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COALITION-FORMATION AS A RESULT
OF POLICY AND OFFICE MOTIVATIONS
IN THE GERMAN FEDERAL STATES
An Empirical Estimate of the Weighting Parameters
of Both Motivations
Susumu Shikano and Eric Linhart
ABSTRACT
In this article, we analyze the policy and office motivations of parties in
coalition-formation processes at the German federal-state level. We utilize
a model developed by Sened that considers both motivations simultan-
eously and introduces a method by which to estimate its key parameters
using data of German state-level coalition-formations.
KEY WORDS coalition-formation Germany office motivation policy moti-
vation
Introduction
Theories of coalition-formation can be categorized within two groups: models
with office motivations and models with policy motivations. The former
assume that only offices motivate parties in the coalition-formation process
(e.g. Riker, 1962; Schofield and Laver, 1985). According to the latter, in
contrast, coalition-formation depends on the programmatic proximity among
parties in the policy space (see Laver and Schofield, 1990, for an overview).
Besides these lines of research, there are also models that combine both
kinds of motivation. The theory of minimal connected coalitions suggested
by Axelrod (1970) is the earliest concept among them. While this model can
be seen as a variation of the office-oriented minimal winning coalition,
Axelrod reduced the number of predicted coalitions by integrating the
connectedness on the unidimensional policy scale. Austen-Smith and Banks
(1988), by contrast, introduced a model in which both kinds of motivation
are considered equal. A similar model suggested by Crombez (1996) and
PARTY POLITICS VOL 16. No.1 pp. 111–130
Copyright © 2010 SAGE Publications Los Angeles London New Delhi
www.sagepublications.com Singapore Washington DC
1354-0688[DOI: 10.1177/1354068809339539]
Baron and Diermeier (2001) assumes that a utility function contains both
an office-motivated and a policy-motivated part. Sened (1995, 1996)
extended this model, allowing the weight of these two motivations to vary
among parties (see also Schofield and Sened, 2006). His model can be seen
as more general, since it includes the purely policy-oriented and purely
office-oriented models as special cases.1
Despite its theoretical innovation, the application of Sened’s model to
empirical data has been meagre. While there are some applications in the liter-
ature (Giannetti and Sened, 2004; Sened, 1996; Linhart and Shikano, 2007),
they remain more akin to a ‘stylized case study’ rather than systematic quan-
titative empirical evidence. Most importantly for the purpose of this article is
that, to date, there are no systematic quantitative estimates of the weights that
parties put on these two complementary motivations. Therefore, one of the
goals of this article is to estimate the parameter for both motivations using
empirical data. For this purpose, we need enough cases to allow us to shrink
the range of possible parameters. German state-level coalition-formations
provide an optimal data basis, since these have similar institutional settings
– the actors involved are almost identical and politically relevant. By ana-
lyzing the German state-level coalition-formations, we also approach a
substantive question, which is the second goal of this article. That is, despite
their programmatic proximity, Germany’s two largest parties, the Christian
Democrats and the Social Democrats, have only infrequently formed grand
coalitions. We show that this aversion to the grand coalition can be explained
partly by the simultaneous consideration of policy and office motivations.
The remainder of this article proceeds as follows: in the next section, we
briefly present Sened’s original model, but since this model has assumptions
that are unrealistic for Germany and/or inappropriate for empirical estima-
tion of the weighting parameters, the third section modifies some elements
of Sened’s original model. By the end of the fourth section, we will have
introduced our data and operationalization. We present the estimated results
in the fifth section and the article ends with some discussions.
Sened’s Model
According to Sened’s model, a party ievaluates a coalition Cin terms of an
office utility uioff(C) as well as a policy utility uipol(C). uioff(C) is conceived as
a relative share of offices which party iobtains in coalition C. To estimate
the policy utility, Sened considers the legislative decision processes after
coalition-formation. Within the framework of a spatial model, one can
identify the position yiprovoked by party iin the electoral campaign as well
as the expected policy output x(C) of coalition Cin a policy space. The
policy utility uipol(C) corresponds to the negative squared distance between
yiand x(C). Furthermore, Sened assumes additive separable utility functions
such that the overall utility uiof coalition Cfor a party i, defined as:
PARTY POLITICS 16(1)
112
ui(C) =
α
iuioff(C) +
β
iuipol(C) =
α
iuioff(C) –
β
i||x(C) – yi||2
with
α
i,
β
i≥0;
α
i+
β
i= 1, where
α
iand
β
iare the party-specific weighting
parameters for the office and policy motivations. We can interpret this utility
function as the gain in the office utility that compensates for the loss in policy
utility caused by distance. Therefore, the overall utility can be positive as well
as negative.
The above utility function assumes that a policy output x(C) can be com-
pletely determined as a result of bargaining during the coalition-formation
process. This appears to be realistic if one considers the existence of coali-
tion agreements in many European countries. Nevertheless, the legislative
processes are not free of uncertainty, since not all future political issues are
known at the time of coalition-formation. Sened integrates this uncertainty
within the model by assuming that some policy outputs are more likely than
others. Denoting Oas the space of all possible policy outputs, one can postu-
late a probability function πCwhich attributes the likelihood πC(x) to every
possible policy output x
∈
O. Assuming risk-neutral actors, the expected
utility of Cfor iis:
ui(C) =
α
iuioff(C) –
β
i∫x
∈
O(πC(x)||x– yi||2)dx.
To define πCmore specifically, Sened uses concepts of legislative decision-
making, e.g. the uncovered set (Giannetti and Sened, 2004; Sened, 1996;
cf. Shepsle and Weingast, 1984), the structural stable core (Sened, 1996; cf.
Schofield, 1986) or the political heart (Schofield and Sened, 2006; cf. Schofield,
1993). It is usually assumed that all outputs inside the corresponding solu-
tion sets are equally probable, while all outputs outside the solution sets have
zero likelihood. Denoting the respective solution set by LCand following
this probability function, we can specify the utility function as follows:
ui(C) =
α
iuioff(C) –
β
i∫x
∈
LC||x– yi||2dx/||LC||.
To predict which coalition rational actors would form, two criteria are
defined: winning and invulnerability. First, rational actors would prefer to
be in the opposition (ui(C) = 0) rather than participate in a coalition which
results in a negative utility. Therefore, the necessary condition for all poten-
tial government coalitions C* is that all participating parties have a non-
negative utility (the winning criterion):2
ui(C*) ≥0 for all i
∈
C*.
The sufficient condition for the formed coalition is that it assures the
highest utility for all participating parties. Denoting Nas the set of all
parties and 2N\Ø the set of all possible coalitions, the sufficient condition,
or ‘invulnerability criterion’, can be formalized as follows:3
ui(C*) ≥ui(C) for all i
∈
C* and for all C
∈
2N\Ø.
SHIKANO & LINHART: COALITION-FORMATION
113
Note that the winning criterion is automatically fulfilled if a coalition is
invulnerable. Invulnerability means that a party ias member of a coalition
C* values this coalition at least as highly as each alternative coalition C.
This holds in particular for coalitions in which iis not a member and which
are valued by ias 0. From this it follows that ui(C*) is not negative if C*
is invulnerable.
Some Adjustments of Sened’s Original Model
For the following analysis, we adjust Sened’s original model in terms of office
utility, the solution set of the legislative stage, the set of potential coalitions
to be investigated and application of the invulnerability criterion.
First, Sened’s original model gives leeway to parties in terms of the policy
output uipol(C) as well as the distribution of offices uioff(C). While on the one
hand this renders the model flexible, it risks including unrealistic outcomes
on the other. In Germany, there are some unwritten norms to be considered.
Imagine, for example, a coalition between highly office-motivated Liberals
and highly policy-motivated Christian Democrats. While – with respect to
their utility functions – both parties would perhaps agree to form a coalition
in which the Liberals held all offices while the Christian Democrats dictated
policy, it would be very difficult for either party to explain to their voters.
Furthermore, a unique prediction cannot be guaranteed, since more than
one solution can be reached through this kind of modelling. To avoid this,
we assume a certain fixed office utility for each party in each coalition. More
specifically, we follow Gamson’s Law, whereby the offices are distributed
proportionally to the participating parties’ share of seats (Gamson, 1961):
uioff(C) = si/Σj
∈
Csjfor all i
∈
C,
where sidenotes party i’s share of seats.
This accommodates the fact that Gamson’s Law holds almost perfectly
in Germany (see Linhart et al., 2008) as well as in other West European
democracies (e.g. Browne and Franklin, 1973; Warwick and Druckman,
2006). The proportional distribution of offices seems to be an accepted
norm; deviations are only possible within a very small margin.4Note that,
by introducing Gamson’s Law, we deviate from another important assump-
tion of Sened’s original model. While Sened game-theoretically modelled the
process in which parties trade policy for office utility and vice versa, our
approach is a more decision-theoretical one – that is, decisions under restric-
tions (Gamson’s Law and ideological constellation of parties) are at stake.
Therefore, the pure office utility for a party is not endogenous, but assumed
to be given on the basis of its share of seats.
Second, Sened’s original model and some of its applications thus far assume
solution concepts for the legislative process that are independent of the co-
alition formed. Accordingly, a coalition game has, for example, only one
PARTY POLITICS 16(1)
114
political heart, and the anticipated policy output in the following legislative
process falls within this set regardless of which coalition has been formed.
Regarding this point, Sened does not follow Austen-Smith and Banks’ (1988)
four-stage model in which the outcome of the coalition-bargaining game
influences the legislative game. In Sened’s view, coalition ‘agreements about
policy positions are usually not binding. Therefore, in this model, the results
of the election, not the composition of any particular coalition, determine
the policy outcome that will be implemented’ (1996: 335). Nonetheless, he
mentions, depending on the context, that alternative modelling – for example
based on the Pareto set – can make sense (Sened, 1996: 335, fn. 5). We are
convinced that the Pareto set is more adequate in the German case mainly
for two reasons:
(1) There are strong indications that, in Germany, the composition of a
coalition government influences the legislative outcome as described by
Austen-Smith and Banks’ original model. In many cases, the existence
of written coalition agreements serve explicitly to regulate the parties,
preventing them from overruling each other with the help of opposition
parties (the interdiction of changing majorities). Even if those agreements
do not exist in written form, they appear to be an accepted political norm
by the parties: the outvoting of parties within the government occurs
only in very exceptional cases, with most heralding the end of the coali-
tion government.
(2) Sened assumes that the opposition parties’ utility equals 0. This assump-
tion is based on the fact that these parties do not hold any offices
(uioff(C) = 0), but are not made responsible for the policy outcome by
the public (uipol(C) = 0). Hence, opposition parties should have little or
no influence on policy outcomes.
Therefore, the Pareto set is a more appropriate means of modelling the
legislative process in Germany. The Pareto set PCof coalition Cincludes the
influence of coalition governments as well as uncertainty (discussed above)
in the legislative processes.
Third, while Sened originally did not restrict the potential coalitions for
investigation, we take only minimal winning coalitions into account. Surplus
majority coalitions and minority governments are excluded from the analysis
for the following reasons: each surplus majority coalition is theoretically
dominated by all minimal winning coalitions in its subset in terms of office
motivation. If any surplus party joins a minimal winning coalition, at least
one original coalition partner gains only a reduced number of distributed
offices. In terms of policy motivation, the Pareto set of a surplus majority
coalition would never be smaller than those of its subset of minimal winning
coalitions. Therefore, the sum of policy distance to the possible policy out-
comes for all parties is larger in the surplus coalition than in any minimal
winning coalitions in its subset. On the contrary, Sened demonstrates the
SHIKANO & LINHART: COALITION-FORMATION
115
possibility that a minority government could be formed. We, however, exclude
this possibility for the following two reasons: first, Sened’s original model
(1996: 361) predicts minority governments only when a central core party
dominates the ideologically polarized party system. This has never occurred
in the German bipolar system (Laver and Schofield, 1990) except when a
single party has won the majority. Second, we assume – by contrast with
Sened’s original model – that the solution set of the legislative stage depends
on the composition of the coalition. If, under this assumption, we allow the
formation of minority governments, every party would prefer its single party
government because it can then monopolize all offices and the solution set
of the legislative state ensuring that it is identical with its policy position.
If we apply the invulnerability criterion to this situation, we cannot predict
any coalition government but all possible single party governments. This
makes no sense and is entirely unrealistic. For the reasons stated above, we
consider only minimal winning coalitions as potential governments. The
exclusion of minority governments is less problematic, at least in this article,
since all German state-level constitutions require the government to have
an absolute majority in the formal investiture vote. Empirically, we can find
only six minority single party governments and five minority coalitions in
our data set out of 111 cases overall.
While the adjustments thus far are more theoretically legitimated, the last
one concerning the invulnerability criterion is for a more empirical reason.
The invulnerability criterion provides deterministic predictions provided the
solution set is not empty. While these kinds of clear predictions are a strength
of formal modelling, they could also lead to the so-called ‘zero-likelihood
problem’ (Signorino, 1999: 281; see also Morton, 1999: 116–18) if the pre-
dictions have to be tested empirically – in particular, when using a maximum
likelihood approach. Within the framework of this standard method of
empirical data analysis, likelihood is defined as a product of empirical obser-
vations and model predictions expressed in probability as follows:
L(
θ
|D) = ∏p(D|
θ
),
where
θ
is the interested parameter and Dis the observed data. Researchers
are interested in finding
θ
given Dis observed. Assume that an interested
variable is discrete with the observation vector z= (z1, z2,..., zM); the like-
lihood function can be further expressed:
L(
θ
|z) = ∏jpj(
θ
)zj,
where pj(
θ
) denotes the predicted probability that jis observed. Obviously,
the likelihood increases if expected outcomes are frequently predicted with
a high probability, and vice versa. Therefore, the set of parameters
θ
which
maximizes the likelihood is sought. This method, however, only works if all
empirically observed outcomes are theoretically predicted with a non-zero
PARTY POLITICS 16(1)
116
probability. If at least one outcome is predicted with probability zero (un-
observed with certainty), the likelihood is zero for every set of parameters
θ
, since the likelihood is a product of predicted probability, as shown in the
equation above. In this case, the identification of
θ
is impossible. And this
is often the case for formal models, since predictions of most formal models
exclude some possible outcomes which definitely do not lie within their
solution set. Thus, the probability is high in that at least one of the observed
outcomes in the empirical data is predicted to have a zero probability. If,
however, model predictions are not deterministic, but probabilistic, this
problem does not arise, because no outcomes are predicted with a proba-
bility of zero. For this reason, we apply the invulnerability criterion prob-
abilistically. Further details concerning this are given below. Furthermore,
we abandon considering the winning criterion since this is included implic-
itly when we test for invulnerability.
Data, Operationalization and Estimation Strategy
As mentioned above in the Introduction, one important goal of this article
is to estimate the weighting parameters of both policy and office motivation
using empirical data. To this end, we need a certain level of information, or,
more concretely, data sets with a certain number of cases. It is not easy to
find such data for coalition-formations, however, since only a limited number
have generally taken place in individual countries in the past. This problem
has at least two solutions: multi-system analysis and sub-system analysis.
Martin and Stevenson (2001) exemplify the first solution through putting
into the analysis the coalition-formations in as many countries as possible.
This produces nothing useful for our purpose, however, since the party sys-
tems (the sets of actors) vary across countries, while we attempt to estimate
the actor-specific weighting parameters.5The second solution is well exem-
plified by Bäck (2003), who analyzed coalition-formations at a sub-national
level – more specifically for Swedish local governments. This solution is
superior to the first in terms of institutional homogeneity and the identical
party system (see also Skjæveland et al., 2007). Coalition-formation processes
analyzed in this way take place in a relatively homogeneous institutional
setting, since the sub-national systems share the same national system. Further-
more, it is likely that the party systems in each sub-system are similar to
each other. One caveat of this solution is that analyzed coalition-formations
at the sub-national level have to be more or less equivalent to those at the
national level (for more details, see, e.g., Bäck, 2003: 35–40).
Being confronted with the case-number problem and two solutions dis-
cussed above, we take the second solution using data of German state-level
coalition-formations. This approach has some advantages besides the points
mentioned above. First, Germany is a federal state in which the states
(Bundesländer) are responsible for many important tasks and, additionally,
SHIKANO & LINHART: COALITION-FORMATION
117
exert influence on national-level policy-making via the Federal Council
(Bundesrat). State-level coalition-formations are therefore politicized equiv-
alently to those at national level. Second, the political systems of the
German states are characterized by parliamentarianism and resemble that
of the federal state.
The data analyzed in the following are taken from the coalition-formations
between the 1983 and 2005 federal elections. The 1983 election was the first
federal election at which the Greens succeeded in entering the national parlia-
ment (the Bundestag). Prior to this, the party system at federal level, as well
as in most states, had consisted of only three parties in the majority of cases:
the Christian Democrats, the Social Democrats and the Liberals. This makes
the analysis less interesting, since there are only a very limited number of
possible coalitions. Despite the relatively short period of time, there have
still been 111 coalition-formations since the 1983 election. However, we are
forced to exclude some cases. First, since we are interested in the coalition-
formation processes, we excluded 47 coalition-formations in which a single
party had an absolute majority. We also had to exclude six further coalition-
formations from the analysis since our analysis focused on the explanation
of minimal winning coalitions in Germany. Thus, one oversized coalition and
five minority governments are not considered here. Two further coalition-
formations had to be excluded, since the coalitions actually formed included
non-established parties whose policy positions were unknown. As a result,
our data set consists of 57 observed coalition-formations.
Our analysis focuses on the five established parties represented in the
national parliament: the CDU/CSU (C; the Christian Democrats), the SPD
(S; the Social Democrats), the FDP (F; the Liberals), the Greens (G) and the
PDS (P; the Socialists, the former GDR Communists). We assume that the
utility of each possible coalition for these five parties determines the coalition-
formation processes. To estimate the policy utility uipol(C), we have to esti-
mate the policy positions of these parties. One problem, therefore, is that we
are modelling the coalition-formation processes among the state-level parties,
for which only little information is available. Therefore, we approximate the
state-level parties’ positions as the estimated ideal points of the corresponding
national parties at the precedent national-level election. This assumption is
less problematic, at least in the German context. Debus (2008) analyzed the
federal- and state-level manifestos and showed overall similarity in the
Benelux-type two-dimensional ideological constellation, despite some indi-
vidual differences. We measure the positions of the national-level parties by
using the Comparative Manifesto Project (CMP) data in the following way
(cf. Klingemann et al., 2007; Linhart and Shikano, 2007): first, we assume
a priori a two-dimensional policy space whose dimensions correspond to
the socio-economic and socio-cultural conflict lines. This kind of two-
dimensional policy space is repeatedly confirmed by multiple empirical
studies (see, e.g., Laver and Hunt, 1992). Second, we classify the 56 coding
categories of the CMP data into three thematic groups corresponding to the
PARTY POLITICS 16(1)
118
two dimensions and a remaining category. Furthermore, we classify the
categories into three groups according to their ideological positions: right,
neutral and left. Third, we construct the positions for each party on each
dimension. The basic idea is similar to the conventional approach, which
sums up the relative frequencies of left and right positions and subtracts one
from the other (see, e.g., Klingemann et al., 1994). While the conventional
approach assumes only one dimension, we implement this separately in the
two dimensions defined as a priori. Furthermore, we do not sum up the raw
frequencies, but the logarithmized relative frequencies are used to reduce
the over-dominating influence of a single category.6Otherwise, the estimated
ideological positions would be too sensitive to the frequency of individual
categories. More details concerning the construction of party positions
appear in the Appendix. Using the party positions constructed in this way,
one can construct the Pareto set for each possible coalition. As discussed
above, we assume that the likelihood of all possible policy outputs inside a
Pareto set is distributed uniformly.
Having measured both components of the utility function, we are now
ready to estimate the weighting parameter for them. As mentioned above,
we assume a probabilistic decision rule to avoid the zero-likelihood problem.
Concretely, this is done by introducing a stochastic term
ε
in the utility
function:
ui(C) =
γ
i[(1 –
β
i)uioff(C) –
β
i∫x
∈
LC||x– yi||2dx/||LC||] +
ε
i.
In favour of estimation economy,
α
iis here replaced by 1 –
β
i(cf. the first
formula in section 2).
γ
iis an additional party-specific term describing the
relative impact of the assumed utility function with respect to an error term
ε
i. The larger
γ
iis, the smaller the relative impact of
ε
ibecomes and, there-
fore, the more important the role of the deterministic component. We can
thus interpret
γ
ias the degree of the deterministic decision.
If we further assume that
ε
iis distributed according to the Gumbel distri-
bution, the probability that party idecides to join coalition C* is:
Probi(C*) = exp{
γ
i[(1 –
β
i)uioff(C*) –
β
i∫x
∈
LC*||x– yi||2dx/||LC*||]}/
Σi
∈
Cexp{
γ
i[(1 –
β
i)uioff(C) –
β
i∫x
∈
LC||x– yi||2dx/||LC||]}.
Note that this probability concerns the individual decision of parties. If
we assume that the individual decision of each party is independent from
that of other parties, the likelihood of a coalition is the product of the prob-
abilities of all participating parties within the coalition:
Prob(C) = ∏i
∈
CProbi(C).
This probability has to be rescaled, since its sum is unequal to 1 in general:
Prob’(C) = Prob(C)/ΣC
∈
MWCProb(C),
where MWC is a subset of 2N\Ø, that is, the set of all minimal winning
coalitions.
SHIKANO & LINHART: COALITION-FORMATION
119
Finally, we can assume that the coalition-formation is based on the multi-
nomial distribution with probabilities Prob’(C).
The estimation of both parameters
γ
iand
β
iis also possible via maximum
likelihood. However, it is more appropriate to assume that
β
iis limited
between 0 and 1. Therefore, we search for the beta distribution which fits
the parameter estimates for
β
i. Furthermore, the beta distribution is highly
appropriate for this purpose, since it is quite flexible in its distribution form.
γ
iis assumed to follow the gamma distribution, which takes only non-
negative values and whose shape of distribution is also flexible. Due to these
distributional assumptions, the parameters are estimated via a Bayesian
approach (Gill, 2002). As prior distribution, a less informative distribution
was used for each parameter:
β
i~
Β
(1, 1)
γ
i~
Γ
(3, 2).
4. Results
Purely Policy-Oriented and Purely Office-Oriented Models
Before we present the estimated results of the parameters specified above,
we make predictions based on the models with only one motivation and
observe their empirical validity. This should allow some impressions to be
drawn from the data analyzed here.
We begin by observing the predictions of the purely office-oriented model.
As discussed above, we assume under Gamson’s Law that each participating
party receives ministerial posts proportionally to its share of seats. Based on
this assumption and the pure office motivation, the prediction based on the
invulnerability criterion corresponds to the so-called minimum winning coali-
tion which has the smallest size of seats among the minimal winning coalitions
(Gamson, 1961; Riker, 1962). The fourth and fifth columns in Table 1 provide
the number of correct and incorrect predictions. Accordingly, the predictions
based on the pure office motivation are poor throughout the time period
analyzed here. The overall rate of correct predictions is only 28 percent.
To make predictions based on the purely policy-oriented model, we observe
the distance from each party to each minimal winning coalition,
∫x
∈
LC||x– yi||2dx/||LC||.
According to the invulnerability criterion, the predicted coalition is one
to which the participating parties have minimal distance on average.7The
second and third columns in Table 1 give the number of correctly and incor-
rectly predicted coalitions. Accordingly, the purely policy-oriented model
shows quite a poor predictive performance between 1983 and 1990. At this
period of time, no single coalition was correctly predicted. In addition, after
1990, the predictive power of this model remains moderate and the overall
PARTY POLITICS 16(1)
120
rate of the correct predictions is 39 percent. This is higher than that of the
purely office-oriented model, but still far from satisfactory. Table 2 gives
more information about which coalitions were well predicted. Accordingly,
the grand coalition of Christian Democrats and Social Democrats is over-
predicted, while the liberal–conservative (CF) and red–green (SG) coalitions
are under-predicted. The visual inspection of party positions in fact confirms
that the two largest parties, the Christian Democrats and the Social Demo-
crats, are programmatically proximate with each other. Nevertheless, the
grand coalition has occurred much less frequently than predicted by prox-
imity. This suggests that one considers not only policy-motivation but also
office motivation, since the grand coalition would promise both large parties
fewer cabinet posts than the other coalitions.
Estimation of the Model Considering Both Motivations
Now we observe the estimated results of the model that considers both moti-
vations. We estimate the parameters using two different model specifications.
The first simple model sets both parameters as generic for all parties, that is
α
i=
α
jand
β
i=
β
jfor all observed parties i, j. The second model, by contrast,
allows both parameters to be variable between parties, i.e. the pair (
α
i;
β
i)
is operationalized as dependent on the actor i. To observe the posterior distri-
butions of the parameters, 10,000 samples are collected for each model
using the Markov–Chain–Monte Carlo method after 10,000 burn-in itera-
tions. Table 3 gives the results for the parameter estimations.
We begin to observe the results of the more restrictive model (model 1)
in which both parameters are estimated generically for all parties. The
γ
parameter expresses the impact of the deterministic components of the utility
function. Accordingly, a relatively high estimated value for
γ
demonstrates
that parties are strongly oriented by the utility consisting of both motivations,
and the error term is quite small. The mixture parameter
β
additionally shows
SHIKANO & LINHART: COALITION-FORMATION
121
Table 1. Predictive performance of the purely policy-oriented and office-oriented
models
Federal-level Purely policy-oriented Purely office-oriented
legislative period Correct Not Correct Not
1983–1987 0523
1987–1990 0853
1990–1994 7429
1994–1998 6639
1998–2002 5739
2002–2005 4518
Total 22 35 16 41
Correctly predicted 39% 28%
that the policy motivation outweighs the office motivation (see also Figure
1). Nevertheless, the office motivation is important as an un-ignorable part
of the utility, since the rate of correct predictions is 62 percent and much
higher than those of the purely office-oriented and policy-oriented models.
If we estimate both parameters specifically for each party, the picture is
different. The estimates of
γ
demonstrate that the CDU/CSU is more oriented
to the deterministic component of utility, while idiosyncratic factors play an
important role in the decisions of the other parties. In terms of the CDU/
CSU’s decision-making, the relative weight of the policy motivation (
β
) is
quite high. Accordingly, the CDU/CSU should be ready to form the grand
coalition when the SPD’s position is not far away in the policy space. This
suggests that the relatively lower frequency of the grand coalition in the
empirical data should be attributed to the other party, the SPD. The esti-
mated results allow us two interpretations: a relatively low level of
γ
implies
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122
Table 2. Predicted and actually formed coalitions
Predicted by the purely
policy-oriented model Actually formed Difference
CS 33 14 19
SG 8 13 –5
SF 6 6 0
CF 5 19 –14
SP 3 3 0
SGP 2 0 2
SFG 0 2 –2
Total 57 57 0
Table 3. Estimated results of the model considering both motivations
(median and 90% confidence interval)
Model 1 Model 2
γ
8.02 (5.87 10.21)
CDU/CSU 9.47 (5.61 14.43)
SPD 2.99 (1.57 4.73)
FDP 2.00 (0.59 5.07)
Greens 2.64 (0.82 5.49)
PDS 1.21 (0.41 2.92)
β
0.79 (0.71 0.88)
CDU/CSU 0.87 (0.74 0.98)
SPD 0.13 (0.01 0.44)
FDP 0.77 (0.18 0.99)
Greens 0.72 (0.31 0.99)
PDS 0.42 (0.05 0.93)
Correct predictions (average) 62% 63%
that the deterministic component consisting of policy and office motivation
plays a less important role in the SPD’s decision-making process. Further-
more, the low estimate of
β
shows that the SPD is more interested in office
than in policy outputs. These interpretations do not exclude each other and
seem to operate simultaneously.
Turning, now, to the estimated results for the smaller parties; the FDP
and the Greens tend to be, like the CDU/CSU, more policy-oriented (see
Figure 2). Their impact on the decision-making process, however, is less than
in that of the CDU/CSU. The most problematic case is the PDS. The low
estimate of
γ
demonstrates that the utility function defined by Sened has the
least impact among the five parties analyzed here. Furthermore, the relative
weight between both motivations is also ambiguous (the lower middle panel
of Figure 2). This might be attributed to the long-standing practice after
reunification of not viewing the PDS as a possible coalition partner.
While this analysis assumes one party’s
β
being common across individual
states, one may wonder whether the Bavarian SPD, for example, weighs policy
differently from the SPD in Hamburg. Regarding this, Strøm (1990a) argued
that a party’s weighting between different kinds of motivations depends on
organizational and institutional determinants. In terms of organizational
factors, German state-level parties have their own relatively independent
organizations. However, Germany’s strict legal regulation makes organiza-
tional features of state-level parties comparable with each other. In terms of
institutions, the party systems in the individual federal states are relatively
homogeneous. All states adopt proportional representation, possess two-
dimensional policy spaces and their ministerial structures and competence
are comparable with each other. One exception is the extent to which elec-
toral competitiveness varies across the federal states. While the CSU – the
Bavarian Christian Democrats – for example, has held a strong position in
Bavaria for a long time, races in East German states are often narrow and
uncertain. In our view, however, this kind of variation in electoral competi-
tiveness can be offset by the other homogeneous factors across the states.
SHIKANO & LINHART: COALITION-FORMATION
123
Figure 1. Posterior distribution of
β
(generic for all parties)
β
Finally, we have to note that this second model with party-specific para-
meters improved the rate of correct predictions only marginally compared
with that of the first model (63 instaed of 62 percent).8Therefore, we should
be cautious in interpreting differences among parties in terms of
β
and
γ
.
Both models, by contrast, show significantly improved prediction rates
compared with those of purely policy-oriented or office-oriented models.
We can thus draw the conclusion that both components in the utility
function are essential and complementary to each other.
Discussion
In this article, we have estimated the weighting parameters for both kinds
of motivation systematically through using empirical data from German
state-level coalition-formations. The results show that it is not sufficient to
consider either policy or office motivations of political parties on their own.
One can achieve a significant improvement in predictive power by inte-
grating both motivations as separable additive components of a combined
utility function. The article shows a systematic way in which this can be
done rather than using ad hoc explanations that switch between both kinds
of motivation.
This article could be criticized for merely conducting a kind of data fitting,
i.e. one assumes an empirical model that consists of multiple theoretical
components and looks for the best parameter estimates for each compo-
nent. For example, Martin and Stevenson (2001), Bäck (2003) and, currently,
PARTY POLITICS 16(1)
124
Figure 2. Posterior distribution of
β
(party-specific)
β β β
β β
Greens
Skjæveland et al. (2007) have already done this kind of research. Further-
more, it is true that these authors also utilized multinomial logit models to
estimate parameters, as in this article. The most important difference be-
tween this article and the data-fitting approach, however, is that we were
not interested in competing theoretical models, but in a single model more
systematically developed by Sened. This model is equipped with a well-
defined utility function at individual actor level. We have realized the para-
meter estimation based on the individual random utility model – entirely
missed in the data-fitting approach.
Besides the innovation, there are still some tasks for the future that need
to be tackled if empirical tests are to be conducted in accordance with
Sened’s original model. One important caveat of this article was the exclu-
sion of minority governments from the analysis. Our main aim was to take
a step towards systematic estimation of weighting parameters. Limiting the
set of considered outcomes to minimal winning coalitions is empirically less
problematic in the context of German state-level coalition-formations. It is,
however, still needed if an estimation strategy is to be realized which can
cope with minority governments when we apply our method to further
contexts, e.g. in Scandinavian countries (Strøm, 1990b). More importantly,
Sened’s original model can predict the formation of minority governments.
One possible solution would be a further modification in terms of the solution
concept for the legislative process. We assumed that minimal winning coali-
tions can implement policy outcomes in their own Pareto set. By contrast,
minority governments can be assumed to implement only policy outcomes in
the political heart or uncovered set, since cooperation with opposition parties
is necessary (cf. Linhart and Pappi, 2009). This would lower the policy utility
of most minority governments and prevent the multiple predictions of all
single party governments via the invulnerability criterion.
Another task will be returning to the game-theoretical modelling approach
as per Sened’s original model. One of the crucial assumptions of model esti-
mation in this article is that individual choices are modelled independently of
one another. In this sense, the predictive model here is a decision-theoretical
model. One can, however, extend the model by endogenizing the parameters,
especially
β
. That is, parties can anticipate the decision of their potential
coalition partners and, correspondingly, adjust their weighting considering
both motivations to maximize their expected utility. This kind of game-
theoretical modelling and the analysis of resulting equilibria would serve to
further broaden the horizon of this field of research.
Appendix: Constructing Party Positions in the
Two-Dimensional Policy Space
Denote the percentage of category jin the manifesto of party iby Mji. We
introduce the following two categorizing functions for coding category j:
SHIKANO & LINHART: COALITION-FORMATION
125
1 if jis classified within the socio-economic category.
d(j) =
2 if jis classified within the socio-cultural category.
3 if jis classified within the other categories.
–1 if jis classified as left position.
sign(j) =
0 if jis classified as neutral position.
1 if jis classified as right position.
Now, we can estimate the ideal position for party ias follows:
Ideal position on the socio-economic dimension:
Ideal position on the socio-cultural dimension:
PARTY POLITICS 16(1)
126
∑∑
=
=
=
=
++⋅=
56
1)(
1
56
1)(
1
)1()1()(
jd
j
ji
jd
j
jii
MlnMlnjsigny
∑∑
=
=
=
=
++⋅=
56
2)(
1
56
2)(
1
)1()1()(
jd
j
ji
jd
j
jii
MlnMlnjsigny
Appendix Table. Categorizing functions for the categories in the CMP data
Category d(j) sign(j)
104 Military: Positive 2 1
105 Military: Negative 2 –1
201 Freedom and Human Rights: Positive 2 –1
202 Democracy: Positive 2 –1
401 Free Enterprise: Positive 1 1
402 Incentives: Positive 1 1
403 Market Regulation: Positive 1 0
404 Economic Planning: Positive 1 –1
405 Corporatism: Positive 1 0
406 Protectionism: Positive 1 –1
407 Protectionism: Negative 1 1
408 Economic Goals 1 0
409 Keynesian Demand Management: Positive 1 –1
410 Productivity: Positive 1 0
411 Technology and Infrastructure: Positive 1 0
412 Controlled Economy: Positive 1 –1
413 Nationalization: Positive 1 –1
414 Economic Orthodoxy: Positive 1 1
415 Marxist Analysis: Positive 1 –1
416 Anti-Growth Economy: Positive 1 –1
Acknowledgement
We would like to thank Hanna Bäck, Thomas Bräuninger, Marc Debus, Patrick
Dumont, Thomas Gschwend, Tasos Kalandrakis, Matthias Lehnert, Johannes Marx,
Franz U. Pappi, Lieven De Winter and three anonymous reviewers for their helpful
comments on a previous version of this manuscript.
Notes
1 Another extension is proposed by Kalandrakis (2007), who combines a bargaining
model that includes a formateur (Baron and Ferejohn, 1989) with a model, similar
to Sened’s, using a combined utility function that allows for both policy and office
motivation.
2 The winning criterion is redefined by Sened with respect to the utility function
applied here. In this context, ‘winning’ does not mean that a coalition holds more
than 50 percent of the seats in a parliament.
3 It is not completely correct to label this criterion as ‘sufficient’, because more than
one coalition can be predicted with it. More precisely, the formation of every
coalition fulfilling this criterion is in equilibrium, since no participating party has
an incentive to leave the coalition and form another. Our definition holds for the
subset of minimal winning coalitions which we research in this article. Regarding
the whole set of all possible coalitions, this definition would become more compli-
cated and have to be refined.
SHIKANO & LINHART: COALITION-FORMATION
127
Appendix Table. Continued
Category d(j) sign(j)
502 Culture: Positive 2 0
503 Social Justice: Positive 1 –1
504 Welfare State Expansion: Positive 1 –1
505 Welfare State Limitation: Positive 1 1
601 National Way of Life: Positive 2 1
602 National Way of Life: Negative 2 –1
603 Traditional Morality: Positive 2 1
604 Traditional Morality: Negative 2 –1
605 Law and Order: Positive 2 1
607 Multiculturalism: Positive 2 –1
608 Multiculturalism: Negative 2 1
701 Labour Groups: Positive 1 –1
702 Labour Groups: Negative 1 1
703 Farmers: Positive 1 0
704 Middle-Class and Professional Groups: Positive 1 1
705 Underprivileged Minority Groups: Positive 2 –1
706 Non-Economic Demographic Groups: Positive 2 0
Categories attributed to none of the dimensions are excluded from this table.
4 Note that we do not necessarily deduce minimum winning coalitions, or coalitions
with the smallest size, from Gamson’s Law, as Gamson did. It is well known that
minimum winning coalitions often fail to predict the coalition actually formed,
which also applies to the empirical test below. In contrast, we add the policy
component to the office component to make predictions. Correspondingly, we can
also predict non-minimum winning coalitions as well.
5 Another drawback of this solution is that it introduces a nearly uncontrollable
institutional heterogeneity across countries. Correspondingly, one needs a number
of control variables at the cost of sacrificing a greater degree of freedom.
6 More precisely, we add 1 to each relative frequency before it is logarithmized.
This is necessary since log(0) equals negative infinity, which cannot be summed
and log(1) = 0, such that this addition is necessary to map the zero-point onto itself.
7 Here, we make predictions using the deterministic decision rule, since we do not
need to estimate the parameters.
8 These rates are an average of 10,000 prediction rates. As stated above, the posterior
distributions of estimated parameters consist of 10,000 samples. This means that
there are 10,000 sets of parameter estimates. Correspondingly, we have 10,000
rates of correct predictions.
References
Austen-Smith, David and Jeffrey Banks (1988) ‘Elections, Coalitions, and Legisla-
tive Outcomes’, American Political Science Review 82: 405–22.
Axelrod, Robert (1970) Conflict of Interest. A Theory of Divergent Goals with
Application to Politics. Chicago, IL: Markham.
Bäck, Hanna (2003) Explaining Coalitions: Evidence and Lessons from Studying
Coalition Formation in Swedish Local Government. Uppsala: Uppsala University
Press.
Baron, David P. and John A. Ferejohn (1989) ‘Bargaining in Legislatures’, American
Political Science Review 83: 1181–206.
Baron, David P. and Daniel Diermeier (2001) ‘Elections, Governments, and Parlia-
ments in Proportional Representation Systems’, Quarterly Journal of Economics
116: 933–67.
Browne, Eric C. and Mark N. Franklin (1973) ‘Aspects of Coalition Payoffs in
European Parliamentary Democracies’, American Political Science Review 67:
453–69.
Crombez, Christophe (1996) ‘Minority Governments, Minimal Winning Coalitions
and Surplus Majorities in Parliamentary Systems’, European Journal of Political
Research 29: 1–29.
Debus, Marc (2008) ‘Party Competition and Government Formation in Multilevel
Settings: Evidence from Germany’, Government and Opposition 43: 505–38.
Gamson, William A. (1961) ‘A Theory of Coalition Formation’, American Socio-
logical Review 26: 373–82.
Giannetti, Daniela and Itai Sened (2004) ‘Party Competition and Coalition
Formation: Italy 1994–96’, Journal of Theoretical Politics 16: 483–515.
Gill, Jeff (2002) Bayesian Methods: A Social and Behavioral Sciences Approach.
Boca Raton, FL: Chapman and Hall.
PARTY POLITICS 16(1)
128
Kalandrakis, Tasos (2007) ‘A Theory of Minority and Majority Governments’.
Mimeo. University of Rochester.
Klingemann, Hans-Dieter, Richard I. Hofferbert and Ian Budge (1994) Parties,
Policies and Democracy. Boulder, CO: Westview Press.
Klingemann, Hans-Dieter, Andrea Volkens, Judith Bara, Ian Budge and Michael
McDonald (2007) Mapping Policy Preferences II: Estimates for Parties, Electors
and Governments in Central and Eastern Europe, European Union and OECD
1990–2003. Oxford: Oxford University Press.
Laver, Michael and W. Ben Hunt (1992) Policy and Party Competition. New York:
Routledge.
Laver, Michael and Norman J. Schofield (1990) ‘Multiparty Government’, Politics
of Coalition in Europe. Oxford: Oxford University Press.
Linhart, Eric and Franz U. Pappi (2009) ‘Koalitionsbildungen zwischen Ämter-und
Politikmotivation. Konstruktion einer interdependenten Nutzenfunktion’ (Coalition
bargaining between office and policy motivation. The construction of an inter-
dependent utility function), Politische Vierteljahresschrift 50: 23–49.
Linhart, Eric, Franz U. Pappi and Ralf Schmitt (2008) ‘Die proportionale Minis-
teriumsaufteilung in deutschen Koalitionsregierungen: Akzeptierte Norm oder das
Ausnutzen strategischer Vorteile?’ (The Proportional Distribution of Portfolios in
German Coalition Governments: Behavioural Norm or Realization of Competi-
tive Advantages?), Politische Vierteljahresschrift 49: 46–67.
Linhart, Eric and Susumu Shikano (2007) ‘Die große Koalition in Österreich:
Schwierigkeiten bei der Bildung, Stabilität und Alternativenlosigkeit’ (The grand
coalition in Austria: Difficulties of formation, stability, and lack of alternatives),
Österreichische Zeitschrift für Politikwissenschaft 36: 185–200.
Linhart, Eric and Susumu Shikano (2009) ‘Ideological Signals of German Parties in
a Multi-Dimensional Space’, German Politics (forthcoming).
Martin, Lanny W. and Randolph T. Stevenson (2001) ‘Government Formation in
Parliamentary Democracy’, American Journal of Political Science 45: 33–50.
Morton, Rebecca B. (1999) Methods and Models: A Guide to the Empirical Analysis
of Formal Models in Political Science. Cambridge: Cambridge University Press.
Riker, William H. (1962) The Theory of Political Coalitions. New Haven, CT: Yale
University Press.
Schofield, Norman J. (1986) ‘Existence of a “Structurally Stable” Equilibrium for a
Non-Collegial Voting Rule’, Public Choice 51: 267–84.
Schofield, Norman J. (1993) ‘Party Competition in a Spatial Model of Coalition
Formation’, in William A. Barnett, Melvin J. Hinich and Norman J. Schofield (eds)
Political Economy. Institutions, Competition, and Representation, pp. 135–74.
Cambridge: Cambridge University Press.
Schofield, Norman J. and Michael Laver (1985) ‘Bargaining Theory and Portfolio
Payoffs in European Coalition Governments 1945–83’, British Journal of Political
Science 15: 143–64.
Schofield, Norman J. and Itai Sened (2006) Multiparty Democracy. Elections and
Legislative Politics. Cambridge: Cambridge University Press.
Sened, Itai (1995) ‘Equilibria in Weighted Voting Games with Side Payments’, Journal
of Theoretical Politics 7: 283–300.
Sened, Itai (1996) ‘A Model of Coalition Formation: Theory and Evidence’, Journal
of Politics 58: 350–72.
SHIKANO & LINHART: COALITION-FORMATION
129
Shepsle, Kenneth A. and Barry R. Weingast (1984) ‘Uncovered Sets and Sophisticated
Voting Outcomes with Implications for Agenda Institutions’, American Journal of
Political Science 28: 49–74.
Signorino, Curtis S. (1999) ‘Strategic Interaction and the Statistical Analysis of Inter-
national Conflict’, American Political Science Review 93: 279–97.
Skjæveland, Asbjørn, Søren Serritzlew and Jens Blom-Hansen (2007) ‘Theories of
Coalition Formation: An Empirical Test Using Data from Danish Local Govern-
ment’, European Journal of Political Research 46: 721–45.
Strøm, Kaare (1990a) ‘A Behavioral Theory of Competitive Political Parties’, Amer-
ican Journal of Political Science 34: 565–98.
Strøm, Kaare (1990b) Minority Government and Majority Rule. Cambridge:
Cambridge University Press.
Warwick, Paul V. and James N. Druckman (2006) ‘The Portfolio Allocation Paradox:
An Investigation into the Nature of a Very Strong but Puzzling Relationship’,
European Journal of Political Research 45: 635–65.
SUSUMU SHIKANO is Professor of Political Methodology at the University of
Konstanz, Germany. His publications have appeared in German Politics, Politische
Vierteljahresschrift, Public Choice and West European Politics.
ADDRESS: Department of Political Science and Management, University of Konstanz,
Postbox 92, D-78457 Konstanz, Germany. [email: susumu.shikano@uni-konstanz.de]
ERIC LINHART is Assistant Professor (Junior Professor) of Applied Political Econ-
omy at the University of Kiel, Germany. His main research foci are coalition theory,
electoral systems and electoral behaviour, legislative studies and decision theory.
ADDRESS: Department of Agricultural Economics, University of Kiel, Olshausenstr.
40, D-24098 Kiel, Germany. [email: eric.linhart@ae.uni-kiel.de]
Paper submitted 19 September 2007; accepted for publication 28 March 2008.
PARTY POLITICS 16(1)
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