Coalition theories
From seats to government
• After elections, parliamentary seats are
assigned and parliamentary party groups
formed
• Then coalition bargaining – if necessary –
begins for the formation of the
government/executive (cabinet)
Parliamentary coalitions
• Coalition theory tries to explain which
government coalitions are more likely to be
formed
• Given the electoral results, what are the
factors that are likely to determine the
formation of certain coalitions?
• These criteria are based on assumptions
about party behaviour
Coalition theories: a map
Minimal connected
winning coalition (Axelrod)
Office-seeking
Minimum
range
(Leiserson)
Policy seeking
Minimal/minimum
Winning coalition
(Riker)
Unidimensional
Bargaining
Proposition (Leiserson)
Bidimensional
De Swann
Institutions free (Laver;Schofield)
Bargaining
theories (Baron,
Diermeir,Merlo etc.)
Institutional rich (Laver, Shepsle)
Cooperative and Non Cooperative Game Theory
1. Cooperative game theory investigates coalitional games with
respect to the relative amounts of power held by various players,
or how a successful coalition should divide its proceeds.
2. In contrast, noncooperative game theory is concerned with the
analysis of strategic choices. The paradigm of noncooperative
game theory is that the details of the ordering and timing of
players’ choices are crucial to determining the outcome of a
game.
In the cooperative games binding agreements are possible
before the start of the game.
Cooperative Game Theory
1. A coalition C is a sub-set non empty of a set N of all players
2. A cooperative game is given by specifying a value for every
(nonempty) coalition. A so called characteristic function v assigns for
each coalition a payment. The function describes how much
collective payoff a set of players can gain by forming a coalition. The
players are assumed to choose which coalitions to form, according to
their estimate of the way the payment will be divided among
coalition members. It is assumed that the empty coalition gains nil or
in other terms v(Ø)=0.
3. v(TS)  v(S) + v(T) if S  T= Ø ;
4. An imputation is a game outcome (a possible solution) or a payoff
distribution (x1, x2…xn) among n players that respects the following
conditions:
a) iNxi = v(N); the players redistribute the “income” of the coalition
b) xi  v(i) for any player i ; None accepts a payoff inferior to what
he/she could earn on his/her own
5. An imputation x dominates an imputation y for a coalition C iff
a) The payoffs from x are higher than the payoffs from y for at least
some member of C (and equal for the others)
b) The sum of the n members payoffs of the coalition C does not
overcome v(C)
6. Definition of Core: the set of non dominated imputations or the set of
Pareto-optimal outcomes in a n-players bargaining game.
7. A simple game is a special kind of cooperative game, where the
payoffs are either 1 or 0. I.e. coalitions are either "winning" or
"losing". In other terms if W is the subset of the winning coalitions,
v(W) = 1. A winning coalition cannot become losing with the
addition of new members
8 A weighted majority game is a simple game in which a weight wi (for
instance percentage of MP’s) is assigned to each player i and a
coalition is winning when the sum of the w of each coalition member
is superior to a level q (for instance 50% of the majority rule) .
Formally iCwi  q;
Office-seeking models
In these models the political actors are motivated only by the interest
for the advantages coming from the office. The coalition making is
represented as a weighted majority game where the payoffs are either
1 or 0. As the payoffs are constant (1) and are not increased by adding
new members to the coalition, winning coalitions with members non
necessary to win give smaller portions of payoffs to its members than
smaller coalitions without unnecessary members
Winning coalition
with 80% of seats
C:Seats
18%
B:seats Po=0,225
D:seats
21%
22%
Po=0,2625
Po=0,275
A:seats
19%
Po=0,2375
Bigger slices!!
Winning coalition
with 58% of seats
C:Seats
B:seats
18%
21%
Po=0,3103
Po=0,3620
A:seats
19%
Po=0,3275
Office-seeking models
A winning coalition without unnecessary members is called “minimal
winning coalition”
The election of June 1952 in Netherlands
Parties
Seats
Minimal winning
coalitions
PvdA
KVP
ARP
VVD
CHU
33
33
14
10
10
PvdA,
KVP
PvdA,
ARP,
VVD
PvdA,
ARP,
CHU
KVP,
ARP,
VVD
KVP,
ARP,
CHU
PvdA,
CHU,
VVD
KVP,
CHU,
VVD
Too many game solutions. Riker hypothesizes that out of the minimal
winning coalitions it will form the coalition requiring as least
resources (seats) as possible: the minimum winning coalition
Office-seeking models
The election of June 1952 in Netherlands
Parties
PvdA
KVP
ARP
VVD
CHU
33
33
14
10
10
PvdA,
KVP
PvdA,
ARP,
VVD
PvdA,
ARP,
CHU
KVP,
ARP,
VVD
KVP,
ARP,
CHU
Seats
Minimal winning
coalitions
Minimum
Winning coalitions
(Size Principle)
VVD:10
0,1754
PvdA :33
0,5789
ARP:14
0,2456
PvdA,
CHU,
VVD
KVP,
CHU,
VVD
PvdA,
CHU,
VVD
KVP,
CHU,
VVD
VVD:10
0,1886
PvdA :33
CHU:10
0,6226
0,1886
Office-seeking models
According Leiserson among the minimal winning coalition
the coalition with the smallest number of parties will form
because of the bargaining costs
The election of June 1952 in Netherlands
Parties
Seats
Minimal winning
coalitions
PvdA
KVP
ARP
VVD
CHU
33
33
14
10
10
PvdA,
KVP
PvdA,
ARP,
VVD
PvdA,
ARP,
CHU
KVP,
ARP,
VVD
KVP,
ARP,
CHU
Minimum
Winning coalitions
(Size Principle)
Bargaining costs
criterion
PvdA,
KVP
PvdA,
CHU,
VVD
KVP,
CHU,
VVD
PvdA,
CHU,
VVD
KVP,
CHU,
VVD
Office-seeking policy “informed” models
According a pure office seeking coalition model policy positions
does not matter and coalition among ideologically different parties
are possible. However parties very different in terms of the ideology
must pay very high bargaining costs.
Axelrod: Minimal connected winning coalitions: The political
actors can be ordered along one dimension . The minimal winning
coalitions must have members ideologically adjacent.
Leiserson: Minimum Range: the winning coalitions must minimize
the ideological distance between the two extreme parties of the
coalition.
Office-seeking policy “informed” models
The election of June 1952 in Netherlands
Parties
Seats
Minimal winning
coalitions
PvdA
Left
KVP
ARP
VVD
CHU
Right
33
33
14
10
10
PvdA,
KVP
PvdA,
ARP,
VVD
PvdA,
ARP,
CHU
KVP,
ARP,
VVD
KVP,
ARP,
CHU
Minimum
Winning coalitions
(Size Principle)
Bargaining costs
criterion
PvdA,
KVP
Minimal
connected winning
coalitions
PvdA,
KVP
Minimum range
PvdA,
KVP
KVP,
ARP,
VVD
PvdA,
CHU,
VVD
KVP,
CHU,
VVD
PvdA,
CHU,
VVD
KVP,
CHU,
VVD
Policy-seeking models in one dimension
In these models the political actors are motivated also by the policy
distance between the expected policies of the government coalitions
and their policy platforms.
de Swann : Cooperative game-unidimensional. The policy positions
are ordered along one dimension. A political actor will prefer the
winning coalition whose policy position is the nearest to its preferred
policy position. In only one dimension any winning coalitions (in a
majority voting game) must include the party where is located the
median voter. This party is called the Core Party, it cannot be
excluded by the winning coalition and it controls its formation.
The coalitions in the Core (or the winning coalitions) can be more than
one.
According that de Swann the Core Party should prefer the coalition
that minimize the difference in terms of seats among the actors on the
left and on the right of the Core Party in the coalition or in other terms
the Core Party should prefer balanced coalitions.
Policy-seeking models
Core Party
Seats=100
L (45)
C (15)
R (40)
a)
L (55)
CL (20)
CR (10)
R (15)
b)
L (25)
CL (15)
C (8)
CR (5)
R (47)
c)
a) According to de Swann L,C,R is better for C than C,R or C,L
as |45-40|<|0-40|<|0-45|
b) Of course the best one is L
c) L,CL,C,CR,R is better for CR as |48-47| < any other
difference.
Policy-seeking models
Seats=100
L (45)
C (15)
R (40)
a)
L (55)
CL (20)
CR (10)
R (15)
b)
L (25)
CL (15)
C (8)
CR (5)
R (47)
c)
Def. Pareto Set: the set of points in the policy space that:
a) For any point not in the set there is in the set a point that is
preferred by all political actors taken in consideration.
b) Given a point in the set none else is considered better by all
political actors
c) For any winning coalition the Pareto set is given by the line
connecting the political actors members of the coalition
Policy-seeking models
Seats=100
L (45)
C (15)
R (40)
a)
L (55)
CL (20)
CR (10)
R (15)
b)
L (25)
CL (15)
C (8)
CR (5)
R (47)
c)
The Core Party is the party present in all Pareto Sets of all
winning coalition. It always exists in a unidimensional world
but..
Policy-seeking models
in a bidimensional policy space (Schofield)
A (20)
B (20)
C (20)
D (40)
Considering to simplify
the analysis, only the
minimal winning
coalitions, in this policy
space no Party is
“member” of all Pareto
Sets of all coalition. There
is always a majority that
can defeat any party
platform.
A (20)
B (20)
D (40)
C (20)
In this situation there is a
a party that is always
included in all Pareto sets
of all winning coalition. It
is D. No majority can
defeat the D’s political
platform.
A (20)
B (20)
C (20)
D (40)
However usually a
centrally located party is a
Core Party if it is quite
big.Otherwise no core
party exists. C is not a
Core party as is not in the
Pareto Set of the
coalitions AD and DB.
Even when a small party
centrally located is a Core
party such a equilibrium is
structurally unstable. ….
The election of June 1952 in Netherlands
Traditionalism
ARP:14
A structurally stable core at
the
KVP position
KVP:33
CHU:10
PvdA:33
Left
Right
VVD:10
Modernization
The election of June 1952 in Netherlands
Traditionalism
ARP:14
A structurally stable core at
the
KVP position
KVP:33
CHU:10
PvdA:33
Left
Right
VVD:10
Modernization
Traditionalism
PvdA:33
A structurally unstable core
at the
ARP position
ARP:14
VVD:10
CHU:10
Left
Right
KVP:33
Modernization
Traditionalism
PvdA:33
ARP:14
A structurally unstable core
at the ARP position: after a
small change in its policy
position, ARP is not a Core
Party any more as the Pareto
set PdvA, KVP,VVD does not
include it.
CHU:10
VVD:10
Left
Right
KVP:33
Modernization
Traditionalism
However even if it does not
exist a Core Party, the area of
the disequilibrium is
delimited by the intersections
of the median lines. The so
called Cycle Set.
Core+Cycle set= Heart
PvdA:33
median
ARP:14
CHU:10
VVD:10
Left
Right
KVP:33
Modernization
median
median
Policy-seeking models
in a bidimensional policy space (Laver-Shepsle)
• Laver-Shepsle theory is a theory about government formation, is
not a theory about “platform” bargaining.
• Laver-Shepsle approach models a real decision making process,
considers an initial status quo: it belongs to non cooperative game
theory.
yes R
P1 sel.
P2 sel
R
Proposes
x1
x1
Vetoed?
Proposes
x2
yes
x2
Vetoed?
Proposes
xi
Proposes
xn
Pn sel
no
R
x2
installed?
xn
Vetoed?
R
no
xi
installed?
yes
R
no
no
R
yes
x1
new SQ
no
yes
yes
xi
Vetoed?
Pi sel
no
x1
installed?
xn
installed?
no
yes
no
yes
R
R
x2
new SQ
R
R
xi
new SQ
R
R
xn
new SQ
R
A government programme
of ideal policies
According to Laver and Shepsle, the choice
of government is not that of a generic policy
programme, but that of a set of ideal policies
of those parties that manage to allocate their
own leaders to the different ministerial
positions
26
Government formation in
parliamentary democracies
• Government formation is also an act of delegation
from the parliamentary support coalition to the
executive
• It is based on a trade-off of benefits (e.g.
efficiency, expertise) and costs (e.g. risk of drift –
ministerial drift)
27
The set of possible governments
Possible governments forms a discrete set of
points on a multi-dimensional space
Each government is characterized by a set of
policies implemented by parties in charge of
those specific policies
‘Being in charge’ of a policy means having a
party representative heading the specific ministry
28
Example
• Three parties A, B and C
• Two key policies: economic policy and foreign
policy
• No party has the majority, but any two parties do
• There are 32=9 possible governments that
correspond to how the two positions (economic
minister, foreign minister) can be allocated to the
two parties
• Of these nine governments, 3 are single party
and 6 are coalition governments
29
foreign policy
forC
forA
forB
The lattice of possible
governments
AC
BC
AA
BA
CC
CA
AB
BB
CB
ecoA
ecoB ecoC economic policy
30
A stable government
• Which of these governments is stable?
• Assume that the status quo government is BA, that
is, the economic minister is from party B while the
foreign minister is from party A (note that BA is
different from AB even if the coalition is the same)
• Is there a majority coalition that prefers a
government to BA among those possible?
• Is the majority winset of BA empty?
31
foreign policy
AC
BC
AA
BA
AB
BB
CC
CA
CB
Party A prefers
governments inside
the circle centered in
AA and radius AA-BA
to the government BA,
and prefers
government BA to
those outside the
circle.
The same applies to
the other parties
economic policy
32
foreign policy
AC
BC
AA
BA
CC
CA
AB
BB
CB
W(BA) is
empty
BA is stable
government
economic policy
33
Defence spending
dC
Winset of BB
B is a strong
party
AC
BC
AA
BA
CC
CA
AB
BB
CB
dA
dB
sA
sB
sC
Social spending
34
• Where A and C can coalesce against B, there
are only coalitions that include B
• Hence B can decide not to join these
coalitions as it prefers government BB
• B is a strong party
• If it exists, there is a single strong party
• A strong party is member of any stable
government coalition
• Merely Strong Party: Although some legislative
majority prefers at least one coalition government
to the government in which a MSP gets all the
portfolios, the MSP is a member of each of these
alternative coalitions (B is a MSP)
• Very Strong Party: A very strong party is a party
to which a majority coalition prefers to give all the
government portfolios rather than support any
other government alternative.
AE
BE
BD
CE
CD
DE
EE
DD
AD
Warfae policy
BC
CC
DC
AC
BB
CB
AB
AA
BA
Welfare policy
CA
DB
DA
Possible
Minority
government
CC stable.
C is a very
strong party
Foreign Policy
German Elections 1987
CDU-FDP
CDU
FDP
SPD
G
Taxation-spending
The W(CDU-FDP) is empty and
CDU-FDP gov confirmed
Foreign policy
W(CDU) has only gov
with CDU
CDU
FDP
SPD
G
Taxation - spending
CDU is a strong party
Optimal government and the risk of
ministerial drift
40
Control mechanisms in parliamentary
governments
•
•
•
Government formation is an act of delegation
Parties may ex-ante negotiate the terms of the
coalition (policy x)
But the risk of ministerial drift remains
•
CONTROL MECHANISMS:
1) Government programs (credibility issue)
2)
3)
4)
5)
Inter-ministerial committees
Overlapping policy jurisdictions
Undersecretaries
Legislative review
41