Political Analysis (2012) 20:501–519
doi:10.1093/pan/mps027
Testing Theories of Congressional–Presidential Interaction
with Veto Override Rates
Gregory J. Martin
Stanford Graduate School of Business, Stanford University,
655 Knight Way, Stanford, CA 94305
e-mail: [email protected]
The ability to veto legislation is the most important formal power of the presidency in the legislative process,
and presidents’ veto behavior has thus attracted a great deal of theoretical interest. Game-theoretic models
of congressional–presidential interactions explain vetoes by incorporating incomplete information over the
distribution of presidential or congressional types. In this article, I examine two prominent such theories, as
well as a simple “noisy” extension of a complete information theory. I show that each makes strong predictions not only about vetoes themselves but also about the resulting override votes; given that overrides
are so closely connected with vetoes, any valid theory of the latter must be able to successfully explain the
former. I test these predictions empirically and show that support for each of these theories in presidential
veto and override data from 1973 to 2008 is quite weak. This negative result suggests that current models
of the veto are incomplete; I sketch some possibilities for extension in the conclusion.
1
Introduction
The power to veto legislation is one of the few formal powers granted to the president by the
constitution, and provides the only directly outcome-relevant and publicly observable action that
presidents take in their interactions with congress. The veto is a straightforward exercise of presidential power in the legislative process with a clear and direct result on policy outcomes: the
president rejects policy change in favor of the status quo. Veto behavior thus provides information
on the president’s policy preferences. In contrast, the other formal and informal legislative powers
of the president—the “power to persuade” members of the congress and the bureaucracy (Neustadt
1980), the power to take unilateral action in unsettled areas of administrative law (Moe and Howell
1999), or the ability to make appeals to the mass public (Canes-Wrone 2001)—do not present the
president with such a cleanly observable binary choice.
Given the relatively simple nature of the veto and its substantive importance in US policymaking, in recent years, scholars have produced a proliferation of theories attempting to explain
its incidence. Theories along these lines address the questions of when presidents deploy the veto
and how members of the congress react when they anticipate being on the receiving end. A critical
design choice in such models is the information structure: how much the players (president,
members of congress, and voters) know about each other.
Models with complete information, like the “pivotal politics” theory of Krehbiel (1998), produce
the prediction that vetoes never occur.1 In situations where the president can credibly threaten
Author’s note: The author acknowledges helpful comments from Keith Krehbiel, Steve Callander, Jon Bendor, and
seminar participants at the GSB Political Economy Seminar, as well as several anonymous referees. The data sets used
in the empirical section, along with all computer programs used to generate the results in this article, are available from
the IQSS Dataverse at http://hdl.handle.net/1902.1/17923.
1
For a formal statement of this prediction, see e.g., Ferejohn and Shipan (1990).
ß The Author 2012. Published by Oxford University Press on behalf of the Society for Political Methodology.
All rights reserved. For Permissions, please email: [email protected]
501
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Edited by Jonathan Katz
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Gregory J. Martin
2
Following Krehbiel, throughout this article, I treat congress as consisting of just a median member and a veto pivot,
and ignore the complication of bicameralism. In the simple models of veto–override interactions presented here, bicameralism does not change any part of the analysis once we take the congressional veto pivot to be the more extreme
of the members at the 67th percentile of the House and Senate, respectively.
3
Not all of these models explicitly include an override stage, however, and doing so can significantly change the equilibrium. I extend the models where necessary to extract predictions.
4
This “noise” formulation of uncertainty is conceptually different from the incomplete–information mechanisms of the
first two models. It allows for members of the congress to simply make mistakes and vote incorrectly on legislation, as
opposed to rationally adjusting their strategy in response to incomplete information. The specification employed is
identical to the statistical voting-error models of Hirsch (2011) and Clinton (2007).
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a veto, the congress sends him a bill sufficiently moderate to be backed by a veto-proof majority
of two-thirds. The pivotal player in this situation—the member of the congress who is just indifferent between the proposed bill and the status quo—is the member whose ideal point lies at the
67th percentile of the distribution of ideal points in the congress.2 The president declines to veto the
bill because he knows the veto will certainly be overridden.
This no-veto prediction is obviously at odds with reality. Consequently, more sophisticated
models of vetoes incorporate some source of incomplete information or noise, so that vetoes
appear in equilibrium. While such theories have had success in explaining the fact that we regularly
observe presidential vetoes, they often neglect the fact that the constitution provides congress with a
means of responding to a veto: congress can, if it musters a two-thirds vote of both chambers,
override a veto and pass a bill over the president’s objection. As I demonstrate, a broad class of
incomplete–information models of veto interactions between the president and the congress yield
predictions not only about vetoes themselves but also about the incidence of successful override votes,
some of which are quite sharp.3 The incidence of successful override votes thus provides a number of
straightforward empirical tests that can be used to discriminate between alternative theories of veto
interactions.
In this article, I consider two prominent such theories, each of which locates the incomplete
information in a different player. The first is one of the models of veto interactions introduced by
Cameron (2000): the “override game,” in which congress does not know which of its members is the
pivotal one when facing down a presidential veto. The second is the alternative formalization of
incomplete information introduced by Groseclose and McCarty (2001) in which it is voters who are
uncertain about the president’s preferences; in situations of divided government, congress may wish
to force the president’s hand and provoke a veto in order to inform the voters about the president’s
true preferences. Finally, in order to consider the possibility that vetoes are generated by stochastic
shocks rather than strategic behavior, I develop an extension of the basic Krehbiel (1998) model,
which adds a pure noise component to voting decisions.4
When subjected to tests employing data on successful override votes, the three models considered here all fare quite poorly. In models with only congress and the president as players,
the observed rate of overrides is far too low to be consistent. In models that introduce voter
perceptions into the mix, voters do not appear to respond to overrides in the way predicted by
signaling theory.
Given that override votes are so closely connected with vetoes—the two have a natural
one-to-one relationship—a successful theory of the latter must be able to explain the former.
Without this constraint, the set of valid models is underidentified. A successful theory needs to
be simultaneously consistent with both veto and override data. The failure of several prominent
models to do so is a puzzle which, I hope, will inspire theorists of the presidency to develop models,
which are consistent with not just the “stylized fact” of vetoes but with all the available relevant
data. The theories considered here provide useful intuition and aid our understanding of the mechanisms that generate vetoes, but they are incomplete in at least one important way.
The remainder of the article proceeds as follows: the following two sections derive theoretical
predictions regarding the incidence of overrides from the three aforementioned models of veto
behavior, and then take these predictions to the data; the final section concludes.
Game-theoretic Models of Congressional–Presidential Interactions
xM
τ
τ
x0
503
P
Fig. 1 Ideal points in the “override game.”
2
Theoretical Predictions
2.1
Uncertain Veto Pivot Model
2.1.1
Lower bound on override probability for general distributions with bounded support
The override game described by Cameron (2000) is a four-stage game played by three players: the
congress (or, more accurately, the congressional median voter), the president, and the congressional
veto player. All players have preferences over bills x of the form Ui ðxÞ ¼ jx xi j, where xi is the
ideal point of player i.
First, nature chooses a type t of the veto player; t is defined as the location of the bill such that
UV ðÞ ¼ UV ðx0 Þ. Second, the congressional median player, who has ideal point xM < , makes a proposal x and votes it up or down against the status quo. Third, the president decides whether or not to
veto. Lastly, the veto player’s type is revealed and she chooses whether or not to override the veto.
5
See Chapter 4, pp. 99–106 for details.
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Cameron (2000) extends the classic spatial voting, or “pivot” theory to the case of incomplete
information over the policy preferences of the players in the game: members of congress and
the president. Cameron’s book describes several variant models of veto interactions, which
locate the uncertainty in different players; I focus on the version with uncertainty over the veto
pivot because, as I will show, it produces clear and testable restrictions on the likelihood of successful override votes.
In this version, Cameron sets up a standard unidimensional spatial model where lawmakers have
single-peaked, linear preferences; the incomplete information is formalized as uncertainty over who is
pivotal.5 Before congress passes a bill, nature chooses a type t of the veto player, unknown to the
congress, where t represents the location of the bill that would make the veto player indifferent
between the status quo and the new bill. Cameron assumes that t is drawn from a uniform distribu where both the status quo x0 and the president’s ideal point are assumed
tion on the interval ½, ,
as depicted in Fig. 1. After the bill goes through initial passage and the president
greater than ,
decides whether to veto or not, the veto player’s location t is revealed, determining whether or not
the veto is overridden. The strategic problem of the congressional proposer is to choose the location
of the bill that maximizes the proposer’s utility from the policy in place at the end of the game.
Cameron proves (in the appendix to Chapter 4) that this model predicts that the probability of
an override, conditional on the occurrence of a veto, must be at least one-half. While the prediction
that the lower bound on override probability is one-half is a consequence of the choice of a uniform distribution, I show below that a lower bound strictly greater than zero exists for any continuous distribution with bounded support. Additionally, for the very general class of symmetric
beta distributions, the lower bound on override probability remains exactly one-half. Right-skewed
beta distributions have lower bound probabilities less than one-half, and left-skewed beta distributions have lower bound probabilities greater than one-half.
Note that all of these derivations apply to the case of linear utility over outcomes on the part of
the median player in the congress. Linear utility implies that the median player is risk-neutral with
respect to the outcome. If we modify the utility function to be strictly concave, risk aversion on the
part of the median player would increase the minimum threshold on override probability.
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Gregory J. Martin
Clearly, in equilibrium, the veto player will override the veto of any bill x, where x x0 .
since there is some chance the veto will be
The president will choose to veto any bill less than ,
sustained and the status quo will prevail. Knowing this, the congressional median player chooses
some optimal proposal x* to maximize his expected utility.
To give the override game its most general formulation, I generalize Cameron’s assumptions
and allow for t to be drawn from an arbitrary continuous distribution with cumulative density
The
function (CDF) F (t), probability density function (PDF) f (t), and bounded support ½, .
probability that the veto of a given proposal x is overridden is just the probability that x, in
other words, F(x). I follow Cameron and normalize the median player’s ideal point xM to be equal
to zero. With these definitions, the median player’s optimal proposal solves:
x ¼ argmaxx PðOverrideÞUM ðxÞ þ PðSustainÞUM ðx0 Þ
There are two possible classes of solution to this maximization problem; either the median player
which passes for sure, or he gambles and chooses some interior x 2 ð, Þ,
which
proposes x ¼ ,
will certainly be vetoed but could potentially survive the override stage. Bills outside of the set ½, are strictly dominated and will not be played in equilibrium. For an interior maximum (the only
type of bill that would provoke a veto from the president), the first order condition on x* is:
fðx Þðx0 x Þ Fðx Þ ¼ 0
After some rearrangement, rewrite this as:
x ¼ x0 Fðx Þ
fðx Þ
Now, the status quo x0 is unknown, in general, but in any situation where a veto threat by the pre This gives us a lower bound on the optimal proposal x*:
sident is credible, it must be the case that x0 .
x Fðx Þ
fðx Þ
From this inequality, we can conclude immediately that x > . Since FðÞ ¼ 0, setting x ¼ in
a contradiction. This observation leads directly to the following
the inequality above gives x ,
proposition:
Proposition 1. The lower bound on the probability of an override conditional on a veto is strictly
greater than zero.
«
Proof. x > , and F is continuous, so Fðx Þ > 0.
Now, it is not particularly surprising that the optimal proposal must have some chance of
surviving a veto, so the mere existence of a nonzero lower bound on override probability
guaranteed byR Proposition
1 does not tell us much. However, if we apply the definition of the
x
CDF Fðx Þ ¼ fðxÞdx, we can rewrite the inequality above as:
Z
x fðxÞ
þ 1 dx fðx Þ
So, the minimum possible optimum proposal xmin must solve:
Z x min
fðxÞ
þ
1
dx ¼ fðxmin Þ
ð1Þ
ð2Þ
For a given distribution f(x), we can solve equation (2) numerically and then evaluate Fðxmin Þ to
get the lower bound on override probability. Later in the article, I evaluate this probability for
various members of the beta family of distributions, and show that so long as the distribution is
symmetric, the minimum probability of overrides is one-half.
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¼ argmaxx FðxÞðxÞ þ ð1 FðxÞÞðx0 Þ
Game-theoretic Models of Congressional–Presidential Interactions
2.1.2
505
Relationship to the upper bound of the t distribution
The Cameron model also implies that the probability of overrides should be weakly increasing
To see this, rewrite the optimization problem that the median player solves in terms of Fðx Þ:
in .
Fðx Þ ¼ argmaxFðxÞ FðxÞðF1 ðFðxÞÞÞ þ ð1 FðxÞÞðx0 Þ ¼ argmaxFðxÞ gðFðxÞ, x0 Þ
Note that because F is a continuous CDF, F1 is well defined.
Proposition 2. The probability of an override is weakly increasing in the upper bound of the distri
bution, .
2.2
The Blame Game
Groseclose and McCarty (2001) provide an alternate explanation for the observation of vetoes.
They propose a model where the uncertainty lies in voters’ perceptions of the president. Vetoes
occur as a result of a hostile congress sending the president a bill it knows will provoke a veto in
order to signal to voters that the president is an extremist. They show that, under certain configurations of the ideal points of the president, congress and voters as well as the status quo, vetoes
can occur in equilibrium.
Groseclose and McCarty’s paper (henceforward referred to as G–M) treats the congress as a
unitary actor and ignores what happens to a bill after it is vetoed by the president. To derive
predictions from their framework relevant to the occurrence of override votes, it is necessary to
extend their model by introducing a fourth player, the congressional veto player, with commonly
known ideal policy cv. The game form is extended by an additional stage in which the veto player
chooses an action 2 foverride, sustaing. I assume that this stage occurs before the voter chooses
his approval rating of the president, but as I will show below, this choice is not relevant to the veto
player’s decision; regardless of the order of the final two stages of the game, the veto player will
choose his action purely on the basis of the policy and without regard to the president’s approval
rating. The following two propositions establish this claim:
Proposition 3. The president will never veto a bill he knows will be subsequently overridden unless
the voter’s equilibrium belief about his expected type (weakly) increases as a result. Formally
ð ¼ veto, ¼ overrideÞ ) a ð , Þ a ðsign, Þ.
Proof: Vetoing a bill that will be overridden is a strictly dominated action if the president’s approval
rating falls as a result. (The president could have signed the bill and gotten the same policy without
taking a hit to his popularity). Therefore, if a president vetoes a subsequently overridden bill in
equilibrium, voters’ expected beliefs about his type, which completely determine their approval,
cannot decrease.
«
Next, we consider whether it is possible to have an equilibrium in which congress proposes a bill,
some presidential type vetoes it and is overridden by the veto player, in which this type’s approval
rating rises as a result. The following proposition shows that the answer is no:
Proposition 4. ð ¼ veto, ¼ overrideÞ ) a ð , Þ a ðsign, Þ.
Proof: The proof is by contradiction. Suppose that a ðveto, Þ > a ðsign, Þ for some presidential
type t0 , who is offered bo in equilibrium. An implication of this statement is that some other type
t00 < t0 must not be offered bo in equilibrium. Note that if ¼ override, as assumed, the optimal bo
is determined only by the location of the veto player cv, and cannot depend on the president’s type.
Hence, an equilibrium involving overrides must be at least a partial pooling equilibrium.
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@g
@g
Proof: Differentiating g with respect to x0 , we find that @x
¼ FðxÞ 1, so @x
is increasing in F(x).
0
0
This is sufficient to show that the function g has increasing differences in ðFðxÞ, x0 Þ; because x0 is
g also has increasing differences in ðFðxÞ, Þ.
Application of Topkis’ theorem
bounded below by ,
completes the proof that Fðx Þ, the solution to the optimization problem and also the probability of
overrides occurring, is weakly increasing in .
«
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Gregory J. Martin
Having established that t00 does not receive bo in equilibrium, and that, therefore, no override
occurs when the president’s type is t00 , there are two remaining options for what t00 could be offered
by congress.
1. Congress offers a bill bv (t00 ) that the president vetoes and is subsequently sustained.
2. Congress offers a bill bs (t00 ) that the president signs.
Option 1 is inconsistent with the existence of a subset of presidential types being offered bo, since
the payoff from this option to congress does not vary with the president’s type. If it were profitable
to offer bv (t00 ) to type t00 , it would also be profitable to offer bv (t00 ) to type t0 , contradicting our initial
equilibrium assumption. To see this, note that the relative payoffs from offering bo versus bv do not
depend on the president’s type but only on the model parameters and the set of types who are
offered bo in equilibrium:
UC ðbV Þ ¼ c jy0 cj BC ð þ ðbV ÞÞ
Option 2 is inconsistent with equilibrium for a similar, though more subtle, reason. If congress is
willing to offer bo to a subset of types whose approval rating rises as a result, then it must be the case
that the policy benefits of the bill are sufficiently large to outweigh the cost of letting the president
increase his approval rating. Without loss of generality, let t0 be the lowest type who is offered bo in
equilibrium, and bs (t0 ) be the optimal bill that congress could offer that would induce t0 to sign it. It
must be true that:
c jbO cj BC ð þ ðbO ÞÞ c jbs ðt0 Þ cj BC ð þ ðbS ðt0 ÞÞÞ
Rearranging gives:
C ðjbO cj jbS ðt0 Þ cjÞ BC ððbO Þ ðbS ðt0 ÞÞ
The right hand side of the above inequality is strictly positive because ðbS ðt0 ÞÞ t0 and
ðbO Þ > t0 by assumption. This implies that the optimal signed bill is strictly closer to the
congress’ ideal point than the optimal vetoed-overridden bill. The continuity of the congress’
preferences and the type space implies that 8e > 0, 9t00 < t0 such that jbS ðt00 Þ bS ðt0 Þj < e, and
thus there exists a type t00 , which in equilibrium is offered and signs a bill closer to the congress’
ideal point than bo. But, why would type t00 sign such a bill? Its policy effect from the president’s
perspective is negative, and voters know that all presidential types would veto a bill to the right of
bo; hence, there can be no negative signaling effect from a veto. Signing bS ðt00 Þ is therefore strictly
dominated. An equilibrium taking the form of Option 2 cannot exist.
«
Propositions 3 and 4 together imply that a veto–override pair can occur only in situations where
the veto does not divide presidential types, and all types are indifferent between vetoing and signing.
A second implication is that the override player’s choice is unaffected by the signaling aspect of the
game; her optimal strategy is the same as in a standard game with only policy concerns.
The first implication means that voters should not update their beliefs about the president’s type
following an overridden veto; hence overrides should not be associated with any change in presidential approval.6 This is in contrast to the prediction, noted in G–M, which sustained vetoes
should be associated with drops in presidential approval. I test this hypothesis below in Section 3.
The second implication necessitates a modification to the G–M specification of the conditions
under which “blame game” vetoes can occur. Specifically, in Proposition 3, equation (3.d) of G–M,
6
This sharp result is in part a consequence of the assumption of full information among the congressional and presidential players. If we added, a la Cameron, some presidential uncertainty over the location of the veto pivot, the logic of
Proposition 3 would no longer hold exactly. Nonetheless, the president’s payoff function is continuous in the probability
of a veto being sustained. Hence, we can expect the propositions to hold approximately if the amount of uncertainty is
small; only very rarely will some proper subset of presidential types find it profitable to veto a bill that is nearly certain
to be overridden. In the presence of small amounts of uncertainty over the veto pivot’s location, an overridden veto
provides only a small amount of information to voters.
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UC ðbO Þ ¼ c jbO cj BC ð þ ðbO ÞÞ
Game-theoretic Models of Congressional–Presidential Interactions
507
2.3
Voting Error
As an alternative specification of the source of noise in veto behavior, I develop a benchmark model
that eliminates the strategic behavior of the previous two models and simply allows members of the
congress to make mistakes in voting. This formulation is conceptually distinct in that it explains
vetoes as the consequence of uncertainty that is unforeseen and unaccounted for by the players in
the game. Here, the median player does not understand the stochastic nature of the veto player’s
location; the observation of vetoes is due to pure voting error on the part of the individual legislators rather than risky proposal behavior on the part of the congressional median player.
I assume that members of the congress have an ideal point that is the additive combination of
two components: a deterministic component that is common knowledge, and a stochastic component that is unknown both to the congress and to the econometrician. I assume the errors are i.i.d.
normally distributed with mean zero and (unknown) variance 2 . (These assumptions are identical
to the specification used in Clinton (2007) and Hirsch (2011)). The ideal point of player i is just:
2
xi ¼ xD
i þ ei , ei Nð0, Þ
Since the deterministic component of preferences is common knowledge, the veto player xv can
be identified. Suppose that the median player behaves as in the complete information pivotal
politics game, and that the ideal points are widely dispersed enough that the probability of the
additive errors causing the relative position of individual congressmen to flip is negligible. Then,
the median player proposes a bill that makes the veto player exactly indifferent between the bill
and the status quo. The probability of the bill being overridden if the president chooses to veto is
just the probability that ev 0, i.e., one-half.
Now, let’s relax the assumption about dispersion in ideal points somewhat, and consider the
congressmen with ideal points on either side of xv: xv1 and xvþ1 (Fig. 2). Define the distances
D
D
D
b ¼ xD
v xv1 and a ¼ xvþ1 xv . If the degree of dispersion in ideal points is such that these three
players are the only three who could conceivably end up in the pivotal position after the addition of
stochastic errors, we can write the probability of a veto override as:
PðOverrideÞ ¼ Pðv votes to overideÞPð v þ 1 or v-1 vote to overrideÞ
þ Pðv votes to sustainÞPðv þ 1 and v-1 vote to overrideÞ
1
1
¼ ð1 ð1 FðbÞÞFðaÞÞ þ ðð1 FðaÞÞFðbÞÞ
2
2
1
¼ ð1 FðaÞFðbÞ þ FðaÞFðbÞÞ
2
where F is the CDF of the normal distribution with mean zero and variance 2 . In the next section,
I estimate the parameters a, b, and 2 using observed veto data and a maximum likelihood estimation technique.
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the president’s type t must be replaced with the veto player’s type, cv, if cv > t. This has the effect of
reducing the set of status quos for which “blame game” vetoes are possible, relative to the case
without the possibility of override votes.
The addition of the override stage to the G–M model nonetheless preserves the important
qualitative features necessary to draw inferences from observed data. Namely, both veto–sustain
and veto–override pairs can occur in equilibrium given appropriate configurations of the players.
The former can occur, just as in the unmodified version of the model, when the status quo is
relatively extreme. The latter can occur if the public’s beliefs are such that the position of even
the most moderate possible presidential type is more extreme than the status quo on some issue,
and both congressional players are on the opposite side. In this case, all presidential types can
costlessly express their disapproval of a moderating proposal by issuing a veto, which is sure to be
overridden. Voters gain no new information from this sequence of events, as required by
Propositions 3 and 4.
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Gregory J. Martin
3
Empirical Tests
3.1
Testing the Lower Bound Prediction
Proposition 1 demonstrates that a nonzero lower bound on the probability of overrides exists for
any bounded distribution of potential veto players in the Cameron model. Equation (2) can be
solved numerically to determine the lower bound for a given distribution. In this section, I compute
the theoretically determined minimum bound for the beta family of distributions, and compare with
the empirically observed rate.
3.1.1
Data
I collected data on vetoed bills from the Library of congress’ THOMAS database7 for the 93–110th
congresses, the period available in the database. For each vetoed bill, I recorded the congress
in which it occurred, the bill number, and whether or not the presidential veto was overridden.
The last classification was determined by examining the database’s “Last Major Action” field.
If this field contained the name of a public law which the bill had become, I considered the
veto overridden; otherwise I considered the veto sustained. There were 181 vetoed bills over
the period, of which 24 were overridden. The data sets used in all the empirical tests, along
with all computer programs used to generate the results in this article, are available from
Martin (2012).
3.1.2
Tests
Estimating a confidence interval for the true override probability is a simple exercise in maximum
likelihood estimation. The likelihood function for the parameter p^ when we observe n vetoes and k
overrides is:
n k
^ nk
^
Lðpjn, kÞ ¼
p^ ð1 pÞ
k
7
http://thomas.loc.gov/.
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Fig. 2 Diagram of voting error with three players.
509
Game-theoretic Models of Congressional–Presidential Interactions
The maximum likelihood estimator (MLE) estimator’s mean and variance are:8
k
n
pð1 pÞ
^ ¼
VarðpÞ
n
p^ ¼
Table 1 Maximum likelihood estimates of true probability of override
Congress
Observations
93
94
95
96
97
98
99
100
101
102
104
105
106
109
110
8
39
19
12
5
9
20
19
1
25
5
4
12
1
2
All
181
Estimate of p (CI)
p-value
0.125
0.205
0.000
0.167
0.000
0.111
0.100
0.158
0.000
0.080
0.200
0.250
0.167
0.000
0.500
.001
.000
NA
.001
NA
.000
.000
.000
NA
.000
.047
.124
.001
NA
.500
(0.104 to 0.354)
(0.078 to 0.332)
(0.000 to 0.000)
(0.044 to 0.378)
(0.000 to 0.000)
(0.094 to 0.316)
(0.031 to 0.231)
(0.006 to 0.322)
(0.000 to 0.000)
(0.026 to 0.186)
(0.151 to 0.551)
(0.174 to 0.674)
(0.044 to 0.378)
(0.000 to 0.000)
(0.193 to 1.193)
0.133 (0.083 to 0.182)
.000
Note. p-value is undefined in congresses in which there were no successful override votes.
8
9
For derivation, see e.g., Casella and Berger (2001), or any other standard econometrics text.
I used MATLAB’s numerical solver function fsolve and numerical integration function quad to compute the solution
to equation (2).
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I construct the asymptotic confidence interval for p using a significance level of 5% in Table 1.
While I believe the pooled estimate over all congresses to be more accurate due to the large
sample size, I calculate the rate for each individual congress as well as a check on stability.
Additionally, I calculate the p-value for the probability that p ¼ 1/2 for each congress and the
pooled data set.
Table 1 shows that the prediction of the Cameron asymmetric information theory with a
uniform distribution of t is rejected with extremely high confidence in all but two congresses,
the 105th and the 110th, each of which had only a few observed vetoes. But perhaps this is not
a failure of the general theory; it might be purely a problem with the choice of the uniform.
To test this conjecture, I solve equation (2) over a range of parameter values of the beta distribution.9 The beta distribution has two shape parameters, and , and takes on a variety of shapes
depending on the values chosen for these parameters. The distribution has expectation equal to
/( þ ); e.g., a higher relative value of shifts the probability mass to the right. If ¼ , the
distribution is symmetric; the special case ¼ 1, ¼ 1 is the uniform distribution.
Figure 3 shows the calculated minimum possible probability for a range of parameters:
1 10, 1 10. The figure shows that as becomes large relative to , the minimum
override probability approaches zero; when becomes large, it approaches 1. Whenever ¼ ,
i.e., whenever the distribution is symmetric, the minimum rate of overrides is exactly one-half, just as
in the special case of the uniform distribution.
Figure 4 takes a slice of the 3D figure at the upper bound estimate of p from Table 1. The figure
shows, in white, the subset of the parameter space that is consistent with the MLE upper bound on p.
510
Gregory J. Martin
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Fig. 3 Minimum override probabilities for the beta family of distributions.
Parameter Space Consistent with Observed Override Rate
10
9
8
7
Beta
6
5
C
4
3
2
B
A
1
1
2
3
4
5
6
7
Alpha
Fig. 4 Beta distribution parameters consistent with observed override rate.
8
9
10
511
4
Game-theoretic Models of Congressional–Presidential Interactions
B
2
A
0. 0
0 .5
1 .0
x
Fig. 5 Representative distributions consistent with observed override rate.
In other words, these are the values of and such that Fðxmin Þ 0:182. Several representative
examples of such distributions, labeled A, B, and C, are shown in Fig. 5. Note that while none of
these distributions can be excluded as inconsistent with observed data at the 5% significance level,
distributions close to B have much higher p-values than do those closer to A or C.
These distributions vary in shape but share the property that they are all strongly right-skewed.
The interpretation of this fact is that, to be consistent with the observed rate of veto overrides, the
distribution of the location of the congressional veto player must be highly skewed in the direction
of the president.
Recall that the derivation of equation (2) depended on the assumption of linear utility on the
part of the median congressional player. In the case of some concave utility function, e.g., a
quadratic loss function UðxÞ ¼ ðx x Þ2 , the median player would tend to be more risk-averse
and hence less likely to tolerate a low probability of veto override. The effect of such a utility
function would be to shrink the subset of the parameter space consistent with the observed veto
rate, relative to that shown in Fig. 4.
3.2
Testing the Relationship of Override Probability to Proposition 2 shows that, if the assumptions of the Cameron incomplete information model are
true, the observed rate of veto overrides should be weakly increasing in the upper bound of the t
distribution. To test this proposition, I run a Monte Carlo simulation of congressional ideal points
using DW-NOMINATE scores and standard errors to determine an estimated upper bound on the
spatial location of the veto pivotal player. I then apply a probit technique to estimate the relationship between override probability and this upper bound.
3.2.1
Data
For this test, I combine the veto and override data described above with DW-NOMINATE estimates of House and Senate ideal points from Carroll et al. (2009). I collected first-dimension ideal
point scores and parametric bootstrapped standard error estimates for each of the congresses for
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0
Probability Density
C
512
Gregory J. Martin
I repeat the folwhich veto data are available.10 To construct from this data, the estimate of ,
lowing Monte Carlo procedure 10,000 times:
For each congress, I compute the 95th percentile of the distribution of the location of the House
and Senate veto player over all 10,000 simulations. I take the maximum of these two values to be
the estimate of the upper bound on the congressional veto player, .
3.2.2
Tests
To test Proposition 2 in actual data, I construct a simple probit specification. Let Y be the vector of
vetoed bills, with yi ¼ 0 indicating that the veto of bill i was not overridden, and yi ¼ 1 indicating
that it was. Let i be the estimate of described above for the congress in which the veto occurred.
Then the model is:
yi ¼ If0 þ 1 i þ ei 0g, ei ji Nð0, 1Þ
Table 2 shows the estimates of the coefficient and marginal effect of on the probability of a veto
being overridden. Inspection of the table shows that the estimated coefficient has the sign predicted
by the theory, although it is not statistically different from zero. (Note that the independent variable
in this specification is subject to obvious measurement error, so the coefficient estimates will tend
to be attenuated toward zero). The estimated probability that the true coefficient is positive is
slightly <80%.
3.3
Testing the Blame Game Model
Groseclose and McCarty’s blame game model gives the prediction that vetoes should be associated
with declines in presidential popularity. As demonstrated above, this prediction does not hold for
overridden vetoes; overrides should only occur in equilibrium when they give voters no information
Table 2 Probit estimates of the marginal effect of tau on probability of override
P(Override)
^
Constant
N
Coefficient
Marginal effect
1.501 (1.20)
1.569 (0.39)
181
0.318 (0.25)
181
Note. Standard errors in parentheses.
10
Scores were downloaded from the DW-NOMINATE page at http://voteview.com/dwnomin.htm on February 23, 2009.
Downloaded from http://pan.oxfordjournals.org/ at Pennsylvania State University on May 12, 2016
1. For every legislator in the sample, I draw an ideal point realization from a normal distribution with mean given by the legislator’s first-dimension DW-NOMINATE score and
standard deviation given by the first-dimension standard error.
2. For each congress, I find the location of the ideal point of the House and Senate veto
players. If the president in a particular congress is a Republican, the veto player is assumed
to be located at the 67th percentile of the distribution, and if he is a Democrat the veto
player is assumed to be located at the 33rd percentile of the distribution.
3. When the president is a Republican, the ideal point of the veto player is typically positive,
and when he is a Democrat, the ideal point is typically negative. To compare across different presidential regimes (and because what I am trying to measure is the distance of the
veto player from the congressional median), I take the absolute value of the difference
between the veto player’s ideal point and the median player’s ideal point.
Game-theoretic Models of Congressional–Presidential Interactions
513
about the president’s type. I construct a test exactly parallel to G–M, but separate out the
overridden and sustained vetoes.
3.3.1
Data
Veto data are identical to that used in the other analyses. The dependent variable, exactly as in G–
M, is Gallup presidential approval ratings, averaged quarterly, and first-differenced. I also include
macroeconomic control variables of quarterly inflation rate and GDP growth rate, from the Bureau
of Labor Statistics and Bureau of Economic Analysis, respectively. As in G–M, I restrict attention
to vetoes occurring in periods of divided government, the situation where “blame game” vetoes are
predicted to occur.
Tests
Like the regressions reported by Groseclose and McCarty,11 which show a negative effect of
“major” vetoes on presidential approval, I regress the quarterly change in presidential approval
on two transformations of the quarterly veto count: a dummy specification with an indicator
variable equal to 1 if there was at least one veto in the quarter and 0 otherwise, and a log transformation equal to logð1 þ vq Þ, where vq is the number of vetoes in quarter q. I construct each of
these variables separately for sustained and overridden vetoes. The specifications are thus:
Appq ¼ D IfvSq > 0g þ D IfvO
q > 0g þ Xq þ eq
ð3Þ
Appq ¼ L logð1 þ vSq Þ þ L logð1 þ vO
q Þ þ Xq þ eq
ð4Þ
where vSq and vO
q are the number of sustained and overridden vetoes, respectively, in quarter q; Xq is
a vector of control variables including macroeconomic indicators and presidential fixed effects; and
eq is an i.i.d. error term.12 The predictions of the blame game model can be stated as follows:
H1 : < 0
H2 : ¼ 0
The results of the regressions are given in Tables 3 and 4. In both specifications, both coefficients
of interest are negative but neither is significantly different from zero. We reject the hypothesis
that the coefficients and differ in both models.13 Equivalently, we could formulate the model
with a general veto term and a marginal override term; the estimated override coefficient in this case
is negative but not significant.14 While these results are obviously inconclusive, there does not seem
to be any evidence that the public treats sustained vetoes differently than overridden vetoes, in
contradiction to the strong distinction predicted by the blame game theory; if anything, overridden
vetoes seem to be worse for a president’s approval than sustained ones.
One caveat to these results is that I do not segregate vetoes into “major” and “minor” categories as
in G–M, for the simple reason that I lack good data to classify the bills in the sample as such. To
address any potential problems from this oversight—for example, that some bills do not have the
salience to get voters’ attention and hence do not affect approval—I performed a simple bootstrap-like
experiment. I randomly assigned bills in the sample to major and minor categories by, effectively,
flipping an unbiased coin, and then recomputed the estimates of specification 3 with separate dummies
11
The results reported here parallel those in G–M’s Table 1.
The specifications are identical to those in G–M with the exception that I do not classify vetoes as “major” or “minor.”
The reason for this is that G–M use the classification scheme of Mayhew (2005), which covers legislation prior to 1994;
my sample extends to 2008. I show below that this is unlikely to affect the overall results.
13
p-values of the heteroskedasticity-adjusted joint F-test are 0.84 in the dummy specification and 0.63 in the log
specification.
14
I also tested a baseline specification with both types of vetoes pooled together, for maximal comparability with the
original G–M paper. I replicate their finding that vetoes are associated with negative changes in approval, with nearly
identical point estimate of 2.1 percentage points. The comparable specification in the original G–M paper, with a
different sample period, found an effect of 2.2 points.
12
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3.3.2
514
Gregory J. Martin
Table 3 Presidential approval regression: Dummy variable specification
(Intercept)
D
D
GDP growth
Inflation rate
Bush II
Clinton
Ford
Nixon
Reagan
Estimate
Std. error
t-value
Pr(> jtj)
4.9914
2.0761
1.5458
0.4699
0.9261
1.6784
2.7130
5.7670
12.8034
1.0490
3.2283
1.7181
2.1511
0.2585
0.4691
2.9437
2.5541
4.0105
3.7981
2.3544
1.55
1.21
0.72
1.82
1.97
0.57
1.06
1.44
3.37
0.45
.1254
.2299
.4742
.0723
.0513
.5699
.2909
.1538
.0011
.6569
Table 4 Presidential approval regression: Log transform specification
(Intercept)
L
L
GDP growth
Inflation rate
Bush II
Clinton
Ford
Nixon
Reagan
Estimate
Std. error
t-value
Pr(> jtj)
5.4768
0.9702
2.2871
0.4745
0.9520
2.0033
2.5338
5.3896
12.9292
0.9551
3.2666
1.3854
2.8559
0.2598
0.4741
2.9802
2.5919
4.1175
3.8090
2.3620
1.68
0.70
0.80
1.83
2.01
0.67
0.98
1.31
3.39
0.40
.0969
.4855
.4252
.0710
.0475
.5031
.3308
.1937
.0010
.6869
N ¼ 104, Adj-R2 ¼ 0.17.
for major and minor vetoes and overrides. I repeated this procedure 100,000 times. The distribution of
coefficients resulting from the experiment is shown below in Fig. 6.
The results of this experiment do not show any indication of bimodality, which would be expected
if there were truly two categories of vetoes, one which affected presidential approval and one which
did not. The lack of any significant distinction between overridden and sustained vetoes in terms of
their effects on presidential approval is also readily evident. Not surprisingly, the effect of overrides—which are comparatively rare—has higher variance, but the average effect is actually slightly
more negative than that of sustained vetoes, again contradicting the blame game theory.
3.4
Testing the Voting-Error Model
Given the weak support for the models described above, one possible conclusion might be that the
assumption of equilibrium played by forward-looking players employed in both models is too
strong. Perhaps the observation of vetoes is due to pure voting error on the part of the individual
legislators rather than risky proposal behavior on the part of the congressional median player, or
strategic grandstanding by an opposition party. In the next section, I estimate the parameters of
such voting error that best fit the observed distribution of veto overrides, and show that this model
is even harder to square with observed data than is the Cameron model.
3.4.1
Data
The data for this analysis are identical to the set used previously and consist of 181 observations of
vetoed bills ranging from the 93rd to 110th congress.
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N ¼ 104, Adj-R2¼ 0.18.
Game-theoretic Models of Congressional–Presidential Interactions
515
3.4.2
Tests
Consider the three-legislator model of additive normal voting error described above. Let p be the
probability of an override conditional on observing a veto; as demonstrated earlier, p is given by:
1
p ¼ ð1 FðaÞFðbÞ þ FðaÞFðbÞÞ
2
The logarithm of the likelihood of observing k overrides out of n vetoes is:
n
log L ¼ log
þ k log p þ ðn kÞ logð1 pÞ
k
Taking derivatives with respect to each of the parameters a, b, 2 and applying the symmetry
properties of the normal distribution gives the following description of the gradient of the log
likelihood function:
@
k @p
n k @p
log LðYjÞ ¼
þ
@
p @
1 p @
@p
1
¼ fðaÞ
@a
2
@p 1
¼ fðbÞ
@b 2 @p
1
@
@
¼ FðaÞ
FðbÞ þ FðbÞ
FðaÞ
@ 2 2
@ 2
@ 2
1
@
@
FðbÞ þ FðbÞ
FðaÞ
FðaÞ
2
@ 2
@ 2
Za
@FðaÞ
x2
FðaÞ
¼
fðxÞdx 2
2
4
@
2
1 2
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Fig. 6 Distribution of “major veto” coefficients.
516
Gregory J. Martin
Fig. 7 Probability of override with standard normal voting error.
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In the above equations, f(x) and F(x) refer to the normal PDF and CDF, respectively, with mean
x and variance 2. Unfortunately, the system described above is not identified—we are effectively
trying to estimate three parameters with two observations, n and k. To identify the estimate,
I normalize b ¼ 1 and estimate the remaining two parameters by numerical maximization of the
log likelihood function. The result of the maximization procedure is effectively a ¼ 1, 2 ¼ 1.
How can this be? Figure 7, which shows the override probability with standard ( 2 ¼ 1) normal
error for various choices of a and b, provides some idea of what is going on.
Even as we let b go to zero and let a become very large relative to the standard deviation, the
probability of override never drops below one-fourth. It is impossible to approach the observed rate
of overrides in the additive normal voting error model with three players.
Of course, the restriction to three potentially pivotal members is an artificial one imposed to
allow for analytic maximum likelihood solution. I next dropped this restriction and estimated a
voting error model with a full complement of legislators potentially occupying the veto-pivotal role.
The complexity of this case requires a resort to simulation.
I performed a separate simulation analysis for each of the congresses (both House and Senate)
in the sample. The method I employed consisted of drawing an ideal point realization for each member
of the chamber from a normal distribution with mean given by the legislator’s first dimension
DW-NOMINATE score and standard deviation given by the legislator’s first-dimension standard error (computed using the bootstrap method of Carroll et al. 2009). In each simulation,
I computed the realized veto player and determined whether a proposed bill at the ideal point
of the pre-error veto player would have passed an override vote. The results, shown in Table 5,
show the percentage of simulations (out of one hundred thousand) in which this hypothetical
override vote was successful.
Two observations, both in the Senate, fall within the estimated confidence interval for the
override rate. Hence, we can conclude that it is not impossible, as it was in the three-player case,
that the voting error model with a full complement of legislators could produce something like the
observed rates of successful override votes. However, the vast majority of legislator ideal point
517
Game-theoretic Models of Congressional–Presidential Interactions
Table 5 Actual override rates and simulated rates under voting-error model
Simulated senate
Simulated house
Observed
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
Mean
0.73
0.28
0.51
0.11
0.78
0.95
0.97
0.42
0.64
0.34
0.75
0.48
0.68
0.88
0.67
0.75
0.13
0.25
0.57
0.83
0.25
0.58
0.80
0.88
0.71
0.26
0.53
0.01
0.39
0.76
0.89
0.40
0.63
0.39
0.84
0.78
0.84
0.60
0.13
0.21
0.00
0.17
0.00
0.11
0.10
0.16
0.00
0.08
NA
0.20
0.25
0.17
NA
NA
0.00
0.50
0.14
Note. Bolded entries indicate values that fall within the 95% MLE confidence interval for the true override rate.
Number of simulations ¼ 100,000.
configurations in the sample period produce override rates that are still far higher than the actual
rate, and on average the simulations generate an override rate close to one-half. Moreover, the variation in simulated rates in the House is only weakly correlated with the actual rate, and in the
Senate, the correlation is negative.15 Adding larger numbers of legislators does not solve the fundamental problem that the voting error model predicts override rates far higher than those that are
actually observed.
4
Conclusion
The very low rate at which presidential vetoes are overridden by the congress is difficult to reconcile
with incomplete–information pivot theories in which legislators have preferences defined over
policy outcomes. The pure policy-motivated models considered here appear to robustly predict
higher rates of override success than are observed. In Cameron’s median proposer model, where
the location of the veto player is uncertain, we have to assume a distribution of possible veto
players strongly skewed in the direction of the president in order to match the observed rate.16
In the voting-error model with three possible veto players, we get a very similar conclusion, that
the legislator to the veto player’s right (toward the president) must be much farther away than the
legislator to the left (away from the president).
One way to interpret these results is similar to the notion of presidential power described in
Krehbiel (1998), following the classic analysis of Neustadt (1980). If the power of the president is
one of persuasion, then the rightward skew of the estimated distribution of veto players may reflect
15
The correlation coefficient of the simulated House rate with the actual rate is 23%; for the simulated Senate rate,
it is 21%.
16
As discussed in Section 2, the results presented here apply to the version of the override game in which a congressional
proposer and the president both have common knowledge ideal points, but the veto player’s ideal point is unknown.
Models in which, instead, the president’s ideal point is uncertain are potentially consistent with low override success
rates: given the right configuration of preferences, any observed rate of override success is consistent. These models
make no unconditional predictions about override rates and hence cannot be rejected on the basis of the evidence in this
article. However, they do make predictions about the joint likelihood of vetoes and overrides, which would need to be
investigated before the results presented here could be considered evidence in their favor.
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Congress
518
Gregory J. Martin
References
Cameron, Charles M. 2000. Veto bargaining: Presidents and the politics of negative power. Cambridge, MA/England:
Cambridge University Press.
Canes-Wrone, Brandice 2001. The president’s legislative influence from public appeals. American Journal of Political
Science 45(2):313–29.
Carroll, Royce, Jeffrey B. Lewis, James Lo, Keith T. Poole, and Howard Rosenthal. 2009. Measuring bias and uncertainty in DW-NOMINATE ideal point estimates via the parametric bootstrap. Political Analysis 17(3):261–75.
Casella, George, and Roger L. Berger 2001. Statistical inference, 2nd ed. Pacific Grove, CA: Duxbury Press.
Clinton, Joshua D. 2007. Lawmaking and roll calls. Journal of Politics 69(2):455–67.
Ferejohn, John, and Charles Shipan. 1990. Congressional influence on the bureaucracy. Journal of Law, Economics and
Organization 6(Special Issue):1–20.
Gilmour, John B. 2011. Political theater or bargaining failure: why presidents veto. Presidential Studies Quarterly
41(3):471–87.
Groseclose, Tim, and Nolan McCarty. 2001. The politics of blame: bargaining before an audience. American Journal of
Political Science 45(1):100–19.
Hirsch, Alexander V. 2011. Theory driven bias in ideal point estimates: a Monte Carlo study. Political Analysis
19(1):87–102.
17
For more systematic evidence along these lines, see the recent work by Gilmour (2011). Gilmour finds that the blame
game narrative appears frequently in contemporary media accounts of vetoes.
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the fact that the president deploys this power to move marginal legislators to his side following
a veto, leading the entire distribution of potentially pivotal players in the final override vote to be
shifted in his direction.
This interpretation, while plausible, does not explain the failure of Proposition 2, which should
hold regardless of the distribution of veto players. Another interpretation is that we cannot explain
well veto and override phenomena without connecting the legislative game to the electoral game
that legislators play simultaneously. If legislators care about their re-election prospects as well as
policy outcomes, they may be motivated to take a stand on a popular issue even if they know that it
will certainly provoke a presidential veto.
The Groseclose–McCarty “blame game” model formalizes this idea in terms of voter uncertainty
regarding the president’s policy preferences. The “blame game” is an intuitively appealing model
that comports well with the observation of vetoes—such as the multiple votes on the S-CHIP bill in
the 110th congress—where both sides appear to have complete information on the other’s
position.17 However, the game form implies that in equilibrium, presidents will act so as to eliminate any signaling effect from vetoes that are subsequently overridden. Knowing this, voters
should not update their beliefs about the president following an override as they do following a
sustained veto. The data examined here show no evidence of this predicted differential treatment of
vetoes versus overrides.
One reason that the approval rating evidence fails to support the theory might be the model’s
assumption of rational voters who know the equilibrium strategies played by congress and the
president, and update their beliefs accordingly in the Bayesian fashion. Voters might use the simpler
heuristic strategy that vetoes indicate presidential extremism; because overridden vetoes are relatively uncommon, this heuristic might not be terribly suboptimal. Another possibility is that the
existence of Cameron-style incomplete information between president and congress blurs the otherwise sharp distinction in the information content of overridden and sustained vetoes, preventing
voters from drawing sharply distinct conclusions.
Neither the Cameron nor the Groseclose–McCarty models are intended as more than partial
explanations, illuminating mechanisms underlying veto behavior but embedded in a larger, messier
reality. It would be premature to conclude from the override evidence alone that these mechanisms
are irrelevant or incorrect; in fact, one way to resolve the puzzle presented here may be to combine
the two into a more general theory. Nonetheless, I have shown that neither mechanism, on its own,
well explains override data. For a theory of vetoes, successfully predicting override votes is a
first-order concern. I hope that these results stimulate future research that builds on our present
understanding to better fit all of the available evidence.
Game-theoretic Models of Congressional–Presidential Interactions
519
Krehbiel, Keith. 1998. Pivotal politics. Chicago: University of Chicago Press.
Martin, Gregory. 2012. Replication data for: testing theories of congressional-presidential interaction with veto override
rates. http://hdl.handle.net/1902.1/17923 (accessed April 17, 2012).
Mayhew, David R. 2005. Divided we govern, 2nd ed. New Haven: Yale University Press.
Moe, Terry, and William Howell. 1999. The presidential power of unilateral action. Journal of Law, Economics, and
Organization 15:132–79.
Neustadt, Richard. 1980. Presidential power. New York: Wiley.
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