coalition theories

Coalition theories

• 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)

From seats to government

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

Office-seeking Policy seeking

UnidimensionalDe Swann

Bidimensional

Institutions free (Laver;Schofield)

Institutional rich (Laver, Shepsle)

Coope

rativ

e

Game T

heor

y Minimal/minimumWinning coalition (Riker)

Bargaining Proposition (Leiserson)

Minimal connected winning coalition (Axelrod)

Minimum range (Leiserson)

Non Cooperative Game Theory

Bargaining theories (Baron, Diermeir,Merlo etc.)

Cooperative and Non Cooperative Game Theory1. 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 Theory1. 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(TS) 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) iNxi = 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 iCwi q;

Office-seeking modelsIn 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

A:seats19%Po=0,2375

B:seats21%Po=0,2625

C:Seats 18%Po=0,225

D:seats22%Po=0,275

Winning coalition with 80% of seats

A:seats19%Po=0,3275

B:seats21%Po=0,3620

C:Seats 18%Po=0,3103

Winning coalition with 58% of seatsBigger slices!!

Office-seeking modelsA winning coalition without unnecessary members is called “minimal winning coalition”

Parties PvdA KVP ARP VVD CHU

Seats 33 33 14 10 10

Minimal winning coalitions

PvdA, KVP

PvdA, ARP, VVD

PvdA, ARP,

CHU

KVP, ARP, VVD

KVP, ARP,

CHU

PvdA, CHU, VVD

KVP, CHU, VVD

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 modelsThe election of June 1952 in Netherlands

VVD:100,1754PvdA :33

0,5789 ARP:140,2456

VVD:100,1886PvdA :33

0,6226CHU:100,1886


Seats 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

Minimum Winning coalitions (Size Principle)

PvdA, CHU, VVD

KVP, CHU, VVD

Office-seeking models



Seats 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


PvdA, CHU, VVD

KVP, CHU, VVD

Bargaining costs criterion

PvdA, KVP

According Leiserson among the minimal winning coalition the coalition with the smallest number of parties will form because of the bargaining costs

Office-seeking policy “informed” modelsAccording 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” modelsThe election of June 1952 in Netherlands

Parties PvdA

Left

KVP ARP VVD CHU

Right

Seats 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


PvdA, CHU, VVD

KVP, CHU, VVD

Bargaining costs criterion

PvdA, KVP

Minimal connected winning coalitions

PvdA, KVP

KVP, ARP, VVD

Minimum range PvdA, KVP

Policy-seeking models in one dimensionIn 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

L (45) C (15) R (40)Seats=100

L (55) CL (20) CR (10) R (15)

L (25) CL (15) C (8) CR (5) R (47)

Core Party

a)

b)

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 Lc) L,CL,C,CR,R is better for CR as |48-47| < any other difference.


L (45) C (15) R (40)Seats=100

L (55) CL (20) CR (10) R (15)

L (25) CL (15) C (8) CR (5) R (47)

a)

b)

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


L (45) C (15) R (40)Seats=100

L (55) CL (20) CR (10) R (15)

L (25) CL (15) C (8) CR (5) R (47)

a)

b)

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)

C (20)

B (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)

C (20)

B (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.

A (20)

C (20)

B (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. ….

ARP:14

KVP:33

VVD:10

PvdA:33CHU:10

Traditionalism

Modernization

Left Right

A structurally stable core at the KVP position


PvdA:33

KVP:33

CHU:10VVD:10

Traditionalism

Modernization

Left Right

A structurally unstable core at the ARP position

ARP:14

PvdA:33

KVP:33

Traditionalism

Modernization

Left Right

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. ARP:14

CHU:10VVD:10

PvdA:33

KVP:33

Traditionalism

Modernization

Left Right

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 ARP:14

CHU:10VVD:10

median

medianmedian

• 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.

Policy-seeking models in a bidimensional policy space (Laver-Shepsle)

R

R

R

R

R

R

R

R

R

R

R

R

R

P1 sel.Proposes x1

Proposes x2

Proposes xi

Proposes xn

P2 sel

Pi sel

Pn sel

x1Vetoed?

x2Vetoed?

xiVetoed?

xnVetoed?

yes

yes

yes

yes

no

no

no

no

x1installed?

x2installed?

xiinstalled?

xninstalled?

yes

no

no

yes

no

yes

no

yes

x1 new SQ

x2 new SQ

xinew SQ

xnnew SQ

26

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

27

• 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 democracies

28

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

29

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

30

AA

BB

CC

BA

AB

AC BC

CA

CB

ecoA ecoB ecoC economic policy

fore

ign

polic

y

forC

forA

forB

The lattice of possible governments

31

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?

32

economic policy

fore

ign

polic

y AA

AB

AC

BA

BB

BC

CA

CB

CC

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

33

economic policy

fore

ign

polic

y AA

AB

AC

BA

BB

BC

CA

CB

CCW(BA) is empty

BA is stable government

34

AA

BB

CC

BA

AB

AC BC

CA

CB

sA sB sC

Social spending

Defe

nce

spen

ding

dC

dA

dB

Winset of BBB is a strong

party

• 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.

Welfare policy

War

fae

polic

y

AA

CD

BA

BB

CC DC

DA

Possible Minority government CC stable.C is a very strong party

DD

EECE

CB

CA

DB

DE

BC

BD

BE

AB

AC

AD

AE

SPD

CDUFDP

GTaxation-spending

Fore

ign

Polic

y

German Elections 1987 CDU-FDP

The W(CDU-FDP) is empty and

CDU-FDP gov confirmed

CDU is a strong party

W(CDU) has only govwith CDU

SPD

CDUFDP

GTaxation - spending

Fore

ign

polic

y

40

Optimal government and the risk of ministerial drift

41

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) Inter-ministerial committees3) Overlapping policy jurisdictions4) Undersecretaries5) Legislative review

coalition theories

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