Weingast B.R., Wittman D. The Oxford Handbook of Political Economy
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chapter 9
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COALITION
GOVERNMENT
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daniel diermeier
1 Introduction:AShift in Perspective
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The year 1990 marked a turning point in the study of governmental coalitions. Laver
and Schofield (1990) published a comprehensive and detailed review of the field
up to the late 1980s. In addition, a significant set of new papers broke with the
established research traditions. First, Baron (1989) published the initial applications
of non-cooperative game theory (the “Baron–Ferejohn” model) to the study of gov-
ernmental coalitions (Baron and Ferejohn 1989). Second, Laver and Shepsle (1990)
used structure-induced equilibrium models to study the formation and stability of
cabinets. Third, Strom (1990) presented a comprehensive account of minority gov-
ernments and coalitional stability.
1
These papers had one important element in common: all focused on the role of
institutions in the study of governmental coalitions. The New Institutionalism had
arrived in the study of coalition government. The point of this new approach was not
that political institutions had been overlooked as a potentially important object of
study. Political institutions—such as party systems, electoral rules, or constitutional
features— have always played an important role in the study of coalition government.
Rather, the claim was methodological: to have explanatory content and empirical ac-
curacy, formal models of politics must incorporate institutional details.
2
This shift in
perspective has had important consequences for the praxis and progress of coalition
research in the last fifteen years.
¹ Laver (this volume) covers many of these issues in greater detail.
² See Diermeier (1997) and Diermeier and Krehbiel (2003) for a detailed discussion of the
methodological aspects of institutionalism.
daniel diermeier 163
It is the distinctive characteristic of parliamentary democracies that the executive
derives its mandate from and is politically responsible to the legislature. This has two
consequences. First, unless one party wins a majority of seats, a rare case in electoral
systems under proportional representation, the government is not determined by an
election alone, but is the result of an elaborate bargaining process among the parties
represented in the parliament. Second, parliamentary governments may lose the
confidence of the parliament at any time, which leads to their immediate termination.
Thus, historically, two questions have dominated the study of coalition government.
Which governments will form? And how long will they last? Institutionalism has
fundamentally changed the way researchers are conceptualizing and answering these
questions.
This chapter is designed as follows. I first discuss important empirical work that
motivated the institutionalist shift in the study of government coalitions. In the
next two sections I discuss the most widely used institutionalist approaches: Laver
and Shepsle’s structure-induced equilibrium approach and the sequential bargaining
model used by Baron and others. I then discuss two alternative approaches (demand
bargaining and efficient bargaining) to model coalition formation that try to over-
come some of the technical difficulties of older approaches. In the next two sections I
discuss the consequences of the institutionalist perspective for empirical work. First,
I review the area of cabinet stability, one of the most active areas in coalition research.
In the penultimate section I discuss recent work that relies on structural estimation
as its methodology to study coalition government empirically. A conclusion contains
a summary and discusses some open questions.
2 The Arrival of Institutionalism
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Institutionalism is difficult to define. It should not be identified with the analysis
of institutions. Rather it is a methodological approach. The common element to all
versions of institutionalism is a rejection of the social choice research program of
finding institution-free properties (as illustrated by McKelvey 1986). Beyond that, in-
stitutionalism consists of rather different research programs that stem from different
methodological approaches.
In the context of the study of government coalition the institutionalist approach
implies a re-evaluation of existing theoretical traditions. Consider Axelrod’s (1972)
theory of proto-coalitions as an example.
3
In his model, ideologically connected
proto-coalitions expand stepwise by adding new parties until they reach political
³ Axelrod’s theory of proto-coalitions is not the only example of an “institution-free” approach to
government coalitions. Other examples include cooperative bargaining theory (e.g. the Shapley value,
bargaining set) or social choice theoretic approaches (e.g. the core, the uncovered set). For a technically
very sophisticated example of recent work in this area see e.g. Schofield, Sened, and Nixon 1998.Their
model combines social choice-based, institution-free models of cabinet formation with Nash equilibria
at the electoral level.
164 coalition government
viability. The important point here is how the explanation works. Note that Axelrod’s
account only relies on the number of parties, their seat share, and their ideological
position. From the perspective of the theory, other aspects of the cabinet formation
process are irrelevant, e.g. who can propose governments, how long the process can
last. Some disregard of existing structure, of course, is the essence of formal modeling.
The question is whether such a stripped-down model of government formation
explains the empirical phenomena. To rephrase the famous quote by Einstein: models
should be as simple as possible, but not simpler.
The answer to this question is, of course, empirical. Are there phenomena that
cannot be explained with an institution-free approach? Before the institutional shift
in the early 1990s much of the empirical study of government coalitions was focused
on one issue: the question of government formation. That is, suppose we know the
number of parties, their seat shares, and (in some models) their ideological position,
which governments would form?
4
The success of this research program was mixed.
Although it consisted of a fruitful interplay of theoretical and empirical work, all told,
institution-free models failed to predict which governments would form.
Two roots in the literature helped introduce institutionalist models into the study
of government coalitions. The first root was empirical. Specifically, two independent
empirical traditions played a critical role: Kaare Strom’s work on minority cabinets
and Browne et al.’s study of cabinet stability. The second root was theoretical and
consistent in the development of institutionalist models of cabinet formation (Laver
and Shepsle 1990;Baron1989).
Strom’s work (1985, 1990) was important in various respects. First, it focused on
a puzzling, but prevalent, case of coalition governments: minority governments,
i.e. cabinets where the parties that occupy portfolios together do not control a ma-
jority of seats in the legislature. As Strom pointed out, their existence is neither rare
(roughly a third of all coalition governments are of the minority type), nor does it
constitute a crisis phenomenon. Denmark, for example, is almost always governed by
minority governments, but hardly qualifies as a polity in crisis. Moreover, many of
the minority governments are surprisingly stable.
The existence of minority governments constituted an embarrassment for existing
theories of coalition formation. Why don’t the opposition parties that constitute
a chamber majority simply replace the incumbent minority government by a new
cabinet that includes them?
The influence of Strom’s work, however, went beyond the mere recognition of
minority governments. It had important methodological consequences for the study
of coalition governments in general. First, it refocused the government forma-
tion question from “which government will form?” to “which type of government
will form?”
5
That is, what are the factors that lead some countries regularly to
choose minority cabinets (e.g. Denmark), while others (e.g. Germany) almost always
choose minimum winning coalitions, while yet others (e.g. Italy) frequently choose
⁴ See e.g. Laver and Schofield 1990 for a detailed overview of this literature.
⁵ See, however, Martin and Stevenson 2001 for a recent, institutional, empirical study of coalition
formation that tried to answer the first question.
daniel diermeier 165
super-majority governments. Second, it gave an account of minority governments us-
ing institutionalist explanations such as the existence of a strong committee system.
6
The second empirical tradition was the study of cabinet stability pioneered by
Browne, Srendreis, and Gleiber (1984, 1986, 1988). Browne et al. viewed cabinet sur-
vival as determined by “critical events,” exogenous random shocks that destabilize an
existing government. These random shocks are assumed to follow a Poisson process
which implies a constant hazard rate for cabinet terminations.
7
Strom’s (1985, 1988)
approach, on the other hand, was institutional. Here the goal was to identify a robust
set of covariates that influence mean cabinet duration. Since government type—
i.e. whether the cabinet had majority or minority status—was one of the proposed
independent variables, Strom’s approach thus integrated his work on cabinet stability
and minority governments.
In 1990 King et al. presented a “unified” model of cabinet dissolutions that com-
bined the attribute approach proposed by Strom (1985, 1988) and the events approach
introduced by Browne, Srendreis, and Gleiber (1986, 1988). Following this insight, a
whole list of papers, especially by Paul Warwick, pointed out that the unified model
isbutaspecialcaseofawholeclassofsurvivalmodels(Warwick1992a, 1992b, 1992c,
1994; Warwick and Easton 1992; Diermeier and Stevenson 1999, 2000).
While this literature provided rich new empirical regularities, an equally com-
pelling theoretical framework was lacking. Competing candidates for such a frame-
work, however, were being developed independently using different versions of game
theory as their models of coalition formation: the Laver–Shepsle model and Baron’s
sequential bargaining models.
3 Structure-induced Equilibrium:
The Laver–Shepsle Model
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In his seminal paper Shepsle (1979) formally introduced institutional structure as a
committee system. The key idea was to assume additional constraints in the spatial
decision-making environments. Specifically, Shepsle assumed that each legislator is
assigned to exactly one issue. This assignment can be interpreted as a committee
system in the context of the US Congress. Intuitively, a committee has exclusive
jurisdiction on a given issue. Using a result by Kramer (1972), it can easily be shown
that structure-induced equilibria exist for every committee assignment.
8
The basic
idea is to have the committees vote sequentially on each issue separately. Since each
issue corresponds to a single-dimensional policy space, the median voter theorem
guarantees that a core exists on that dimension. The final outcome then is the
composite of the sequence of committee decisions. The key methodological idea of
⁶ See Diermeier and Merlo 2000 for a critical discussion of Strom’s theory of minority cabinets.
⁷ For a detailed discussion of the cabinet termination literature see Laver 2003. Laver also discusses
alternative conceptualization of the lifespan of governments, such as party turnover (e.g. Mershon 1996).
⁸ For a thorough formal analysis see e.g. Austen-Smith and Banks 2005.
166 coalition government
SIE theory thus consists in transforming a social choice problem in which the core
does not exist (multidimensional choice spaces) into a more structured problem in
which the core (as the issue-by-issue core) does exist. Formally, issue-by-issue voting
corresponds to an agenda restriction, since in later states of the process decisions on
earlier dimensions cannot be revisited. What made this particular agenda restriction
plausible is that it corresponded well to features of real legislative decision-making
such as a committee system.
Laver and Shepsle (1990) apply this methodology to the study of cabinets. In
the context of coalitional government, however, the key decision-makers are not
committees and individual legislators, but cabinets and parties. Laver and Shepsle
thus interpret the issue assignments from Shepsle (1979) as cabinet portfolios assigned
to parties. Holders of portfolios can unilaterally determine the policy choice on that
dimension.
Going beyond the original SIE analysis, Laver and Shepsle then ask under what
circumstances such portfolio assignments are in the majority core of a voting game
on cabinet assignments. Consider the example in Figure 9.1.
9
In this example there
are three parties A, B, and C with their ideological positions along two policy dimen-
sions represented by small circles. Each combination of letters represents a possible
coalition government. Suppose that every two-party coalition represents a majority,
while each single-party government is a minority government. The idea of their
model is that it takes a government (modeled as an allocation of portfolios) to beat a
government. Government BA, for example, is stable because there is no alternative
government in its win set even though there are policies strictly preferred to the
policy implemented by BA. But according to Laver and Shepsle’s model these policies
do not constitute credible alternatives to BA since they cannot be implemented by
any government. As in the case of congressional committee systems discussed above,
the Laver–Shepsle results therefore depend on an agenda restriction. The twin as-
sumption is that in a parliamentary system policies are decided in cabinets, not by
the legislature and that each minister effectively can exercise dictatorial control over his
respective portfolio dimension.
Laver and Shepsle show not only that portfolio assignments can be stable, but
that the stable assignments may be of the minority type. Finally, by perturbing the
key parameters of the equilibrium governments, Laver and Shepsle also hint at an
explanation for cabinet stability.
10
With one model, so it seems, Laver and Shepsle succeeded in addressing all the
major empirical themes discussed above. Moreover, their methodology also promised
to shed some new light on the old question of which specific cabinet would form. The
appeal of the Laver–Shepsle model is that it maintains the basic features of spatial,
institution-free models, but seems to add just enough structure to account for the
new empirical challenges.
⁹ Adapted from Laver and Shepsle 1990, 875.
¹⁰ See Laver and Shepsle 1994, 1996 for rich analyses of various institutional features of government
formation and termination using their framework. Laver and Shepsle 1998 model cabinet stability using
random perturbations.
daniel diermeier 167
AB
A
AC
B
BA
BC C
CA
CB
Y
Dimension
X
Dimension
Fig. 9.1 Ideal points and win-sets of credible proposals
As in the case of Shepsle’s model for the US Congress, the explanatory power of
the Laver–Shepsle model depends on the empirical plausibility of its key assumption
about cabinet decision-making. The results, for example, do not go through in a
model where ruling parties bargain over policies in cabinets.
11
But there is a more
serious, methodological problem with the model. This problem has nothing to do
with the plausibility of any of the assumptions, but with the solution concept used by
Laver and Shepsle.
This problem, ironically, was pointed out by Austen-Smith and Banks (1990)ina
paper in the same issue of the American Political Science Review where the Laver–
Shepsle article was published. Austen-Smith and Banks show that except in the
very special case of three parties, two dimensions, and Euclidean (“circular”) pref-
erences, structure-induced equilibria in the portfolio assignment game may not exist.
Figure 9.2 (adapted from figure 5 in Austen-Smith and Banks 1990) demonstrates this
point. In this example there is one large party, D, with 49 per cent of the vote share
and three smaller parties with a vote share of 17 per cent each. Note that parties D and
C each prefer cabinet D to cabinets A, B, and AB, while parties A, B, C, which jointly
constitute a majority, prefer B to D. Finally, A and D prefer D over C. Therefore, the
core of cabinet assignment problem is empty.
The methodological problems uncovered by Austen-Smith and Banks consist in
the insight that core existence in the Laver–Shepsle model cannot be guaranteed. Note
that in cases of an empty core the Laver–Shepsle theory has no empirical content; it
does not predict anything. Put differently, the agenda restrictions considered by Laver
¹¹ See the next two sections for such models.
168 coalition government
D
C
B
A
AB
BC
Fig. 9.2 Core-existence cannot be extended to more than three parties
and Shepsle are not sufficienttoavoidthewell-knowncorenon-existenceproblems
(Plott 1967).
Elsewhere (e.g. Diermeier 1997; Diermeier and Krehbiel 2003) I have argued that
the root cause of these problems lies in the use of the core as a solution concept
while non-cooperative game theory (with Nash equilibrium as its solution concept)
does not suffer similar problems. One could, for example, reformulate the Laver–
Shepsle framework as a non-cooperative bargaining model among party leaders.
The theoretical literature on coalition government, however, has not taken this path.
Rather, a whole variety of alternative frameworks, all based on non-cooperative game
theory, have been proposed over the last fifteen years. It is to those applications of
non-cooperative game theory that we turn next.
4 Sequential Bargaining:The
Baron–Ferejohn Model
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The Baron–Ferejohn (“BF”) model of legislative bargaining (Baron and Ferejohn
1989) is one of the most widely used formal frameworks in the study of legislative
politics. One of the first direct applications of the model to a specific problem in
political science was the problem of government formation (e.g. Baron 1989, 1991).
In all variants of the BF model, a proposer is selected according to a known rule.
He then proposes a policy or an allocation of benefits to a group of voters. According
to a given voting rule, the proposal is either accepted or rejected. If the proposal is
daniel diermeier 169
accepted, the game ends and all actors receive payoffsasspecifiedbytheaccepted
proposal. Otherwise, another proposer is selected, etc.
12
The process continues until
a proposal is accepted or the game ends.
Consider a simple version of the model where there are three political parties with
no party having a majority of the votes in the legislature. The BF model predicts that
the party with proposal power will propose a minimal winning coalition consisting
of him- or herself and one other member, leaving the third party with a zero payoff.
The proposing party will give a proposed coalition partner just the amount necessary
to secure an acceptance. This amount (or continuation value) equals the coalition
partner’s expected payoff if the proposal is rejected and the bargaining continues.
Proposals are thus always accepted in the first round. Note that the proposing party
maximizes its payoff by choosing as a coalition partner one of the parties with the
lowest continuation value. The division of spoils will in general be highly unequal,
especially if the parties are very impatient.
Consider a simple, two-period, example of the model where three parties divide $1.
If the money is not divided after two periods, each party receives nothing. Suppose
further that each party has an equal amount of seats and that in each period the
probability that any given party is chosen as the proposer is proportional to seat
share, i.e. each party is selected with probability 1/3. In the last period each recognized
proposer will propose to keep the entire $1 and allocate nothing to the other two
parties. This proposal will be accepted by the other parties.
13
Now consider each
party’s voting decision in period one. If the proposal is rejected, each party again
has a probability of 1/3 of being selected as proposer in the second period. But as we
just showed, in that case the proposer will get the entire $1. Therefore, the expected
payoff from rejecting a proposal is 1/3 for each party. This expected payoff is also called
the “continuation value.” Call it D
i
for each party I (here D
i
=1/3 for each i). Now
consider the incentives of a proposer in period one. By the same argument as above
14
each proposer will make a proposal that allocates $1 − D
i
(here $2/3) to himself, D
i
to one other party (his “coalition partner”), and nothing to the remaining party. This
proposal will be accepted.
15
¹² A variant of this set-up allows (nested) amendments to a proposal before it is voted on. This is the
case of an open amendment rule (Baron and Ferejohn 1989).
¹³ Why would the non-proposing parties vote for a proposal where they receive nothing? The idea is
the following. Since the model assumes that all parties’ relevant motivations are fully captured by their
monetary rewards, parties would accept any ε-amount for sure. But then the proposer can make this ε as
small as he wishes. The technical reason is that a proposal that allocates everything to the proposer is the
only subgame perfect Nash equilibrium in the second period. From the proposer’s point of view offering
ε more than $0 cannot be optimal since he can always offer less than ε. From the other parties’ points of
view accepting $0 with probability one is optimal (they are indifferent), but voting to accept with any
probability less than one cannot be optimal, since in that case the proposer would be better off offering
some small ε which the parties would accept for sure.
¹⁴ See also the previous footnote.
¹⁵ In their general model, Baron and Ferejohn show that an analogous argument also holds if the
game is of potentially infinite duration. That is, parties are selected to propose until agreement is
reached. To ensure equilibrium existence future payoffs need to be discounted. The more they are
discounted, i.e. the more impatient the parties, the higher the payoff to the proposer. In subsequent years
Baron systematically applied the model to various aspects of government formation such as different
170 coalition government
Compared to the Laver–Shepsle model, the Baron–Ferejohn model has many
methodological advantages. Because of the use of non-cooperative game theory,
equilibrium existence is assured even in environments (e.g. dividing a fixed benefit
under majority rule) where the core is empty.
16
These features make the model very suitable for institutional analysis.
However, compared to the Laver–Shepsle model, the Baron–Ferejohn model is
much more difficult to work with, especially if one leaves the purely distributive
(“divide-the-dollar”) environment and includes policy preferences. In that case only
the simplest environment of three symmetric parties with Euclidean preferences is
reasonably manageable.
17
Also, the model is only about coalition formation, not
stability.
Therefore, even though the Baron–Ferejohn model does not have the same
methodological challenges as the Laver–Shepsle model, its applicability in the study of
coalition government is constrained by its technical difficulties. These shortcomings
have limited its use in explaining, for instance, minority government formation or
cabinet stability.
18
5 Alternative Frameworks:
Demand Bargaining and
Efficient Negotiations
.............................................................................
The methodological shortcomings of the Laver–Shepsle framework and the techni-
cal challenges of using the Baron–Ferejohn model in an environment with policy
preferences have led to a search for alternative bargaining models over coalition
governments. Two candidates have received the most interest: demand bargaining
and efficient negotiations.
voting and proposal rules (Baron 1989), parties with spatial preferences (Baron 1993), and multistage
decision-making (Baron 1996). See Baron 1993 for a detailed overview.
¹⁶ The curious reader may ask why the Baron–Ferejohn model does not face the same
methodological issues as the Laver–Shepsle model. Suppose parties would vote over selection
probabilities. Don’t we face similar non-existence problems as discussed in the Laver–Shepsle model?
Such a question confuses two different methodologies. Laver and Shepsle use the core as their solution
concept. If we use the core, non-existence problems reappear at the level of institutional choice. But if
we use Nash equilibrium, then the collective choice over selection probabilities again needs to be
modeled as a non-cooperative game and this game generally will have a Nash equilibrium. For a more
detailed discussion of this subtle point see Diermeier 1997; Diermeier and Krehbiel 2003. For a model of
voting over proposal rights see Diermeier and Vlaicu 2005.
¹⁷ See Austen-Smith and Banks 2005 and Banks and Duggan 2000, 2003, for a thorough analysis of
the Baron–Ferejohn model. In the general case of convex preferences we also have to worry about
multiple equilibria. See also Eraslan and Merlo 2002.
¹⁸ See, however, Baron 1998 who proposed a model based on Diermeier and Feddersen 1998 where
minority governments could be stable, but would not be chosen in equilibrium. See also Kalandrakis
2004.
daniel diermeier 171
The demand bargaining approach in the study of coalition government is due
to Morelli (1999). In Morelli’s approach agents do not make sequential offers (as in
the Baron–Ferejohn model), but make sequential demands, i.e. compensations for
their participation in a given coalition. Specifically, the head of state chooses the first
mover. After that, agents make sequential demands until every member has made
a demand or until a majority coalition forms. If no acceptable coalition emerges
after all players have made a demand, a new first demander is randomly selected;
all the previous demands are void, and the game proceeds until a compatible set of
demands is made by a majority coalition. The order of play is randomly determined
from among those who have not yet made a demand, with proportional recognition
probabilities.
19
To see the difference from the Baron–Ferejohn model consider the three-party
example as above. Morelli (1999,proposition1) shows that in this case the distrib-
ution of benefits is ($1/2,$1/2) among some two-party coalition. In contrast to the
Baron–Ferejohn model there is no proposer premium. Intuitively, each party has the
same bargaining power in the demand bargaining game and that is reflected in
the equilibrium outcome.
An alternative approach was proposed by Merlo (1997) based on the work of Merlo
and Wilson (1995). As in the original Baron–Ferejohn model and in Morelli’s model,
a set of players bargain over a perfectly divisible payoff by being recognized and
then making offers. If the offer is accepted by all parties, the government forms; if
not, bargaining continues. However, there are two key differences. First, all players
need to agree to a proposed distribution. Second, the value of the prize changes
over time. Merlo interprets this change as shifting common expectations about the
lifespan of the chosen coalition caused, for example, by shifting economic indicators
(e.g. Warwick 1994). Merlo and Wilson (1995, 1998) show that this game has a unique
stationary subgame perfect equilibrium.
20
Second, the equilibrium of the bargaining
game satisfies the so-called separation principle:anyequilibriumpayoff vector must
be Pareto efficient, and the set of states where parties agree must be independent
of the proposer’s identity. A very rough intuition for the result is that because all
members of the coalition need to agree to an allocation, the coalition behaves as if
it desired to maximize the joint payoff.Withchangingpayoffs this implies that for
some states the parties would be better off to delay agreement to wait for a better
draw. Therefore, bargaining delays can occur in equilibrium.
21
In contrast to earlier
accounts (e.g. Strom 1988) that had interpreted long formation times as evidence of
a crisis, Merlo and Wilson showed that delays may be optimal from the point of view
of the bargaining parties. By not agreeing immediately (and thus forgoing a higher
¹⁹ Earlier models of demand bargaining used an exogenous order of play. See e.g. Selten 1992;Winter
1994a, 1994b.
²⁰ Both unanimity and randomly changing payoffs are important for both the uniqueness result and
the efficiency property (Binmore 1986; Eraslan and Merlo 2002). Majority rule, for example, leads to
multiple equilibria and inefficiency. Parties agree “too early” to ensure that they will be included in the
final deal.
²¹ For an empirical studies of the cabinet formation processes see Diermeier and van Roozendaal
1998; Diermeier and Merlo 2000; Martin and Vanberg 2003.