0521 0.0563 0.0558
Portugal 0.0266 0.0521 0.0563 0.0558
Sweeden 0.0236 0.0432 0.0502 0.0501
Austria 0.0215 0.0432 0.0502 0.0501
Denmark 0.0142 0.0312 0.0414 0.0412
Finland 0.0137 0.0312 0.0414 0.0412
Ireland 0.00998 0.0312 0.0414 0.0412
Luxembourg 0.00114 0.0203 0.0326 0.0319
Number of decisive coalitions in the 15-EU
The total number of coalitions in the 15 European Union is 32768.
We calculate the number of winning coalitions to which the country
i is critical, that is, his defection implies that the coalition
to become losing. These coalitions are called swings for the country.
The total number of winning coalitions to wich a country is critical,
under the votes rule with q=169, is 16685. The total number of winning coalitions
to wich a country is critical, under the votes, majority and the population rules,
is 16550.
Swings 1 Swings 2 Swings 3 Sw3-Sw1
Germany 1989 1989 2004 15
United Kingdom 1989 1989 1984 -5
France 1989 1989 1984 -5
Italy 1989 1989 1984 -5
Spain 1853 1853 1838 -15
Netherlands 925 925 910 -15
Greece 869 869 854 -15
Belgium 869 869 854 -15
Portugal 869 869 854 -15
Sweeden 721 721 712 -9
Austria 721 721 712 -9
Denmark 521 521 512 -9
Finland 521 521 512 -9
Ireland 521 521 512 -9
Luxembourg 339 339 324 -15
The total number of winning coalitions to wich a country is critical,
under the Nice weighting of votes, the two thirds and the population
rules, is 15622.
Swings1 Swings2/3 Swings3 Sw3-Sw1
Germany 1989 1637 1652 -337
United Kingdom 1989 1637 1632 -357
France 1989 1637 1632 -357
Italy 1989 1637 1632 -357
Spain 1853 1551 1536 -317
Netherlands 925 943 928 3
Greece 869 887 872 3
Belgium 869 887 872 3
Portugal 869 887 872 3
Sweeden 721 791 782 61
Austria 721 791 782 61
Denmark 521 653 644 123
Finland 521 653 644 123
Ireland 521 653 644 123
Luxembourg 339 513 498 159
When all the candidates countries have
acceded:
Acts of the Council shall require for their adoption at least 255 votes in favour
cast by at least a majority of the members where this Treaty requires them to be
adopted on a proposal from the Commission.
When a decision is to be adopted by the Council by a qualified majority, a
member of the Council may request verification that the qualified majority
comprises at least 62% of the total population of the Union.
If that condition is shown not to have been met, the decision in question shall
not be adopted.
The Banzhaf Power in the 27-EU with the
majority Nice rule
The distribution of population and Banzhaf power indices, under the
Nice weighting of votes with the quota q = 255, the mayority of
the members and the 62% of the total population is:
Countries People Banzhaf V Banzhaf V+M Banzhaf V+M+P
Germany 0.170 0.0778 0.0778 0.0778
United Kingdom 0.123 0.0778 0.0778 0.0778
France 0.123 0.0778 0.0778 0.0778
Italy 0.120 0.0778 0.0778 0.0778
Spain 0.0819 0.0742 0.0742 0.0742
Poland 0.0804 0.0742 0.0742 0.0742
Romania 0.0467 0.0426 0.0426 0.0426
Netherlands 0.0328 0.0397 0.0397 0.0397
Greece 0.0219 0.0368 0.0368 0.0368
Czech Republic 0.0214 0.0368 0.0368 0.0368
Belgium 0.0212 0.0368 0.0368 0.0368
Hungary 0.0210 0.0368 0.0368 0.0368
Portugal 0.0207 0.0368 0.0368 0.0368
Sweeden 0.0184 0.0309 0.0309 0.0309
Bulgaria 0.0171 0.0309 0.0309 0.0309
Austria 0.0168 0.0309 0.0309 0.0309
Slovak Republic 0.0112 0.0218 0.0218 0.0218
Denmark 0.0110 0.0218 0.0218 0.0218
Finland 0.0107 0.0218 0.0218 0.0218
Ireland 0.00778 0.0218 0.0218 0.0218
Lithuania 0.00769 0.0218 0.0218 0.0218
Latvia 0.00507 0.0125 0.0125 0.0125
Slovenia 0.00411 0.0125 0.0125 0.0125
Estonia 0.00301 0.0125 0.0125 0.0125
Cyprus 0.00156 0.0125 0.0125 0.0125
Luxembourg 0.000892 0.0125 0.0125 0.0125
Malta 0.000788 0.00942 0.00942 0.00942
The power of the countries, under the triple Nice rule and
the first voting rule, coincides. Their differences are less or equal than 1/10000.
The Banzhaf Power in the 27-EU with the
2/3 Nice rule
In other cases, for their adoption acts of the Council in the 27-EU shall require at least
255 votes in favour, cast by at least two thirds of the members.
The distribution of population and Banzhaf power indices, under the
Nice weighting of votes with the quota q = 255, the two thirds of
the members and the 62% of the total
population is:
Countries People Banzhaf V Banz V+(2/3) Banz V+(2/3)+P
Germany 0.170 0.0778 0.0665 0.0665
United Kingdom 0.123 0.0778 0.0665 0.0665
France 0.123 0.0778 0.0665 0.0665
Italy 0.120 0.0778 0.0665 0.0665
Spain 0.0819 0.0742 0.0631 0.0631
Poland 0.0804 0.0742 0.0631 0.0631
Romania 0.0467 0.0426 0.0407 0.0407
Netherlands 0.0328 0.0397 0.0386 0.0386
Greece 0.0219 0.0368 0.0366 0.0366
Czech Republic 0.0214 0.0368 0.0366 0.0366
Belgium 0.0212 0.0368 0.0366 0.0366
Hungary 0.0210 0.0368 0.0366 0.0366
Portugal 0.0207 0.0368 0.0366 0.0366
Sweeden 0.0184 0.0309 0.0325 0.0325
Bulgaria 0.0171 0.0309 0.0325 0.0325
Austria 0.0168 0.0309 0.0325 0.0325
Slovak Republic 0.0112 0.0218 0.0263 0.0263
Denmark 0.0110 0.0218 0.0263 0.0263
Finland 0.0107 0.0218 0.0263 0.0263
Ireland 0.00778 0.0218 0.0263 0.0263
Lithuania 0.00769 0.0218 0.0263 0.0263
Latvia 0.00507 0.0125 0.0198 0.0198
Slovenia 0.00411 0.0125 0.0198 0.0198
Estonia 0.00301 0.0125 0.0198 0.0198
Cyprus 0.00156 0.0125 0.0198 0.0198
Luxembourg 0.000892 0.0125 0.0198 0.0198
Malta 0.000788 0.00942 0.0177 0.0177
The power of the countries, under the triple Nice rule and
the double Nice rule (votes with q = 255 and two thirds of the countries), coincides.
Their differences are less or equal than 1/10000.
Number of decisive coalitions in the 27-EU
The total number of coalitions in the 27-European Union is 2^27 = 134217728.
We calculate the number of winning coalitions to which the country i is critical,
that is, his defection implies that the coalition to become losing.
The total number of winning coalitions to wich a country is critical,
under the votes Nice rule, is 28 186 428.
The total number of winning coalitions to wich a country is critical,
under the votes, majority of the countries and population Nice rules, is 28 186 324.
Countries Sw1 (V) Sw2 (V+M) Sw3 (V+M+P) Sw3-Sw1
Germany 2193664 2193648 2193654 -10
United Kingdom 2193664 2193648 2193650 -14
France 2193664 2193648 2193650 -14
Italy 2193664 2193648 2193650 -14
Spain 2091380 2091364 2091358 -22
Poland 2091380 2091364 2091358 -22
Romania 1200504 1200488 1200482 -22
The Netherlands 1120138 1120122 1120116 -22
Greece 1038492 1038482 1038476 -16
Czech Republic 1038492 1038482 1038476 -16
Belgium 1038492 1038482 1038476 -16
Hungary 1038492 1038482 1038476 -16
Portugal 1038492 1038482 1038476 -16
Sweeden 871654 871660 871654 0
Bulgaria 871654 871660 871654 0
Austria 871654 871660 871654 0
Slovak Republic 614702 614718 614712 10
Denmark 614702 614718 614712 10
Finland 614702 614718 614712 10
Ireland 614702 614718 614712 10
Lithuania 614702 614718 614712 10
Latvia 352374 352390 352384 10
Slovenia 352374 352390 352384 10
Estonia 352374 352390 352384 10
Cyprus 352374 352390 352384 10
Luxembourg 352374 352390 352384 10
Malta 265568 265584 265584 16
TOTAL 28186428 28186444 28186324 -104
The total number of winning coalitions to wich a country is critical,
under the votes, 2/3 of the countries and population Nice rules, is 24 502 539.
Countries Swings1 Swings2/3 Swings3 Swin3-Swin1
Germany 2193664 1628747 1628753 -564911
United Kingdom 2193664 1628747 1628749 -564915
France 2193664 1628747 1628749 -564915
Italy 2193664 1628747 1628749 -564915
Spain 2091380 1547305 1547299 -544081
Poland 2091380 1547305 1547299 -544081
Romania 1200504 996561 996555 -203949
Netherlands 1120138 946969 946963 -173175
Greece 1038492 897313 897307 -141185
Czech Republic 1038492 897313 897307 -141185
Belgium 1038492 897313 897307 -141185
Hungary 1038492 897313 897307 -141185
Portugal 1038492 897313 897307 -141185
Sweeden 871654 796493 796487 -75167
Bulgaria 871654 796493 796487 -75167
Austria 871654 796493 796487 -75167
Slovak Republic 614702 643339 643333 28631
Denmark 614702 643339 643333 28631
Finland 614702 643339 643333 28631
Ireland 614702 643339 643333 28631
Lithuania 614702 643339 643333 28631
Latvia 352374 484411 484405 132031
Slovenia 352374 484411 484405 132031
Estonia 352374 484411 484405 132031
Cyprus 352374 484411 484405 132031
Luxembourg 352374 484411 484405 132031
Malta 265568 434737 434737 169169
TOTAL 28186428 24502659 24502539 -3683889
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The Treaty of Nice contains the Declaration on the enlargement of the
European Union and the Declaration on the qualified majority
threshold and the number of votes for a blocking minority in an
enlarged Union, which includes agreements that are a
contradiction in terms.
So, on the pages 82-83 of the Treaty after of the table 2, which
establishes the weighting of votes in the Council of 27 countries, it
says textually:
Acts of the Council shall require for their adoption at least 258 votes in
favour, cast by a majority of members, where this Treaty requires them to be
adopted on a proposal from the Commission. In other cases, for their
adoption acts of the Council shall require at least 258 votes in favour cast
by at least two-thirds of the members. When a decision is to be adopted by
the Council by a qualified majority, a member of the Council may request
verification that the Member States constituting the qualified majority
represent at least 62% of the total population of the Union. If that
condition is shown not to have been met, the decision in question
shall not be adopted.
Consequently, the qualified majority of 258 votes over a total of 345 votes
represents a percentage of the 74,78%. On the other hand, on the page 85 of
the Treaty, the Declaration on the qualified majority threshold
establishes that:
Insofar as all the candidate countries listed in the Declaration on the
enlargement of the European Union have not yet acceded to the Union
when the new vote weightings take effect (1 January 2005),
the threshold for a qualified majority will move, according to the
pace of accessions, from a percentage below the current one to a
maximum of 73,4%. When all the candidate countries mentioned above
have acceded, the blocking minority, in a Union of 27, will be
raised to 91 votes, and the qualified majority threshold resulting
from the table given in the Declaration on enlargement of the
European Union will be automatically adjusted accordingly.
When all candidate States are acceded, the total of votes in the Council
will be n = 345. Therefore, a blocking minority of b = 91 votes
will automatically imply a qualified majority of q = n + 1 - b = 255 votes,
which corresponds to the 73,91% of the votes. As a result:
The two qualified majorities of 258 and 255 votes, adopted in the
Treaty of Nice for the Council of 27 countries, are superior to the maximum
percentage of 73,4%, fixed in the Declaration on the qualified
majority threshold.
The qualified majority of 258 votes will never be able to be applied.
The reason is that the inclusion of all the candidates force to fix the
majority in 255 votes. In the case that all adhesions do not
take place, the majority threshold has to be smaller or equal
to 73,4% from a maximum of 342 votes
(345 minus 3), that is, less or equal than 251 votes.
Go to MBilbao Lab
December 9, 2003
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El poder
de las naciones en la Unión Europea
Computing power indices in weighted multiple majority games