Pivotal Politics and Initiative Use in the American States
Frederick J. Boehmke
Tracy L. Osborn
Emily U. Schilling
University of Iowa
June 08, 2015
ABSTRACT
We incorporate the role of pivotal players in the legislature into a spatial model of the direct
initiative process to study the interplay between these two policymaking institutions. We show
that the size of the standard gridlock interval relates to the ability of the legislature to preempt
initiatives, and that the presence of the initiative process often reduces the size of the traditional
gridlock interval. Further, we find that initiatives can also arise in situations without legislative
gridlock because pivotal players sometimes prefer to block legislation in order to ensure an
initiative proposal passes. Specifically, we find that as the distance between the median voter and
the pivot player closest to the initiative proposer increases, initiative use also increases.
Empirical analysis of initiative use in the American states supports this prediction.
Corresponding author: [email protected]. Boehmke is Professor of Political Science and Director of
the Iowa Social Science Research Center; Osborn is Associate Professor of Political Science; Schilling is a Ph.D.
candidate in Political Science. We thank Edward Lascher, Justin Esarey, and seminar participants at Emory
University, the Unversity of North Carolina, Chapel Hill, and Washington University for helpful comments and
suggestions.
1
Introduction
The direct legislation process, particularly the initiative and referendum, is portrayed as a
way for citizens and organized interests to influence public policy when state legislatures refuse
to act. As envisioned by Progressive reformers over a century ago, institutions such as the direct
initiative process would serve as a “gun behind the door” to encourage legislatures to pass
policies concordant with citizens’ preferences. Despite valid concerns about the contemporary
practice and use of direct legislation, existing scholarship suggests that the initiative process still
generally serves the interests of the many rather than the few (Matsusaka’s 2004; Gerber 1999;
Boehmke 2005a).
The relatively infrequent use of the initiative process comports with its intended role as a
corrective rather than a primary means of policymaking. Even during the resurgence in initiative
use in recent decades, the most frequent users only experience an average of two successful
measures per year (Boehmke 2005a). The success of such measures embodies the direct effect of
the initiative process, whereby citizens and organized interests influence policy directly through
the passage of proposals rather than through the legislative arena.
In addition, theoretical accounts of the initiative process highlight a less observable – though
perhaps more important – indirect effect. These models suggest that legislators, cognizant of the
threat of a ballot measure, strategically pass policies closer to the median voter in order to
preempt a successful proposal (see, e.g., Gerber 1996; Matsusaka and McCarty 2001; Boehmke
2005a). Both forms of influence thereby lead direct legislation to facilitate policy responsiveness
to the median voter.
An alternate stream of work focuses on the role of legislative institutions that foster gridlock
and thus hinder policy responsiveness (Binder 1999; Brady and Volden 1998; Cox and
2
McCubbins 1993). Krehbiel (1998) embodies one strand of this research by arguing that
procedures such as the filibuster and the executive veto create obstacles that may thwart elected
officials’ ability to implement policy change and thereby decrease policy responsiveness.
As political institutions, therefore, the initiative process and legislatures often sit in
opposition to each other: direct legislation provides an incentive for policymakers to moderate
policies towards voters; whereas, supermajoritarian legislative procedures can have a deterrent
effect on policy movement. While academic work has overlooked the interplay between these
institutions, the initiative process’ ability to counteract legislative inaction has long been
recognized in the popular dialogue. For example, the Los Angeles Times stated that “groups are
trying to fill the Sacramento power vacuum by bypassing the legislative gridlock and going
directly to the voters” (Skelton 2011).
We show that simultaneously considering supermajoritarian legislative procedures and direct
legislation in the policymaking process advances our understanding of both institutions. Further,
by assessing gridlock and the initiative in tandem, we also speak to the common perception that
direct legislation serves as a release valve when gridlock thwarts policy change. We do this by
developing a formal model of the policymaking process in initiative states that fuses the pivotal
politics model of legislative policymaking (e.g., Krehbiel 1998) with spatial models of the
initiative process (e.g., Gerber 1996).
Our integrated model generates predictions about the conditions under which legislative
preemption fails and initiatives appear on the ballot. Primarily, we find that initiatives are not a
response to legislative gridlock; rather, they occur because pivotal actors in the legislature prefer
to block legislation in favor of their preferred outcome offered by the initiative process. We also
find that the initiative process generally reduces the size of the traditional legislative gridlock
3
interval. We assess the first prediction by modeling initiative use as a function of the relative
locations of pivotal actors with three distinct tests drawing on different measures of state
legislators’ ideal points, finding consistent support for our theory. Overall, our work highlights
the importance of considering the interplay between multiple institutions in a political system.
Modeling the Initiative Process and Pivotal Politics
In this section we present our model that combines policymaking via the legislature and the
initiative process, provide an overview of equilibrium conditions, and discuss the model’s
testable predictions. Particularly, we focus on predictions about the conditions under which the
initiative process will change policy outcomes vis-à-vis the simple pivotal politics model. The
theoretical appendix to the paper presents a detailed presentation of the model.
Models of Direct Legislation
Models of the direct legislation process typically originate from Romer and Rosenthal’s
(1978; 1979) one dimensional spatial model of agenda setting in which the setter makes a “take it
or leave it” offer to voters. If the offer fails, policy reverts either to the status quo or to some
legislatively prescribed reversion point. Gerber (1996) adapts this model to direct legislation by
giving proposal power to an outside actor, (e.g. an organized interest group). After the legislature
passes its policy, the proposer can pay some cost, c, to place an alternate proposal on the ballot.
Voters then decide between the two options.
The model’s central conclusion highlights the indirect effect of the initiative process: by
usurping the legislature’s policymaking authority, the initiative process forces the legislature to
moderate its proposals toward the median voter in order to preempt ballot measures. With this
4
policy moderation, the legislature deters the group from using the initiative process to pass a less
desirable policy. This legislative moderation occurs whenever the legislature and proposer
compete over the median voter’s ideal point: either when the voter lies between the legislature
and the proposer or when the proposer lies between the voter and the legislature. Variations on
this basic model (e.g., Matsusaka and McCarty 2001; Boehmke 2005a) allow for uncertainty
over the median voter’s ideal point; yet, the equilibrium remains similar in spirit. 1
Empirical tests of this model focus on whether the ability to propose initiatives engenders
policies that better reflect the median voter’s preferences. On balance, the evidence supports this
prediction across a variety of policies, such as tax rates (Matsusaka 1995, 2004), abortion laws
(Burden 2005; Gerber 1999), gaming policy (Boehmke 2005a), or laws restricting same sex
marriage (Lupia et al. 2010); though not all studies find such an effect (e.g., Burden 2005;
Lascher, Hagan, and Rochlin 1996; Lax and Phillips 2009).
The initiative stage of our model begins from the same premises as Gerber’s (1996)
canonical model. Policymaking and ideal points exist in a one dimensional policy space with
three relevant actors: the legislature, L, which acts first by selecting a policy, denoted 𝑥𝐿 ; the
proposer, P, who then has the option of paying a cost, c, to qualify a measure, 𝑥𝑃 , for the ballot;
and the median voter, V, who chooses between the policies of the legislature and the proposer,
provided the latter opts to make a proposal. We adapt this model by relaxing the assumption that
the legislature (and executive) is a unitary actor and instead include multiple players in the
government as in Krehbiel’s (1998) pivotal politics model. 2
Modeling Legislative Policymaking
5
In the pivotal politics model, passing legislation requires the support of “pivotal” actors.
Legislative rules and procedures determine the identities and the spatial location of these actors.
The first pivot point is the filibuster. The filibuster allows a minority group of legislators to stall
a vote by (the threat of) indefinite debate until cloture is invoked, often via a supermajority vote.
In a one-dimensional spatial model, the filibuster pivot, F, represents the member whose support
must be won in order to ensure sufficient votes to invoke cloture, allowing movement from the
status quo, denoted by 𝑥0 .
Once a bill receives a majority vote in the legislature the executive must approve it; however,
the executive possesses veto power. In the states, we refer to the pivotal role of the Governor, G,
who has varying ability across the states to veto legislation. Should such a veto occur, the
legislature could override the veto with a supermajority vote. The override rule identifies a
second pivot known as the veto override player. The roles of the governor and veto override
player interact since the veto override legislator, O, only matters if the governor’s veto poses a
credible threat.
The legislative process in the pivotal politics model often results in gridlock. In order to pass,
new legislation must benefit at least three pivotal players: the median legislator, since a majority
of legislators must prefer a new proposal to the status quo; the filibuster pivot, since a minority
can indefinitely stall a proposal until a successful cloture vote; and either the governor or the
veto override pivot, since if the former chooses to veto, the latter must vote to override it. As
with the initiative process, adding the filibuster and override rules into legislative policymaking
models empowers certain actors (i.e. pivots) and leads to final policy outcomes that can diverge
from the median legislator’s ideal point. Further, the combination of these requirements leads to
6
a subset of policies falling between the veto and filibuster pivots in which policy cannot be
moved – the gridlock interval.
Combining the Initiative and Pivotal Politics Models
We combine these two models by retaining the legislative process in the pivotal politics
model and adding two additional stages from the initiative model. 4 First, after the pivotal politics
legislative process ends with policy, 𝑥𝐿 , the initiative proposer can pay a cost, c, to place its own
proposal, 𝑥𝑃 , on the ballot. Second, if the measure, 𝑥𝑃 , appears on the ballot, the median voter, 𝑉,
in the state selects her preferred policy, 𝑥𝐿 or 𝑥𝑃 . The game then ends.
The equilibrium outcome of our game depends on the arrangement of the six players’ ideal
points, but we can reduce the number of combinations due to restrictions on the ordering of
legislative actors’ ideal points, i.e., 𝐹 ≤ 𝐿 ≤ 𝑂. The median legislator must always lie between
the filibuster and veto override players by construction. 5 Further, we assume that the proposer
has an “extreme” ideal point to capture the idea that organized interests tend to represent either
more liberal or conservative positions. For presentational purposes we assume a liberal interest
group; in the appendix we discuss the results if we assume a conservative proposer. Similarly,
we assume that the governor lies outside the gridlock interval, just to the right of the veto
override legislator. If the governor lies inside the gridlock interval between the median legislator
and the override legislator, then the governor becomes the veto pivot and similar results hold.
Finally, we locate all actors’ ideal points and the status quo between zero and one for
presentation.
We present the results of our model based on four different configurations of ideal points
given by the location of the median voter: to the left of the gridlock interval (𝑉 < 𝐹); between
7
the filibuster pivot and the median legislator (𝐹 < 𝑉 < 𝐿); between the median legislator and
the veto pivot (𝐿 < 𝑉 < 𝑂); and, finally, to the right of the veto pivot (𝑂 < 𝑉).
The equilibrium outcome then depends on the location of the status quo, creating multiple
possible policy outcomes within each of these four configurations. To summarize these, we
present the equilibrium policy outcome (focusing on subgame perfect equilibria) in Figure 1. The
horizontal and vertical axes represent the policy space, and notations along the axes indicate the
location of each actor’s ideal point. The red line plots the equilibrium outcome of our gridlockinitiative game on the vertical axis against the location of the status quo on the horizontal axis.
For comparison, the blue line does the same for the solely pivotal politics game, while the orange
line plots the optimal initiative for every policy (i.e., initiatives without a legislature). We set the
cost of proposing an initiative to 0. In the appendix we present a similar graph with a small cost
of proposal; generally, as long as the cost of the initiative is not too large, the main results hold
with only minor modifications to reflect the cost of proposal.
[Figure 1 about here.]
Figure 1 shows that the possibility of initiatives often changes the equilibrium outcome in the
pivotal politics model. Generally, these deviations result from the threat of an initiative. The
initiative threat either leads the legislature to alter its policy choice to preempt an initiative or
leads the proposer to place a measure on the ballot. Initiatives can occur in equilibrium when the
legislature can make no better policy through the legislative process (i.e., the preemptive policy
change fails to happen). This occurs when one of the non-median pivotal actors in the legislature
blocks legislation to secure something better from the initiative than what the legislature will do.
Such a failure of preemptive legislation can only happen when the median voter and the proposer
sit on opposite sides of that pivotal actor. As we show in the appendix, initiatives only occur
8
when the optimal ballot measure falls into the gridlock interval, though this constitutes a
necessary rather than a sufficient condition. Intuitively, when a ballot measure falls into the
gridlock interval at least one of the veto or filibuster pivots would be made worse off by passing
any other policy, thereby creating an incentive to block the legislative process in favor of the
initiative policy.
Overall, the equilibrium outcome represents a combination of the forces operating in
Gerber’s initiative model and Krehbiel’s pivotal politics model. In configuration 1, for example,
when the median voter sits between the proposer and the filibuster pivot, the result mirrors
Gerber’s (1996) model: the legislature preempts an initiative by moving policy to the voter’s
ideal point. Moving policy anywhere to the right of the voter’s ideal point results in an initiative
that pivots around the median voter towards the proposer.
In the other three configurations, however, the median voter’s ideal point lies to right of the
filibuster pivot, leading to conflict among the pivotal players over where to move policy given
the threat of an initiative. If the legislature passes a policy to the right of the voter’s ideal point,
the proposer can select an initiative that it prefers to the left of the median voter that is also
closer to the median voter’s preferred policy. This decision by the proposer changes the dynamic
in the legislature, since gridlock now leads to the proposer’s policy via the ballot instead of
reverting to the status quo ante in the legislative process. When the proposer’s policy lies in the
gridlock interval, the legislature again finds itself trapped; in order to preempt a ballot measure in
the gridlock interval, the median legislator would have to move policy away from at least one of
the two other pivots. This move is impossible, since both of the pivots must approve of the
proposed policy change and can thwart the change if they disapprove. Thus, the legislature can,
at best, propose the same policy as the proposer, rendering itself indifferent between legislative
9
action and a ballot proposal. Once the optimal initiative moves back out of the gridlock interval,
there again exists a policy that the legislature prefers to the expected initiative policy. This
legislative policy makes at least two pivots strictly better off (and the other weakly better off) –
thus precluding use of the initiative process.
Findings and Predictions
Table 1 summarizes the predictions of our gridlock-initiative game for each of the four main
configurations. We highlight three main testable propositions. First, our game implies that the
presence of the initiative process in a state alters the traditional gridlock interval. When the
initiative is considered in tandem with the legislative process, gridlock only occurs when the
legislative gridlock interval overlaps with the initiative gridlock interval. This interval may be
zero, as in configuration 1, smaller than the traditional gridlock interval as in configurations 2 or
3, or identical, as in configuration 4. Scholars testing pivotal politics style theories in the states
should be cognizant of these changes stemming from direct democracy.
[Table 1 about here]
Second, our model demonstrates that the initiative process can make the median voter better
or worse off relative to legislative-only policy outcomes. The possibility of being worse off has
previously occurred in models with uncertainty (Matsusaka and McCarty 2001), but here it
occurs due to the actions of the pivotal players. For example, consider case three in Figure 1 with
a status quo just to the right of the veto override player. In the game without the initiative, policy
would pivot around O back towards the median voter. With the initiative process, however, the
filibuster pivot blocks this move since it prefers the initiative that pivots around V (taking the
outcome further from the median voter). Further, note that this utility loss occurs despite a
10
successful initiative. This prediction speaks to debates over whether the initiative is a positive or
negative institutional feature.
Third, our model shows that initiatives occur over a wide range of status quo points. Thus,
initiatives can occur with regularity where permitted by state law, because a multitude of
legislative configurations result in equilibria involving a successful ballot measure. 6 Since this
third prediction forms the basis for our subsequent empirical tests, we explore it in more detail.
Consider the outcomes summarized in Table 1. 7 In configuration 1, no initiative occurs since
the legislature can always preempt it. In configurations 2 and 3, initiatives can occur whenever
the proposer will benefit and the resulting optimal measure, given the status quo ante, lies in the
gridlock interval. However, the proposer cannot pass anything until the status quo lies opposite
the median voter, so the region in which initiatives can occur begins at L. When policy moves to
the right of L, the median legislator and veto pivot would like to preempt an initiative at V, but
the filibuster pivot stops them since the resulting initiative will be closer to his ideal point. The
resulting initiative measure continues to lie in the gridlock interval until it crosses F. This
happens when the status quo passes V + |V − F|. Therefore, the size of the policy space that can
lead to initiatives therefore corresponds to |V − F|.
Configuration 4 looks similar, except that the legislature can initially preempt a ballot
measure when the status quo crosses V. Thus, the optimal initiative would lie to the right of the
veto override. An initiative to the right of the veto override allows the median legislator to
propose a legislative policy equidistant to the left of O, which it and the filibuster pivot prefer.
Once the optimal initiative moves into the gridlock interval, pivoting ends since no policy to the
left of the ballot measure would make the veto override pivot better off. Thus, the permissive
initiative interval starts at V + |V − O| and continues as before until V + |V − F|. The size of the
11
policy space that can lead to initiatives in configuration 4, therefore, corresponds to |O − F|, the
familiar pivotal politics gridlock interval. 8
Pivotal Politics and Initiative Use
In order to evaluate the relationship between the size of our gridlock intervals and initiative use,
we require data on the number of citizen-sponsored initiatives appearing on statewide ballots and
the location of various actors’ ideal points. 10 The Initiative and Referendum Institute’s website
provides information on the former from the year the state adopted the initiative process through
2010. Of the twenty-four states that currently permit initiatives, some allow them only on general
election ballots, while others allow them on primary and off-year ballots. We follow convention
in the literature by analyzing the number of ballot measures per biennium.
To measure the location of pivotal actors’ ideal points, we draw on three available data
sources. First, we rely on Clark, Osborn, Winburn, and Wright’s (2009) data on state legislative
ideology for the 1999-2000 and 2003-2004 sessions. For these data, one concern is the ideology
scores are calculated one state at a time, so that they are not directly comparable across states.
Because the intervals measure the difference between ideal points, however, problems of
location do not affect our measures in these data. Differences in scale across chambers and states
do remain a concern, though. Second, we use Shor and McCarty’s (2011) data on state legislative
ideal points for 1993-2009. 11 These data cover a longer time period and are comparable over
time and across states, as the authors use the Project Vote Smart National Political Awareness
Test (NPAT) to put legislators’ ideological scores in a common ideological space. 12 Finally, we
utilize Masket’s (2004) data on California Assembly ideal points from 1901-2003. These data
provide us an extended time series for one state. Like the Shor and McCarty data, Masket’s data
12
allow ideological comparison across legislators in different sessions on a common ideological
scale. These data sources represent a near universe of the available roll call data collection in the
U.S. states, and thus the available ideological estimators of legislators’ positions, at the time of
our study.
Measuring Initiative Intervals
Across our four configurations of the median voter’s location, we find that three different status
quo regions permit initiatives. When we have a liberal proposer, the size of the permissible status
quo region in configurations 2 and 3 corresponds to the distance between the median voter and
the filibuster pivot, i.e., |F-V|. With a conservative proposer the distance between the median
voter and the veto override pivot, |O-V|, measures the analogous interval and gives our second
permissible status quo region. From configuration 4, the third status quo region is the traditional
gridlock interval given by |F-O|.
To identify the filibuster and veto pivots, we examined state legislative procedures to
determine the veto override threshold and whether a state allows the filibuster and the threshold
necessary to invoke cloture. Only thirteen of the fifty states allow filibusters, including five of
the twenty-four initiative states. In states that do not, the median legislator effectively serves as
the filibuster pivot. For the veto pivot, the legislative bound of the permissive status quo range
depends on whether the governor or the veto threshold legislator lies closer to the median voter.
Unfortunately, we lack data on gubernatorial ideal points and therefore must calculate the veto
interval as the distance between the median voter and the veto override pivot. 13
For the California data, we initially calculate the veto interval as the distance between the
median voter and the 66th percentile legislator for the veto pivot. 14 Two rule changes, however,
13
potentially increase the filibuster interval for revenue bills. In June of 1933 voters passed
Proposition 1, requiring a two-thirds vote to pass a budget with more than a 5% increase in
spending. 15 In 1978, voters passed Proposition 13, which applied this same supermajority
requirement to tax bills. These two supermajority requirements potentially mimic the possibility
of a filibuster by requiring a supermajority to pass certain bills. We calculate the filibuster pivot
using the 33rd percentile legislator during the period 1979-2003. We use this filibuster measure in
all analyses for the post Proposition 13 period since the 1933 change targeted only the budget
and only under certain circumstances; whereas, Proposition 13’s tax requirement likely affects
more bills and has spillover effects into other policy areas that entail raising revenue. 16
These calculations provide us with direct measures of two of the three points – the filibuster
pivot and the override pivot. For the third key point, no data as of yet provide sufficiently
comprehensive coverage of the location of the median voter in a common space with legislators
for our use here. Bafumi and Herron (2010) estimate the median voter at the national level with a
battery of questions about legislative proposals; Masket and Noel (2012) create common space
legislator and median voter ideal point estimates using legislator and district votes on
referendums as a bridge. Unfortunately, neither approach currently provides the broad crosssectional and temporal coverage we require to test our model. The extant work on median voter
estimates suggests a reasonable interim solution, however. To place the median voter, we
measure the distance between the median voter and the veto and filibuster pivots with the
distance between the median legislator and each pivot.
While imperfect, we believe this provides a good proxy measure for our theoretical concept.
While the median voter and median legislator will not necessarily have the same ideal point, our
approach only requires a positive correlation between the relevant intervals: as long as |V − F|
14
correlates with |L − F| (and similarly for the veto interval), the latter will provide a useable
proxy for our preferred measure. We subject this assumption to an extensive robustness check
through a series of simulations.
A second complication lies with identifying the correct preference configuration. Without
knowing the median voter and proposer’s ideal points, we do not know which of our measures of
the permissive status quo interval to use. 17 In configurations two and three our model predicts
that |V − F| or |V − O| measures the correct interval (depending on the location of the proposer);
whereas, in the fourth configuration, |O − F |captures it. But since |V − F|+|V − O| = |F − O|
whenever the median voter lies between O and F we can not include all three measures, since
they would be perfectly collinear. Since |V − F| matters with a proposer on the left and |V − O|
matters with a proposer on the right, our first approach includes both. Thus, if an observation
corresponds to a configuration where one of them matters, our theory predicts a positive
relationship; if it does not, our theory predicts no relationship. These expectations simply make it
less likely that we would find a significant effect since in some cases the included interval will
be incorrect and have no effect. Our second approach includes just the gridlock interval, which
forms the permissive zone in case four (and is captured by the sum of the two separate intervals
in the first approach). This effectively captures the two separate intervals if the data are roughly
evenly split between left and right proposers in configurations two and three and has the added
benefit of not requiring us to measure the median voter’s ideal point. 18
Additional Control Variables
In addition to our key independent variable–the size of the initiative-permissive status quo
intervals–we also control for a number of other factors known to influence the frequency of
15
initiative usage across the states (see, e.g., Banducci 1998, Boehmke 2005b, and McGrath 2011).
To protect empirical parsimony, we focus only on a small number of additional variables. First,
in order to rule out the possibility that divided government rather than the gridlock interval per se
leads to more initiatives, we utilize Klarner’s (2003) data to construct a measure of whether one
party controls all three branches of state government from 1959-2007.
Second, demographic characteristics of a state also influence initiative use. Matsusaka and
McCarty’s (2001) model predicts that legislators in larger states will experience greater
uncertainty about constituent preferences which then increases the frequency of initiatives. We
add a control for state population from the Bureau of Economic Analysis (BEA) from 19292009. We also control for real per capita state income using BEA data.
Third, liberal states tend to see more initiatives. This tendency may stem from the initiative’s
Progressive Era origins in the United States or from the fact that the initiative process tends to be
utilized at a greater rate by citizen-oriented groups (Boehmke 2005b), which form in direct
democracy states at a greater rate (Boehmke 2002). For our purposes, a greater number of
potential proposers may exist in more liberal states; the presence of more proposers should
increase initiative use. We control for state liberal citizen ideology using Berry, Ringquist,
Fording, and Hanson’s (1998) measure for 1960-2010.
Finally, the rules governing ballot measure qualification explain much of the variation in
initiative use in the American states. Previous studies find that signature requirements,
distribution requirements, petition circulation periods, and whether states permit statutory or
constitutional measures influence the number of measures (see, e.g., Boehmke 2005b; McGrath
2011; Hicks 2013). 19 We measure the signature requirement in percentage terms and average it
across distinct requirements for statutory and constitutional measures if both are allowed. We
16
measure the circulation period with two variables: one for the maximum number of days in
circulation and an indicator variable for those without a maximum. We account for the
distribution requirement with a dichotomous indicator for whether the state requires thresholds
for signatures across geographic subunits in addition to overall (e.g., the statewide signature
threshold must be met in 40% of counties).
Initiative Use across the American States
We link our cross-sectional time-series data on initiative use to Clark et al. (2009) and Shor
and McCarty’s (2011) data on state legislator ideal points, from which we construct a measure of
the filibuster and veto intervals for each legislative session. The first sample we use is the two
legislative sessions (1999-2000 and 2003-2004) in the Clark et al. data (2009). 20 We also
consider an extended sample for these data, in which we use initiative use data from 1997-2006,
substituting the gridlock interval measure from 1999-2000 for the missing one in 1997-1998, the
2003-2004 value for 2005-2006, and the mean of the 1999-2000 and 2003-2004 values for 20012002. This quadruples our sample size, but likely introduces some error into our key independent
variable. 21 We then use the Shor and McCarty data, which cover a longer time period.
[Table 2 about here.]
We present the results of our negative binomial models of initiative use across states in Table
2. We find generally strong support for our hypotheses, with the coefficient on the filibuster
interval positive and significant in all models, the coefficient on the gridlock interval significant
in two of three models, and the coefficient on the veto interval significant in one model. In all
three cases, the standard errors decrease as the sample size increases and, notably, all variables
achieve significance in the model with the greatest number of observations. First difference
17
calculations show that an increase from the 16th to the 84th percentile for the veto interval
produces about 1.9 more initiatives per biennium in this model. The same change in the
filibuster interval produces 0.2 more initiatives per biennium with the Shor and McCarty data
and 0.4 to 0.7 more initiatives per biennium using the Clark et al. data. 22 The first difference for
the gridlock interval ranges from 1 to 1.7 to 2.1 over the three models. Over the ten-year time
period in our extended sample, states average 3 measures per biennium, making these sizable
effects.
Our other variables perform largely as expected. As expected, distributional requirements
and greater signature requirements decrease the number of initiatives on the ballot while the
number of circulation days, the population of the state, and the real income per capita have a
positive effect.
Initiative Use in California, 1911-2003
Our second test uses a purely time series data set on the number of ballot measures in California
from 1911-2003 using Masket’s first dimension DW-nominate estimates of legislator ideal
points. We again use the legislative session as our unit of analysis and estimate a negative
binomial model of the number of initiatives.
[Figure 2 about here.]
Figure 2 presents a smoothed, lowess plot of initiative use per biennium and the filibuster and
veto intervals over time. Initiative use follows the familiar pattern of high frequency early in the
twentieth century shortly after adoption, followed by a long fallow period and resurgence in use
in the early 1970s. The filibuster interval follows a broadly similar trend, with a moderate but
steady decline from 1911 to the late 1950s, followed by a small surge in the 1960s and a steep
18
increase in 1979 with the introduction of the supermajority requirement for budgets and tax
measures in 1979. The veto interval trends with the filibuster interval until 1979, after which it
experiences a steep decline. We now turn to a regression analysis to determine if this correlation
remains with the addition of various control variables.
Because most of our independent variables only have valid measures back to about 1960, we
estimate two models. The first model includes the two permissive initiative intervals or the
gridlock interval as the substantive independent variables and a cubic spline in order to model
changes in other forces that we do not measure directly. We use a natural cubic spline with knots
placed at each quintile. 23 Using a cubic spline with more knots should capture possibly complex
changes in omitted variables over time, though robustness checks indicate that our results do not
depend on this particular functional form. In the second model we add demographic and
ideological control variables. Since this restricts our sample to the period 1961-2003, we account
for complex changes stemming from time with a quadratic function of time rather than with
splines.
[Table 3 about here.]
Table 3 presents the results for all four models. In the models with the separate permissive
zones, the coefficient for the filibuster interval is always positive and significant. The veto
interval coefficient is only significant in the full sample. In the two models that use the gridlock
interval, we again find significance in both models. Calculations show the gridlock interval led to
between one and five more initiatives per biennium prior to Proposition 13 in 1979 while the
combination of the filibuster and increased gridlock interval led to five to fourteen more
initiatives per year thereafter (see appendix). This change in legislative rules demonstrates
handily the real effect of legislative gridlock on initiative use.
19
Robustness Check
While we argued earlier that the distance between the median legislator and the pivots serves as a
good proxy for the distance between the median voter and the pivots, we attempt to bolster this
claim by summarizing the results of an extensive robustness check reported in detail in our
supplemental appendix. To execute this test, we assume the existence of a representation
function that maps district median voter ideal points into legislator ideal points. While we do not
know the exact shape of such a function, we set the general structure based on reported results in
the literature at the state (Masket and Noel 2012; Tausanovitch and Warshaw 2012) or federal
level (Bafumi and Herron 2010). We then simulate district median voter ideal points from our
observed legislator ideal points to impute a predicted state median voter ideal point. We assume
that the relationship between the median voter and a district’s legislator is generally linear with a
slope near one, an intercept near zero, and an extremism bias such that a representative is more
extreme. We add a random error term to capture variation around this relationship. We repeat
this exercise over 1800 different combinations of the parameters of this representation function,
calculate the two theoretical variables of interest, and run our regression model with these
imputed values. In brief, this exercise indicates that our findings for both key variables prove
quite robust and do not change sign or lose significance across broad combinations of changes,
though the findings for the veto interval appear slightly more persistent. Not surprisingly,
though, as the size of the random error increases, the results eventually weaken.
Conclusion
20
Uniting standard spatial models of the initiative process with the pivotal politics model of
legislative policymaking leads to a more nuanced understanding of each. We identify the
conditions under which the initiative process breaks legislative gridlock, and alternatively, when
the legislature cannot successfully preempt a ballot measure. Thus, we provide predictions about
when the initiative might serve as the Progressives’ proffered “gun behind the door” via
legislative policy moderation or direct voter decision making. Importantly, our theoretical results
indicate that initiatives do not merely result from legislative gridlock; they can in fact create
legislative gridlock that would not have existed otherwise. Initiatives do not arise simply because
the status quo lies in the gridlock interval; rather, they arise because the legislature’s optimal
policy in the absence of the initiative lies in the gridlock interval. Pivotal actors exploit the threat
of an initiative to force policy changes that make them better off, whether through the legislature
or the ballot box. Ultimately, this exploitation can leave the median voter worse off than without
the initiative process, meaning a state institution designed to express the public’s wishes may
actually thwart the public will.
We find evidence consistent with our hypotheses across several state data sets, suggesting
that our findings do not emerge purely due to the limitations of our data. Extensive robustness
analysis also bolsters our results. As state data sets continue to improve, we believe it will be
possible to test more precisely our predictions and yield further evidence of the success or failure
behind one of the Progressives’ key reforms.
Our model produces a number of novel theoretical and substantive implications for
legislative and state politics. First, our results highlight the interdependence of political
institutions and, consequently, the potential unintended consequences of reforming one
institution on the other institutions in the state. Just as state legislative term limits
21
unintentionally limit the legislature’s bargaining power with the governor (Kousser 2005), the
response of pivotal legislative actors to the initiative process determines whether the initiative
generates helps produce policy closer to the median voter’s ideal point. Yet, multi-institutional
studies that trace the dynamics between institutions are rare in American politics relative to
single institution studies, particularly about legislative dynamics. Considering multiple
institutions in tandem offers greater insight into how a rule change in one institution affects the
other. For example, supermajority requirements may slow the legislative process and make it
more cautious, but they also increase the permissive space for the initiative process. In turn, the
initiative process can both decrease overall gridlock and change the balance of power between
pivotal actors in the legislature. As Figure 2 shows, California’s two-thirds majority tax rule
introduced by Proposition 13 (i.e., the initiative process itself changing the gridlock interval!)
resulted immediately in a huge expansion in the filibuster-median voter interval, which was
promptly followed by a doubling in the number of initiatives.
Second, our results identify nuance in translating the pivotal politics model to state
legislatures. In states that allow initiatives, the initiative process can break the traditional
legislative gridlock interval, leading to a smaller initiative-adjusted gridlock interval. Policies
that formerly would have been gridlocked can now be moved, either through legislative
preemption or through the ballot box. Further, the variety in state legislative rules affects the
placement of the filibuster and veto pivots, and thus the applicability of congressional theory to
legislatures more generally. As we note earlier, not all states allow for filibusters; similarly, a
few states, such as Arkansas, place their veto override threshold at a simple, rather than a super,
majority. From our initial application of the pivotal politics model to the states, additional
variations in rules, such as supermajority vote requirements on particular types of bills (which
22
exist in at least nine states) and line-item and/or amendatory veto powers, could be added to
further specify the identification of the filibuster and override pivots. 25 These observations speak
to the generalizability of theories across institutions, as the application of pivotal politics to state
legislatures (or more generally, comparative legislatures) is not always straightforward.
Furthermore, a number of testable outcomes regarding legislative behavior should be pursued
in future work. For example, differences in patterns of bill sponsorship, legislative vote margins,
“rolling” of the legislative majority, and bill passage rates might all result from changes to the
effective gridlock interval under the initiative process. Our theory could also inform models of
the sequential process of legislative bargaining under initiative and non-initiative conditions.
Other legislative rules, such as the thresholds required for discharge petitions in the U.S. states,
could also place additional pivotal actors on the spatial spectrum. As state legislative data
become more commonly available, these institutional variations to our basic initiative-gridlock
model will become testable propositions. In the meantime, the model we present in this work
demonstrates the importance of both institutional interplay in the creation of public policy and
the importance of assessing the consequences of government reform.
23
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Study of American Voters and their Members in Congress.” American Political Science
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Todd Donovan, and Caroline J. Tolbert. Columbus: Ohio State University Press.
Berry, William; Evan Ringquist; Richard Fording; and Russell Hanson. 1998. “Measuring
Citizen and Government Ideology in the American States, 1960-1993.” American Journal of
Political Science 42 (1): 327-48.
Binder, Sarah A. 1999. “The Dynamics of Legislative Gridlock, 1947-1996.” American Political
Science Review 93 (3): 519–33.
Boehmke, Frederick J. 2002. “The Effect of Direct Democracy on the Size and Diversity of State
Interest Group Populations.” The Journal of Politics 64(3): 827–844.
Boehmke, Frederick J. 2005a. The Indirect Effect of Direct Legislation: How Institutions Shape
Interest Groups Systems. The Ohio State University Press.
Boehmke, Frederick J. 2005b. “Sources of Variation in the Frequency of Statewide Initiatives:
The Role of Interest Group Populations.” Political Research Quarterly 58(4): 575–585.
Brady, David W., and Craig Volden. 2006. Revolving Gridlock: Politics and Policy from Jimmy
Carter to George W. Bush. Boulder, CO: Westview Press.
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Clark, Jennifer Hayes; Tracy Osborn; Jonathan Winburn; and Gerald C. Wright. 2009.
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Cox, Gary and Mathew McCubbins. 1993. Legislative Leviathan: Party Government in the
House. Berkeley: University of California Press.
Cronin, Thomas E. 1989. Direct Democracy: the Politics of Initiative, Referendum and Recall.
Cambridge: Harvard University Press.
Gerber, Elisabeth R. 1996. “Legislative Response to the Threat of Popular Initiatives.” American
Journal of Political Science 40(1): 99-128.
Gerber, Elisabeth R. 1999. The Populist Paradox: Interest Group Influence and the Promise of
Direct Legislation. Princeton: Princeton University Press.
Hicks, William D. 2013. “Initiatives within Representative Government Political Competition
and Initiative Use in the American States.” State Politics & Policy Quarterly 13(4): 471-494.
Keele, Luke J. 2008. Semiparametric Regression for the Social Sciences. New York, NY: John
Wiley & Sons.
Klarner, Carl. 2003. “The Measurement of the Partisan Balance of State Government.” State
Politics and Policy Quarterly, 3 (3): 309-319.
Krehbiel, Keith. 1998. Pivotal Politics: A Theory of U.S. Lawmaking. Chicago: University Of
Chicago Press.
Lascher, Edward L. Jr; Michael G.Hagen and Steven A. Rochlin. 1996. “Gun Behind the Door?
Ballot Initiatives, State Policies and Public Opinion.” The Journal of Politics 58: 760-775.
25
Lax, Jeffrey R. and Justin H. Phillips. 2009. “Gay Rights in the States: Public Opinion and
Policy Responsiveness.” American Political Science Review 103 (3): 367-386
Lupia, Arthur; Yanna Krupnikov; Adam Seth Levine; Spencer Piston; and Alexander Von
Hagen-Jamar. 2010. “Why State Constitutions Differ in their Treatment of Same-Sex
Marriage.” The Journal of Politics 72: 1222-1235.
McGrath, Robert J. 2011. “Electoral Competition and the Frequency of Initiative Use in the U.S.
States.” American Politics Research 39 (3): 611-638.
Magleby, David B. 1984. Direct Legislation: Voting On Ballot Propositions in the United States.
Baltimore: Johns Hopkins University Press.
Masket, Seth E., 2004. “California Assembly Ideal Points, 1901-2003.” University of Denver.
http://mysite.du.edu/~smasket/research.html.
Masket, Seth E. and Hans Noel. 2012. “Serving Two Masters Using Referenda to Assess
Partisan versus Dyadic Legislative Representation.” Political Research Quarterly 65 (1):
104-123.
Matsusaka, John G. 1995. “Fiscal Effects of the Voter Initiative.” Journal of Political Economy
103: 587-623.
Matsusaka, John G. 2004. For the Many or the Few: The Initiative Process, Public Policy, and
American Democracy. Chicago: Chicago University Press.
Matsusaka, John G. and Nolan M. McCarty. 2001. “Political Resource Allocation: Benefits and
Costs of Voter Initiatives.” Journal of Law, Economics, and Organization 17: 413-448.
Romer, Thomas and Howard Rosenthal. 1978. “Political Resource Allocation, Controlled
Agendas, and the Status Quo.” Public Choice 33: 27-44.
26
Romer, Thomas and Howard Rosenthal. 1979. “Bureaucrats versus Voters: On the Political
Economy of Resource Allocation by Direct Democracy.” Quarterly Journal of Economics
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Shor, Boris and Nolan McCarty. 2011. “The Ideological Mapping of American Legislatures.”
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Tausanovitch, Chris, and Christopher Warshaw. 2013. “Measuring Constituent Policy
Preferences in Congress, State Legislatures, and Cities.” The Journal of Politics 75 (2): 330342.Waters, M. Dane. 2003. Initiative and Referendum Almanac. Durham, NC: Carolina
Academic Press.
27
Table 1.
Summary of Theoretical Predictions about When Initiatives can Occur in Equilibrium
Configuration 1
Configuration 2 Configuration 3
Configuration 4
Location of the Median Voter
V<F
F<V<L
L<V<O
O<V
Initiative range with left proposer
No
V<SQ<V+|V-F| V<SQ<V+|V-F| V+|V-O|<SQ<V+|V-F|
Size of initiative range
0
|V-F|
|V-F|
|F-O|
Initiative range with right proposer V-|V-O|<SQ<V-|V-F| V-|V-O|<SQ<V V-|V-O|<SQ<V
No
Size of initiative range
|F-O|
|V-O|
|V-O|
0
Note. P represents the Proposer’s ideal point, F the filibuster pivot’s ideal point, L the median legislator’s ideal point, O the veto override’s ideal point, V the
median voter’s ideal point, and SQ the status quo ante.
28
Table 2.
Negative Binomial Model of Initiative Use in the American States
Clark et al.
Clark et al. extended
Shor & McCarty
(2000&2004)
(1998-2006)
(1994-2008)
0.915**
1.307**
0.790**
Filibuster interval, |F-L|
(0.461)
(0.357)
(0.230)
0.110
0.456
0.843**
Veto interval, |O-L|
(0.433)
(0.282)
(0.218)
0.418
0.759**
0.824**
Gridlock interval, |F-O|
(0.354)
(0.229)
(0.193)
1.610** 1.657** 1.826** 1.891** 1.464** 1.469**
Statutory Initiatives
(0.754)
(0.770)
(0.467)
(0.482)
(0.387)
(0.384)
0.373
0.165
0.774** 0.505** 0.444** 0.453**
Constitutional Initiatives
(0.414)
(0.355)
(0.339)
(0.256)
(0.215)
(0.208)
-0.546* -0.504
-0.628** -0.589** -0.479** -0.481**
Distribution Requirement
(0.316)
(0.342)
(0.201)
(0.219)
(0.155)
(0.154)
-0.019
-0.019
-0.039
-0.037
-0.067** -0.067**
Signatures - Average
(0.065)
(0.066)
(0.034)
(0.035)
(0.028)
(0.028)
0.166** 0.153** 0.165** 0.151** 0.128** 0.129**
Circulation Days
(0.059)
(0.061)
(0.035)
(0.035)
(0.030)
(0.029)
0.153
0.091
0.737
0.614
0.566
0.564
Unlimited Circulation
(0.671)
(0.732)
(0.504)
(0.502)
(0.426)
(0.424)
-0.176
-0.169
-0.173
-0.170
0.009
-0.005
Unified control
(0.263)
(0.251)
(0.157)
(0.155)
(0.168)
(0.147)
0.005
0.022* -0.009
0.011
-0.014
-0.014
Total Population
(0.017)
(0.013)
(0.013)
(0.009)
(0.012)
(0.012)
0.643
0.749
0.928** 1.008** 0.617** 0.610**
Real Income per Capita
(0.597)
(0.584)
(0.345)
(0.352)
(0.235)
(0.233)
0.017
0.015
0.002
0.002
0.002
0.002
Citizen Ideology
(0.014)
(0.013)
(0.008)
(0.008)
(0.006)
(0.006)
-3.901
-4.120
-4.549** -4.747** -2.820** -2.797**
constant
(2.475)
(2.519)
(1.398)
(1.427)
(0.940)
(0.936)
-1.125** -1.141* -1.597** -1.497** -1.632** -1.632**
ln(alpha)
(0.545)
(0.590)
(0.490)
(0.472)
(0.358)
(0.360)
46
46
115
115
154
154
Observations
-92.05
-92.62
-223.45 -225.22 -301.04 -301.06
Log-Likelihood
Note. * Indicates p<.1, ** indicates p<.05, two tailed tests. Robust standard errors in parenthesis.
29
Table 3.
Negative Binomial Model of Initiative Use in California
Filibuster interval, |F-L|
Veto interval, |O-L|
Gridlock interval, |F-O|
Spline (1)
Spline (2)
Spline (3)
Spline (4)
1911-2003
1.370**
(0.561)
1.253**
(0.568)
1.243**
(0.569)
-0.015
-0.016
(0.022)
(0.022)
-0.126
-0.125
(0.134)
(0.134)
0.598
0.596
(0.437)
(0.436)
-1.070*
-1.057*
(0.601)
(0.599)
Citizen Ideology
Total Population
Real Income per Capita
Unified control
Time
Time Squared
constant
ln(alpha)
Observations
Log-Likelihood
2.081**
(0.516)
-2.666**
(0.503)
45
-107.15
2.086**
(0.517)
-2.657**
(0.495)
45
-107.18
1961-2003
2.361**
(1.191)
0.874
(1.035)
1.672*
(0.865)
0.088
(0.054)
0.002
(0.304)
-0.768
(1.397)
-0.577
(0.451)
0.411*
(0.224)
-0.002*
(0.001)
-18.769**
(9.496)
-3.822**
(1.473)
21
-49.66
0.044
(0.048)
-0.003
(0.342)
-0.608
(1.412)
0.023
(0.326)
0.265
(0.228)
-0.001
(0.001)
-11.689
(9.727)
-2.854**
(0.705)
21
-51.14
Note. * Indicates p<.1, ** indicates p<.05, two tailed tests. Robust standard errors in parenthesis.
30
Equilibrium Outcome
F VL
O G
Gridlock
Outcomes
P
P
Equilibrium Outcome
V F L
O G
Gridlock
Outcomes
Initiatives
Figure 1.
Equilibrium Outcomes as a Function of the Location of the Status Quo
Initiatives
P
P
P
F LV O G
Location of the Status Quo
With Initiative
F VL
O G
Location of the Status Quo
Gridlock
Outcomes
Equilibrium Outcome
F L
O VG
Gridlock
Outcomes
P
Equilibrium Outcome
F LV O G
P
V F L
O G
Location of the Status Quo
Initiatives
P
Without Initiative
F L
O VG
Location of the Status Quo
Without Legislature
Note. Vertical axis represents the equilibrium policy outcome as a function of the actors’ ideal points and the value
of the status quo ante, which is given by the horizontal axis. Ideal points are displayed for the initiative proposer (P),
filibuster pivot (F), median legislator (L), veto override pivot (O) governor (G), and the median voter (V). Here we
assume that the cost of proposing an initiative is 0. Cases depend on the location of the median voter relative to the
other actors. The regions labeled “Initiatives” correspond to locations of the status quo ante that correspond to the
proposer qualifying and passing an initiative in equilibrium.
31
.75
.5
10
.25
5
0
0
|F-L| & |O-L| Interval
Number of Initiatives
15
1
Figure 2.
Trends in the Gridlock Interval and Initiative Use in California, 1898-2003
1950
year
1900
Initiative Use
Filibuster Interval
2000
Veto Override Interval
Note. Source: filibuster and veto intervals calculated from Masket (2004). Initiative use from the Initiative and
Referendum Institute, aggregated to legislative session. California added a supermajority requirement for budgets
and tax measures in 1978, creating the filibuster interval. The blue line represents a lowess plot of the filibuster
interval, the green line represents the veto override interval, and red line represents a lowess plot of initiative use.
32
1
One important difference occurs via the introduction of uncertainty in Matsusaka and
McCarty’s (2001) model, which leads to situations in which the median voter may be worse off
due to the initiative process.
2
Here we focus on Krehbiel’s initial 1998 model. There is a rich literature developed from
Krehbiel’s argument both theoretically and empirically, as well as a competing literature
regarding party, rather than preference, effects. In this piece, we focus on the integration of these
two basic models of the initiative and legislative policy-making processes.
4
We assume that all players’ utilities decline linearly in the policy space. We denote players’
ideal points for convenience by their names (e.g., L is the median legislator’s ideal point),
proposals by subscripting by the proposing player’s name (e.g., 𝑥𝑃 represents the policy chosen
by the Proposer), and the status quo ante by 𝑥0 .
5
Note that the inequality is not strict since many states only require 50% to invoke cloture or a
simple legislative majority to override the governor.
6
While the legislature could pass the identical policy itself, a sustained gubernatorial veto
weakly dominates moving policy in the legislature for G and O, suggesting that it would be in
those actors’ best interest to block legislation and make the proposer go forth with a ballot
measure.
7
We present results for a liberal proposer, but we show in our appendix that analogous outcomes
obtain with conservative proposer. In this arrangement, initiatives can occur when the status quo
lies between V and V- |V-O| in cases 2 and 3 and between V-|V-O| and F-|V-F| when the voter is
on the opposite side of the gridlock interval from the proposer. The size of the policy spaces that
can lead to initiatives therefore corresponds to |V-O| in configurations 2 and 3 and |O-F| in
configuration 4.
8
The ordering we have on players’ ideal points (i.e., that F<V<O) allows us to simplify across
the two absolute values.
10
All data and code needed to replicate the analyses in this paper and its appendix will be made
available on the Dataverse.
11
Variation in data availability for each state leads to incomplete coverage for some of them
from 1993-2009.
12
For details on the scaling process, see Shor, Berry, and McCarty (2010).
13
The locations of the veto and filibuster pivots were determined using the governor’s party. If
the governor was (e.g.) a Republican, the veto pivot was determined from the left and the
filibuster pivot from the right since in order to override a veto the party in opposition to the
governor would have to support.
14
The locations for the veto and filibuster pivots in the California data were determined in the
same way as in the cross-sectional data using the party of the Governor.
15
See the text of this measure online at http://library.uchastings.edu/ballot_pdf/1933s.pdf
(accessed July 2, 2012).
16
We estimated a model with both definitions of the gridlock interval, i.e., one based on a
straight majority requirement and one accounting for the change after the 1978 rule change, and
the supermajority version emerged as the significant one, providing statistical support for our
coding decision.
17
Astute readers will note that since we measure V with L, we implicitly assume that all our
observations fall into cases 2 and 3. If correct, then we have done no harm and the measure of
33
the initiative interval for case 4 will not affect initiative use. If incorrect, we can still rely on our
weaker assumption that our proxy interval correlates with the true measure, which permits the
median voter to lie outside the traditional gridlock interval.
18
If, for example, cases are split evenly between left and right proposers, then it
corresponds exactly since |𝑉 − 𝐹|/2+|𝑉 − 𝑂|/2 = |𝐹 − 𝑂|/2. Rescaling the gridlock interval
by half does not affect the sign or significance level of our results. To the extent that the mixture
of cases deviates somewhat from half and half, there would still be a strong correlation between
the gridlock interval and the convex combination of the two components.
19 Data for these variables come from a variety of sources (Matsusaka 2004; Boehmke
2005b; Waters 2003; the Book of the States for various years; the National Conference of
State Legislatures’ website; Ballotpedia’s website; Secretaries of State websites; and state
legislatures’ databases of passed bills).
20
A few observations are lost as a result of Nevada not having enough final passage votes in the
Senate for Clark et al. (2009) to calculate the ideal points of the legislators for 2003-2004.
21
Note that the session-to-session correlation in the Masket data is over 0.9, which suggests that
our strategy of extending our sample may be reasonable, though recall that the Masket data
utilize a common space whereas the Clark et al. data do not.
22
The change from the 16th to the 84th percentiles corresponds to a change from one standard
deviation below the mean to one standard deviation above the mean for a normally distributed
variable. Our measure of the intervals are skewed, somewhat bimodal, and bounded below at
zero, so we use percentiles instead. All other variables were set to their mean (for continuous) or
modal (for discrete) values for this calculation.
23
See Keele (2008) for more information on splines.
25
See, for example, National Conference of State Legislatures Legisbrief 6:48
(http://www.ncsl.org/research/fiscal-policy/supermajority-vote-requirements-to-pass-thebudget.aspx) or the National Governors Association
(http://www.nga.org/cms/home/management-resources/governors-powers-and-authority.html).
34