Shepsle Laver Events Equilibria

Events, Equilibria, and Government Survival

Michael laver; Kenneth A. Shepsle

American Journal of Political Science, Vol. 42, No. 1. (Jan., 1998), pp. 28-54.

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Events, Equilibria, and
Government Survival*
Michael Laver, Trinity College, Dublin
Kenneth A. Shepsle, Harvard University

Theory: A game-theoretic model of government formation yields an equilibrium govern-
ment, the robustness of which may be explored by subjecting it to exogenous shocks.
This permits an examination of government durability and survival in a cruel political
world.
Hypotheses: The vulnerability of a government to exogenous shocks depends upon the
nature of the shock. A government may be quite resistant to some classes of shock, while
it is highly vulnerable to others.
Methods: Game-theoretic analysis yields equilibrium results. A simulation technology is
crafted which allows us to subject this equilibrium to perturbations of its underlying pa-
rameters (much in the spirit of wind-tunnel experiments in engineering).
Results: The technology does indeed allow the systematic examination of well-defined
cases. We find, for the case of two European governments in the 1980s and 1990s, that
they differ considerably in their vulnerability to exogenous shocks.

Introduction
In order to understand the workings of parliamentary government, one
must determine what it takes for a government to survive in a cruel political
world. In order to do this we must understand the circumstances that led to a
particular government taking office in the first place, and the circumstances
in which this government would be replaced by some alternative. This con-
centrates our attention on how radically circumstances must change before a
government falls and is replaced. If a government can survive dramatic
changes in its political environment while still managing to hold on to the
reins of power, we think of it as relatively stable. If a government cannot
survive even quite small changes to the environment in which it originally
took office, we think of it as being relatively unstable.
This paper is concerned with government survival in parliamentary de-
mocracies, exploring factors that might destabilize equilibrium govern-
ments. This is not just an abstract academic problem. In practical political
terms, the survival potential of any real-world government is of obvious in-
terest to the wide range of actors who must deal with it. These include,
among many others: opposition parties, citizens, interest groups, revolution-
*This paper was originally prepared for the Annual Meeting of the American Political Science As-
sociation, San Francisco, 1996. We are grateful for the comments there from Sven Feldmann and
Barry Weingast. For programming assistance we thank Paul Doyle. We also gratefully acknowledge
the comments of three anonymous referees.
American Journal of Political Science, Vol. 42, No. 1, January 1998, Pp. 28-54 O 1998 by the
Board of Regents of the University of Wisconsin System

29
EVENTS, EQUILIBRIA, AND GOVERNMENT SURVIVAL

aries, investors, foreign governments and international organizations. For
both practical and theoretical reasons, therefore, one of the most important
applications of any model of parliamentary politics is to analyze the ability
of an incumbent government to survive changes in its political environment.
The discussion that follows is developed in several stages. First, we re-
view briefly the main themes in the surprisingly small political science lit-
erature on government survival, concluding that what is missing from this
literature is a theoretical account of what it takes to disequilibrate a govern-
ment or, put differently, why one equilibrium government should be re-
placed by another. Second, we propose various ways in which recent theo-
retical developments might be elaborated into a more comprehensive
approach to the analysis of government survival. Third, we propose a simu-
lation technology that allows substantive progress to be made in this analy-
sis despite major analytical puzzles that remain to be solved. Fourth, we use
the technology we develop to explore the survival potential of two particu-
lar real-world governments.

Government Survival: The Story So Far
Considering that it is such a self-evidently important topic, government
survival in parliamentary systems has been rather neglected by political sci-
entists. The most striking evidence of this neglect is that the first book-length
treatment of the subject appeared only in 1994 (Warwick, 1994). Fortunately
Paul Warwick, who has been one of the most consistent and innovative con-
tributors to the literature so far, provides an excellent review of the literature
on government survival and it would be pointless to repeat this here.' A
simple sketch will suffice.
Most previous discussions of government survival have shared two
striking features. They have been heavily inductive in their logic and they
have concentrated upon government duration as the key variable to be ex-
plained. The quot;government survival debates,quot; as Warwick aptly titles his re-
view, have essentially concerned two issues. The first has been the identity
of independent variables to be included in multivariate statistical analyses of
government duration. The second has been the determination of the most
appropriate statistical model for conducting such an analysis.
The debate over the most appropriate statistical model for analyzing
government durations has been unusual and interesting in political science
terms. Rather than being an arcane discussion on statistical technique among
methodologists, as it might appear on the surface, it has actually been a
debate on how best to conceive of government stability and the processes
that underlie this.
'An earlier review can be found in the chapter on government stability in Laver and Schofield
(1990).

30 Michael Laver and Kenneth A. Shepsle

On the one hand is a group of deterministic models that implicitly as-
sume the durability of a particular government to be an attribute it pos-
sesses, one conditioned by features of the government fixed at the time of its
formation. (Examples of this quot;attributes approachquot; include Sanders and
Herman 1977; Strom 1985; Taylor and Herman 1971; Warwick 1979.) On
the other hand is a stochastic model generated by Browne, Frendreis, and
Gleiber (1984, 1986, 1988), for whom governments exist in a world of criti-
cal events, each event having some probability of destroying the govern-
ment in a process that is essentially random. The methodological debate
arises because, if this quot;events approachquot; to government stability is accepted,
then it is quite inappropriate to analyze cabinet durations using OLS regres-
sion models (which apart from anything else often predict negative govern-
ment durations for feasible configurations of parameter values).
Browne, Frendreis, and Gleiber stated what with the benefit of hindsight
was an extreme version of the events approach that implied government du-
rations were entirely a product of the flow of critical events, so that no gov-
ernment was inherently more durable than any other. Since the deterministic
attributes approach had achieved some empirical success in analyzing gov-
ernment durations, this did not seem entirely plausible. King et al. (1990)
showed that it is possible to specify a statistical model derived from event
history analysis that reconciles a view that government survival was an in-
herently stochastic process, one in which real-world governments exist in a
flow of potentially fatal critical events, with a view that some governments
have attributes that make them inherently more stable than others. The most
obvious attribute that can enhance government stability is a legislative ma-
jority, but several other attributes do improve empirical accounts of govern-
ment duration.
Subsequently, Warwick (1994) developed and enhanced this quot;unifiedquot;
approach. The results of his extensive research in this tradition are reported
and discussed in his book and this work now represents the prevailing ortho-
doxy in empirical accounts of government survival. It remains characterized
by an inductive approach. The style of analysis is to identify a set of inde-
pendent variables with prima facie relevance to government duration. The
variables are then operationalized and an empirical analysis is performed
using an event history model. Causal modeling is essentially inductive. The
result of the empirical analysis is a best-fitting statistical model.

The Way Forward
The Need for a Theory of Government Survival
What is missing from these orthodox accounts of government stability
is a theoretical model of what causes one government equilibrium to be re-
placed with an alternative. Without such a model, it is not possible to pro-

31

vide a comprehensive account of the survival of governments in parliamen-
tary democracies.
It should hardly be necessary to go into much detail on why a purely
empirical account of government survival will always leave us short of a
theoretical explanation for what is going on. An empirical account identifies
factors associated with government survival or duration. These regularities
must be embedded in a model in order to ascertain the mechanisms by which
these factors do, in fact, translate into longer lasting governments or higher
probabilities of survival. Purely empirical accounts, in other words, are the
stuff of Hume's quot;constant conjunction,quot; not of his quot;necessary connection.quot;
The latter is required to know why particular factors are associated with gov-
ernment survival.
Actually, the events theorists did have an explicit model of government
equilibrium, albeit a very simple one. In some ways it is unfortunate that
their work has been presented within the prevailing orthodoxy as a method-
ological argument for a change in statistical method from OLS regression to
event history analysis. Epistemologically, it is much more than this. The
theoretical contribution made by Browne, Frendreis, and Gleiber was to ar-
gue that every government is an equilibrium government in some sense at
the moment of its formation, and that the duration of this government can be
modeled by treating it as if it is forced to survive bombardment by critical
events, any one of which has some probability of destroying the government
equilibrium. They did not concern themselves with why the original govern-
ment was in equilibrium. But their argument implies that it must have been
the equilibrium outcome of some unmodeled process, since it was the gov-
ernment that did indeed form. Of course this means that Browne, Frendreis,
and Gleiber are utterly silent on what follows the disequilibration reflected
in a government defeat. For them, in effect, the unmodeled government for-
mation process then generates a new equilibrium, which they take as it
comes, and which is immediately subjected to relentless bombardment by
critical events.
It seems to us that the notion that governments must survive bombard-
ment by critical events is very persuasive, both substantively and epistemo-
logically. We argue in this paper that the way forward is not to continue the
inductive search for stability-inducing attributes, but rather is to derive a rig-
orous theoretical model that builds upon and extends the idea that a govern-
ment must be in equilibrium at the moment of formation by virtue of the
simple fact that it formed.

Public Opinion Shocks in Three-Party Legislatures
The model we have in mind sees an equilibrium government as the out-
come of the strategic choices faced by the people whose actions result in its


formation. A change in the government equilibrium, the end of one govern-
ment and the beginning of another, must therefore be the result of a change
in the political incentives for one or more pivotal actors, leading them to
change strategies in such a way as to create a new government equilibrium.
One recent theoretical exploration has developed precisely along these
lines (Lupia and Strom 1995). They consider a status quo government in the
aftermath of a particular type of critical event, one that changes the electoral
expectations of key actors. We might think of this as apublic opinion shock.
This shock changes the political environment in which the status quo gov-
ernment must exist, with the result that some actors may change their minds
about whether or not to bring down the government. Lupia and Strom's cen-
tral argument is developed for a three-party legislature and derives from the
plausible assumptions that, first, bringing down a government has opportu-
nity costs for government members (the loss of the remainder of their consti-
tutionally mandated term of office) while, second, both fighting elections
and getting involved in coalition renegotiations have transaction costs for all
involved.
Driven by these assumptions, their model shows that government coali-
tion parties who find as a result of a public opinion shock that they stand to
gain seats at the next election (were one held immediately) may nonetheless
have an incentive either to continue to accept the status quo, or to renegoti-
ate a new coalition agreement without an election, rather than to force an
election and thereby realize anticipated electoral gains. This result is inter-
esting because it runs counter to what on the face of things might seem the
common-sense assertion that coalition members bring down governments
when they anticipate electoral gains (Grofman and van Roozendaal 1994).
A further important insight emerging from the Lupia-Strom model is
that, as a consequence of the declining opportunity costs of a government
collapse as any administration steadily approaches the end of its constitu-
tionally imposed maximum term, the likelihood of the same event destabi-
lizing the government increases throughout the life of the government. This
provides a theoretical justification for the empirical finding of a rising haz-
ard rate-that, other things being equal, the probability of government ter-
minations appears to increase throughout a government's term of office
(Warwick 1994).
There are several ways in which the Lupia-Strom model could be ex-
tended to incorporate interesting features of the government termination
process. One is the strategic asymmetry that exists in many countries by vir-
tue of the fact that only the Prime Minister (and hence the PM's party) has
the constitutional power to request a dissolution of the legislature; the oppo-
sition parties and the other government party or parties do not. Thus a major-
ity coalition consisting of opposition parties and non-PM government par-
ties can make the PM's life a misery, to be sure. But they cannot directly

33

impose a dissolution on a PM who stares them down. In order to force a dis-
solution, a majority coalition excluding the PM's party must bring down the
government, install a rival PM, and then have him or her seek to dissolve the
legislature. In other countries, such as Norway, Finland, and Switzerland,
the government has very little strategic control over the timing of elections.
The Lupia-Strom model could be extended in interesting ways to capture
these variationsa2
Another possibility that is not fully covered by the Lupia-Strom treat-
ment of opportunity costs arises if government parties form the view, after
a public opinion shock, that potential electoral gains accruing to them are
likely to continue to be available for some time in the future. In this event,
government parties need not incur the opportunity costs of bringing down
the government and having an immediate election, but can effectively
quot;bankquot; their public opinion windfall with a view to forcing an election and
cashing it in at some future date, thereby extending their expected tenure of
office.
A further issue is the restriction of the Lupia-Strom model to three-party
systems. They make the claim in a footnote that quot;we can use our three-party
model to explain the dynamics of an n-party bargaining situation by assum-
ing that at least one of our parties is actually a protocoalition. This expansion
is problematic only to the extent that the unitary-actor assumption does not
carry over well in the case of a protocoalitionquot; (Lupia and Strom 1995,
663n). However, it is not at all self-evident that the complex proofs tendered
by Lupia and Strom would go through in a situation in which one quot;partyquot;
was in fact a protocoalition of two or more parties, each with different pref-
erence schedules, each affected differently by the public opinion shock, each
negotiating separately with other actors, and each capable of choosing dif-
ferent coalition partners in any renegotiation. Suppressing all of that politi-
cal action by imposing the unitary actor assumption on a protocoalition does
seem impla~sible.~
These are all matters for a second-generation model, however. There is
no doubt that Lupia and Strom have made significant progress in under-
standing the impact of public opinion shocks on coalitions in three-party
legislatures. This is a very important first step along the road to a fuller theo-
retical account of government survival, allowing us to see that it is indeed
possible to model the impact of events on government survival in a logically
rigorous manner.

2For further details on confidence votes and parliamentary dissolution, see Huber (1995,
1996). Country-by-country detail on these matters in tabular form is found in Gallaher, Laver, and
Mair (1995,30).
3We should also note that in other contexts (for example, entry models of electoral competi-
tion) n = 3 parties is not a good proxy for generalizing to n > 3 parties. Equilibrium may exist for the
latter circumstance, but not for the former. For details, see Shepsle (1991).

Michael Laver and Kenneth A. Shepsle
34

A Broader Treatment of Critical Events
The next steps along this road will involve developing more convincing
accounts of n-party legislatures, and dealing with the impact of critical
events other than public opinion shocks. One relevant approach has recently
been suggested by Laver and Shepsle (1996), elaborating a model first put
forward as a result of independent work by Laver and Shepsle (1990) and
Austen-Smith and Banks (1990). They develop a game-theoretic model of
equilibrium government that can be applied to a legislature with any number
of parties. The capacity of any particular equilibrium government to survive
perturbations of key model parameters can then be explored.
Laver and Shepsle's portfolio allocation model of equilibrium govern-
ment in parliamentary democracies is based upon a set of assumptions that
can of course be debated bur which we will not debate here in the interests of
arriving quickly at a model of government survival. Their core assumption is
that governments are fundamentally characterized by the particular alloca-
tion of key cabinet portfolios among parties. This is because cabinet minis-
ters in practice have considerable influence over policy outputs in areas un-
der the jurisdiction of their portfolios. The partisan allocation of portfolios in
this way forms the basis of forecasts about the policy output of any given
government. Thus health policy is heavily conditioned by the partisan politi-
cal agenda of the minister of health, defense policy by the views of the poli-
tical party of the minister of defense, and so on. Equilibrium governments in
the Laver-Shepsle model emerge in several different ways. Here we focus on
one form of equilibrium. The dimension-by-dimension median cabinet is the
cabinet in which each key portfolio is allocated to the party with the median
legislator on the policy dimension characterizing the jurisdiction of that port-
folio. It is an equilibrium if it has an empty winset-that is, if no other port-
folio allocation is preferred to it by a parliamentary m a j ~ r i t y . ~
Laver and Shepsle explore the issue of government survival by first us-
ing their model to identify equilibrium cabinets, and then investigating the
sensitivity of such equilibria to perturbations in model parameters. Each
model parameter in effect identifies a particular class of critical events that
have an explicit theoretical bearing on the stability of government equilibria.
One class is the sort of public opinion shock that forms the basis of the Lupia-
Strom model. Other things being equal, an equilibrium cabinet that ceases to
be in equilibrium as a result of relatively small perturbations in model param-

4Surely majorities will prefer many policies to the one associated with a putative equilibrium
cabinet. This is the well-known fact of life about majority rule institutions in multidimensional con-
texts. The Laver-Shepsle claim is that it is entirely more likely to find that the dimension-by-dimen-
sion median cabinet is preferred by a majority to every other cabinet (each of which is associated
with a forecast policy that some majority likes less than the multidimensional median policy).

35

eters is forecast to be less likely to survive in the real world than an equilib-
rium cabinet that requires larger perturbations in the same parameters before
it ceases to be an equilibrium. Statistically, a higher proportion of critical
events should destabilize the former than the latter government.
This way of doing things thus builds upon both the purely stochastic
quot;eventsquot; approach used by Browne, Frendreis, and Gleiber and the deduc-
tive approach used by Lupia and Strom. It involves constructing an explicit
deductive model of parliamentary government, then unpacking the substan-
tive implications of this model for government survival according to the
epistemological assumptions of the quot;eventsquot; a p p r ~ a c hIn effect, we are
.~
recommending a form of sensitivity analysis in which we ask whether a par-
ticular configuration of parameters sustaining an equilibrium is robust to
shocks and, if so, then how robust.

What Do Shocks Shock?
We have just argued that the best way to model the government survival
process is to take a model of government equilibrium and analyze the impact
on equilibrium of shocks to key parameters. This means that our account of
government survival will be driven by the variables assumed to condition
government equilibrium. The key variables used by the portfolio allocation
model (and of course by many other extant or conceivable models) to iden-
tify equilibrium governments are:
party positions on key policy dimensions;
party specific saliency weights attached to these dimensions;
the distribution of seats among parties;
the legislative decision rule used to sustain a government in office.
Change in the values of any one of these variables may, according to
the portfolio allocation model, destabilize an existing equilibrium govern-
ment. The variables identified by this model are hardly exotic, however,
and have an important role in most accounts of government formation that
take party policy seriously. They are thus likely to figure in any compre-
hensive account of government survival. These variables thus help us to
specify classes of critical event that have a bearing upon government sur-
vival. Any critical event that has an effect on government survival that we

5An important point to make at this stage is that this way of using a model of government equi-
librium to generate a model of government survival is generic-the methodology does not require
any particular model of government equilibrium. Government survival could be analyzed using any
model generating a clear specification of an equilibrium government and the parameters that under-
pin this. Given any such model, the underlying technique of investigating the sensitivity of particu-
lar government equilibria to the perturbation of key model parameters could be employed.

36

Table 1. Classification of Critical Events
Type of critical event
Model parameter perturbed
Party ideal points Policy shock
Party-specific dimension weights Agenda shock
Public opinion shock
Expected seat distribution in immediate election
Decision rule shock
Effective majority required for government survival

can explore analytically must do so because it causes a disequilibrating
shock to the value of one of the basic model variables. These are summa-
rized in Table 1.

Events That Shock Party Policy Positions: Policy Shocks
The original Laver-Shepsle (1996) discussion of cabinet stability con-
centrated on shocks to the matrix of distances between party ideal points.
Such shocks were used to model quot;genericquot; critical events on the grounds
that many critical events have the effect of changing how the parties feel
about each other's policy commitments, thus changing the matrix of inter-
party distances.
However, an important matter that is brought into focus by Lupia and
Strom's more explicit modeling of the impact of a particular type of shock
concerns the precise substantive meaning of modeling shocks by perturbing
party ideal points. After all, party ideal points represent the tastes of parties,
which Laver and Shepsle take in all other parts of their argument to be
primitives, not strategic variables. Even assuming party ideal positions on a
given set of issues to reflect fundamental tastes, however, it is possible to
conceive of ways in which party positions on policies within the jurisdiction
of various cabinet portfolios might change over time. This is because politi-
cians and parties are agents for constituencies in the broader polity. Party
ideal points reflect preferences induced by this agency relationship. And
constituency interests (the principles of the principals, so to speak) surely
change as events impinge upon markets, factors of production, income, and
many other things besides.
Thus foreign policy positions, for example, are of their very essence
open to the impact of exogenous shocks. The Berlin Wall is torn down; civil
war flares up in Bosnia or Rwanda; Britain dispatches a task force to retake
the Falkland Islands from Argentina. Few of these events could reliably have
been foreseen, yet each creates a need for government and opposition parties
in many other countries to assess their present policy position or, in some
instances to take altogether new policy positions. Unanticipated events-

37

sudden runs on foreign currencies, unexpected major bankruptcies-can ob-
viously have similar effects on economic policy. Indeed it is not hard to
think of examples of the way in which this type of quot;policy shockquot; can stimu-
late policy reconsideration and, indeed, add new issues to any important
policy jurisdiction. In this way events can constitute the exogenous shocks
that perturb party positions in major policy jurisdictions.

Events that Rearrange the Policy Agenda: Agenda Shocks
A second class of political event identified in Table 1 may disturb an
equilibrium by affecting the relative salience of key policy jurisdictions.
Such events do not effect a reconsideration of specific issues positions, and
thus do not shock party ideal points. Rather, they affect the relative impor-
tance of policy jurisdictions. Even after the Balkans conflict has become
part of the foreign policy issue bundle, for example, and even if party posi-
tions on it have done all the adjusting they are going to do, particular dra-
matic events and atrocities in Bosnia may raise the overall profile of foreign
policy, forcing it higher up the political agenda. We might therefore think of
these events as agenda shocks.
Each political actor (or political party if we use the assumption of par-
ties as unitary actors) gives a relative weight to each policy jurisdiction.
These weights may well be very different for different parties in the same
~ y s t e mThe perceived aggregate policy distance between two parties is
.~
then a function of policy distances between them on each key policy dimen-
sion, weighting the distance on each dimension, for each party, by the party-
specific dimension eight.^ This of course creates a situation in which it is
likely that Party A's view of the distance between Party A and Party B will
differ from Party B's view of precisely the same thing, since each applies
different weights to their differences on each dimension.
We can think of agenda shocks as changing party-specific dimension
weights. This allows for the possibility that an event can change how Party
A feels about Party B in a way that is different from the change in how Party
B feels about Party A . Imagine two parties, one a social democratic party
~
and one a fundamentalist religious party. The social democratic party gives
a much higher weight to the economic policy dimension than to the social1
moral policy dimension; the fundamentalist religious party does the reverse.
An example of an agenda shock might be a supreme court decision unex-
pectedly changing abortion law. This would be a much bigger deal for the
6Empirical evidence of just how different party-specific dimension weights can be was col-
lected by Laver and Hunt (1992).
'This is, it will be a function of the salience-weighted Euclidean distance.
8 ~ oprecisely this reason, it is difficult to illustrate the impact of shocks to party-specific di-
r
mension weights in a simple diagram.


fundamentalist religious party than for the social democratic party. Even
though the party positions on abortion would not change, the increased sa-
lience of the abortion issue for the religious party would create a situation in
which it perceived a quot;widening gapquot; between it and the social democratic
party, a change that might be considerably less visible to the latter. If the two
parties happened for some reason to be in coalition together, the relative in-
centives for each to end the arrangement may change as a result of this
agenda shock, despite the fact that their policy positions remained the same.

Events that Shock Expected Election Results: Public Opinion Shocks
Lupia and Strom base their model of government survival on the impact
of an event that affects quot;commonly held expectations concerning the out-
come of a potential electionquot; (1995,648)-we will call these public opinion
shocks. Parties in the Lupia-Strom model are assumed to quot;care about con-
trolling seats in parliamentquot; (1995,652). Indeed the payoffs they assume for
each party derive from a simple additive function of legislative seat share
and coalition payoff (1995, 653).9 Thus an event that affects the expected
result of the next election, for example an unexpected opinion poll finding,
potentially affects the incentives of various parties to destroy the govern-
ment, even if the event is expected to result in no change whatsoever to the
set of winning coalitions, which we refer to as the decisive structure.1°
In the three-party world of the Lupia-Strom model, of course, almost
every public opinion shock will leave unchanged the decisive structure an-
ticipated after the next election. The only decisive structure with coalition
potential makes any two parties capable of forming a winning coalition; the
only type of shock to the decisive structure that can change this is one big
enough to give a single party an overall majority. Thus, if Lupia and Strom
did not assume parties value legislative seat shares intrinsically, and thus re-
negotiate the coalitions to which they belong so as to realize the utility gains
deriving from changes in forecasts about seat shares, then the only time any-
thing would happen in their model is when a big enough public opinion
shock arrived to offer one party the prospect of a single-handed legislative
majority.
Laver and Shepsle, in contrast, regard the legislative seat share as an
entirely instrumental concern for each party, important only to the extent it

gLupia and Strom actually conceptualize party objective functions in a more general fashion,
so that in their model shocks also affect things other than expected election results. Nevertheless,
their examples and running commentary focus primarily on the latter, so we think of theirs mainly
as an analysis of public opinion shocks.
'OThat is, since parties care about seat share, they may he motivated to bring down a sitting
government and provoke new elections in order to capture a seat-share dividend, even if such
changes in seat shares leave the original decisive structure intact.

39

affects the party composition of the government that is forecast to result
from a particular seat distribution. This implies that the only public opinion
shocks that can have an effect on model predictions are those that change the
decisive structure. Public opinion shocks thus have very discontinuous ef-
fects. Some large shocks will have no effect whatsoever but, as the seat dis-
tribution moves close to a threshold, quite small shocks can have quite big
effects. In the three-party case, for example, if three parties each have 33
seats in a 99 seat legislature, only whopper public opinion shocks, big
enough to lead to the prediction that one party will gain at least 17 seats to
give it an overall majority, will change the parties' calculations. In another
99 seat legislature in which two parties have 49 seats and the third party has
one seat, a teeny-weeny shock forecast to result in a single seat gain by one
of the two big parties would have the same destabilizing effect.quot; It is as well
to be aware, therefore, that our own exploration of government survival is
concerned solely with incentives arising from the composition of the gov-
ernment, rather than from any intrinsic satisfaction associated with doing
well in legislative elections.
We should further note that we assume public opinion shocks to affect
the calculations only of parties in a position to bring about an immediate
election. As we pointed out earlier when discussing the Lupia-Strom account
of public opinion shocks, there is an important asymmetry in the making and
breaking of governments that we must consider if we are to develop a con-
vincing account of the impact of public opinion shocks on government stabil-
ity. Not all parties are equally able to force an election when the circum-
stances favor them. Opposition parties are typically quite unable to force an
election when, as is very often the case, they do well in public opinion polls
during the lifetime of the government. In fact, it is usually the case that only
the Prime Minister's party can directly impose an early election, so that the
only public opinion shocks likely unambiguously to result in an election are
those that improve, for the PM's party, the government equilibrium antici-
pated to result from a forced election.12 Since the PM's party is already in
government and already controls the Prime Ministership, the only real strate-
gic benefit of an early election in this sense arises from an anticipated result
that allows the PM's party to get rid of some or all coalition partners and form
a new government in which it controls more key portfolios.

quot;As the number of parties increases, the number of possible decisive structures goes up at a
very rapid rate, and the probability that a small change in seat shares will change the decisive struc-
ture increases accordingly. The difference between shocks to seat shares and shocks to decisive
structures thus narrows as the number of parties increases.
I20ne bit of ambiguity remains. It is possible that the PM's party could elicit agreement from
other government parties to reshuffle some of the portfolios, effectively impounding the import of
the public opinion shock while avoiding the necessity of holding an early election.


Government parties other than the PM's party may, however, have the
indirect power to force an election. If a public opinion shock makes a non-
PM government party very strong,13 then it can resign, form an alternative
administration in which it controls the prime ministership, then force an elec-
tion from this position. Opposition parties would facilitate this since they too
favor a minority government run by the non-PM government partner. l4 Thus
public opinion shocks making a non-PM government partner very strong are
also destabilizing according to the portfolio allocation model.

Events that Shock the Decision Rule
While every aspect of the institutional environment of parliamentary
democracies is of course an endogenous product of politics in the long term,
it is conventional to treat certain institutional features as being fixed exog-
enously within the timescale of the process under consideration. When look-
ing at the making and breaking of governments, analysts almost always take
the legislative decision rule - typically majority voting - to be fixed in the
sense that changing the decision rule is not considered to be a feasible part
of the process of making or breaking a government. Both the Lupia-Strom
and the Laver-Shepsle accounts follow this convention. Looking at things in
more general terms, however, it may happen that the majority decision rule
underpinning the formation of a particular equilibrium government may ef-
fectively (if not formally) be changed during the lifetime of that government,
potentially undermining its stability.
We know of no real-world situation in which the majority rule for votes
of confidencelno confidence in the government has been abandoned for-
mally. However, some constitutions do require qualified majorities in parlia-
ment for certain policy changes, for example those involving alterations of
the constitution. A government that forms when no constitutional issue is on
the agenda, or foreseen, may in such cases be destabilized if a shock not
only causes such an issue to emerge out of the blue but also is of sufficient
importance that the government cannot govern effectively if it cannot make
the necessary constitutional revision. It may be in equilibrium given the ma-
jority decision rule, but out of equilibrium given the qualified majority rule
implied if it is to continue effectively in office. The reemergence of commu-
nal strife in Belgium, and the need for constitutional engineering to address
this, is one prima facie example of such a mid-term rule change.
A more prosaic, and more common, situation in which a qualified ma-
jority decision rule can effectively be imposed unexpectedly arises from the
13Avery strong party, in Laver and Shepsle's terms, is a party with an ideal point that has an
empty winset. That is, there is no portfolio allocation (i.e., government) preferred by a parliamentary
majority to the one in which the party in question receives all key portfolios.
14Sincethis party is very strong, the opposition parties by definition prefer it to the status quo.

41

emergence in the legislature of an anti-system party, or of one or more inde-
pendents.15 An anti-system party that votes against everything as part of a
wider strategy to destabilize legislative politics as a whole, or independents
whose preferences are not well-known and who vote apparently at random,
effectively add votes to the anti-government side of every division, regard-
less of its content. This leaves the remaining parties needing a majority vote
in the legislature when all legislative votes are not available to them. Thus if
there are 10 maverick voters in a 200 seat legislature, the decision rule re-
quires 101 out of 190 available voters, not out of 200, and a qualified major-
ity decision rule is effectively in operation. If the maverick votes come into
being as a result of some shock to the system during the lifetime of a particu-
lar government, then this is a de facto decision rule shock and it may under-
mine government stability.16
To om knowledge nothing has been written on government survival un-
der qualified majority decision rules, and strategic interaction in such cir-
cumstances is clearly complex and difficult to characterize. We certainly do
not have the space to go into such matters here-the important point to note
is that a decision rule shock resulting from the unexpected emergence or dis-
appearance of mavericks can destabilize an existing equilibrium.

Classes of Critical Event
Putting all of this together, we see that having a model of government
equilibrium allows us to identify classes of critical event that might desta-
bilize that equilibrium. A model has variables that contribute towards iden-
tifying an equilibrium. A particular equilibrium outcome is conditioned on
certain values of these variables, these values being parameters of the equi-
librium concerned. Each variable is associated with a class of relevant criti-
cal event, an event capable of perturbing the values of the variable enough
to destroy the equilibrium. Indeed in the world as conceived by any model,
all relevant critical events rnust derive their relevance by perturbing the
values of some model variable since, if all such values remain unchanged,
the equilibrium analysis derived from the model must remain unchanged
also and the status quo remain intact.
Thus having a model of government equilibrium is an essential step in
any systematic analysis of the impact of events on government survival; and
it is in this sense that we observed earlier that purely inductive approaches
are incomplete. The Lupia-Strom account of government survival derives
15Althoughfor this to happen mid-term the anti-system party would need to be a split from an
existing pro-system party.
160ne of the anonymous referees observed that exogenous decision-rule shocks are especially
plausible when applied to parliaments operating under something short of full sovereignty, such as
subnational assemblies or, increasingly, national parliaments within the EU.


from a model of government equilibrium driven by expectations about fu-
ture election results. This leads to a concentration on public opinion shocks
as a class of critical event. The Laver-Shepsle account is based on a range of
different variables, as we have seen, each of which defines a different class
of critical event.17 In what follows we explore the impact of different types
of critical event on the stability of some real-world equilibrium govern-
ments. Before this, however, we set out the simulation technology that al-
lows us to do so.

Simulating Critical Events
In principle it should be possible to use the analytic methods of com-
parative statics to evaluate the impact of perturbing key model parameters
on a particular government equilibrium. This is in effect what Lupia and
Strom do for the three-party case. Laver and Shepsle (1993) also explore
government equilibrium in the three-party two-ditnensional case analyti-
cally. In practice when using the portfolio allocation model to consider more
complex cases, however, the impact of interactions between model param-
eters on equilibrium forecasts is not only complex, but is fundamentally
characterized by sudden discontinuities in the face of continuous changes in
individual variables. Strategic thresholds, for example the indifference
curves of pivotal actors, are suddenly crossed, generating new voting ma-
jorities, when party ideals or party-specific salience weights are continu-
ously varied. New sets of winning coalitions are suddenly generated from
smooth changes in party weights, and so on. Analytical expressions about
the relationship between model parameters and government equilibrium can
be written down, but they are large and ugly and lack any intuitive connec-
tion to the real world. l s
Since analytical techniques are impractical, we use simulations to ex-
plore the ability of particular equilibrium cabinets to survive perturbations in
model parameters. We simulate a stream of political shocks by adding a se-
ries of random disturbance terms to key party system parameters and ob-
serving the proportion of these that destabilize a given equilibrium. Compar-
ing two equilibrium cabinets, the cabinet that is destabilized by the higher
proportion of random shocks is taken to be the less stable. The proportion of
a stream of random shocks of fixed amplitude that a given equilibrium cabi-
net survives can be taken as an estimate of its relative stability vis ZI vis com-
parable equilibrium cabinets exposed to the same shock stream.

171nfact, the Laver-Shepsele model allows for several different forms of equilibrium, only the
most prominent of which we have described here.
I8Some large, ugly, and nonintuitive expressions derived from the portfolio allocation model
are on display in Laver and Shepsle (1993).

43

In practice if we want to estimate, for example, the impact of agenda
shocks on a given equilibrium government, we generate a set of quot;shocked
cases, each representing a perturbation in the base case under investigation
after an event alters party-specific dimension weights. In the results that we
report in this paper, we used 1,000 shocked cases for each simulation. In the
case of an agenda shock, each shocked case is derived by adding a random
disturbance term to the base case weight attached by each party to each di-
mension. This disturbance term is randomly drawn from a normal distribu-
tion with a mean of zero and a standard deviation of s, where the magnitude
of s determines the amplitude of the shock stream to which we expose the
base case. A larger s is likely to expose dimension weights to larger perturba-
tions. The standard deviation, s, of the shock term is thus a parameter that
characterizes the variation in the size of the shocks being modeled-in effect
the amplitude of the shock stream to which the base case is subjected.19 By
increasing s a more vigorous and destructive shock stream can be simulated.
The stability of the equilibria generated by two different base cases can
be compared using simulated shock streams such as these. Each base case is
perturbed a fixed number of times by random shocks drawn from a stream of
fixed amplitude. Some of these shocks will create a shocked case in which
the model's predicted equilibrium cabinet is identical to that in the base
case. Some will create a shocked case in which the anticipated outcome is
not the same as in the base case. The higher the proportion of shocked cases
in which the newly created equilibrium is identical to the base case equilib-
rium, the more stable the base case is taken to be. An identical technique can
be used to explore the effects of policy or public opinion shocks, while the
effects of decision-rule shocks can be explored using more conventional
analytical means.20
Our theoretical approach of modeling cabinet stability in terms of ro-
bustness to perturbations in party system parameters, as well as our basic
simulation technology, is appropriate for any well-specified model of cabinet
equilibrium. Provided a model of cabinet equilibrium can be well-enough

I9It is worth noting that holding s constant over a given set of simulated shocked cases
amounts to assuming, in the language of event history analysis, that the cabinet under investigation
has a constant hazard rate. It is in principle possible to simulate variable (most often thought of as
rising) hazard rates, by varying s in some well-specified way during the simulation. But we do not
attempt this in the present paper. See Warwick (1994) for a discussion of constant and variable haz-
ard rates.
201nfact, this proves to be a conservative measure of stability, for we count every instance in
which a parameter shock no longer quot;supportsquot; the prior equilibrium as actually disequilibrating it.
But, as Sven Feldmann has pointed out to us, not all destabilizing events are disequilibrating events.
Forward-looking institutional actors may not desert the prior equilibrium, deciding to '?jump shipquot;
only if they are certain they will be better off when the process their desertion sets into motion
settles down into a new equilibrium.


specified to be programmed, a particular party system configuration under
investigation can be taken as comprising a quot;base case,quot; to which random per-
turbations of key parameters can systematically be applied. The equilibrium
can be recalculated in the light of each perturbation, allowing the investiga-
tor to estimate the proportion of such perturbations to which the base case
equilibrium is robust, using this to generate an estimate of relative stability.
There is nothing about this methodology that is specific to the portfolio allo-
cation approach.

The Relative Stability of Real Cabinets
In this section we use the Laver-Shepsle portfolio allocation model of
government equilibrium and the simulation technology we have just de-
scribed to explore the relative ability of two real-world governments to sur-
vive different types of critical event. The two cases we consider in some de-
tail are, first, the Christian Democrat (CDU)-Free Democrat (FDP) coalition
that formed in Germany in 1987 and, second, the Fianna FBil (FF)-Labour
(Lab) coalition that formed in Ireland in 1992.
Our choice of these cases is far from accidental. The most persuasive
two-dimensional representation of each case generates a very clear cut equi-
librium government according to the portfolio allocation model. In each
case, taking the key portfolios as Finance and Foreign Affairs, the cabinet
that actually formed was one allocating each key portfolio to the party con-
trolling the median legislator on the main policy dimension over which the
portfolio had jurisdiction. This quot;dimension-by-dimension medianquot; cabinet
gave the Finance portfolio to the CDU and Foreign Affairs to the FDP in
Germany. In Ireland, it gave Finance to FF and Foreign Affairs to Labour.
Crucially in each case, no alternative portfolio allocation was preferred by a
legislative majority to the portfolio allocation that occurred; the latter alloca-
tion's winset was empty. In each case, therefore, the government that formed
was in equilibrium. No actor with an incentive to bring down the incumbent
government also had the ability to do so, while none with the ability to do so
also had the incentive.
It may on the face of things seem to be cheating to concentrate only
upon equilibrium governments when we analyze government survival. A
moment's thought, however, reveals that this is in fact the only thing that we
can sensibly do, given our argument that we must analyze government sur-
vival by using an explicit model to explore the events that knock an equilib-
rium government out of equilibrium. In a very real sense we have nothing at
all to say about the stability of out-of-equilibrium governments. Since our
model cannot account for why they formed in the first place, it cannot possi-
bly account for why they fall. This is not a problem unique to our approach,
but applies to any approach that sees the fall of a government as the collapse

45

of an equilibrium (e.g., Austen-Smith and Banks 1988, 1990; Baron 1991;
Schofield 1993). If the equilibrium in place is not anticipated by a model,
then its collapse must depend upon factors outside the model's scope.
We operationalize our exploration of the two governments concerned
using the same dataset as Laver and Shepsle (1996) to identify equilibrium
governments. These data involve specifications of key policy dimensions
and cabinet portfolios, of actual party policy positions and party-specific di-
mension weights, and of legislative seat distributions and the actual alloca-
tion of key portfolios. While most of these operationalizations could of
course be discussed at great length, it is not our purpose in the current paper
to do so. The basic data for both cases are given in Table 2.21
Using these data, we first confirmed that the status quo portfolio alloca-
tion in the Irish and German cases was indeed in equilibrium, using the com-
puter program developed by Laver and Shepsle for applying the portfolio al-
location The Finance-Foreign Affairs portfolio allocation to FF-Lab
in Ireland and CDUICSU-FDP in Germany had an empty winset in each in-
stance. We then used the same program to perform a wide range of simula-
tions that explored the sensitivity of each equilibrium government to pertur-
bations of party-specific dimension weights, party policy positions, and party
seat distributions. These simulations thus explored the ability of the Irish and
German governments under investigation to survive agenda shocks, policy
shocks, and public opinion shocks, respectively.

Agenda Shocks
We first explored the susceptibility of the two equilibrium governments
to agenda shocks. We did this by exposing each base case to a series of
shock streams, each stream of increasing amplitude, and observing the pro-
portion of shocked cases in each stream for which the base case equilibrium
cabinet remained in equilibrium. Each shocked case was generated by tak-
ing each party-specific dimension weight in the base case and adding a ran-
dom disturbance term, as described earlier. The first shock stream of 1,000
cases had a relatively low amplitude. Each successive shock stream applied
to a particular equilibrium government had a greater amplitude, causing
greater perturbations to the party-specific dimension weights in the base

2'In Laver and Shepsle (1996) we developed the German and Irish cases both as a two-dimen-
sional and a three-dimensional portfolio allocation situation. Here we present only the former to
keep exposition simple and the running of the simulations manageable.
quot;The program itself (called WINSET), program manuals, and sample data files can be down-
loaded over the Internet for personal academic use by connecting to FTP.TCD.IE, logging on as
user quot;anonymousquot; and supplying a complete e-mail address as a password. The latest release ver-
sions of all files are located in the directory /PUB/POLITICS. All analyses in this paper can be rep-
licated using this program and the data in Table 2.


Table 2. Party Positions, Legislative Seats, and Dimension Weightings
Germany 1987

FOREIGN
FINANCE AFFAIRS
Increase taxes ( 1) Pro ( I ) vs.
vs. cut services (20) anti (20) U.S.S.R.
Seats Position Weight Position Weight
Christian Democratic Union1
223 13.5 13.9 9.8 12.4
Christian Social Union (CDUICSU)
186 6.5 12.5 4.6 13.2
Social Democratic Party (SPD)
46 15.7 15.2 6.6 13.8
Free Democrats (FDP)
42 5.2 9.8 4.0 9.8
Greens (G)

Total
Majority threshold
Source: Party positions taken from Laver and Hunt (1992, 197).

Ireland 1992

FOREIGN
FINANCE AFFAIRS
Pro (1) vs.
Increase taxes ( 1 ) anti (20) British
vs. cut services 120) aresence in N.I.
Seats Position Weight Position Weight
68 13.1 12.6 15.8 12.4
Fianna FBil (FF)
45 15.0 15.5 10.0 12.3
Fine Gael (FG)
33 6.9 13.0 12.4 10.5
Labour (Lab)
10 17.6 16.4 10.6 10.7
Progressive Democrats (PD)
4 4.5 12.5 7.6 15.3
Democratic Left (DL)
5
Others

Total
Chair
Maioritv threshold
Source: Party positions taken from Laver (1994, 163)

case. In effect, this amplitude-the standard deviation, s-was a knob that
we could turn to increase the violence of the shock stream to which we ex-
posed each government.

47

Party-specific dimension weights in the dataset were denominated on a
scale from one to 20. The mildest shock stream we report was generated by
adding to these weights random disturbance terms drawn from a normal dis-
tribution with a mean of zero and a standard deviation of 1.00, and holding
all other parameters constant. Since the standard deviation of the shock
terms in this most tranquil shock stream was 5% of the maximum party-spe-
cific dimension weight, almost all shocks would leave dimension weights
within 10% of their original base case value. After a thousand quot;runsquot; (sets of
random draws) at this setting for s , we then produced another stream of
1,000, using a standard deviation of 1.50; we then generated a shock stream
using an s of 2.00, and so on. The effect was rather like putting a model of
the government under investigation into a wind tunnel, then exposing the
modeled government to ever more violent winds so that we could observe
when and how it was ultimately blown apart.
In order to estimate the maximum possible susceptibility to agenda
shocks of the equilibrium government under investigation, given a fixed
configuration of party policy positions and decisive structure, we also gener-
ated a shock stream in which party specific dimension weights were simply
random numbers drawn from a uniform distribution on the [I, 201 interval.
On these most extreme assumptions, the stream of agenda shocks is so vio-
lent that party specific dimension weights in each shocked case cannot be
predicted at all from those in the base case.
The results of exposing the governments under investigation to shock
streams with amplitudes from 1 to 3.5 are given in Table 3, each cell of
which reports the results of a 1,000 case ~ i m u l a t i o nThis also shows the
.~~
results of the maximal shock stream, with totally random dimension
weights. The results in Table 3 show, for a given amplitude of shock stream,
s, the proportion of cases for which the base case equilibrium was no longer
an equilibrium in the shocked case. This is reported as the governmental
death rate per shock in the table. Note in this instance that a shock to party-
specific dimension weights cannot change the identity of the dimension by
dimension median cabinet, which must remain the same as the base case in
all shocked cases, since party positions are not being altered. What changes
with the shocks is the relative salience of each dimension to a party. This in
turn determines whether or not some alternative cabinet is preferred by a
majority to the base case dimension-by-dimension median cabinet.
To take a specific example from Table 3, if exposed to an agenda shock
stream of amplitude 2.00, then the German government in 1987 had a death
rate per shock of 0.057. In other words 57 out of 1000 agenda shocks in a
23Shock streams of amplitude greater than 3.5 caused problems in simulations of agenda
shocks using this dataset since, given the base case configurations of party specific dimension
weights, they sometimes generated negative dimension weights.


Table 3. Simulated Agenda Shocks; Germany 1987,

Ireland 1992

Dimwt(p, d) = BaseDimwt(p, d) + Normal (0, s)
Shock streanz Governn~ental
anzplitude, s. death rate/shock
Gernzany Ireland

random
dimension
weights

stream of this amplitude destabilized the status quo. This gives an expected
duration of 1,000157, or 17.5 of the shocks in this stream.24In contrast, the
Irish government forming in 1992 had an estimated death rate per shock of
0.004 in a shock stream of similar amplitude, giving an expected duration of
250 of the shocks in this stream.
If we attempt to relate these simulations to the absolute real-time sur-
vival rates of the governments under investigation, of course, we are ham-
strung by having no idea whatsoever of the most appropriate value of s to
model agenda shock streams in a particular real-world case. The simulations
do nonetheless give us some very useful insights. In the examples explored
in Table 3, for example, we do observe that the German government has a
higher death rate than the Irish government for every value of s investigated.
(And, given the figures in the table, it seems reasonable to extrapolate and
interpolate results for other values of s to infer that this finding holds for all
values of s.) These results do, therefore, indicate strongly that, other things
being equal, the German government in 1987 was distinctly more suscep-
tible to agenda shocks than was its Irish counterpart in 1992.25

241f we know the mean real-time frequency of agenda shocks in a stream of amplitude s = 2,
then this would allow us to estimate an expected duration in real time. But of course we do not.
quot;To reiterate, however, if such shocks were decidedly less frequent in real-time Germany than
in real-time Ireland, it is perfectly legitimate to expect a German government lasting longer than its
Irish counterpart.

49

Table 4. Simulated Policy Shocks: Germany 1987,

Ireland 1992

Position(p, d) = BasePosition(p, d) + Normal (0, s)
Shock stream Governmental
an~plitude, . death ratehhock
s
Germany Ireland

random

party

positions

Policy Shocks
The susceptibility of each government to policy shocks is explored in a
closely analogous way in Table 4. The results in this table were estimated by
simulating streams of shocked cases, each of which was generated by add-
ing random disturbance terms to the party policy positions reported in Table
2, holding all other parameters constant. Party policy positions were also
expressed in the data on a scale running from one to 20 for each dimension.
The random disturbance term added to each policy position on each dimen-
sion was independently drawn from a normal distribution with a mean of
zero and a standard deviation of s. The most tranquil shock streams had a
standard deviation of 0.5, so that most shocked policy positions were once
more within 10% of their original value. Ever more violent shock streams
were generated, up to a maximum amplitude of 5.0. Once more the effects
of a maximal shock stream were calculated as a benchmark, given base case
dimension weights and decisive structure, using a shock stream in which
party policy positions were drawn completely at random from a uniform dis-
tribution on the [ I , 201 interval.
The results of applying streams of policy shocks to the two cases under
investigation is shown in Table 4. In striking contrast to the impact of
agenda shocks, policy shock streams of equivalent amplitude had a much

50

more destabilizing effect. This almost certainly arises from the vital role of
the dimension-by-dimension median cabinet in determining the equilibrium
in this model, and the fact that perturbations of party policy positions can
obviously change this in a way that perturbation of party-specific dimension
weights cannot. Table 4 also shows that equivalent streams of policy shocks
had a more destabilizing effect on the 1992 Irish government than on the
1987 German government. The Irish government was in particular much
more sensitive to relatively small perturbations in party policy positions,
with a death rate per shock of 0.257 in the shock stream of amplitude 0.5, as
opposed to a death rate in equivalent circumstances of 0.001 for the German
government. The Irish government is more susceptible than the German
government to policy shock streams of every amplitude investigated or rea-
sonably interpolated.
This suggests very strongly that the configuration of Irish policy posi-
tions puts the Irish case much closer to one or more strategic thresholds than
was the German case, the latter thus requiring more vigorous policy shocks
to destabilize it. The net result was that the Irish government was much more
vulnerable to policy shocks.

Public Opinion Shocks
The susceptibility of each government to public opinion shocks is ex-
plored in Table 5. Streams of public opinion shocks were generated by per-
turbing party seat totals to simulate party expectations about the results of an
immediate election. Each party seat total was perturbed by adding a random
disturbance term drawn from a normal distribution with a mean of zero and
a standard deviation of (s) x (S,)/20, where S, was the number of seats won
by party p in the base case and s was once more a parameter describing the
violence of the shock stream. Thus, when s was set to one, the standard de-
viation of shocks was 5% of the original party seat total, making it broadly
analogous to values of s in other types of shock stream. In this relatively
tranquil shock stream, almost all shocks would change seat totals no more
than 10% from their original value. The impact of ever more violent shock
streams was also modeled, to a maximum of s = 5. In addition, as a bench-
mark of the impact of maximal public opinion shocks, a series of shocked
cases was generated in which party seat totals were randomly drawn from a
uniform distribution on the [O, 1001 interval. In all cases, the number of seats
controlled by each party in each shocked case was totaled, and the majority
threshold recalculated accordingly.
The quot;overallquot; results in Table 5 show the vulnerability of the two equi-
librium cabinets under investigation to public opinion shocks that give some
party an incentive to force an early election. The results of these simulations
show the Irish government in 1992 to have been much more susceptible to

51

Table 5. Simulated Public Opinion Shocks:

Germany 1987, Ireland 1992

+ Normal (0, s BaseSeats(p)/20)
Seats(p) = BaseSeats(p)
Shock stream Governmental
amplitude, s. death rate/shock
Germany Ireland
CDU very FF very
overall strong overall strong

0.046 0.011
random
(0.047 FDP) (0.066 Lab)
party
seats

relatively modest levels of this type of public opinion shock than was the
German government in 1987. In a shock stream that almost never perturbs
party seat totals by more than 10% of their original value (s = I), the Ger-
man government has a death rate per shock of 0.005, while the Irish govern-
ment had a death rate of 0.264.
We should recall, however, that the portfolio allocation model identifies
as destabilizing only those public opinion shocks that make some member of
a coalition cabinet quot;very strongquot; (see Laver and Shepsle 1996, chap. 4)
when before it was not. Public opinion shocks improving the strategic posi-
tion of the opposition, however dramatically, should have no effect on the
stability of the government; neither should shocks improving the electoral
prospects of government members somewhat, but not enough to secure for
them a more favorable equilibrium government. Thus Table 5 also shows the
proportion of shocks in each shock stream that made the PM's party very
strong. While other public opinion shocks might destabilize governments if
we ignore the PM's control over the calling of elections, only these more re-
stricted types of shock can give the PM an incentive to force an election and
be in this way d e ~ t a b i l i z i n g . ~ ~

26As it happens, never in the shock streams investigated was the non-PM government party
made very strong.

52

These figures show that the asymmetry between the PMS party and oth-
ers in regard to calling an election makes a very substantial difference to the
impact of public opinion shocks on government survival. In both countries,
the government was much less vulnerable to public opinion shocks once the
PM's control over calling an election was taken into account. Many of the
simulated public opinion shocks helped opposition parties, which have no
control over calling an election. Other public opinion shocks may have fa-
vored the government parties, but not enough to improve their position in
the government expected to result from an immediate election. We once
more have striking evidence that institutional details such as this can make a
big, big difference.

Where Are We Now?
The essential point of this paper has been to develop a theoretical ac-
count of government survival within the critical events tradition. Our ap-
proach develops the ideas of the original events theorists, who had no model
of government equilibrium and thus took every government as an equilib-
rium in its own terms. Instead, however, we take a well-specified model of
government equilibrium and explore ways in which critical events affect
particular equilibrium governments. Our approach complements the one re-
cently put forward by Lupia and Strom, who use a model of government
equilibrium to characterize government survival analytically, with analytical
complexities restricting the substance of their account to only one type of
critical event in (untypical) three-party systems. We use simulations to side-
step analytical complexities, and apply these to a model that identifies the
impact of different classes of critical event in party systems of any size.
Our simulation technology allows us to explore exhaustively aspects of
the stability of individual quot;basequot; cases, and in this paper we explored the
cases of Germany in 1987 and Ireland in 1992. For the particular cases un-
der investigation, we can use simulations based on the portfolio allocation
model to look at the susceptibility of different governments to different
types of shock. As a result of this we see that cases which might on the face
of things look rather similar can in fact be unstable in different ways, with
some types of critical event being more dangerous for some governments
and other types of critical event being more dangerous for others. The ap-
proach thus allows us to use the model to make what is really quite a system-
atic and fruitful exploration of individual cases. As such it is an example of
something that is relatively rare in political science-the use of a rigorous
general model in specific case studies.27

27B~t nothing comes free, o f course. The very richness that commends the approach to case
studies, that characterizes each case in terms o f a range o f parameters, and that thereby identifies dif-
ferent types o f critical event which may have a bearing on government stability, makes each case

53

The question that remains concerns whether it is actually useful, or even
possible, to talk about government survival in general. Two five-party sys-
tems with identical decisive structures, for example, can have very different
stability characteristics, according to our approach, arising from different
configurations of party ideal points. One configuration of ideal points may
leave some crucial indifference curve very close to a strategic threshold-
the other may not. Two five-party systems with identical configurations of
party ideals and dimension weights may also have identical decisive struc-
tures, but one decisive structure may derive from a set of party weights for
which small changes in seat totals change the decisive structure, while the
other requires much larger changes in seat total to change the decisive struc-
ture. Again, the two superficially identical governments may have very dif-
ferent stability characteristics as a consequence.
Given all of this, and despite the fact that we can use a model to analyze
individual cases in a rigorous manner, general statements about government
stability should only be made with caution. This implies that previous gen-
eral statements about government stability may perhaps have been rather too
sanguine, and that we should be grateful for the solid ground that the model
places under our feet when we attempt the systematic analysis of individual
cases.

Manuscript submitted 9 October 1996.

Final manuscript received 18 February 1997.

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