The Logic of Pre-Electoral Coalition Formation

SONA NADENICHEK GOLDER

Florida State University

Question

Under what conditions are pre-electoral coalitions likely to form?

Electoral coalitions formed in the 2002 legislative elections in France and Germany but not in the

Netherlands.

Why?

Definitions

Most parties who wish to exercise executive power are forced to enter some type of coalition.

Parties can form coalitions:

After elections (government coalitions). Before elections (pre-electoral coalitions).

Definitions

A pre-electoral coalition is a collection of parties that do not compete independently in an election. Rather, they publicly agree to coordinate their campaigns by running joint candidates/lists or agreeing to enter government together following the election.

Criterion I: An electoral coalition must be publicly stated. Criterion II: Member parties in an electoral coalition

cannot compete in elections as truly independent entities. Criterion III: The electoral coalition must be at the national

level.

Types of Electoral Coalitions

Pre-Electoral Coalition Type Degree of Electoral Coordination

Nomination Agreement

Joint Lists

Dual Ballot Instructions

Vote Transfer Instructions

Public Commitment to Govern Together

Why do we care?

Electoral outcomes

Policy implications

Normative implications Commonplace

Some Figures

Data from 19 West European countries 1946-2002

Average of 11 electoral coalitions at any one time.

Average electoral coalition size is 2.6.

25% of these coalitions end up in government.

1/3 of written government coalition agreements based on pre-electoral agreements (Müller & Strøm).

Coalition Literature

Government Coalition Literature

Austin-Smith & Banks (1988)

Laver & Schofield (1988)

Baron & Ferejohn (1989)

Laver & Shepsle (1990)

Strøm, Budge & Laver (1994)

Lupia & Strøm (1995)

Merlo (1997), Warwick (1999)

Diermeier et al. (1999, 2003)

Warwick & Druckman (2001, 2006)

Martin & Vanberg (2003)

Etc., etc…

See Laver (1998) in Annual Review of Political Science for an overview of models.

See Martin & Stevenson (2001) for an empirical analysis of the main hypotheses in the literature.

See Müller & Strøm (2000), Coalition Governments in Western Europe for case studies.

Electoral Coalition Literature

Powell (2000); Kaminski (2001)

“One area that cries out for more serious theoretical and empirical work is the appearance of announced pre-electoral coalitions between political parties. We know too little about the origins of such coalitions . . .”

Powell (2000, p. 247)

What determines electoral coalition formation?

State of the Art

Disproportionality Story“The more disproportional the electoral system, the greater the incentives for pre-electoral alliances”

Strom, Budge & Laver (1994, p. 316)

Signaling Story

No empirical tests

State of the Art: An Empirical Test

405 legislative elections, 25 countries, 1946-2002

Disproportionality

Electoral coalitions are more likely to form and be successful in disproportional electoral systems so long as there is a sufficiently large number of parties.

Signaling

State of the Art: Limitations

Costs of electoral coalition formation• Ideological and distributional issues

Within-country temporal variation

No bargaining model

Theory

Bargaining Model

Just as with government coalitions, electoral coalitions emerge from a bargaining process.

There are some differences . . .

• Government coalitions cannot affect the probability of electoral victory, but pre-electoral coalitions can.

• Ideological compatibility constraint stronger forelectoral coalitions than government coalitions.

What does the bargaining model look like?

What does the bargaining model look like?

Actors: Party A, Party B (Potential Coalition Partners) Non-Strategic Opposition Party

Party leaders care about: Office Policy

Decision: Party A and Party B must decide whether to

form an electoral coalition or run separately.

Timeline for Bargaining Game

Period 1

Period 2

(No)

Party A makes an offer

(Yes)

Party B accepts(Yes)

PEC

(No)

Party A accepts

(Yes)

PEC

(No)No PEC

Party B makes an offer

(Yes)

(No)No PEC

Party A accepts

(Yes)

PEC

(No)No PEC

Party B makes an offer

(Yes)

(No)No PEC

Bargaining Model

Party leaders will form an electoral coalition whenever the expected utility from an agreement is greater than the expected utility from running alone (reservation price).

Payoffs

Probability of winning and losing:

Probability that you enter government running divided (Pi-d).

Probability that you enter government running united (Pt

u), where P1u> P2

u.

Payoffs

Office Benefits (S)

If parties form an electoral coalition, they divide the office benefits (o1

A,1-o1A) or (o2

B,1-o2B).

If parties do not form an electoral coalition but still enter government, they receive share si of the office benefits, where si=seatsi/(seatsi+seatsj ).

Payoffs

Policy

If not in government, you suffer utility loss from having opposition set policy (λi-opp), where λi-opp = - (Pi – Popp)2

If in government as electoral coalition, you suffer utility loss from coalition policy λi-pec, where

1. λi-pec = -(Pi–Ppec)2

2. Ppec = pA+suB|pA-pB| or Ppec = pB-suA|pA-pB|

3. SuA = seatsA/(seatsA+seatsB) and SuB = seatsB/(seatsA+seatsB)

Actors, Actions, and Payoffs

If A makes offer and B accepts in Period 1

Pu1 (oA

1 – λA-PEC) - λA-OPP(1-Pu1) ; Pu

1 ((1- oA1) – λB-PEC) - λB-OPP(1-Pu

1)

If B rejects A’s offer in Period 1, and A accepts B’s offer in Period 2

Pu2 (oB

2 – λA-PEC) - λA-OPP(1-Pu2) ; Pu

2 ((1- oB2) – λB-PEC) - λB-OPP(1-Pu

2)

(same payoffs if A makes no offer in Period 1, and A accepts B’s offer in Period 2)

If neither actor makes an offer in either period

PA-d (sA -λA-GOV) - λA-OPP(1-PA-d) ; PB-d

(sB -λB-GOV) - λB-OPP(1-PB-d)

(same payoffs if offers are made, but rejected)

Equilibria

Depending on parameter values, 3 possible sub-game perfect Nash equilibria in this game.

In two equilibria, electoral coalitions form in the first round.

In one equilibrium, electoral coalitions never form.

Comparative Statics

The probability of electoral coalition formation increases when:

Ideological distance between coalition partners (λAB) decreases.

Ideological distance to opposition (λi-opp) increases, so long as coalition is beneficial (Pt

u> Pti-d).

Probability that coalition wins (P1u, P2

u) increases.

Probability that party wins running alone (Pi-d) decreases.

What does the model get us?

Surprising result Party system polarization does not have an

unconditional effect on electoral coalition formation.

Is this a Good Explanation?

Hypothesis 1

The probability of electoral coalition formation increases when:

Ideological distance between coalition partners (λAB) decreases.

Hypothesis 1

Pre-electoral coalitions are less likely to form as the ideological distance between potential coalition members increases.

Hypotheses 2 and 3

The probability of electoral coalition formation increases when: Ideological distance to opposition (λi-opp) increases, so long as

coalition is beneficial (Ptu> Pt

i-d).

Hypotheses 2 and 3

Party system polarization increases the likelihood of electoral coalitions when the electoral system is sufficiently disproportional. An increase in the disproportionality of the electoral system will increase the probability of forming a pre-electoral coalition. This positive effect should be stronger when the party system is polarized.

Hypothesis 4

The probability of electoral coalition formation increases when:

Probability that coalition wins (P1u, P2

u) increases. Probability that party wins running alone (Pi-d) decreases.

Hypothesis 4

The probability that an electoral coalition forms is a quadratic function of the size of the potential electoral coalition. It should be increasing in the first term (size) and decreasing in the second term (size2).

Hypothesis 5

Hypothesis 4

Hypothesis 5

If the expected coalition size is sufficiently large, then pre- electoral coalitions are less likely to form if there is an asymmetric distribution of electoral strength among the potential coalition parties.

Data

292 legislative elections in 20 advanced industrialized parliamentary democracies between 1946 and 1998.

Data

292 legislative elections in 20 advanced industrialized parliamentary democracies between 1946 and 1998.

Dyadic format 4,460 potential two-party coalitions.

234 potential coalitions actually formed (5%)

Pre-electoral coalitions formed prior to 44% of elections in dataset

Specification

Random-Effects Probit Model

PEC* = β0 + β1Incompatibility + β2Polarization

+ β3Threshold + β4Polarization*Threshold

+ β5Coalition Size+ β6Coalition Size2

+ β7Asymmetry + β8Asymmetry*Coalition Size + ε

Results

Regressor Model 1 (random effects) Model 2

Ideological Incompatibility -0.007*

(0.002)

-0.005*

(0.002)

Polarization 0.002

(0.004)

-0.001

(0.02)

Electoral Threshold 0.026*

(0.01)

0.021*

(0.005)

Polarization*Electoral Threshold 0.0003

(0.0003)

0.0002

(0.0001)

Coalition Size 0.043*

(0.01)

0.041*

(0.008)

Coalition Size2 -0.0005*

(0.0001)

-0.0004*

(0.0001)

Asymmetry -0.144

(0.286)

-0.01

(0.22)

Asymmetry*Coalition Size -0.025*

(0.008)

-0.024*

(0.006)

Constant -2.46*

(0.29)

-2.10*

(0.18)

N

Log Likelihood

3495

-613.49

3495

-663.95

Dependent Variable: Pre-Electoral Coalition (0,1)

* p < 0.05 (two-tailed)

Interaction Terms in Non-Linear Models: An Aside

Imagine I have some conditional hypothesis whereby some variable Z modifies the effect of X on Y.

One question we might ask is how the value of Z modifies the effect of X on Y.

What is ? We refer to this as the “interaction effect”.

ZX

Y2

Interaction Terms in Non-Linear Models: An Aside

OLS World

Y = β0 + β1X + β2Z + β3XZ + ε

= β1 + β3Z

= β3

The coefficient (and standard error) on the interaction term tells us the direction, magnitude, and significance of the “interaction effect”.

X

Y

ZX

Y2

Interaction Terms in Non-Linear Models: An Aside

Logit World

P(yi = 1) = = Λ(xiβ) = Λ

= [Λ(1-Λ)][β1 + β3Z]

= β3Λ(1-Λ) +

(β1 + β3Z)(β2 + β3X)Λ(1-Λ)(1-2Λ)

X

1) P(yi

ixe1

1

ZX

1) P(yi

Interaction Terms in Non-Linear Models: An Aside

Logit World

The coefficient (and standard error) on the interaction term does NOT tell us the direction, magnitude, or significance of the “interaction effect”.

The interaction effect depends on the values of all of the other variables.

Interaction Terms in Non-Linear Models: An Aside

P(yi = 1) = = Λ(xiβ)

xiβ = β0 + β1X + β2Z + β3XZ

Let β0 = β1 = β2 = β3 = 1

A simulation…

ixe1

1

Second Derivative of Pr(Y=1) [b0=b1=b2=b3=1, Z=0] plotted against X

-0.1

0

0.1

0.2

0.3

-6 -5 -4 -3 -2 -1 0 1 2 3 4

X

seco

nd

der

ivat

ive

Second Derivative of Pr(Y=1) [b0=b1=b2=b3=1]plotted against p

-0.1-0.05

00.05

0.10.15

0.20.25

0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

p

se

co

nd

de

riv

ati

ve

Regressor Model 1 (random effects) Model 2

Ideological Incompatibility -0.007*

(0.002)

-0.005*

(0.002)

Polarization 0.002

(0.004)

-0.001

(0.02)

Electoral Threshold 0.026*

(0.01)

0.021*

(0.005)

Polarization*Electoral Threshold 0.0003

(0.0003)

0.0002

(0.0001)

Coalition Size 0.043*

(0.01)

0.041*

(0.008)

Coalition Size2 -0.0005*

(0.0001)

-0.0004*

(0.0001)

Asymmetry -0.144

(0.286)

-0.01

(0.22)

Asymmetry*Coalition Size -0.025*

(0.008)

-0.024*

(0.006)

Constant -2.46*

(0.29)

-2.10*

(0.18)

N

Log Likelihood

3495

-613.49

3495

-663.95

Dependent Variable: Pre-Electoral Coalition (0,1)

* p < 0.05 (two-tailed)

Quantities of Interest

Predicted probabilities What’s the predicted probability that y = 1 (i.e., that a pre-electoral

coalition forms)? Note that we often report this for probit/logit models, but not when we use

OLS…

Marginal effects What’s the effect of a very, very small change in x on the probability that y

= 1?

First differences How does the probability that y = 1 change when we increase x by one unit

(or some number of units)?

0

.00

5 .0

1 .0

15

0 10 20 30 40 50 60 70 80 90 100

Effect of a One Unit Increase in Electoral Thresholds on the Probability of Electoral Coalition Formation

Party System Polarization

Eff

ect o

f E

lect

oral

Thr

esho

lds 95% Confidence Intervals

0

.00

1 .0

03

.00

5 .0

07

0 5 10 15 20 25 30 35

Effect of a One Unit Increase in Party System Polarization on the Probability of Electoral Coalition Formation

Eff

ect o

f P

arty

Sys

tem

Pol

ariz

atio

n

Electoral Threshold

95% Confidence Intervals

-.

00

1 -.

00

05

-.0

00

1 0 .

00

01

0 10 20 30 40 50 60 70 80 90 100

Effect of a 0.01 Unit Increase in Asymmetry on the Probability of Electoral Coalition Formation

Eff

ect o

f A

sym

met

ry

Expected Coalition Size

95% Confidence Intervals

-.003

-.002

-.001

0 .0

01

.002

.003

0 10 20 30 40 50 60 70 80 90 100

Effect of a One Unit Increase in Expected Coalition Size on the Probability of Electoral Coalition Formation

(When Asymmetry is one standard deviation below its mean)

Eff

ect o

f E

xpec

ted

Coa

liti

on S

ize

Expected Coalition Size

95% Confidence Intervals

-.00

3 -.

002

-.00

1 0

.001

.0

02

.003

0 10 20 30 40 50 60 70 80 90 100

-.00

15 -

.00

1 -.

0005

0

.00

05

.00

1 .0

015

0 10 20 30 40 50 60 70 80 90 100

-.00

15 -

.00

1 -.

0005

0

.00

05

.00

1 .0

015

0 10 20 30 40 50 60 70 80 90 100

Expected Coalition Size

Effect of a One-Unit Increase in Expected

Coalition Size

Asymmetry is one standard deviation below its mean

Asymmetry is at its mean

Asymmetry is one standard deviation above its mean

Shifts to the left as Asymmetry increases

Substantive Effect of Explanatory Variables on Electoral Coalition Formation

Holding all other variables at their means

Example

If all countries had the electoral threshold of Denmark in the 1970s (2%), and moved to the slightly higher threshold used by Norway in the 1970s (8.9%), the predicted probability of pre-electoral coalitions forming would jump by 181% and we would see an additional 59 electoral coalitions.

Conclusions

Summary: Before

Electoral coalitions are a simple function of electoral rules.

“The more disproportional the electoral system, the greater the incentives for pre-electoral alliances”

Summary: After Electoral rules do not have a direct unconditional effect on

electoral coalition formation.

Pre-electoral coalitions are more likely when: Potential coalition partners share similar ideological preferences. Parties are of roughly equal size. The coalition size is large, but not too large. The party system is polarized and the disproportionality of the electoral

rules creates an electoral bonus from forming a coalition.

Model explains cross-national variation and temporal variation within countries.

Why might you care about this?

Electoral coalitions offer the opportunity of combining the best aspects of the ‘majoritarian’ and ‘proportional’ visions of democracy. We could increase the likelihood of electoral

coalition formation by making electoral rules more disproportional.

The actual effect of changing the electoral rules will depend on the size and ideological polarization of the party system in each country.

Why might you care about this?

Electoral coalitions have an effect on various aspects of post-election government formation. Governments based on electoral coalitions are more

ideologically compatible than other governments and they form more quickly.

Electoral coalitions increase the likelihood that member parties enter government.

Differences between governments that form in the post-election versus inter-election periods.

The End