Policy Preferences in Coalition Formation: Instability, Minority, and
Surplus Governments
Anna Bassi
[email protected]
UNC–Chapel Hill, Department of Political Science
2nd R&R at the Journal of Politics
Abstract
In parliamentary democracies, political parties bargain over cabinet portfolios when forming coalition
governments. While most of the theoretical literature predicts that only minimal winning coalitions form
in equilibrium, the empirical evidence shows that they are as frequent as minority or surplus coalitions. In
this article, I bridge the gap between the theoretical predictions and the empirical evidence by developing
a noncooperative bargaining model in which parties are both office seeking and policy pursuing. Parties
bargain over cabinet portfolios, which in turn determines the government policy. Parties are farsighted,
and when they coalesce with other parties, they take into account not only the expected cabinet portfolios
allocation, but also how this allocation would affect the government coalition policy. The model predicts in
equilibrium the formation of minimal winning as well as minority and surplus coalitions as a function of a
party’s size, ideal policies, and relative preference over policy and office.
1
Introduction
In parliamentary democracies the executive branch (the government) is elected by and accountable to the
legislative branch (the parliament). The government needs to be supported by the majority of the legislators
in order to be installed and remain in power. A distinguished stream of literature claims that governments
should include the number of parties sufficient to secure the majority quota in the legislature but no more (i.e.,
the coalition of governing parties should be minimal winning).1 However, as Laver and Schofield (1998) note
in their analysis of government in Western European countries, only 39% of the governments formed in the
postwar period (1945-1987) are minimal winning coalitions, while 37% are minority governments (coalitions of
parties not commanding a majority of legislative seats) and 24% are surplus governments (coalitions including
more parties than strictly necessary to control the legislative majority).
This is one of the most-discussed unsolved puzzles in the study of coalition formation. Most theories
on this matter analyze the coalition formation process as a bargaining game over distributive benefits (i.e.,
offices).2 But if only the parties included in the government coalition receive the perks, why are minority
governments supported by a legislative majority? Why don’t the opposition parties (which constitute the
majority) coalesce and come to power? Surplus governments are also puzzling, as in this case spoils are
allocated to parties whose removal from the government coalition would not affect the ability of the coalition
to come to and stay in power. Why should coalition parties which are pivotal in obtaining the majority vote
tolerate sharing the perks with parties that are essentially superfluous?
This article answers all of these questions by providing a unified theoretical model of government formation
that generates equilibrium coalitions that can be of minimal winning, minority, or surplus size. The model
proposed here explains the rationality of minority and surplus governments and the reasons that these types
of coalitions are neither a rare contingency nor a temporary solution to a political impasse.3
Besides Golder et al. (2012), who propose a government formation model with zero-intelligence agents
1
See the pioneering work of Riker (1962), in which he postulates the “size principle”: the claim that in n-person, zero-sum
games with side payments, players create coalitions just large enough to ensure winning and no larger.
2
From the work of Riker (1962) to the alternating offer and demand games of Baron and Ferejohn 1989 and Morelli 1990,
respectively.
3
See Strøm (1990) for a comprehensive literature review.
1
able to predict government coalition types that come very close to those observed in the real world, few formal
theoretical models have predicted the occurrence of other than minimal winning coalitions.
In an effort to account for the wider range of government coalition types, noncooperative theories of
government formation have started to take a more ideological stance, assuming that parties are not only office
motivated but also policy oriented. Diermeier and Merlo (2000) propose models in which the government
coalition may exchange side payments and policy concession with other parties to obtain the support of the
majority. Such models predict minority, minimum winning, or surplus coalitions in equilibrium. Baron et
al. (2012) extend the pioneering legislative bargaining model of Baron and Ferejohn (1989) to two periods
by endogenizing the status quo. Martin and Stevenson (2001) find that ideologically connected coalitions are
more likely to form than others, while Duch et al. (2010), Indriðason (2011) and Cho (2014) present models of
elections in which voters’ behavior depends on the forecasted policy outcome determined by the postelection
bargaining over policy. Kalandrakis (2015) shows that minority coalitions form with positive probability when
the office rents are sufficiently small compared to the policy motivations.
All the models described above analyze the effects of policy and office motivations on the government
formation process as two independent factors. The bargaining over the distribution of cabinet portfolios and
over the government policy platform as treated as two distinct elements of the model. Once the parties reach
an agreement and their proposal obtains the vote of confidence, the ministers who control different portfolios
are delegated to implement the government policy. Hence, party leaders may effectively treat policy as a
trading device to buy office or votes, explaining the rationality of either minority or surplus coalitions.
In reality, however, parties may significantly affect policy through the control of the cabinet portfolios,
making the two factors dependent upon one another. In fact, each ministerial position affects the policymaking
activity of the government, by exerting a discretionary power over policies that fall within its jurisdiction. As
Gallagher, Laver, and Mair (2001: 56) explain “... only the minister in charge of the relevant department is
in a position to present the policy proposal at cabinet, giving him or her a privileged position in the policy
area in question.” Bäck et al. (2011) shows that when parties bargain to allocate the cabinet portfolios, they
try to obtain the cabinet posts that give them control of the policy areas about which they care the most to
2
secure this privileged position. Furthermore, parties controlling ministerial posts have considerable impact on
the collective decisions of the cabinet via the ministers’ votes on policies of general interest. Even if coalitions
have previously agreed on prospective policies, coalition parties can help or derail their implementation by
supporting or stalling the discussion and vote in the council of ministers. Hence, the more offices a party
controls, the more it will be able to influence the overall government policy.4
Given the considerable power that ministers have in deciding on and implementing the government policies,
we should assume that the policy of a government coalition is a function of the allocation of the cabinet
portfolios. This means that when parties choose to coalesce, they anticipate not only how the portfolios are
allocated among the coalition parties, but also how that allocation will affect the policy of the governing
coalition. This is consistent with the “ministerial government” model defined by Laver and Shepsle (1996: 8):
...a powerful executive in which individual ministers, by virtue of their positions as the political
heads of the major departments of state, are able to have a significant impact on policy in areas
that fall under their jurisdiction. This entails a division- and specialization-of-labor arrangement
in which effective policy of any government depends upon the allocation of cabinet portfolios upon
politicians....Knowing the policy preferences of cabinet ministers, and the process of interaction
among them, it should be possible to forecast the policy outputs that will emerge from a particular
cabinet once it has taken office.
In this study I propose a model to bridge the gap between the predictions of the extant theoretical
literature and the phenomena observed in the empirical analysis of government formation. Two main features
distinguish this model from the existing theories in the literature.
First, government policy is derived from the cabinet portfolio allocation. Parties bargain over the allocation
of cabinet portfolios, which in turn generates the policy of the government coalition.5 Parties’ utility is a
function of both the office benefits and the distance between the government policy and the parties’ ideal
4
This does not prevent a principal-agent problem from occuring (as studied by Strøm, 2000; Huber and Lupia, 2001; and
Martin and Vanberg, 2004, among others) where ministers have an incentive to use their discretion in drafting bills to deviate
from the policy decided upon by the cabinet in an attempt to move government policy toward outcomes they prefer.
5
Similarly to the voting game of Indriðason (2011), who assumes the government policy to be the weighted average of the ideal
policies of the coalition parties.
3
policies. The model explicitly analyzes coalition formation in terms of the relative importance of ideology
and the office rents from holding ministerial positions, using a noncooperative bargaining framework in which
coalitions form endogenously as in Bassi (2013).
In equilibrium, the share of cabinet portfolios that coalition parties receive is proportional to their share
of legislative seats, no matter their policy preferences (consistently with the findings of Gamson, 1961; Laver,
1998; Warwick and Druckman, 2001; Warwick and Druckman, 2006; and Bassi, 2013). However, the coalition
that emerges in equilibrium is a function of the parties’ sizes and their relative policy preferences. In trying to
form a government coalition, all parties are farsighted (as in Penn, 2009, and Bassi, 2013) when considering
other parties as potential coalition partners. Hence, parties take into account the spoils that they would need
to allocate to a partner as well as the associated effect of the partnership on the coalition policy. Thus, the
composition of the government coalition and its policy platform are simultaneously determined in equilibrium.
Second, the endogenous nature of the coalition formation makes the equilibrium coalition robust to deviations (i.e., nonconfidence motions) by any subcoalition of parties. The robustness to group deviations
required by the strong equilibrium solution concept (Aumann, 1959) sets this model apart from most theories
of coalition formation.6 While existing coalition formation models are concerned with predicting the existence of other than minimal winning coalitions, the objective of this model is to predict coalitions that can
not only form, but also survive for the entire legislative term. In this respect, this model is fundamentally
different from the legislative bargaining models building on the Baron and Ferejohn’s (1989) pioneering work
in which coalitions form but can always be beaten in a dynamic setting by alternative coalitions (through the
redrawning of a different proposer). In the model proposed here, parties foresee the utility that every party
would get for any viable coalition and only participate in (or support) the government coalition that is best
for them. Hence the coalitions that form in equilibrium are stable in a dynamic setting.
This article breaks new ground by proposing a unified approach able to produce the full range of government coalition types that are empirically observed: single-party minority governments, minority coalitions,
6
The importance of coalition stability and durability has been studied by Indriðason (2010), who analyzes how concerns about
coalition survival might explain the willingness of the formateur to allocate larger shares of cabinet portfolios to the coalition
partners.
4
surplus coalitions, and minimal winning coalitions (connected or disconnected). This innovative model represents an improvement relative to previous studies, which have successfully predicted only a few government
coalition types at a time. For example, Cho (2014) proposes a model in which minimal winning coalitions and
minority single-party governments are formed with positive probability and alternate over time. Kalandrakis
(2015) develops a model able to produce both single-party minority and majority coalitions, but he does not
discuss the conditions that would make minority coalitions or surplus governments equilibria of the game.
The few studies that do predict the full range of government types impose relatively strict assumptions on the
players’ rationality or utility function. Golder et al. (2012) propose an agent-based model in which players
are minimally (or not) rational, while Diermeier and Merlo (2000) assume that parties can extract (rather
than distribute) utility from the coalition partners to explain the emergence of surplus governments.
In the model presented here, minority governments form in equilibrium when there exist some parties
outside the coalition that prefer to support the minority government rather than to vote against it and form
a majority coalition with the other external parties. This occurs when the external supporters (i) have ideal
policies closer to the minority government policy than to the prospective policy of the alternative majority
coalition, and (ii) care more about policy than about office. Because external supporters would be worse off
by deposing the minority government and becoming formateurs of alternative coalitions than by supporting
it, the minority government is not only an equilibrium of the game, but a dynamically stable one.
Surplus governments form in equilibrium and are stable for a similar reason. A party proposes a majority
coalition that includes a “dummy partner” when the oversized coalition is preferable to a minimum winning
coalition. This happens when (i) the introduction of the dummy partner moves the government policy closer
to the party’s ideal policy; (ii) the loss of office due to the introduction of the dummy partner is less than
the policy benefit; and (iii) the other “nondummy” coalition partners are better off by participating in the
surplus coalition than by deviating to alternative coalitions.
In the present study I provide an empirical test of the equilibrium predictions generated by the theoretical
model using coalition formation data from Western European countries. The degree of agreement between
the equilibrium predictions and the actual data is remarkable, providing support for the theoretical model
5
and evidence of its ability to generate reliable predictions about the composition of government coalitions.
The empirical analysis also highlights the pivotal role of parties’ preferences regarding policy and office for the
understanding of the government coalition process, without which minority and surplus governments could
not be explained.
2
A government formation model with policy-pursuing parties
In this section I construct a general model of multiparty competition in which parties are simultaneously
interested in policy outcomes and in the perquisites obtained from office. This model enables us to better
understand multiparty competition of the kind found in European parliamentary democracies.
The model is a version of the legislative bargaining model with an endogenous formateur that builds on
the baseline framework of Bassi (2013). The main feature of this approach is that the distribution of office
benefits and the policy chosen by the potential government coalition (i.e., proto-coalition) depend only on
parties’ preferences regarding cabinet portfolio allocations and policy and not on the details of the bargaining
process, such as the recognition of the formateur.
The model presented here considers a legislature with N ≡ {1, 2, ..., n} parties. Each party has a legislative
weight wi ∈ [0, 1], where wi < 1/2 for i ∈ N and
P
i wi
= 1. The utility function of a party is represented
by the aggregate utility of each of the legislator members of the party, Ui =
X
ul with i ∈ N . Individual
l∈i
legislators l ∈ {1, 2, ..., L} are loyal to the party line, meaning that (i) they support the policy of the party;
(ii) they do not switch from one party to another; and (iii) they cannot be excluded from enjoying the benefits
(both in terms of policy and office perks) to which the party is entitled. For the sake of simplicity, I assume
that each member of a party has the same weight, and that the ideal policy of each party member overlaps
perfectly with the “policy line” of the party. Hence, each party acts as a unitary actor7 and its utility function
can be rewritten as Ui = wi ul , where ul is the utility of the legislator members of party i.
Each party’s utility is a function of both the share of cabinet portfolios that it controls and the distance
7
The incentives for the parties to act cohesively, both in terms of office rents and in terms of electoral chances, are particularly
strong in the process of government formation. Parties’ members are urged to act in a unitary fashion, and betrayal of party
loyalty is severely punished by party leaders.
6
between the joint policy of the government coalition and the party’s ideal policy. Let X ≡ {(x1 , x2 , ..., xn )|xi ≥
0,
P
i xi
≤ 1, ∀i ∈ N } denote the set of feasible allocations of the cabinet portfolios, where xi is the share
party i receives. Let Z c (with 0 ≤ Z c ≤ 1) denote the joint policy of the government coalition c, and
Zb ≡ {(zb1 , zb2 , ..., zbn )|0 ≤ zbi ≤ 1, ∀i ∈ N } denote the parties’ ideal policies set. Both the parties’ ideal policies
and the government policy are points chosen in a one-dimensional ideological space [0, 1] (one can think of a
policy being placed somewhere between “extreme left” and “extreme right”).
In a parliamentary democracy, the government policy Z c is implemented by the cabinet or council of
ministers. Each party affects the overall government policy through the control of the ministries in the
council. Let Z ≡ {(z1 , z2 , ..., zn )|0 ≤ zi ≤ 1, ∀i ∈ N } denote the set of prospective policies that the parties
would implement should they serve in government,8 the government policy can then be expressed as a linear
combination of the policies implemented by the parties weighted by the portfolio share they control:
Zc =
X
xi zi = x1 z1 + x2 z2 + ... + xn zn
i=1
Denote party i’s utility as a quasi-linear function in which the utility is increasing in the cabinet portfolio
allocation xi and decreasing in the distance between the government policy Z c and its ideal policy zbi .
Ui (xi , Z c ; zbi ) = xi + γi (1 − |Z c − zbi |),
∀i ∈ N
where γi is a parameter that captures the policy concern of party i. The policy concern γi can be interpreted
as a measure of how party i trades off policy closeness for office. If γi is equal to 1, policy closeness and office
affect the utility of party i equally. If γi is less than 1, party i requires more than a unit of policy closeness to
trade off for a unit of office. In other words, party i is motivated more by office than by policy. The opposite
occurs when γi is greater than 1.
For simplicity, assume that the policies outlined in the parties’ manifestos are binding and perfectly depict
the parties’ true ideal policies (zi = zbi ). We then can describe the utility of the parties as a function of three
variables: the allocation of cabinet portfolios, the parties’ ideal policies, and their office-policy trade-off,
8
The prospective policies of the parties are outlined in the party’s manifestos and consequently are common knowledge.
7
Ui (xi , zbi , zb−i ) = xi + γi [1 − (1 − xi )κci ]
where κci = |zbi −
1
1−xi
P
j∈N \i
xj zbj |.
Notice that the parties’ utility is a positive function of the distributive share of cabinet portfolios that
they control and a negative function of the share controlled by the coalition partners. An increase of xi has
two positive effects on the overall utility of party i. On the one hand, it increases the office benefits associated
with holding ministerial positions; on the other hand it decreases the loss determined by the distance between
the party’s ideal policy and the government policy.
The bargaining game proceeds as follows. Parties behave noncooperatively and decide how to allocate
a perfectly divisible homogeneous bundle of ministerial posts (normalized to sum to 1) among themselves.
Each party is assumed to know all other parties’ preferences, and all actions are assumed to be observable.
The interaction between parties is modeled as in Bassi (2013). In each period t ∈ T , government formation
proceeds in four stages (Ht ≡ {h1 , h2 , h3 , h4 }Tt=1 ).
In the first stage, h1 , parties simultaneously propose a coalition with other parties. Let cJi ∈ Ci denote
party i’s proposal, where J is the set of parties in the proposed coalition and Ci is the set of all party i’s
feasible coalition proposals.9 The parties with matching proposals (cJj = cJ ,
∀j ∈ J) form a proto-coalition
and proceed to the next stage. Notice that a single-party government constitutes a degenerate proto-coalition.
In the second stage, h2 , parties in the same proto-coalition (i ∈ cJ ) compete to be the formateur. Each
party i offers a share Λij ∈ [0, 1], ∀j ∈ cJ , j 6= i of the cabinet portfolios to each proto-coalition partner j in order
to be formateur. The party offering the largest share to each and every partner (let us denote this as party m)
wins the privilege of being formateur and signs a proto-proposal Sem that allocates the share Λm
j to the coalition
partners j ∈ cJ \m and the remainder (1 −
X
m
m
em
Λm
j ) to itself: S = (Λ1 , Λ2 , ...1 −
j∈cJ \m
P
j∈cJ \m
Λm
j , 0, ..., 0).
In the third stage, h3 , the coalition parties bargain over the allocation of the cabinet portfolios, with
the formateur proposing an allocation and the partners accepting or rejecting it. If the partners reject the
formateur’s proposal S m = (x1 , x2 , ..., xn ), they can either fall back to the proto-proposal vector Sem or
9
{1,2}
For example, c1
denotes the party 1’s proposal for a coalition composed of party 1 and party 2.
8
terminate the coalition negotiations (going back to stage h1 of the game).
In the fourth stage, h4 , every legislator votes on the proto-coalition proposal (either the formateur proposal
or the proto-proposal). If it obtains the quota required to pass, the newly formed government takes office;
otherwise the game repeats, beginning at the first stage, up to T periods, until a proposal receives the required
number of votes. If at the end of period T no proposal has been passed, a “caretaker government,” composed
of nonpartisan individuals, is established that proposes S = (xi , Z) = (0, z) ∀i ∈ N , according to which no
party receives cabinet portfolios and the government continues to implement the status quo policy.
The solution concept, following Bassi (2013), is the subgame perfect equilibrium. I now solve the subgame
at period t = T by backward induction, starting from the last stage of the game.
2.1
Stage 4: Voting stage
In the last stage of the game of period t = T , the coalition proposal is brought to the floor and voted on by
the legislators. If it does not receive the quota of votes required to pass, a caretaker government is established
that implements the status quo policy. Let (ScJ ) denote the proposal of coalition cJ and vi (ScJ ) denote the
vote of party i. A party votes in favor of the proposal (vi (ScJ ) = 1) if and only if it expects to receive a utility
which is greater than or equal to the utility that it would receive from the caretaker government:
vi (ScJ )




 1
J
if xi + γi [1 − (1 − xi )κci ] ≥ γi (1 − κi ) ∀i ∈ N



 0 otherwise
J
where κci = |zbi −
1
1−xi
P
j∈N \i
xj zbj | and κi = |zbi − z| denote the distances between party i’s ideal policy and
the policies determined by the proposal SecJ and the caretaker proposal, respectively.
The equilibrium strategies of this voting game are very different from the standard legislative bargaining
models in which agents are exclusively office seekers. Here, as Strøm (1990) suggests, a majority for office
does not guarantee a majority for policy, as members of the coalition receive a positive utility from the status
quo policy. Hence, there are two types of equilibrium strategy profiles in which a proposal is passed:
Proposition 1 A coalition proposal ScJ receives the majority of the legislators’ votes if
9
(1)


∀i ∈ cJ
J
xi + γi [1 − (1 − xi )κci ] ≥ γi (1 − κi ) &

(2)





∀i ∈ cJ


X
wi >
i∈cJ
J
xi + γi [1 − (1 − xi )κci ] ≥ γi (1 − κi )
&
X
1
2
; or
wi ≤
i∈cJ


J


/ cJ s.t. xk + γk [1 − (1 − xk )κck ] ≥ γk (1 − κk ) &

 ∃k ∈
X
k∈c
/ J
wk >
1
2
1 X
wi
−
2
J
i∈c
Proposition 1 implies that control of the majority of the seats is neither a sufficient nor a necessary
condition for a coalition’s proposal to obtain a majority vote. First, the proposal of a majority coalition
passes the vote of confidence only if enough members of the coalition prefer the coalition proposal to that of
the caretaker government (condition 1). Second, a coalition can gather the majority vote without controlling
the majority of the seats if enough members outside the coalition prefer its proposal to that of the caretaker
government (condition 2).
2.2
Stage 3: Bargaining over cabinet portfolios and government policy
In the bargaining stage, the formateur of the proto-coalition brings a proposal for allocation of the cabinet
portfolios to the proto-coalition partners. If the partners accept it, the formateur’s proposal will be brought
to the floor and voted on by the legislature, as discussed in the previous section; otherwise, either the protoproposal will advance to the fourth stage of the game or the proto-coalition’s negotiations will terminate.
Without loss of generality, assume that the formateur of a generic proto-coalition cJ is party m and that it
proposes ScmJ . The formateur is farsighted and chooses the proposal that maximizes its own utility and that it
believes will able to pass the vote of confidence in the legislature. To secure the proto-coalition partners’ vote,
the formateur has to make the partners better off or at least indifferent to the choice between the formateur’s
proposal ScmJ and both the proto-proposal SecmJ and the caretaker proposal S:
max
xm ∈X
J
xm + γm [1 − (1 − xm )κcm ]
10
J
J
m
ei c ],
s.t. xi + γi [1 − (1 − xi )κci ] ≥ Λm
i + γi [1 − (1 − Λi )κ
J
xi + γi [1 − (1 − xi )κci ] ≥ γi [1 − κi ]
where κei c
J
= |zbi −
1
1−Λm
i
P
j∈cJ \i
(1)
∀i ∈ cJ \m.
(2)
Λm
j zbj | denotes the distance between party i’s ideal policy and the policy
determined by the proto-proposal SecmJ .
The first constraint is an incentive-compatibility constraint that ensures that the proto-coalition partners
will voluntarily choose ScmJ over SecmJ .10 The second is a participation constraint that ensures that the protocoalition partners will vote in favor of the proposal at the voting stage.
The participation constraint guarantees that the parties want to participate in forming the government,
in that they are at least as well off by participating as they would be by not participating. The incentivecompatibility constraint in contrast makes sure that the parties are motivated to behave in a manner consistent
with the formateur’s optimal solution. Intuitively, the formateur needs to compensate the partners for the
alternative utility they could earn if they were to turn down the formateur’s proposal.
Any solution must satisfy the two constraints. By nonsatiability, the most stringent constraint must be
satisfied with equality, while the others remain nonbinding. A solution always exists because U is a continuous
concave function defined on a compact, nonempty set.
Proposition 2 The equilibrium allocation of cabinet portfolios is as follows:
∗
ScmJ =



















where xi =
γi (κ∗i −κi )
1+γi κ∗i
∀i ∈ cJ \m
max [Λm
i , xi ]
1−
P
j∈cJ \m
h
max Λm
j , xj
i
i=m
∀i ∈
/ cJ
0
is the share of portfolios that makes party i indifferent to the caretaker proposal and κ∗i
∗
is the distance in policy generated by the equilibrium allocation ScmJ .
m
J
If the incentive-compatibility constraint is binding for all partners (max [Λm
i , xi ] = Λi , ∀i ∈ c \m), the
10
I assume that whenever a receiver is indifferent, it chooses the formateur’s proposal. This assumption is innocuous since a
sufficiently small increase of xi could induce the receiver to accept xi without changing the utility of the players.
11
equilibrium proposal ScmJ coincides with the proto-proposal SecmJ . In contrast, if for some partners the participation constraint is binding and the incentive-compatibility constraint is not, the formateur needs to allocate
to these partners a share of the cabinet portfolios that makes them at least indifferent to the status quo,
while allocating the proto-proposal share to the rest of the partners. The formateur allocates no offices to the
parties outside the proto-coalition.
2.3
Stage 2: Formateur selection
The formateur is endogenously selected, as parties are willing to offer to the partners a share of the spoils in
exchange for the right to be the formateur. Each party i in the proto-coalition cJ offers a share Λij to each
partner j ∈ cJ \i. As proved in Bassi (2013),11 the equilibrium bid vector for every party is proportional to
the coalition partners’ weight vector: Λij = λi wj . Hence, the equilibrium bid vector is equal to the partners’
weight vector multiplied by a constant “per capita” bid. The party offering the largest “per capita” share
λi becomes formateur. Each party has a well-defined reservation price that makes it indifferent between the
roles of proposer and receiver. In equilibrium a party needs to offer this share to each partner in order to win
the role of formateur.
Proposition 3 The equilibrium bid is unique and identical for every party in the same proto-coalition:12
i∗
λ =λ
cJ
=















P1
wj
h
J
J
if ∀i ∈ cJ
:
wi λc = max wi λc , xi
if ∃k ∈ cJ
:
xk = max wk λc , xk
i
j∈cJ
∗
1−xk
P
wj
h
J
i
j∈cJ \k
J
where xk =
γk (κck −κk )
J
1+γk κck
.
The equilibrium bid is less than or equal to 1 divided by the total weight of the proto-coalition. Parties
know that, should they become formateurs, they would need to allocate to the partners either the share of
J
cabinet portfolios that they are offering in exchange for the role of formateur (wi λc ), or the share that makes
the parties indifferent to the caretaker government (xi ), whichever is greater. When the latter is greater for
some partners, it translates into a shrinkage of the pie, i.e., a reduction of the value of being formateur. As a
11
12
See Proposition I in Bassi (2013), p. 784.
See the proof in the on-line supplemental appendix.
12
consequence, parties are willing to bid less. Hence, more valuable status quo policies lead to a decline in the
equilibrium bid for being formateur.
Having solved for the equilibrium bid, we can now proceed to the quantitative analysis of the equilibrium
formateur proposal of the previous stage. If no coalition party prefers the caretaker proposal to the protoproposal, the formateur proposal allocates to each and every partner a share of portfolios perfectly proportional
to the party’s nominal voting weight ( Pwiw ).
j
j∈cJ
When instead there is a coalition party that is better off with the caretaker proposal than with the protoproposal, this party is allocated a more-than-proportional share of portfolios (xi > Pwiw ), while the remaining
j
j∈cJ
∗
w (1−x )
parties (those preferring the proto-proposal) receive a less-than-proportional share ( iP wk < Pwiw ).
j
j∈cJ \k
2.4
j
j∈cJ
Stage 1: Coalition formation game
In the coalition formation stage, each party proposes a proto-coalition. Parties are farsighted and form
expectations on the share of cabinet allocation that each party in the coalition would control and the policies
that the coalition parties would implement.
The coalition formation game has multiple Nash equilibria. However, I focus on those strategy profiles
that are robust not only to individual deviations but also to improving deviations by any subcoalition of
players. Hence, I adopt the strong equilibrium refinement (Aumann, 1959).
Proposition 4 A strong equilibrium of the coalition formation game does not always exist.13
Intuitively, a strong equilibrium does not exist when there is a cycle of preferences. If the group preference
is not transitive, for any strategy profile there exists a profitable deviation for a subcoalition of parties.
Proposition 5 If unlimited but nonbinding communication is allowed, the strong equilibrium of the coalition
formation game can be a minimal winning, a minority, or a surplus coalition.
Proposition 5 suggests that in equilibrium the government coalition can be either majority or minority,
relatively large or small, and ideologically connected or disconnected. This departs from the majority of the
13
See the proof in the on-line supplemental appendix.
13
theoretical literature, which predicts either minimal winning coalitions (when parties are office seeking) or
ideologically connected coalitions (when parties are policy pursuing). This is because parties trade off policy
proximity and office perks differently. Parties that prefer office over policy are more willing to coalesce with
ideologically distant parties if these are smaller and therefore are expected to be allocated a smaller share
of the cabinet portfolios. In contrast, parties that prefer policy over office are more willing to coalesce with
larger parties that are ideologically adjacent (even though these parties are expected to be allocated more
office seats).
If the number of periods is finite, in every period of the game each party proposes the same proto-coalition;
bids the same share to be the formateur; and proposes the same portfolio allocation as in the last period of
the game. Hence, the equilibrium strategies are unique.14
To explore the intuitions behind the model’s results, and how the equilibrium coalition changes as a
function of the parties’ parameters, in the sections that follow I examine the conditions that cause the
equilibrium coalition to be minimal winning, minority, or surplus.
3
Minimal winning coalitions
Let us assume the simplest scenario of a three-party legislature where wi ≤ 1/2 with ∀i ∈ N . Every coalition
of two parties is a minimal winning coalition. Let us assume for simplicity that no party prefers the status
quo to the proto-proposal. Then, party i’s equilibrium coalition proposal is
ci




 cij
i
if
Ui (cij ) ≥ Ui (cik )
⇐⇒
1−wi λij
1−wi λik
≤
1+γi κik
1+γi κij



 cik
i
if
Ui (cij ) ≤ Ui (cik )
⇐⇒
1−wi λij
1−wi λik
≥
1+γi κik
1+γi κij
ij
where cij
i denotes party i’s proposal to coalesce with party j; λ =
1
wi +wj ,
the equilibrium bid for both party
i and party j; and κij = |zbi − zbj |, the distance between the ideal policies of parties i and j.
The left-hand side of the inequality represents the relative loss of perks for party i in coalescing with j
rather than with k, i.e., how much party i must offer to party j (the numerator) relative to what it needs to
14
As discussed in Bassi, 2013 (Proposition VI, p. 786.)
14
offer to party k (the denominator). The right-hand side, in contrast, can be interpreted as party i’s relative
loss of policy closeness in coalescing with k relative to that in coalescing with j. If the relative loss of perks
in coalescing with party j is less than the relative loss of policy closeness in coalescing with party k, party i
will be better off by proposing a coalition with party j.
Without loss of generality, assume the parties’ ideal policies to be zbi < zbj < zbk , with party j being closer
to party i than to party k (κij < κjk ). The equilibrium of the game depends on the parties’ sizes, the location
of their ideal policies, and the their preferences.
In the simplest case, when the median party (party j) is the smallest party and the party that is farther
away from it is the biggest party (party k), the unique equilibrium coalition is always composed of parties
i and j (ci,j ). This is because for both parties i and j coalescing with each other is strictly dominant: it
maximizes both the office benefits and the policy proximity.
However, in all other cases, parties may face the trade-off described earlier, and the equilibrium coalition
depends on how the parties value policy relative to office. Consider the case in which the most extreme party
(party k) is the smallest party and the median party is the biggest party (wj > wi > wk ): all three parties
face a tradeoff, and the equilibrium coalition could be any permutation of two parties or it might not exist.
∗
c





cij








 cik




cjk








 @
if
1−wi λij
1−wi λik
≤
1+γi κik
1+γi κij
if
1−wi λij
1−wi λik
≥
1+γi κik
1+γi κij
if
&
1−wj λij
1−wj λjk
1−wj λij
1−wj λjk
≤
≥
1+γj κjk
1+γj κij
1+γj κjk
1+γj κij
&
1−wk λjk
1−wk λik
≥
1+γk κik
1+γk κjk
&
1−wk λjk
1−wk λik
≤
1+γk κik
1+γk κjk
e.w.
In this case, each minimal winning coalition might be the strong equilibrium. However, given the sizes,
the ideal policies, and the policy concerns of the parties, the model is able to predict not only the type of
government, but also its composition. This is a major step forward toward the analysis and the understanding
of government formation.
15
4
Minority governments
In the model proposed here, a government is a coalition composed of one or more parties with control over
cabinet posts (Laver and Shepsle, 1996). A coalition that does not control the majority of seats in the
parliament but garners a majority in a vote of confidence or investiture is considered a minority government.
Minority governments are viable thanks to the support of one or more parties outside of the government
coalition, called external supporters. External supporters are not allocated any distributive (office) benefits,
and they do not bargain over policy with the government coalition because the coalition government promises
would not be credible. However, the minority coalition can indirectly distribute policy benefits to external
supporters when the allocation of cabinet portfolios yields a government policy that is close to the external
supporters’ preferred policies.
In this section I analyze the conditions that make a minority coalition government the strong equilibrium
of the game. Since external parties do not bargain with coalition partners over either office or policy, they do
not take part in either the third stage of the game (in which parties inside the coalition allocate the cabinet
portfolios), or the second stage (in which a formateur is selected), but only in the coalition-proposal and voting
stages. Hence, I focus here on just the first and fourth stages, which are fundamental to an understanding of
the puzzle of minority governments. The analysis of the voting stage will help explain why parties without
portfolio are willing to support a government and make it a viable option, while the analysis of the coalition
formation stage will help answer a more essential question: why opposition parties do not simply depose the
minority government and propose an alternative government.
In the voting stage, party k supports a minority coalition cJ if the utility that it receives from the
J
government coalition proposal γk [1 − κck ] is greater than or equal to the utility that it would receive from the
proposal of the caretaker government γk (1 − κk ).
Proposition 6 (Viability of a Minority Government). A party without portfolio votes in favor of a
J
coalition proposal if its ideal policy is closer to the coalition’s policy than to the status quo (κck ≤ κk ).
A minority government is a strong equilibrium if the opposition parties do not have an incentive to deviate
16
and propose an alternative coalition together in the coalition-proposal stage. Party k does not propose a
majority coalition with the other parties, which we shall denote as c0 , if the utility that it would receive by
coalescing with the other parties is less than or equal to the utility that it would receive from the minority
coalition’s proposal:
0
J
0
0
γk [1 − κck ] ≥ xck + γk [1 − (1 − xck )κck ]
0
where κck = |zck −
1
1−xk
P
j∈c0 \k
xj zbj | defines the distance between the ideal policy of party k and the policy
that the coalition c0 would implement. This occurs when the policy of the external supporter is closer to the
minority government policy than to that of the alternative majority coalition and when the external supporter
is more motivated by policy than by office considerations.
Solving the inequality for party k’s policy concern, we have that for sufficiently large values of γk , party k
is willing to sacrifice the office benefits that it could gain by coalescing with other parties in order to achieve
a more desirable government policy offered by the minority government:
Pwk
wj
c0
xk
j∈c0
γk ≥ γ k =
0
0
J
0
J =
wk
c
c
c
P
)κck − κck
(1 − xk )κk − κk
(1 −
w
(3)
j
j∈c0
The value γ k denotes the cutoff value of the policy concern that makes a party indifferent between being an
external supporter and part of an alternative government coalition. The higher the value of γ k , the higher the
hurdle for a minority government to be a stable equilibrium. The policy concern cutoff level γ k is a positive
∂γ k
function of party size ( ∂w
> 0) and the distance from the prospective alternative coalition policy ( ∂γci0 > 0),
k
∂κk
and a negative function of the distance from the minority government policy (
∂γ i
J
∂κck
< 0).
Proposition 7 (Comparative Statics). External supporters are more likely to support a minority government without trying to depose it and propose an alternative government when
(i) the external supporter’s size (wk ) decreases;
(ii) the distance between the external supporter’s ideal policy and the ideal policies of the other opposition
0
parties (κck ) increases; or
J
(iii) the distance between external supporter’s ideal policy and the minority government policy (κck ) decreases.
17
When a party’s size increases, the party’s share of cabinet portfolios increases, increasing the value of
being in a coalition government. A party needs to be highly policy motivated (i.e., to have a high value for
γk ) when the spoils that it would have to renounce are larger. In contrast, when either the distance from
the prospective alternative coalition policy increases, or the distance from the minority government policy
decreases, the value of being in a prospective alternative majority coalition decreases, lowering the cutoff level
for the policy concern.
This result is consistent with a large stream of theoretical literature focusing on the predominance of
parties’ policy motivations over office benefits, starting with Dodd (1976), who suggests that high polarization
is the main cause of the existence of minority governments, up to Laver and Shepsle (1996), who claim that
the key for the birth of minority governments lies in the ideological divisions of the remaining parties.
A minority government is a strong equilibrium of the coalition formation game when no party or no
subcoalition of parties wants to deviate.
Proposition 8 (Stability/Effectiveness of a Minority Government). The strong equilibrium of the
coalition formation game is a minority proto-coalition cJ if it is optimal for all parties in the minority coalition
and if there exists an external party or subset of parties k that would be better off by supporting the minority
government proposal than by proposing an alternative coalition c0 :
cJ = arg maxci ∈C
if
∃k ∈ N
b c , zbi )
U i (xi , yi , Z|ci , λ
i
J
κck ≤ κk
0
γk ≥
X
j∈cJ
4.1
0
xck
0
J
κck (1−xck )−κck
wj +
X
k
wk >
1
2
Example
Let us analyze again the simplest scenario of a three-party legislature where no party controls the majority
of the legislative seats and zbi < zbj < zbk . Assume that party j proposes a single-party minority government.
18
Proposals
cij
cik
cjk
ci
cj
ck
S
Table 1: Minority single-party Strong Equilibrium.
Cabinet portfolio share
Government policy
xi
xj
xk
Z
0.42
0.58
0
0.22
0.56
0
0.64
0.41
0
0.64
0.36
0.48
1
0
0
0.10
0
1
0
0.30
0
0
1
0.80
0
0
0
0.40
Parties’ utility
Ui
Uj
5.73
1.04
4.72
0.45
3.71
1.05
7.00
0.40
4.80
1.50
1.80
0.25
4.20
0.45
Uk
0.21
0.74
0.70
0.15
0.25
1.50
0.30
Notes. The table reports for each coalition proposal the equilibrium allocation of cabinet portfolio, the government
policy, and the utility for each party. The sizes of the three parties are wi = 0.32, wj = 0.44, and wk = 0.25. The ideal
policies of the three parties are zi = 0.1, zj = 0.3, and zk = 0.8. The status quo policy is z=0.4. The policy concerns
for the three parties are γi = 6 and γj = γk = 0.5.
Since party j is the median party, its proposal will always be viable, because the party with an ideal policy on
the other side of the median with respect to the status quo would vote for the minority government proposal.15
The single-party minority government is a stable government if the external supporter (assume this is
party i) does not have an incentive to form an alternative coalition with the other opposition party. This
occurs when the external supporter’s policy concern is greater than a cutoff value γ i :
γi ≥ γ i =
wi λik
(1 − wi λik )κik − κij
Minority governments might be an equilibrium of the game along other minimal winning equilibrium
coalitions, or they might provide a solution for a government impasse when there is no majority coalition that
can be robust to group deviations. Let us consider the following example. Assume a three-party legislature,
with party sizes wi = .32, wj = 0.44, and wk = 0.25; ideal policies zbi = 0.1, zbj = 0.3, and zbk = 0.8; and policy
concerns γi = 6, γj = 0.5, and γk = 0.5. Let us also assume the status quo policy is z = 0.4. Hence, according
to the above condition, a single-party minority government proposed by party j is a strong equilibrium of the
game (party i’s policy concern is greater than γ i = 5.19).
In table 1 I report the utilities for all feasible strategies of the three parties. None of the three minimal
winning coalitions is a strong equilibrium. The coalition cij is not a strong equilibrium of the game: parties j
and k would prefer to coordinate and deviate by proposing a coalition cjk . The same applies to cjk and cik .
15
Notice, however, that median-party status is a sufficient but not necessary condition in a three-party legislature. If a nonmedian
party proposes a single-party minority government, its proposal can still be viable if the median party prefers it to the status quo.
19
Minority single-party governments proposed by either party i or party k are not viable: in both cases
the opposition parties will vote against the proposals, since the status quo policy is preferable. A minority
single-party government proposed by party j is, however, not only viable (party i would prefer it to the
caretaker government proposal), but also a strong equilibrium: party i does not have any incentive to deviate
and coalesce with party k. The minority government j yields the maximum utility for party j and it is Pareto
efficient for party i, since there are no alternative profitable coalitions to which party i can deviate.
5
Surplus governments
Proposition 4 suggests that any majority coalition can be the strong equilibrium of the government formation
game, including majority coalitions that are not minimal winning. In this section, we analyze the conditions
that need to be satisfied for such coalitions to be strong equilibria.
Non-minimal winning majority coalitions are coalitions which include more parties than are necessary to
control the majority in the legislature. For this reason, they are often called “surplus” coalitions. A surplus
coalition would still control the majority of the seats in the legislature even after the departure of one of the
coalition partners.
The extant literature claims that surplus governments form mainly to overcome political crises that call
for institutional reforms or changes to the constitution and that often require supermajorities;16 to garner
insurance against potentially reneging legislators, or to fulfill pre-electoral coalition agreements.
However, surplus governments do not form only to provide insurance against future changes in the political environment or qualified majorities in times of crisis. As Laver and Schofield (1998) indicate, surplus
governments are quite frequent (they constitute 24% of all coalition governments formed in Western European
countries), they form in periods when no qualified majority is required for institutional change, and they are
not necessarily more stable than minimal winning coalitions or minority governments (for example Italian
surplus coalitions). In what follows I analyze the rationality of surplus governments and what makes them an
equilibrium of the government formation game.
16
This was the case for the governments formed in many Western European countries immediately after World War II.
20
Let us assume, for the sake of simplicity, that no party prefers the status quo to the proto-coalition
proposal, and that all party members of a proto-coalition are treated the same.17 The mechanism that rules
the selection of the formateur, the allocation of the cabinet portofolio, and the voting is as described in section
3. I then focus on the analysis of the conditions that make parties better off by proposing a surplus coalition.
Party i proposes a majority coalition including a “dummy partner” (which we shall denote as surplus
coalition cs ), if the utility that it would receive is greater than or equal to the utility that it would receive by
proposing the same majority coalition without the dummy partner (which we shall denote as coalition cm ):
m
s
m
m
s
s
(xci − xci ) ≤ γi [κci (1 − xci ) − κci (1 − xci )]
s
(4)
m
where κci and κci define the distances between the ideal policy of party i and the coalition policies of cs and
cm , respectively. This happens when (i) the introduction of the dummy partner moves the government policy
closer to the ideal policy of party i (the right-hand side of the inequality is positive); and (ii) the loss of office
due to the introduction of the dummy partner is less than the policy benefit.
Condition (i) is satisfied when party i’s relative distance from the minimal winning and the surplus coalition
policies is greater than party i’s relative loss of office with the surplus and minimal winning coalition:
1 − xsi
κm
i
>
κsi
1 − xm
i
Condition (ii) is satisfied when the policy concern γi is:
γi ≥ γ i =
(1 −
s
xm
i − xi
m
m
xi )κi − (1
−
xsi )κsi
=
(λm − λs )wi
s s
(1 − wi λm )κm
i − (1 − wi λ )κi
(5)
The value γ i denotes the cutoff value of the policy concern parameter that makes a party indifferent
between proposing a surplus and a minimal winning coalition. For sufficiently large values of γi , party i is
willing to tradeoff the office benefits that it would need to allocate to the dummy party in order to obtain a
government policy closer to its ideal policy.
17
All parties have the same action set. Every coalition party member (pivotal to obtain the majority vote or not) compete
to become formateurs, are allocated a share of cabinet portfolios if other partners win the role of formateur, and vote for the
formateur’s proposal or proto-proposal.
21
Proposition 9 (Comparative Statics). A party is more likely to propose a surplus government when
(i) its size (wi ) decreases;
(ii) the loss of office benefits from including a dummy party (λm − λs ) decreases;
(iii) the distance between the surplus government policy and its ideal policy (κsi ) decreases; or
(iv) the distance between the minimal winning coalition government and its ideal policy (κm
i ) increases.
This model provides a new explanation for the emergence of surplus governments. A party might be better
off by adding a dummy party to its coalition proposal if this introduction moves the government policy closer
to its ideal policy and it is more motivated by policy than by office.
This is consistent with the view of Powell (1982), who claims that surplus governments emerge when parties
need to coalesce with distant parties to secure viability but try to include in the government coalition extra
parties with policy positions closer to their own to move the government policy toward their ideal policies.
A surplus government is a strong equilibrium when the other nondummy coalition partners are better off
with the surplus coalition than with any alternative coalitions that they could form.
Proposition 10 (Stability/Effectiveness of a Surplus Government). Assume that there exists a minimal winning coalition cm which is a strong equilibrium. A surplus coalition cs composed of all of the parties
included in cm and some dummy parties d might be a strong equilibrium of the game if there exists at least
one coalition partner i ∈ cm that would be better off by proposing the surplus coalition cs than the minimal
winning coalition cm and and if there is no subcoalition of parties that has an incentive to deviate and propose
an alternative coalition c0 .
5.1
Example
Let us analyze the scenario of a four-party legislature where wi ≤ L/2 with ∀i ∈ N and no party prefers the
status quo to the proto-proposal (xi = wi λij
i
∀i, j ∈ N ). Let us also assume party sizes wi = 0.30, wj = 0.05,
wk = 0.25, and wl = 0.40; ideal policies zbi = 0.10, zbj = 0.35, zbk = 0.40, and zbl = 0.90; policy concerns γi = 1,
γj = 2, γk = 5, and γl = 1; and the status quo policy z = 0.7.
22
Proposals
cik
cil
ckl
cij
cjk
cjl
ci
cj
ck
cl
cijk
cjkl
cijl
S
Table 2: Surplus coalition strong equilibrium.
Cabinet portfolio share
Government policy
Parties’
xi
xj
xk
xl
Z
Ui
0.55
0
0.45
0
0.24
1.41
0.43
0
0
0.57
0.56
0.97
0
0
0.38
0.62
0.71
0.39
0.86
0.14
0
0
0.14
1.82
0
0.17
0.83
0
0.39
0.71
0
0.11
0
0.89
0.84
0.26
1
0
0
0
0.10
2.00
0
1
0
0
0.35
0.75
0
0
1
0
0.40
0.70
0
0
0
1
0.90
0.20
0.50
0.08
0.42
0
0.25
1.35
0
0.07
0.36
0.57
0.68
0.42
0.40
0.07
0
0.53
0.54
0.96
0
0
0
0
0.70
0.40
utility
Uj
1.77
1.59
1.28
1.71
2.08
1.13
1.50
3.00
1.90
0.90
1.87
1.41
1.68
1.30
Uk
4.64
4.21
3.85
3.68
5.79
2.81
3.50
4.75
6.00
2.50
4.65
3.95
4.28
3.50
Ul
0.34
1.23
1.42
0.24
0.49
1.83
0.20
0.45
0.50
2.00
0.34
1.35
1.18
0.80
Notes. The table reports for each coalition proposal the equilibrium allocation of cabinet portfolio, the government
policy, and the utility for each party. The sizes of the four parties are wi = 0.30, wj = 0.05, wk = 0.25, and wl = 0.40.
The ideal policies of the four parties are zi = 0.10, zj = 0.35, zk = 0.40, and zl = 0.90. The status quo policy is z=0.70.
The policy concerns for the four parties are γi = 1, γj = 2, γk = 5, and γl = 1. The first six proposals are minimal
winning coalitions proposals; the following four ones are minority government proposals, and the last three are surplus
coalition proposals.
In table 2 I report the utilities for all feasible strategies of the four parties. All the coalition proposals are
viable with the exception of the minority single-party government proposed by party l (cl ) and the coalition
composed of party j and l (cjl ), that would be rejected at the voting stage. Of all the other viable coalitions,
only two are strong equilibria: the minimal winning coalition composed of party i and k (cik ), and the surplus
coalition composed of party i, j, and k (cijk ). Notice that the surplus coalition includes all the parties of
the equilibrium minimal winning coalition plus the dummy party j. This is because one of the nondummy
parties (party k) prefers to include the dummy party in order to move the policy closer to its ideal policy
(the coalition policy moves from 0.24 to 0.25). For the other partner (party i) there is no profitable deviation
from the surplus government proposal. Hence, the surplus coalition is a strong equilibrium of the game.
6
Empirical validity
In this section, I compare the model’s predictions for both the type and composition of coalitions with coalition
formation data from Western European countries for the period 1986–1989.
23
A significant component of the data in this analysis is derived from the Experts Survey of Laver and Hunt
(1992), the only expert survey to date that seeks to evaluate parties’ willingness to trade off office perks versus
policy.18 In the on-line supplemental appendix I discuss the method used to estimate the trade-off parameter
γ from the ratings in the survey.
The parties’ ideological positions are constructed from the public ownership scale of the Expert Survey
of Laver and Hunt (1992), the party position on the left-right scale of the Expert Surveys of Castles and
Mair (1984) and Morgan (1976), and the party position on the left-right scale of the content analysis of party
manifestos by Laver and Budge (1992).
The sample consists of 15 governments in 15 Western European countries19 over the period 1986–1989,
which is the period immediately preceding the Laver and Hunt (1992) survey. The countries represented
in the sample are Austria (1986), Belgium (1987), Britain (1987), Denmark (1988), Finland (1987), France
(1988), Germany (1987), Iceland (1987), Ireland (1989), Italy (1987), Luxembourg (1989), Netherlands (1989),
Norway (1989), Spain (1989), and Sweden (1988).
In table 3 I present a summary of the model’s theoretical predictions compared to the actual governments
formed in the 15 countries under study. Besides the cases in which a strong equilibrium does not exist
(Finland, Iceland, and Netherlands),20 in about 75% of the governments (9 out of 12) the strong equilibrium
predicted by the model matched the actual government. In both Britain and Spain, a single party controlled
the absolute majority of the parliamentary seats. In this case, the single majoritarian party proposed a solo
government, as it is trivially predicted by the model. In three cases (Belgium, Germany, and Ireland), the
strong equilibrium is a minimal winning coalition, and its composition matches the actual government formed.
In four cases (Denmark, France, Norway, and Sweden), the strong equilibrium is a minority coalition, and its
composition matches the actual government formed.
18
Question 14 of the survey asks respondents to answer the following question: Forced to make a choice, would party leaders
give up policy objectives in order to get into government, or would they sacrifice a place in government in order to maintain policy
objectives? Respondents can assign a score between 1 and 20, where (1) = give up a place in government, and (20) = give up
policy objectives.
19
I analyzed only those countries for which a set of policy positions was generated by at least two different sources.
20
In these cases, there are multiple Nash equilibria; however, these government coalitions might collapse at any time because
of profitable deviations by subcoalitions of parties (which in fact happened profusely in Iceland). In such cases, the fact that the
theoretical model does not provide a unique strong equilibrium prediction does not mean that it fails to describe the government
formation process realistically.
24
Table 3: Theoretical predictions vs. actual governments
Country
Austria
Belgium
Britain
Denmark
Finland
France
Germany
Iceland
Ireland
Italy
Luxembourg
Netherlands
Norway
Spain
Sweden
Theoretical predictions
Type
Composition
MWC
OVP, FPO
MWC
CVP/PSC, PRL/PVV
Maj.
CON
Min.
KF, V, RV
@ SE
Min.
PS, MRG
MWC
CDU/CSU, FDP
@ SE
MWC
FF, PD
Sur.
DC, PSI, PRI, PSDI
MWC
CSP, DP
@ SE
Min.
H, KRF, SP
Maj.
PSOE
Min.
SD
Type
MWC
MWC
Maj.
Min.
Sur.
Min.
MWC
MWC
MWC
Sur.
MWC
MWC
Min.
Maj.
Min.
Actual government
Composition
SPO, OVP
CVP/PSC, PRL/PVV
CON
KF, V, RV
SDP, KOK, SPP, RP
PS, MRG
CDU/CSU, FDP
IP, SDP, PP
FF, PD
DC, PSI, PRI, PSDI, PLI
CSP, LSAP
CDA, Lab
H, KRF, SP
PSOE
SD
X
X
X
X
X
X
X
X
X
Notes. The table reports for each country (leftmost column) the type of coalition predicted by the model (second
column), the composition of the equilibrium government coalition (third column), the actual type of coalition formed
(fourth column), and the actual composition of the government coalition (fifth column). A check mark in the rightmost
column describes a perfect match between the theoretical predictions and the actual government formed. Abbreviations
for government types are used (MWC = minimal winning coalition; Maj. = single-party majority; Min. = minority
government; Sur. = surplus coalition). The abbreviation @SE denotes the absence of any strong equilibrium. Political
party names are abbreviated: CDA = Christian Democratic Appeal; CDU/CSU = Christian Democratic Union and
Christian Social Union; CON = Conservative Party; CSP = Christian Social Party; CVP/PSC = Flemish Christian
People’s party and Francophone Christian Democratic Party; DC = Christian Democrats; DP = Democratic Party;
FDP = Free Democratic Party; FF = Fianna F´ail; FPO = Freedom Party; H = Conservatives; IP = Independence
Party; KF = Conservative People’s Party; KOK = National Coalition; KRF = Christian People’s Party; Lab = Labor
Party; LSAP = Socialist Party; MRG = Left Radicals; OVP = People’s Party; PD = Progressive Democrats; PLI =
Liberal Party; PP = Progressive Party; PRI = Republican Party; PRL/PVV = Francophone Reform Liberal Party and
Flemish Party of Liberty and Progress; PS = Social Party; PSDI = Social-Democratic Party; PSI = Socialist Party;
PSOE = Socialist Party; RP = Rural Party; RV = Radical Liberal Party; SD = Social Democrats; SDP = Social
Democratic Party; SP = Center Party; SPO = Socialist Party; SPP = Swedish People’s Party; V = Liberal Party.
In the last three instances (Austria, Italy, and Luxembourg) the predictions of the theoretical model do
not match the government coalition that occurs in the data. These departures can be explained by the fact
that in Austria the government formation process was dominated by the turn to extremism of the Freedom
Party,21 which led the Social Democratic Party and the People’s Party to make a commitment to exclude
the Freedom Party from the government (Müller and Strøm, 2000). A similar commitment between the
Christian Democrats and the Socialist Party to exclude the Communist Party from government yielded the
emergence of the “Pentapartito” government in Italy (Pridham, 1988), which I discuss in greater detail below.
21
In 1986 Jörg Haider defeated Austrian Vice Chancellor Norbert Steger in the race for the party leadership. Since then, the
Freedom Party has moved toward the extreme right, consistent with Haider’s nationalist, anti-immigration, and anti-EU views.
25
In Luxembourg, instead, the government formation process has been affected more by electoral shifts than
by office or policy motivations: the Christian Social Party preferred to propose a coalition with the Socialist
Party rather than with the Democratic Party (DP) because coalitions with the DP in the past had resulted
in greater electoral losses (Müller and Strøm, 2000).22
To illustrate the logic of the government formation process and the rationale for the emergence of minimalwinning, minority, and surplus equilibrium coalitions, I focus here on three cases: Ireland, Sweden, and Italy.23
6.1
Ireland 1989: Minimal winning coalition
The government that formed in Ireland in the aftermath of the 1989 election provides an example of an
equilibrium minimal winning coalition (see table 4). Both Fianna F´ail (FF) and the Progressive Democrats
(PD) obtain the highest utility by coalescing. Hence the model predicts that they will propose a government
coalition. This coalition is robust to individual and group deviations, as neither coalition party has any
incentive to deviate. The coalition between FF and the Workers’ Party (WP), although optimal for WP, is
not an equilibrium coalition, since FF would deviate and propose a coalition with PD (obtaining a utility
equal to 1.34 rather than 1.32). The coalition between Fine Gael (FG), the Labor Party (Lab), WP, and PD
would not be an equilibrium coalition for the same reason: PD would deviate and propose a coalition with
FF (obtaining a utility equal to 0.63 rather than 0.60). The coalitions between FF and FG and between FF
and Lab are not equilibrium coalitions because all of the governing parties have an incentive to deviate.
The equilibrium coalition predicted by the model matches the government coalition formed after the 1989
general election. The election results deprived Fianna Fáil of four seats and of the overall majority. This did
not prevent Charles Haughey, the leader of FF, from proposing a minority single-party government, but his
proposal failed to pass the investiture vote in the Dáil. After about a month of bargaining and negotiations, a
coalition government formed between Fianna Fáil and the Progressive Democrats, the first time that Fianna
Fáil had entered into a coalition with any party. Charles Haughey’s 21st Government of Ireland ended in
22
The rule of thumb until 1989 was that if a coalition party lost a significant number of seats in favor of an opposition party, this
coalition party would be replaced in the next election. As a consequence, the principle “do change a losing team” was constantly
applied from 1959 to 1989.
23
The on-line supplemental appendix reports the analyses of all countries not discussed in detail in this section (see tables 1-12).
26
Table 4: Ireland 1989
Panel A: Parties’ size and preference
FF
wN
77
ẑ
0.60
γ
0.42
Panel B: Parties’ utilities
Coalitions
(FF, FG)
(FF, Lab)
(FF, WP)
(FF, PD)*
(FG, Lab, WP, PD)
UF F
0.99
1.24
1.32
1.34
0.41
parameters
FG
Lab
55
15
0.69
0.31
0.51
0.70
WP
7
0.16
3.00
PD
6
0.825
0.70
SF
1
0.25
9.19
DSP
1
0.19
3.44
UF G
0.90
0.44
0.45
0.47
1.12
UW P
1.57
1.82
1.87
1.63
1.82
UP D
0.57
0.51
0.52
0.63
0.60
USF
5.64
6.41
6.31
5.82
6.13
UDSP
1.91
2.19
2.16
1.97
2.09
ULab
0.47
0.69
0.52
0.49
0.70
Notes. Panel A reports the legislative seats allocated to each party (out of a total of 166), the estimated ideal policy
ẑ, and the trade-off coefficient γ. Political party names are abbreviated (FF = Fianna F´ail; FG = Fine Gael; Lab =
Labor Party; WP = Workers Party; PD = Progressive Democrats; SF = Sinn Fein; DSP = Democratic Socialist Party).
Panel B reports, for each coalition, the utility for each party. The coalition in bold is the strong equilibrium coalition.
The coalition with the asterisk is the actual government formed.
January 1992, when Haughey was involved in a scandal and resigned. Albert Reynolds immediately replaced
him as the new Prime Minister of the 22nd Government of Ireland, and the government coalition between FF
and PD continued for its full term (Wilsford, 1995).
6.2
Sweden 1988: Minority government
The Swedish government formation process after the 1988 elections in contrast provides an example of the
emergence of equilibrium minority governments in a situation where no majority coalitions can form in equilibrium (see table 5).24 No coalition is a strong equilibrium of the game, but the minority single-party
government proposed by the Swedish Social Democrats (SD) is a strong equilibrium. Trivially, SD does not
have any incentive to deviate, as it receives the highest utility. But one might ask why the other parties do
not coalesce and propose an alternative majority coalition. While the Moderate Unity Party (M), the People’s
Party (PP), the Center Party (CP), and the Greens (G) would like to deviate together, they could not achieve
a majority without the Communist Party (COM), which would prefer to support the minority coalition rather
24
The on-line supplemental appendix provides the analysis of three examples of proper equilibrium minority coalitions: Denmark
(1988), France (1988), and Norway (1989).
27
Table 5: Sweden 1988
Panel A: Parties’ size and preference parameters
SD
M
wN
156
66
ẑ
0.32
0.87
γ
1.14
1.61
Panel B: Parties’ utilities
Coalitions
(SD, M)
(SD, PP)
(SD, CP)
(SD, COM)
(SD, G)
(M, PP, CP, COM, G)
(SD)*
USD
1.66
1.83
1.86
1.98
1.99
0.77
2.14
UM
1.29
0.85
0.81
0.68
0.77
1.59
0.72
PP
44
0.66
0.62
CP
42
0.58
0.73
COM
21
0.11
3.52
G
20
0.55
5.42
UP P
0.51
0.68
0.44
0.39
0.43
0.84
0.41
UCP
0.66
0.59
0.79
0.52
0.56
0.90
0.54
UCOM
2.20
2.52
2.59
2.99
2.69
1.75
2.78
UG
5.06
4.58
4.47
4.04
4.43
5.02
4.17
Notes. Panel A reports the legislative seats allocated to each party (out of a total of 349), the estimated ideal policy
ẑ, and the trade-off coefficient γ. Political party names are abbreviated (SD = Social Democrats; M = Moderate Unity
Party; PP = People’s Party; CP = Center Party; COM = Communist Party; G = Greens). Panel B reports, for each
coalition, the utility for each party. The coalition in bold is the strong equilibrium coalition. The coalition with the
asterisk is the actual government formed.
than coalescing with them (by supporting the minority coalition it obtains a utility equal to 2.78 rather than
1.76). For a party extensively motivated by policy, coalescing with conservative to very-conservative parties is
less appealing than supporting an adjacent parties even if this means staying out of government. Hence, the
minority government is not only viable but durable, because there is no coalition of parties that can defeat it
and propose a viable alternative government.
The equilibrium coalition predicted by the model matches the government coalition formed after the 1988
general election. The Social Democratic Party lost three seats in the election, but remained the largest party
with 156 seats, and together with the support of the Communists controlled the majority of the Riksdag
(Sainsbury, 1989). Carlsson, the leader of the SD, maintained the incumbent government. The single-party
government was successful, except in 1990, when it failed to gain a majority for economic reforms. Although
the speaker of the Riksdag asked the Moderate party leader to explore the possibility of a conservative
government coalition, this was ultimately considered to be nonviable and Carlsson’s cabinet was immediately
reinstated with a slightly modified political agenda. Carlsson continued to lead the single-party government
for a full term until the 1991 elections.
28
Table 6: Italy 1987
Panel A: Parties’ size and preference
PCI
wN
101
ẑ
0.02
γ
3.14
Panel B: Parties’ utilities
Coalitions
(DC, PCI)
(DC, PSI, PLI)
(DC, PSI, PSDI)
(DC, PSI, PRI)
(DC, PSI, Rad)
(DC, PSI, DP, G)
(DC, PSI, PSDI, PRI)
(DC, PSI, PSDI, PLI)
(DC, PSI, PRI, PLI)
(DC, PSI, PSDI, PRI, PLI)*
UP CI
2.63
1.65
1.69
1.70
1.66
1.68
1.69
1.67
1.68
1.69
parameters
PSI
PSDI
36
5
0.20
0.32
1.42
1.38
PRI
8
0.32
1.76
DC
125
0.57
1.10
PLI
3
0.80
1.98
MSI
16
1.00
1.82
DP
1
0.01
10.91
G
1
0.44
9.86
Rad
3
0.71
5.69
UP SI
1.24
1.22
1.23
1.24
1.22
1.24
1.24
1.22
1.22
1.23
UP RI
1.75
1.46
1.47
1.52
1.46
1.47
1.53
1.46
1.51
1.52
UDC
1.38
1.78
1.75
1.74
1.77
1.77
1.71
1.75
1.73
1.70
UP LI
1.04
1.39
1.35
1.34
1.37
1.35
1.35
1.38
1.37
1.36
UM SI
0.59
0.90
0.88
0.87
0.89
0.88
0.87
0.89
0.88
0.87
UDP
7.48
5.64
5.76
5.79
5.66
5.74
5.78
5.70
5.72
5.78
UG
8.72
9.34
9.44
9.47
9.36
9.43
9.46
9.39
9.41
9.46
URad
3.55
4.51
4.45
4.43
4.52
4.40
4.38
4.43
4.41
4.44
UP SDI
1.37
1.14
1.18
1.16
1.14
1.15
1.19
1.17
1.15
1.18
Notes. Panel A reports the senatorial seats allocated to each party (out of a total of 324, i.e., 315 elected and 9 life
senators), the estimated ideal policy ẑ, and the trade-off coefficient γ within the 95% confidence interval. Panel B
reports, for each feasible minimal winning coalition (first block) and surplus coalition (second block), the utility for
each party. Political party names are abbreviated (PCI = Communist Party; PSI = Socialist Party; PSDI = Social
Democratic Party; PRI = Republican Party; DC = Christian Democrats; PLI = Liberal Party; MSI = Social Movement;
DP = Proletarian Democracy; G = Greens; Rad = Radicals). Coalitions in bold are strong equilibrium coalitions. The
coalition with the asterisk is the actual government formed.
6.3
Italy 1987: Surplus government
The Italian government formation process after the 1987 elections provides an example of the emergence
of surplus governments in equilibrium (see table 6). There are four different equilibrium minimal winning
coalitions: every equilibrium coalition includes the Christian Democrats (DC) and the Socialist Party (PSI)
plus either the Liberal Party (PLI), the Social Democratic Party (PSDI), the Republican Party (PRI), or the
Proletarian Democracy (DP) and the Greens (G).
There is also an equilibrium surplus coalition which includes DC, PSI, PSDI, and PRI. As in the example in
the previous section, the surplus coalition includes all the parties of the equilibrium minimal winning coalition
composed of DC, PSI, and PSDI plus the dummy party PRI. This is because both PSI and PSDI prefer to
include PRI to move the policy closer to their ideal policy. For the other partner (DC) no profitable deviation
from the surplus government proposal exists. Hence, the surplus coalition is a strong equilibrium.
29
Although the equilibrium surplus coalition predicted by the model matches the type of government coalition formed after the 1987 general election, it does not perfectly match its composition. In fact, the Pentapartito coalition (composed of DC, PSI, PSDI, PRI, and PLI) continued to govern Italy until 1991, when the
Republican Party defected from the coalition. It is claimed that the origins of the Pentapartito coalition go
back to an informal alliance (or pact) forged between the leader of the Christian Democratic Party, Arnaldo
Forlani, and the leader of the Socialist Party, Bettino Craxi, during the XXXV PSI’s general meeting (Colarizi and Gervasoni, 2005). The pact aimed to oppose extreme left-wing (Communist) and right-wing (Social
Movement) parties by including in the coalition the three historic parties: PSDI, PRI, and PLI.
7
Conclusions
Most formal theories of government formation analyze the formation process as a bargaining game over
government resources, virtually always predicting equilibrium coalitions that are minimal winning. The
predictions of these theories, however, are contradicted by the empirical evidence, which shows that minority
and surplus governments form as often as minimal winning coalitions.
Recently, legislative bargaining theories have begun to take a more ideological perspective, assuming
that parties bargain over both distributive benefits (i.e., office) and the government policy when forming
a government (Diermeier and Merlo, 2000; Martin and Stevenson, 2001; Cho, 2014; Kalandrakis, 2015).
However, these theories assume office and policy concerns to be independent of one another. In these theories,
parties bargain over the cabinet portfolios and policy as two distinct items: the portfolios are allocated, and
the government coalition is bound to implement the agreed-upon government policy. In reality, however,
parties significantly affect policy through the control of the cabinet portfolios, because ministerial offices
have a significant impact on policy in areas that fall under their jurisdiction, consistent with the model of
government described by Laver and Shepsle (1996). Hence, the larger the share of cabinet portfolios a party
controls, the greater the impact of that party on the government policy, rendering policy and office dependent
upon one another.
30
This article proposes a theoretical framework that departs from the existing literature by analyzing the
government formation problem in a framework in which parties bargain over the allocation of cabinet portfolios, which in turn determines the government policy. This provides a more realistic perspective on how parties
affect the policy-making activity of a coalition government. Parties are forward-looking and, when deciding to
coalesce with other parties, they anticipate how the portfolios will be distributed among the coalition parties,
and how this will ultimately affect the policy of the coalition. In fact, as Bäck et al. (2011) show, parties are
aware of the policy power that comes with a ministerial position and aim to obtain the ministries that will
give them jurisdiction in the policy areas about which they care the most.
The fact that parties are not only interested in dividing up the spoils of office but also in achieving policy
objectives helps to explain why parties form smaller or wider coalitions than those required to achieve the
confidence vote. Policy-concerned parties might prefer to trade off cabinet portfolio perquisites in order to
achieve a more desirable government policy, leading to an enlargement of the government coalition, and even
a surplus coalition. When the policy concern of a party is sufficiently large, the party might even prefer to
renounce altogether the value of being part of the government coalition in order to give external support to
a minority government whose government policy is close to its ideal policy.
The theoretical model described in this article provides important insights on the emergence of minority
and surplus governments in multiparty parliamentary systems. Minority governments form in equilibrium
when there are external supporters that prefer a minority government over forming a majority coalition with
other external parties. Because external supporters would be worse off by deposing the minority government
and being formateurs of alternative coalitions than they would by supporting it, the minority government
is not only an equilibrium of the game, but a dynamically stable one. Surplus governments, in contrast,
form when a party is better off by including a superfluous party that moves the government policy closer to
the party’s ideal policy. The theoretical model developed here improves on the literature by analyzing the
conditions that guarantee the emergence and the stability of minority and surplus governments, which are
explained as rational outcomes of parties’ strategic considerations.
The endogenous nature of the coalition-formation process sets my model apart from most theories of
31
coalition formation. While extant legislative bargaining models are concerned with predicting the existence
of minority or surplus government coalitions, the objective of my model is to predict coalitions that not only
can form in equilibrium, but are also durable and can survive for the entire legislative term. In this respect,
this model is fundamentally different from the legislative bargaining models building on Baron and Ferejohn’s
(1989) pioneering work in which coalitions form but can always be beaten in a dynamic setting by alternative
coalitions (through the redrawning of a different proposer). In my model, parties foresee the utility that every
party would get for any viable coalition and only participate in (or support) the coalition that is optimal for
them. Hence the coalitions that form in equilibrium are stable in a dynamic setting.
Coalition stability has been studied by Indriðason (2010), who analyzes how concerns about government
survival affect the allocation of cabinet portfolios, and Penn (2009), who analyzes a dynamic voting game
in which players trade off the current value of a proposal for its long-run stability value. Furthermore, the
concept of endogenous government formation described in this article is related to the endogenous equilibrium
agenda of Penn (2008: 208), who analyzes a game of agenda formation in which “...players bargain informally
by tossing out ideas, and stop only when there is no alternative remaining that is better than every previously
proposed alternative.” While any coalition can be an equilibrium of the game, allowing parties to negotiate
in a free-style manner without a time limit narrows the set of potential equilibrium coalitions to a unique
coalition that is robust to group deviations.
In this article I offer an empirical analysis that compares the theoretical predictions and the actual governments formed in 15 Western European parliamentary legislatures. The limited availability of data on
parties’ preferences regarding policy and office confines the analysis to the government formation processes
that occurred in the period 1986–1989. The model’s predictions match the actual government composition in
75% of the cases, highlighting its strong predictive power. This suggests that the model could be productively
employed to forecast the composition of future government coalitions, the share of cabinet portfolios allocated
to each coalition party, and, to a certain extent, even the type of ministries that they will obtain. Furthermore, by providing exact predictions about the composition of the government and the government policy
outcome, this model could be fruitfully used to analyze how forward-looking voters are affected by changes in
32
the institutional features or the political environment.
The empirical analysis shows the relevance and the pivotal role of parties’ preferences regarding policy and
office benefits. Without an understanding of these, minority and surplus governments cannot be explained.
A detailed analysis of parties’ preferences regarding office and policy is an enterprise that political science
scholars have not yet undertaken. However, it would be valuable to determine whether these preferences
are fixed or are affected either by the conditions of the environment or by the history of the game. The
data appear to indicate that across countries, cultures, and political positions, small or extreme parties seem
to have one thing in common: they value policy more than office objectives. But it remains unclear what
happens when these parties become larger, more popular, or more moderate. Do they aspire to a greater
share of cabinet portfolios, with a concomitant decrease in the importance of achieving policy objectives?
Or do they continue to value policy as their number one priority? Estimating parties’ preferences over time
and analyzing how these preferences are affected by the history of the game and other exogenous variables
would help to answer these questions and provide scholars with a richer understanding of party politics in
parliamentary legislatures.
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