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chapter 12
..............................................................
PIVOTS
..............................................................
keith krehbiel
Institutional analysis of political behavior is increasingly common in political
economy and political science. In its most complete form, such analysis begins with
a blend of substantive knowledge, good instincts, or possibly just lucky guesses,
about which constitutional, legal, or organizational features politicians regard as
constraining their behavior. Constraints are then characterized in a game form, an
equilibrium concept is specified, the game is solved, predictions are derived, and
tests are conducted. Comparative institutional analysis is a logical extension in which
a common political setting—such as a legislature—is studied by juxtaposing and
testing the predictions of two or more institutional theories.
Pivot theories are increasingly common in such research. Their key characteristics
can be classified as exogenous (assumed) or endogenous (derived). Exogenous fea-
tures include preferences, players, policy space, and a status quo point: a policy that
remains in effect if no other policy displaces it in the course of decision-making.
Endogenous features include statements of equilibrium behavior, characterization
of stable outcomes, and identification of a corresponding gridlock interval:asetof
potential status quo points where in the status quo policy does not change in equi-
librium even though a majority of voters prefers change. Once solved, pivot theories
earn their adjective by focusing on pivot points (or simply pivots): the preferences and
identities of a subset of players who, in equilibrium and for some status quo point(s),
are crucial in the outcome.
1
This chapter has two objectives: to provide an accessible overview of pivot theo-
ries, and to develop and illustrate a new form of comparative institutional analysis
as a means for discriminating between such theories. Although in principle the
substantive focus could be on any collective choice organization, in practice more
∗
Discussions with Nolan McCarty and Jon Woon and comments from Brian Crisp, Ken Shepsle,
Barry Weingast, and Donald Wittman are gratefully acknowledged.
¹ Increasingly precise notions of crucial are given below.
224 legislative pivots
pivot theories have been developed to study US national decision-making than other
types of decision-making. Consequently, the substantive motivation and empirical
application center on US politics.
1 ABaseline:Median Voter Theory
.............................................................................
The simplest pivot theory is undoubtedly the well-known median voter theory (Black
1958).
2
In the present context, the median voter model has several noteworthy charc-
teristics that make it a useful baseline against which to compare alternative models.
First, because the final collective choice in this model is always the policy correspond-
ing with the most preferred policy (or ideal point) of the median voter, the status quo
has no effect on outcomes. Second, the median voter is always pivotal: that is, he is not
only a member of all winning coalitions but also a necessary and sufficient member
of all minimum winning coalitions. Third, gridlock never occurs: that is, new policies
are passed whenever there exists a majority favoring such passage. Finally, although
the median voter can be seen as a pivot theory, it should be viewed as a special case
inasmuch as none of these results hold once institutional details are added to the
framework.
2 Super-majority Pivots:The Pivotal
Politics Theory
.............................................................................
The pivotal politics model as introduced (Krehbiel 1996) and elaborated (Brady
and Volden 1998;Krehbiel1998;WawroandSchickler2004) embraces US national
law-making as its substantive focus.
3
Previously, a rich tradition of scholarship had
addressed the consequences, or perhaps lack thereof, associated with the increasingly
regular pattern in US politics of split party control in the executive and legislative
branches. The conventional wisdom was that the ostensibly increasing tendency for
policy stalemate—gridlock in the vernacular of the 1980sand1990s—was predomi-
nantly attributable to divided government. For example, when a Republican president
confronted a Democratic Congress, as was common in the post-Second World War
period, it seemed only natural that Democrats would dig in their heels to impede,
if not deny, enactment of the president’s agenda. In contrast, when party control is
unified across branches of government, Congress is supportive rather than resistant
to presidential initiatives, so major policy change can occur. Or, so it was said.
² The standard model assumes a unidimensional choice space, single-peaked preferences, an odd
number of voters, simple-majority voting, and an open amendment procedure. These assumptions will
likewise hold for other pivot theories to be considered.
³SeealsoMo2001 and Nacif 2003 for applications in Korea and Mexico, respectively.
keith krehbiel 225
Conventional wisdom is meant to be challenged, and few if any scholars of the US
political system have amassed a more impressive set of challenges to received wisdom
than David Mayhew. In his 1991 tour de force Divided We Govern,Mayhewexecuteda
novel, laborious, and deeply insightful research design to address the question: does
it matter much whether the government is divided or unified? In terms of passing
major legislation (coded subjectively but convincingly), the answer was an emphatic
“no.” Governing regimes in US politics invariably need to exert substantial effort to
overcome various obstacles to policy-making, but, as an empirical matter, this is true
in unified as well as divided government. Moreover, when the natural propensity
for gridlock is overcome, the winning coalitions credited for such achievements
are almost invariably larger than minimum majority in size and thus bipartisan in
composition.
In this context, two stylized facts served as the impetus for the development
of the pivotal politics theory of law-making. First, why is gridlock common and
seemingly independent of party control? Second, why, when gridlock ceases to exist,
are winning coalitions large and bipartisan? The answer offered by pivotal politics
theory fits in a nutshell with room to spare: super-majoritarianism. Its concrete
manifestations and analytic characterizations are somewhat more intricate but, nev-
ertheless, can be made transparent to anyone with a basic grasp of spatial voting
models.
Borrowing from median voter theory, the pivotal politics model postulates that,
for any given issue the government may consider, a single, primary dimension is
sufficient for representing decision-makers’ essential conflicting interests. Formally,
each player (legislators in a unicameral law-making body plus a president) has sym-
metric, single-peaked preferences over a unidimensional policy space, x ∈ R. These
assumptions on preferences have been common, beginning with the median voter
theory and extending through the important movement of “new institutionalism”
pioneered by Shepsle (1979) and his colleagues (e.g. Denzau and Mackay 1983; Shepsle
and Weingast 1987). Also common has been the assumption that, on any given
dimension, there exists an exogenous status quo point, q, which represents the policy
outcome in the event that the players of the game fail to come to an agreement on the
new policy, x.
The pivotal politics theory deviates from its predecessors in its specification of
voting rules. A noteworthy feature of the US Senate is its conferral, first by precedent
and eventually codified in its standing rules, of the right of any of its individuals to
engage in “extended debate,” i.e. to filibuster. Depending upon the period of history
studied, such rights effectively raised the voting threshold for law-making activity
from a simple majority standard of (n +1)/2 to a super-majority standard of 3/5or
2/3. (For present purposes, we will confine attention to the contemporary case of
3/5 cloture.) Furthermore, the pivotal politics theory puts the president into the law-
making equation in a similarly super-majoritarian way. In this instance, the justifica-
tion lies in the US Constitution. The president’s signature is a sufficient condition for
policy change on any legislation Congress passes, but, in the absence of the president’s
signature, legislation either fails or requires a veto override by two-third majorities in
the legislative body.
226 legislative pivots
1 2 3...
35 40 45 50
cut-point if m
were proposed
9950...
q
f
m
2f−q
p
∗
Fig. 12.1 Cloture super-majoritarianism makes f pivotal
Whereas prior spatial models relied upon constraints on amendment activity to
obtain results different from those of median voter theory,
4
the incorporation of
super-majoritarian voting rules in pivotal politics theory is consequential even in
the absence of such constraints. Figure 12.1 illustrates the central intuition, which is
generalized and illustrated more completely in Figure 12.2. Suppose there are ninety-
nine legislators distributed uniformly over the interval [1, 99]. Suppose also that
the collective choice the last time government considered the issue in question was
q = 35. Clearly, a majority coalition exists that would like to move the policy to the
point x = 50, the median voter’s ideal point. If this were attempted, however, every
legislator whose ideal point lies to the left of 42.5 (the midpoint between 35 and 50)
has an incentive not to let the policy proceed to a vote. Armed with the right to
filibuster the bill, these legislators have a credible threat. The only way to proceed is to
invoke cloture, which, according to contemporary Senate rules, requires a 3/5vote.
The question from the perspective of the proponents of a rightward shift in policy
becomes: by how much can the proposed bill exceed the status quo and yet persuade
the pivotal voter on cloture to cast his vote in favor of closing debate?
The identity of the filibuster pivot f is determined by the cloture rule. Specifically,
the filibuster pivot in this 99-person scenario is the 40th voter from the left and whose
ideal point equals 40.
5
If he votes to invoke cloture, the filibuster is terminated by a
vote of 60–39 > 3/5. If he votes against the cloture motion, however, the filibuster
persists by a vote of 59–40 < 3/5. Given this fact, and a somewhat more subtle
fact that the filibuster pivot—so defined—has interests congruent with the thirty-
nine legislators to his left in this scenario, the optimal proposal strategy of any bill
proponent is 45.
⁴ For example, Romer and Rosenthal 1978 characterized an agenda setter as a first-stage player who
crafts a proposal for an electorate that is restricted to accepting or rejecting the single proposal (and
where rejection is tacit acceptance of an exogenous status quo). This is, in effect, the denial of
amendment rights to the second-stage players, i.e. a closed rule. Shepsle and Weingast 1987 impose
similar constraints in the legislative context, but subsequent to open-rule consideration on the floor.
⁵ A common error is to designate the 40th voter in the US Senate as the filibuster pivot because, with
N = 100, a 60–40 vote invokes cloture. However, then the Senate’s filibuster pivot is actually the 41st voter
(the 60th from the right), because hers is the last, and thus pivotal, vote needed for the cloture motion to
carry. I use N = 99 in the example only because it simplifies matters to have a unique median of 50.
keith krehbiel 227
Gridlock Interval
Outcomes
Status quo q
p
p
v
v
m
m
f
f
I II III
No policy change
IV V
Fig. 12.2 Equilibrium in the pivotal politics theory
It is merely an analytic convenience that the proposer is the median voter. Any
right-of-median voter would make the same proposal because he or she faces the
same optimization problem: to make the filibuster pivot indifferent between the
optimal proposal p
∗
and the status quo q. Any proposal less than 45 is not optimal
for such proposers because it fails to extract all available rents. Any proposal more
than 45 is not optimal for such proposers because it triggers a successful filibuster
and leaves the undesirable status quo point in effect. Only with x =45isthereno
alternative proposal that can both beat a filibuster and gain a majority. Therefore, the
equilibrium proposal in such cases is, in general, 2 f − q.
From the opposite end of the spectrum—that is, a status quo point that lies on the
upper end of the spectrum—the president and the veto pivot (the 66th legislator in
this scenario) are the constraints against which bill proponents optimize. Dispensing
with an example, suffice it to say the equilibrium proposal is 2v −q.
6
With only a couple of qualifications, these two examples of pivotal voters serve
effectively as building blocks for the complete statement of equilibrium in the pivotal
politics game. Figure 12.2 graphs all possible equilibrium outcomes (vertical axis) as
a function of variable status quo points and fixed ideal points (horizontal axis). As
many as five types of behavior occur in the model, defined in terms of the extremity
of the status quo relative to pivotal legislators’ ideal points. For status quo points
in the most extreme intervals, I and V, the super-majoritarian constraint does not
bind proposal-making, and the median voter outcome results. Therefore, the graph is
⁶ This example assumes that the president’s ideal point p is greater than 66. Substitute p for v
otherwise. Formally, the game is multistage, finite, and complete information in structure. As an analytic
convenience, it suffices to focus on the behavior of at most four players: the median voter, a president, a
2/3 veto pivotal voter on the president’s side of the median, and a 3/5 filibuster pivot on the side of the
median opposite the president (see Krehbiel 1996)
228 legislative pivots
flat at m throughout these intervals. For moderate status quo points, intervals II and
IV, the pivot constraints do bind and the behavior results in partial convergence as
characterized in Figure 12.1. Finally, for moderate status quo points, defined precisely
as those in the closed set [ f,v], gridlock occurs. That is, any policy that a majority
coalition prefers to the status quo elicits opposition of one of the pivotal voters, f or v.
Moreover, the pivotal voters have a credible threat of opposition stemming directly
from the super-majority requirement.
Several empirical implications emerge from the pivotal politics analysis. For in-
stance, the model accommodates the two stylized facts about American national law-
making. First, gridlock is common in unified and divided government alike. Indeed,
the primitives of the model exclude any direct reference to partisan identities. Players
are simply agents who have preferences over policies and who optimize accordingly.
Second, when gridlock is broken and a new policy is chosen, the coalition that sup-
ports such a policy is invariably greater than a minimum majority set of legislators.
In addition to accounting for these stylized facts, the theory also has implications for
variation in legislative productivity, coalition sizes, switching behavior in roll calls on
cloture and veto overrides, and budget processes. With mostly positive findings, these
predictions are explored extensively in Krehbiel (1998) and Brady and Volden (1998).
However, the pivotal politics theory is also subject to widespread criticism, with
two sins of omission drawing the most attention. First, the theory strays from the
new institutionalism tradition of legislative modeling based on assumptions about
restrictive amendment procedures and agenda-setting by preference outliers. Second,
the theory is deafeningly silent about political parties.
3 Party Pivots:The Procedural
Cartel Theory
.............................................................................
Attributed to John Dingell, the former and formidable chairman of the House
Committee on Energy and Commerce, a favorite quotation of congressional scholars
is: “You take substance and give me procedure, and I’ll screw you every time.” In this
vein, it is not surprising that students of legislative behavior are sensitive to the many
ways in which institutional features can give rise to outcome-consequential strategic
behavior. Nor is it surprising that procedural control and partisan motivations
regularly go hand in hand. So, for example, in an industrious research agenda
spanning more than a decade, Gary Cox and Matthew McCubbins have been at
the forefront of efforts to advance the thesis that, through procedures, the majority
party is the dominant entity in legislative politics, both in the USA and abroad. The
foundational model on which the thesis is built is called procedural cartel theory
which—while presented as a much different substantive model of law-making from
median voter or pivotal politics theory—nevertheless satisfies the defining analytical
features of pivot theories.
keith krehbiel 229
Outcome
I II III IV
Gridlock Interval
No policy change
Status quo, q
m
m
r
2r−m
r
2r − m
Fig. 12.3 Equilibrium in the procedural cartel theory
Consider analytics first. The core model in Cox and McCubbins’s (2005) Setting the
Agenda is clearly recognizable as the gatekeeping model of Denzau and Mackay (1983).
Much as the pivotal politics theory is reducible to four players and four stages, the
Denzau–Mackay/Cox–McCubbins theory is reducible to two players and two stages.
In stage one, an agenda-setter denoted by r—e.g. the Republicans’ median voter—
has “unconditional agenda power,” by which the authors mean the ability to block
any and all attempts to change the exogenous status quo. In stage two, if and only if
a stage-one bill is proposed, the full legislature selects the median voter’s ideal point
under an open rule. The gatekeeping assumption has an immediate implication: a
necessary condition for policy change is that a majority of the majority party prefers
the legislature’s median voter’s ideal point to the status quo. Conversely, gridlock
prevails whenever this condition is not met.
Figure 12.3 illustrates the equilibrium of the gatekeeping model in parallel fashion
with the pivotal politics diagram in Figure 12.2. Clearly, the majority party median, r,
resembles the pivotal voters f and v in pivotal politics theory. His consent, like that of
the veto or filibuster pivot, is a necessary and sufficient condition for policy change.
Although the party cartel theory satisfies the generic features of pivot theories,
several distinctions between it and the earlier pivotal politics model are subjects of
ongoing debate in the field.
First, the procedural pivot (i.e. majority party gatekeeper) in the cartel model is not
in general indifferent between the final policy (the legislative median) and the status
quo, as is often the case for pivots in the pivotal-politics model. This observation
follows from the fact that the majority party median r is not a constraint against
which other players optimize but rather plays the role of dictatorial obstructionist
whenever the status quo lies within |r −m| units of his ideal point, r .
Second, like the pivotal politics theory, the procedural cartel theory also pro-
vides an account for gridlock. However, within the cartel theory’s relatively large
range of status quo points that cannot be changed in equilibrium—namely, those in
(m, 2r −m)—half of these policies (r, 2r −m) are not Pareto optimal with respect to
230 legislative pivots
the two potential pivots. That is, both pivots can be made strictly better off by policies
in the other half of the gridlock interval. Furthermore, alternative procedures exist
that can address this problem. For example, suppose the House gave the committee
an ex post veto instead of a gatekeeping right (which is equivalent to an ex ante
veto). Then for any q in (r, 2r −m),themedianvotercanpre-emptthevetoby
selecting a policy between m and r that both pivots prefer to q, and such a policy
will be adopted to their mutual benefit.
7
This fact leads to the following puzzle:
why would the majority party median (as the presumed procedural dictator) and the
legislative median (as the implicit constitutionally stipulated chooser of “the rules of
[the House’s] proceedings”) consent to using a gatekeeping rule when other available
rules lead to Pareto-superior outcomes?
8
Third, it is questionable empirically whether the majority party in fact has a
monopoly agenda setting right in the manner presumed in the procedural cartel
theory. If codified procedures are consulted, the assumption of an institutionalized
majority party gatekeeping right is difficult to defend. Under Rule XV of the House,
for example, a simple majority of the House can discharge legislation from obstruc-
tionists or so-called gatekeepers. In the Senate, the roughly comparable procedural
mechanism is for an individual to propose a non-germane amendment to legislation
before the body.
Finally, the designated gridlock interval in the party cartel theory is distinctively
lopsided relative to the legislative median. Gridlock favors the majority party at the
expense not only of the minority party but also the chamber median voter. Yet, the
theory predicts that in all observable instances of successful law-making, the outcome
is the legislative median, not the majority party median. For policies to be non-
centrist, therefore, depends crucially upon a historical path in which erstwhile median
outcomes somehow become stuck away from the center and within the current-
period gridlock interval. This inescapable historical endogeneity of the status quo
is a critical concern below.
4 Comparative Empirical Analysis
.............................................................................
A recent and instructive instance of comparative institutional analyis focuses on two
of the three pivot models reviewed above. In order to test the procedural cartel and
median voter models “head to head,” Cox and McCubbins (2005,ch.3)advocate
empirical analysis of roll rates.Apartyissaidtoberolledwhenamajorityofits
members vote against a measure, a majority of the opposite party’s members vote for
a measure, and the measure is enacted.
9
The rate at which a party is rolled, therefore,
⁷ The optimal such proposal is b =2r − q. This is an instance of the Romer–Rosenthal model (1978).
⁸ Crombez, Krehbiel, and Groseclose 2006 generalize this argument.
⁹ In principle, enactment is not a necessary condition for a roll to occur. In practice, however, the
authors confine their attention to votes on final passage. They defend this choice on grounds that such
votes uniquely and clearly represent binary choices between the exogenous status quo and the proposal
keith krehbiel 231
No rolls
−1
No rolls
Minority party rolls
Majority party
gatekeeping
I III
0
II IV V VI
1
q
2d − m 2r − m
|d − m|
dm r
|r − m|
Fig. 12.4 Roll rate dependence on the distribution of the status quo
is defined as the proportion of final-passage roll calls on which these conditions are
met. A party with a low roll rate is presumed to have agenda power, while, conversely,
a party that is rolled often is said to be weak.
An immediate implication of the procedural cartel model is that a rational gate-
keeper, in this case the majority party, is never rolled. Consequently its roll rate
should be constant and zero. The minority party is expected to be rolled regularly
because it has no presumed gatekeeping rights. In contrast, the median voter model,
which Cox and McCubbins call the “floor agenda model,” implies that roll rates
for each party will be a function of the distance between that party’s median voter
and the legislature’s median voter. Cox and McCubbins then attempt to explain
variation in roll rates via regression analysis. Let r and d respectively denote the
majority and minority party medians, respectively. They estimate regressions of the
form:
Minority roll rate = · + ‚|d −m|+ ε. (1)
Majority roll rate = · + „|r − m| + ε. (2)
The logic of the test is illustrated in Figure 12.4. Assume that at any given law-making
opportunity, legislators’ ideal points are spread out over a finite interval, say [−1, 1].
For ease of illustration, suppose the median of the minority party is d = −1/3, the
chamber median is m = 0, and the majority party median is r =1/3. Reflection
points
10
of the two parties therefore lie at −2/3and2/3, and the policy space is
conveniently partitioned into six segments, I–VI.
Clearly, predicting roll rates under the cartel theory (or any given pivot model)
requires assumptions about the distribution of status quo points. In the simplest case,
suppose q is distributed uniformly over [−1, 1]. Then status quo points will arise in
segmentsIorVIwithprobability1/6+1/6=1/3. None of these status quo points
elicit rolls, because majorities of both parties prefer the cartel-theoretic equilibrium
as possibly amended. Accordingly, such votes are regarded as more appropriate grounds for inference
than would be, say, procedural votes, frivolous amendments, etc.
¹⁰ A reflection point of, say, a party median p with respect to the chamber median m,denoted
R(p, m), is the point whose distance from p equals that between p and m butthatliesonthenon-m
side of p. With distance-based (Euclidean) preferences, R(p, m)=2p − m. By construction the pivotal
player with ideal point p is indifferent between m and its reflection point about p,i.e.R(p, m).