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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)

Minimum range (Leiserson)

Office-seeking

Policy seeking

Cooperative Game Theory

Minimal/minimum

Winning coalition (Riker)

Unidimensional

De Swann

Bargaining

Proposition (Leiserson)

Bidimensional

Institutions free (Laver;Schofield)

Bargaining theories (Baron, Diermeir,Merlo etc.)

Non Cooperative Game Theory

Institutional rich (Laver, Shepsle)

Cooperative and Non Cooperative Game Theory

- 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.
- 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.

A coalition C is a sub-set non empty of a set N of all players

- 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.
- v(TS) v(S) + v(T) if S T= Ø ;
- An imputation is a game outcome (a possible solution) or a payoff distribution (x1, x2…xn) among n players that respects the following conditions:
- iNxi = v(N); the players redistribute the “income” of the coalition
- 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

- The payoffs from x are higher than the payoffs from y for at least some member of C (and equal for the others)
- 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 iCwi 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

Winning coalition

with 58% of seats

Bigger slices!!

C:Seats

18%

Po=0,225

C:Seats

18%

Po=0,3103

B:seats

21%

Po=0,3620

B:seats

21%

Po=0,2625

D:seats

22%

Po=0,275

A:seats

19%

Po=0,3275

A:seats

19%

Po=0,2375

Office-seeking models

A winning coalition without unnecessary members is called “minimal winning coalition”

The election of June 1952 in Netherlands

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

VVD:10

0,1754

VVD:10

0,1886

PvdA :33

0,5789

PvdA :33

0,6226

CHU:10

0,1886

ARP:14

0,2456

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

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

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 in one dimensionPolicy-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)

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:
- For any point not in the set there is in the set a point that is preferred by all political actors taken in consideration.
- Given a point in the set none else is considered better by all political actors
- 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)

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.

B (20)

C (20)

D (40)

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.

B (20)

D (40)

C (20)

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. ….

B (20)

C (20)

D (40)

The election of June 1952 in Netherlands

Traditionalism

A structurally stable core at the

KVP position

ARP:14

KVP:33

CHU:10

PvdA:33

Left

Right

VVD:10

Modernization

The election of June 1952 in Netherlands

Traditionalism

A structurally stable core at the

KVP position

ARP:14

KVP:33

CHU:10

PvdA:33

Left

Right

VVD:10

Modernization

A structurally unstable core at the

ARP position

PvdA:33

ARP:14

VVD:10

CHU:10

Left

Right

KVP:33

Modernization

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.

Traditionalism

PvdA:33

ARP:14

CHU:10

VVD:10

Left

Right

KVP:33

Modernization

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

Traditionalism

PvdA:33

median

ARP:14

CHU:10

VVD:10

Left

Right

KVP:33

median

Modernization

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.

R

yes

R

Proposes

x1

no

x1

installed?

P1 sel.

x1

Vetoed?

x1

new SQ

R

no

yes

Proposes

x2

yes

R

R

P2 sel

x2

Vetoed?

no

x2

installed?

no

x2

new SQ

R

Proposes

xi

yes

yes

R

R

R

Pi sel

xi

Vetoed?

no

xi

installed?

no

xi

new SQ

Proposes

xn

R

yes

yes

Pn sel

xn

Vetoed?

R

R

no

xn

installed?

xn

new SQ

R

no

yes

A government programmeof 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 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)

Government formation in parliamentary democracies27

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

forC

forA

forB

AC

BC

CC

AA

CA

BA

AB

BB

CB

ecoA ecoB ecoC

economic policy

The lattice of possible governments

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

BC

CC

AA

CA

BA

foreign policy

AB

BB

CB

economic policy

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

32

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.

BE

CE

DE

EE

CD

DD

BD

AD

Possible Minority government CC stable.

C is a very strong party

CC

DC

BC

AC

BB

CB

AB

DB

Warfae policy

AA

CA

DA

BA

Welfare policy

Foreign Policy

FDP

SPD

G

Taxation-spending

German Elections 1987 CDU-FDP

The W(CDU-FDP) is empty and

CDU-FDP gov confirmed

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:

Government programs (credibility issue)

Inter-ministerial committees

Overlapping policy jurisdictions

Undersecretaries

Legislative review

41

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