Course: The Institutions of the EU
Topic of the session: Decision – making and voting in the EU
Tutor: Sophie Wulk (MA/MSc)
Notes from: 07th of May 2010
By: Martyna Pelczynska
Chair: Kenan Çarpan
DECISION - MAKING AND VOTING IN THE EUROPEAN UNION
Outline of the main issues discussed during the session:
1. Introduction
2. Statistical approach to weighted voting system with regard to the concept of power
- Banzhaf Power index
- Shapley – Shubik Power index
3. Banzhaf Power index
- Key concepts and the formula
- Calculating the index
- Practical example
4. Shapley - Shubik Power index
- Key concepts and the formula
- Calculating the index
- Practical example
5. Questions and Ideas for next week session
1. Introduction
Decision - making process in European Union is based on interaction between The
European Commission, The European Parliament and The Council. In this constellation The
Council is claimed to be the main decision-making body. The process itself is very
complicated and might vary depending on the subject. The main point is that in every scenario
close interinstitutional collaboration is required and all the decisions are reached by votes
which are organized in special systems.
Presently in EU policy making practice, 3 types of voting methods can be differentiated:
A) Unanimity
B) Simple majority
C) Qualified majority
Currently, the most important function is subscribed to Qualified Majority Voting (QMV)
which has become the feature of decision- making in The Council and is used at the large
scope of policy making cases. QMV is a weighted voting system in which votes are
distributed between Member States according to the size of population. The bigger the
country’s population, the more votes it has. In the present situation, taking into account that
there are 27 Member States, the qualified majority is reached if at least 255 votes in favour
are cast by at least 14 Council members. In addition, it has to be confirmed that the votes in
favour represent at least 62% of the EU population.
2. Statistical approach to weighted voting system with regard to
the concept of power
Weighted voting system is simply a mechanism in which “the preferences of some
voters carry more weight than the preferences of other voters”. It has always been the subject
of many discussions between politicians, lawyers and sociologists. One could find many
materials tackling this issue from different points of views. Among all the perspectives that
could be used for analysis of this method, the statistical approach usually receives less
attention than political or legal one.
Weighted voting system is based on mathematical models which could be examined with
statistical tools. Thanks to this apparatus, it is possible to analyze the distribution of the
decision power of each voter or each country as it is the case with the EU. Nevertheless, to be
able to study this matter, we need special formulas or indexes. Among all the methods, the
two mostly used to calculate the power of each voter are:
1) Banzhaf Power index developed by John Francis Banzhaf III
2) Shapley – Shubik Power index invented by Lloyd Stowell Shapley Martin Shubik
3. Banzhaf Power index
John Francis Banzhaf III (02.07.1940 - )
 Legal activist
 Law professor at George Washington University Law
School
 The inventor of the Banzhaf Power Index for
examining weighted voting systems according to their
members' abilities to force quorums.
 Key concepts and the formula
The formula is based on the fact that each player is an individual who has certain
amount of votes and in this way is worth a certain weight. All players (voters) can form
coalitions of different sizes and leave them freely. It has to be noted that the weight of
a player is not equal to his power. Usually in each coalition we can find more than one critical
player. In this context, the influence of the player is proportional to the number of times he is
critical.
Key concepts:
Quota- the number of votes that is required to pass a motion
Player – individual who posses votes (power) and is worth certain weight
Critical player – individual who can cast critical vote and whose departure would turn
winning coalition into a losing one
Winning coalition- the group of players whose votes joined together can pass a motion.
Loosing coalition- the group of players who cannot pass a motion.
Banzhaf Power Index for a Player P:
BPI (P) =
# of times Player P is critical
Total # of times all Players (together) are critical
 Calculating the Banzhaf Power Index
Step 1
Determine all the winning coalitions
Determine the critical players in each
Step 2
winning coalition.
Find the number of times all players are
Step 3
critical
Step 4
Find the number of times Player P is critical
Calculate BPI index for each Player
according to formula :
Step 5
BPI(P) = (# of times player P is critical) /
(# times all are critical)
THE BANZHAF POWER DISTRIBUTION IS COUNTED.
 Practical Example
Quota
4
Which player has the most power?
P1
3
P2
2
P3
2
Solution
Step 1 – determine all the winning coalitions
Step 2 - determine the critical players in each
winning coalition.
Step 3 - find the number of times all players
are critical
Step 4 - Find the number of times Player P is
critical
{P1, P2}; {P1, P3}; {P2, P3}; {P1, P2, P3}
There are 4 winning coalitions
Winning coalition
Critical player
{P1, P2}
P1 & P2
{P1, P3}
P1 & P3
{P2, P3}
P2 & P3
{P1, P2, P3}
none
There are 6 critical players
Altogether all players are critical 6 times
P1 – is critical 2 times
P2 – is critical 2 times
P3 – is critical 2 times
Each player is critical twice
Step 5 - Calculate BPI index for each Player BPI(P1)= 2/6 = 1/3
according to formula
BPI(P2)= 2/6 = 1/3
BPI(P3)= 2/6= 1/3
Each player has the same power even
though the weights are different.
4. Shapley - Shubik Power index
Shapley – Shubik Power Index

Was formulated by Lloyd
Shapley and Martin Shubik in
1954
 Is used to measure the powers
of players in a voting game.
Martin Shubik (24.03.1926 - )
 Seymour H. Knox Professor of
Mathematical Institutional
Economics at Yale University
 The author of approximately twenty
books and over 200 articles
 Specializes primarily in strategic
analysis.
Lloyd S. Shapley (02.06.1923 - )



American mathematician and
economist.
Professor Emeritus at University of
California, Los Angeles.
Specializes in fields of mathematical
economics and game theory
 Key concepts and the formula
The formula is also founded on the same assumption that each player is an individual
who has certain amount of votes and in this way carry certain weight. All players can form
sequential coalitions which are of the same size dependant on numbers of players. Unlike in
Banzhaf Power Index players enter coalitions in certain order and cannot freely leave them. In
each coalition one pivotal player can be determined. It has to be again noted that the weight of
a player is not equal to his power. A player’s power is proportional to the number of times the
player is pivotal.
Key concepts:
Quota- the number of votes that is required to pass a motion
Player – individual who posses votes (power) and is worth certain weight
Pivotal Player – the player whose votes cause the coalition's votes to equal or exceed the
quota.
Sequential Coalition - is one in which the players are listed in the order that they entered the
coalition.
Winning coalition – the group of players whose votes joined together can pass a motion.
Losing Coalition - the group of players who cannot pass a motion
Shapley – Shubik Power Index for a Player P:
SSPI (P) =
# of times Player P is pivotal
Total # of times all Players (together) are pivotal
 Calculating the Shapley – Shubik Power Index
Make a list of all N! sequential coalitions
containing N players
Determine the pivotal player in each of these
Step 2
coalitions,
Determine the number of times Player P is
Step 3
pivotal
Calculate SSPI index for each Player
according to formula :
Step 4
SSPI(P) = (# of times player P is pivotal) /
(# times all are pivotal)
THE SHAPLEY – SHUBIK POWER DISTRIBUTION IS COUNTED.
Step 1
 Practical Example
Quota
4
Which player has the most power?
P1
3
P2
2
P3
2
Solution
Step 1 – Make a list of all N! sequential
coalitions containing N players
3!=3*2*1 = 6 variations
{P1, P2, P3};{P1, P3, P2};{P2, P1, P3};
{P2, P3, P1};{P3, P1, P2};{P3, P2, P1}
Step 2 - Determine the pivotal player in each of Sequential Coalition
Pivotal player
these coalitions ( only on per coalition)
{P1, P2, P3}
P2
{P1, P3, P2}
P3
{P2, P1, P3}
P1
{P2, P3, P1}
P3
{P3, P1, P2}
P1
{P3, P2, P1}
P2
Step 3 - Determine the number of times Player P1 – is pivotal 2 times
P is pivotal
P2 – is pivotal 2 times
P3 – is pivotal 2 times
Each Player is pivotal twice
Step 4 - Calculate SSPI index for each Player BPI(P1)= 2/6 = 1/3
according to formula:
BPI(P2)= 2/6 = 1/3
SSPI(P) = (# of times player P is pivotal) / BPI(P3)= 2/6= 1/3
(# times all are pivotal)
Each player has the same power even
though the weights are different. The
distribution of power is equal.
5. Questions and Ideas for next week session
What comes to our mind when we think about informal aspects of decision – making process?
(keywords, phrases, questions)
-
Corruption
Lobbying
Not public
Efficiency
Legitimacy
Priorities
Multispeed Europe
Backwards justification
Personal relations
Individual Interests
Open method of coordination
Who has the power in decision-making?
The average of agreements made on formal and informal level
How are decisions really made?