Models of Vetoes and Veto Bargaining
Charles Cameron
Department of Political Science
and
Nolan McCarty
DRAFT
Key words: executive-legislative relations, presidents, separation of powers, gridlock
Running title: Veto Bargaining
Abstract: Models of veto bargaining have become an important tool for formal institutional analysis. In this chapter, we review the core model of veto bargaining and some of its more interesting and useful extensions, focusing on one of the best developed applications, the presidential veto over legislation. One of the primary attractions of these models is that they often produce crisp, testable empirical predictions. Our review focuses on seventeen such predictions. We conclude with a brief review of the empirical evidence related to these hypotheses.
Acknowledgements: We thank Tim Groseclose, Stuart Jordan,
and Eric Magar for comments on this review.
Variable |
Definition |
X |
Policy outcome |
Q |
Status Quo |
C |
Congress |
P
|
President |
O
|
Override pivotal voter |
V |
Voter |
C
|
Congress’s ideal point |
P |
President’s ideal point (complete information) |
O |
Override pivot’s ideal point |
M |
Moderate presidential type |
E |
Extreme presidential type |
V |
Voter’s ideal point |
B |
Legislative proposal |
p |
Probability that president is extreme type |
|
|
Probability bargaining breaks down following a veto |
|
|
Congress’s utility function |
|
|
President’s utility function |
|
|
Override pivot’s utility function |
|
|
Voter’s utility function |
1. Introduction
Consider the following situations:
o A legislature passes a bill and sends it to the executive, who may veto the bill.
o A legislature passes a bill and a constitutional court reviews it, possibly striking it down as unconstitutional.
o A legislative committee brings a bill to the floor of the legislature under a closed rule (no amendments allowed).
o An executive presents a legislative body with a treaty, which it may reject or accept but not modify.
o An executive promulgates an executive order, which the legislature may tacitly accept or explicitly reject.
o An executive or a board presents voters (or a legislature) with a proposed budget, which they may accept or reject.
o An interest group places an initiative on the ballot for a decision by the voters.
o An executive agency writes a regulation, which an administrative law court may review and strike down as incompatible with the agency’s statutory authority or direction.
o A subordinate presents a bureaucratic superior with an alternative to current policy, which the superior may accept or reject.
All these examples, and many more, involve “veto bargaining,” one of the most ubiquitous of all forms of political bargaining.
A defining feature of veto bargaining is that a proposer makes a take-it-or-leave offer to a receiver. But oft-times this simple procedure is embedded in more complex procedures, reflecting different institutional structures. For example, rejections of offers (“vetoes”) may themselves be over-ridden. Or, the proposer may follow a rejected offer with a subsequent offer. Or, the receiver may issue a veto threat before the proposer makes her offer. Or, third parties monitor the bargaining and may reward or punish the bargainers. Or, behavior in one episode of bargaining may offer hints about likely behavior in subsequent episodes involving somewhat different issues. And so on. In order to study the implications of any of these situations, a political analyst can modify and extend the simple models of veto bargaining to capture the critical strategic features in question. This flexibility has made models of veto bargaining an essential component in the tool kit of rational choice institutionalists.
In addition, models of veto bargaining often yield crisp empirical predictions, for example, about the circumstances under which rejections are likely or unlikely, the character (e.g., ideological make-up) of offers as reversion points shift, and so on. Many of these comparative static predictions have received systematic empirical support across a variety of institutional settings (briefly reviewed below). Thus, models of veto bargaining have also been at the forefront of work on the empirical implications of formal, game theoretic models of politics.
In this chapter, we review the core model of veto bargaining and some of its most interesting and useful extensions. While the substantive applications of veto bargaining are numerous, we will focus on one of the more developed applications, the presidential veto over legislation. Throughout we keep technical considerations to a minimum, expositing the models using very simple set-ups. More complex modifications – some hitherto restricted to advanced research articles – then develop naturally from the simpler ones. All employ a common framework and notation. Students who have received as little as a single semester of instruction in game theory ought to be able to follow most of the exposition, and advanced researchers who have been curious about the new developments should be able to see the essential ideas quickly and easily.
The chapter is organized as follows. In sections 2 and 3, we present the basic model of veto bargaining derived from the seminal work of Romer and Rosenthal (1978) and present the results derived from the complete information version of that model. Noting the inability of the complete information model to produce vetoes, we explore a simple incomplete information model in section 4. This model indicates that uncertainty about the president’s position can produce vetoes so long as legislative and presidential preferences are sufficiently divergent. In section 5, we proceed to application of the incomplete information model focusing on veto threats, sequential bargaining, presidential reputations, and the role of electoral politics. Finally, we conclude with a brief discussion of empirical research and current research opportunities.
2. Preliminaries
To keep the models relatively simple, we abstract from bicameralism and other features of the internal institutional process to model the proposer – typically a legislature such as the U.S. Congress – as a unitary actor, whom we denote as C (“Congress”).[1] Similarly, we treat the receiver – typically an executive such as the U.S. President – as a unitary actor, whom we denote as P (“President”). These assumptions allow us to model veto bargaining as bilateral between the proposer and the receiver. For ease of exposition, we often refer to the proposer as “Congress” or “she,” and the receiver as the “president” or “he.”
Also, all of the models presented in this chapter focus on political bargaining over a one dimensional policy space. The assumption of unidimensionality is not particularly consequential, except in the more advanced models incorporating signaling. Most of the predictions in the simpler models would hold for a multidimensional model, so long as the players are treated as unitary actors.
For simplicity of exposition, we
assume C and P evaluate policy alternatives solely on their
proximity to their most preferred policies, which we denote c and p,
respectively. Thus, the policy utility
functions for C and P are 
and 
given any alternative x. These functions are plotted in figure 1.
Insert Figure 1 about here
In some of the models discussed in
this chapter, an additional player will be relevant for determining whether or
not President’s veto will be overridden.
The override pivot is
denoted O has an ideal point o. This pivot is defined as the legislator closest to the
president for whom exactly 1/3 of the legislature has ideal points either lower
or higher than hers.[2]
We assume O’s utility function has the same form as C and P,
or 
. For clarity of exposition, we refer to the override pivot
as “it.”
3. The Basic Model: Complete Information
In the core model, the sequence of play is as follows: 1) C makes a proposal b ( a “bill”) to change the status quo or reversion policy q. 2) P accepts or vetoes the offer. If P accepts the offer, the final policy outcome x is the bill b, and the game ends. 3) If P vetoes the offer, a vote on a motion to override occurs. If O supports the motion, the bill is successful and again x = b is the new policy. If O does not support the motion, the bill fails and x = q , so the status quo remains the policy in effect.
A typical point of departure for analyzing veto power is the assumption that all actors are perfectly informed about the preferences and actions of all other players. Under these assumptions, there is no uncertainty about how the receiver or override pivots will respond to a proposal. Therefore, C can choose b optimally given her correct expectations about the future.
Given that
there is no uncertainty, the game can be solved via backward induction. First
consider the decision of the override pivots on an override motion. Clearly, a pivot will vote to override if it
prefers b to q. Thus, we
can define a set of bills 
that O prefers
to q so that an override motion would always be successful if b
is an element of this set. This set is
shown in panel a of Figure 2. Given the assumptions about the symmetry of
the utility functions, this set is just 
or 
depending on whether
or not 
. As long as C
makes a proposal in , the veto will be overridden and the proposal becomes the
new policy.
Having
determined which proposals survive a veto, we can now compute which proposals
will be accepted by the receiver. First,
it is reasonable to assume that the president will accept any bill that would
have been overridden.[3]
Thus, the bills in will not be
vetoed. Nor will P veto any bills
that he prefers to the status quo.
Formally, let 
be the set of bills for which 
, that is, 
. Under the specified
assumptions, is given by either 
or 
depending on whether
or not 
, as shown in panel b of Figure 2.
Since C is perfectly
informed about P’s preferences, she knows for certain that any bill in
either or will be
successful. She need only offer her
most-preferred bill from these sets. If q
is her favorite bill in these sets, she shouldn’t legislate at all, any small cost of legislating will lead her to strictly
prefer not to pass a bill destined to be vetoed. Thus, it is straightforward to compute C’s
optimal behavior.
In the Appendix of this chapter, we formally present Proposition 1 which fully describes the proposal, veto, and override behavior in the subgame perfect Nash equilibrium to the basic veto game. This proposition generates a number of specific predictions that will be useful in understanding the power of the veto.
The first prediction deals with the usage of the veto. In the basic model, the president never vetoes any bill that can be overridden and the legislature never makes any proposal that will be vetoed, therefore the only bills we observe in equilibrium are passed bills.
Prediction 1 (Complete information: veto frequency). If all actors are perfectly informed about the preferences of all other actors, vetoes should not occur.
While seemingly simple (or even absurd), Prediction 1 it has a very powerful implication. Most importantly, it demonstrates that it is impossible to infer anything about the extent of veto power from the frequency of vetoes. In this very simply model, P’s veto power moves policy away from that preferred by C – yet we never see vetoes actually employed. Thus, it would be incorrect to infer that the veto is impotent based solely on the infrequency of its use.
The second
prediction, which we present graphically, is that the executive veto has policy
consequences even if it not used. In
Figure 3, we present the equilibrium policy outcomes 
for all status quo
points and a several illustrative preference configurations. These policy outcomes with the veto can be
compared with the policy outcome that would prevail without an executive veto,
namely, 
. Note that for status
quo points around p and o, the veto moves policy away from c
towards the positions favored by P and the override pivot.
Prediction 2 (Complete information: policy outcomes). Policy may be responsive to the preferences of the receiver or the override pivot.
Insert Figure 3 about here
In the case of executive-legislative relations in separation of powers systems, Proposition One also leads to some important predictions about presidential support for legislation. Suppose for the moment that the president does not have veto power. Then policy will be determined solely by C’s preferences, and often legislation will pass that the president opposes. In other words, he would veto these bills if he could. Of course, whether the president will get “rolled” in this way depends on the position of the status quo. Figure 3 indicates the set of q in which policy will move contrary to the president’s preferences. Now suppose instead the president can utilize the veto. Not surprisingly, the circumstances under which he gets rolled are much rarer. In fact, if the president’s ideal point lies between c and o (as in Figure 3), he never gets rolled. If the president’s preferences are more extreme than the override pivot’s (as in figure 2), he may get rolled when veto-proof legislation is passed. Critically, however, rolls will occur far less often when P posses the veto power than when P lacks it.
Prediction 3 (Complete information: roll rates). The probability of passage of offers opposed by the chooser is lower when he has a veto.[4]
This is an obvious prediction, but it can be useful when
considering the history of the veto in different institutional structures. For
example, some have argued that during the 18th and 19th centuries a norm of
legislative deference prevented the
Extension: Sequential Veto Bargaining Under Complete Information
In many cases, the proposer can make repeated offers if the receiver uses the veto, and the receiver can veto and re-veto offers. Cameron (2000) calls such situations “sequential veto bargaining.” Maintaining the assumption of complete and perfect information, what happens to the proposer C’s offers under sequential veto bargaining? One might expect that the receiver can implicitly threaten to veto early offers, and extract concessions from the proposer. However Primo, in an interesting recent paper (2002), examines this question and finds that the proposer makes exactly the same offers in finitely and infinitely repeated versions of the basic model – and this holds for [almost] any discount rates for the proposer and receiver.
We merely sketch Primo’s results. First, assume both players receive 
in a period t if P
vetoes the bill or C makes no offer. However, if a bill is ever
accepted, then both players receive 
for that and all
succeeding periods in the game (which may be infinite in length). Hence, the
payoff function for C becomes 
, and similarly for P
, where 
is a discount factor
for C and 
that for P.
(We abstract for the moment from veto over-rides).
First,
Primo proves the following result: for any game with finite periods T,
for any allowable discount factors, the equilibrium offers, vetoes,
acceptances, and policy outcomes specified in Proposition One remain the unique
subgame perfect equilibrium. The intuition for the result is that if the game
reaches the last period, the outcome will be identical to that of Proposition
1. Consider first the case of proposition
1 where the president is indifferent to accepting and rejecting the equilibrium
proposal so that 
. Thus his payoff in
the last period is 
. Backing up one more
period, his utilities from vetoing is therefore 
while the utility of
accepting any 
is 
. Since the 
simply scales up both
utilities, the president’s calculus is the same as it is in the last
period. Thus, 
. This logic will
continue for any finite number of periods.
The case where 
is very similar.
Next, Primo extends his result to the infinitely repeated case. Again, the same offers, vetoes, acceptances, and policy outcomes are the unique subgame perfect equilibrium, for all discount rates in (0,1).[6] This result may seem surprising to those familiar with the many Folk Theorems for repeated games, which typically generate a plethora of equilibria. However, as Primo notes, “We should not expect a Folk Theorem to be operative. Intuitively, Folk theorem results emerge when there are credible punishment or reward strategies that can be invoked. This is not possible in this game, because each player (implicitly) has veto authority over the policy outcome, either by not proposing a particular policy, in the case of the proposer, or by rejecting a proposal, in the case of the receiver.” (419). Absent these punishment strategies, only the unique equilibrium from Proposition 1 can exist.
What happens if we add veto over-rides to this game? Cameron (2000) considers a two-period model that is almost identical to Primo’s, except a veto over-ride player is randomly selected each period (Cameron 2000 pp. 99-106 and 117-120).[7] Again, the one-shot offers and acceptances and vetoes remain the unique equilibrium. This result surely extends to any finite number of periods, while Primo’s results strongly suggest the same for infinitely repeated offers with vetoes. Thus, we have
Prediction 4 (Complete information: sequential veto bargaining). In complete information settings, sequential veto bargaining yields the same behavior and outcomes as one shot veto bargaining, and this holds for any period game and even if one player is more patient than the other.
An important implication of Prediction 4 for modelers is that the results from one-shot versions of veto bargaining will be robust to repetition – if incomplete information is not a critical feature of the environment. Primo suggests a number of empirical implications, for example, term limits may not affect presidential veto power very significantly.
4. Simple Incomplete Information
The complete information model provides an excellent tool for studying veto power. But it cannot provide a basis for studying vetoes, for the obvious reason that it predicts vetoes will not occur. We now turn to a simple model for studying vetoes, rather than veto power. In this model, vetoes do occur. This simple incomplete information model in turn provides the foundation for building more complex models of veto bargaining that incorporate reputation, learning, and dynamics.
If one wants to explain the fact that vetoes occur, one must dispense with at least one of the assumptions underlying the basic model. While the model presented in the last section has a number of very restrictive assumptions, few of them are actually consequential in the prediction of no vetoes. One important exception is the assumption that C has complete information about the preferences of P and O. When there is such uncertainty, vetoes may occur because the legislature overestimates its ability to extract concessions from the president or the override pivot.
Relaxing the assumption of complete
information has been the starting point for most of the recent work on veto
bargaining (Matthews 1989, McCarty 1997, and Cameron 2000). To present the
basic flavor of these models, we consider a model without an override possibility so that q
remains the policy in the event of a veto. To capture the uncertainty that the
proposer C faces about the receiver P’s preferences, we assume
she believes P is one of two preference “types,” a moderate with ideal
point m or an extremist with ideal point e. We assume throughout that 
. Following the usual
practice in applied game theory, we assume C’s beliefs are common
knowledge.[8] Let 
be the probability
that P is the extreme type.
The main implication of the
uncertainty about preferences is that C no longer knows for sure which
bills the president will accept and which he will veto. To see this, consider Figure 5 where we
assume that 
. Here the set of
bills the extremist type of receiver is willing to accept over the status quo
is only a subset of those the moderate type is willing to accept. Thus, C can force a more attractive
bill (from her perspective) on the moderate receiver than she can on the
extremist one. C’s dilemma is
whether to propose a bill she finds relatively less attractive but that both
types will accept – a bill like 
– or be more aggressive and propose a bill – like 
– she finds more attractive but only the moderate receiver
will accept. Clearly, the attractiveness of the gamble depends on C’s
beliefs about P’s type. If p is
high (so C believes P is probably an extremist), C will
likely be deterred from making the aggressive proposal. On the other hand, if p is low (so C
believes P is probably a moderate), C may well find an attractive
gamble. If she offers it, on occasion it
will prove a poor choice: the receiver will turn out to be the extreme type and will veto
it.
In the Appendix to this chapter, we calculate the necessary conditions for a veto to occur. For the preference configuration in Panel A, we show that C will make the risky proposal (possibly generating a veto) if and only if:
However, the necessary conditions change as c moves closer to m, as in Panel B. Here C’s best risky proposal is her ideal point c. This fact alters the necessary condition somewhat to:
It can easily be shown the right hand side of is lower than that of , implying that a veto is less
likely to occur. This is because in the
preferences illustrated by panel B, the policy concession required to avoid a
veto (i.e. 
) is much smaller.
Finally, note that in the extreme case shown in Panel C, where C’s
ideal point is acceptable to both types, no veto will occur. These results lead to prediction number 4:
Prediction 4: (Incomplete information: veto frequency) Vetoes will be more likely when the expected difference between the ideal points of P and C is larger.
In the interest of brevity, we omit an analysis of this model with a veto override. But such an analysis produces a parallel result:[9]
Prediction 5: (Incomplete information: veto frequency) Vetoes will be more likely when the expected difference between the ideal points of O and C is larger.
5. Models with Reputation, Learning, and Dynamics
An interesting feature of the incomplete information model is that a moderate receiver P does better if the proposer C believes P is the extreme type. This raises the possibility that P might attempt to manipulate C’s beliefs about his type, his reputation. In this section, we examine three models in which the actors try to manipulate P’s reputation. All are signaling models, because an informed player takes an action that conveys information about P’s type. In the first two models, the veto threat and sequential veto bargaining (SVB) models, the informed player is the receiver P himself. In the third model, the blame game veto model, both C and P take actions to convey information to uninformed voters.
Veto Threats
Ranging from the dramatic “read my lips” variety to the much more mundane “statements of administration policy” routinely produced by the Office of Management and Budget, the veto threat is an important feature of legislative politics in the U.S. However, none of the models reviewed thus far provide any leverage on understanding this phenomena. Matthews (1986) however provides an influential model of veto threats where the president may use a costless signal or “cheap talk” to reveal information about preferences and veto intentions.
To
illustrate this model, it is helpful to increase the number of presidential
types from two to four. Therefore, in
addition to m and e, we add the two following types: r the
“recalcitrant” type and a the “accommodating”
type. We assume that 
as in Figure 6. President r is called recalcitrant
because he will veto any bill that C prefers to the status quo while a is accommodating because he prefers c to the
status quo. We will also assume that the
probability of these types are 
. In this game, the
president first makes a “speech” which is simply a costless signal to the
legislature. Each of these messages has
no literal meaning, just a contextual one derived from the equilibrium that is
being played. Following the speech, C
updates her beliefs about the president’s preferences and then makes a proposal
which the president can either accept or reject.
As a
baseline, first consider an equilibrium where the
president’s speeches contain no information because each type makes the same
speech. In this babbling equilibrium, C
will simply choose the bill from 
,, or 
that maximizes her utility.
For any such choice, those with lower types will veto. For example, if C chooses
, e and r will veto so that the veto
probability is 
. Rather than
present the formulae for the conditions for each proposal, they are illustrated
graphically in Figure 7. The first
figure shows which proposal will be made in the babbling equilibrium for
different values of 
and 
for given values on 
and 
. Note that the
proposal is never made since C
always does at least as well with a vetoed proposal. Note that this equilibrium is somewhat bad from
the president’s perspective. If the
president is type a, there is a utility loss associated with the fact
that C may propose the less desirable policies and . For president m,
there are losses associated with the fact that C might propose c
(which he then vetoes) rather than his preferred . Since r and e,
only get their status quo utility from all proposals, they are not
affected. C is also affected by
the lack of information as it may force her either to accommodate more than
necessary or to risk a veto.
So given
the bad outcomes from the babbling equilibrium, it is reasonable to ask whether
there are other equilibria where more information is transmitted. Matthews shows that some information can be
revealed in presidential speeches, but not all of it. First, consider why a separating equilibrium
where every presidential type gives a distinct speech cannot be an equilibrium. If C
could learn the president’s type from the speech, she would optimally propose 
to r, to e, etc. However, since m prefers to , m would prefer to defect and give e’s speech.
Thus, a separating equilibrium cannot exist. Matthew’s shows that the most informative
equilibrium is one where type a reveals his type with an “accommodating”
speech and the other types all make the same “threatening” speech. Following an accommodating speech, C
correctly infers that the president will accept her ideal point and thus
proposes c. Type a is
willing to make the accommodating speech since she clearly prefers c to or . Following the
threatening speech, C learns that the president is not a and updates her beliefs accordingly. Given these beliefs, C chooses between
and . The second panel of
Figure 7 illustrates the optimal proposal as a function of and for given values on and . Two
important things to note. First,
it is more likely that C proposes because the knowledge
that the president is not type a makes the probability that will be vetoed much
higher.
Prediction 6 (Concessions to veto threats) Congress makes a larger concession to the president’s preferences following a veto threat.
It is important to note that
an informative equilibrium is not guaranteed to exist. Suppose type a preferred to c to , an informative
equilibrium would exists only if C’s best response to the threatening
message was . Otherwise, a would defect to the threat. Similarly, if a
prefers to c, no
informative equilibrium can exist.
It is possible for some
configurations of preferences that the veto threat is simply a bluff. Consider what would happen if m were
moved in Figure 6 sufficiently to the right that he preferred c to q
(thus became an accommodator) but still preferred to c. In the informative equilibrium, m
would still give the threatening speech, but it is a bluff in the sense that he
would have signed C’s ideal point.
Prediction 7 (Veto threats: bluffing) The president may issue a veto threat even though he would accept C’s ideal point.
The informative equilibrium makes C better off (if it
didn’t she could just turn off the TV and ignore the speech). However, it is possible that some
presidential types will be worse off.
Suppose that a were repositioned so that his preference ordering
were such that were preferred to c
which was preferred to . Further, suppose
that the babbling equilibrium produced while a threat in the
more informative equilibrium produced . Then a would clearly prefer the outcome of the babbling
equilibrium to the c she gets from make her accommodating speech in the
informative equilibrium.
Sequential Veto Bargaining with Incomplete Information
Often, the proposer can make multiple offers, learning about the receiver as she does so. For example, if the receiver rejects a tough offer early, the proposer may believe the receiver is genuinely tough. If so, the proposer’s next offer is apt to be more accommodating. This “haggling” dynamic is very common in many types of bargaining, and one might well expect to see it in veto bargaining as well. But a complicating factor is misdirection: the proposer will often have an incentive to reject early offers in order to build a reputation that leads to better later offers. But knowing this, why should the proposer actually make the compromises? The sequential veto bargaining model (SVB) model explores these questions about learning and credibility.
A simple example conveys many of the
basic ideas. First, consider a situation in which q = 0, e = ¼, m
= .6, and c = 1. By now it should be clear that in a one-shot game
(without a veto threat) 
and 
. Using the techniques discussed in Section 4 and equation , it is easy to see that C
will offer if 
, and otherwise. But suppose this is not a one-shot game, so that C
may make a second offer if the first is rejected. More specifically, suppose
bargaining breaks down with probability
, but otherwise a second offer can be made. (The probability
of a bargaining breakdown reflects the inherent uncertainty of the legislative
and other political processes.) Is a
haggling equilibrium possible, that is, one in which C first makes a
tough offer then, following a veto and no bargaining break down, makes a more
accommodating offer?
In such a haggling equilibrium, the moderate president must accept the tough offer in the first round (if both types rejected the tough offer, then C should make the accommodating offer lest a break down saddle her with the unappealing status quo). Therefore, the following “incentive compatibility constraint” must hold:
or
.
(The incentive compatibility constraint indicates that
accepting the tough offer in the first round is better for the moderate type
than rejecting the offer and holding out for the more proximate accommodating
offer, taking into account the probability of a bargaining breakdown). In the
example, the critical value for the break down probability is .6. Let 
be C’s belief that the president is the extreme type,
following a veto. Note the following: in a haggling equilibrium, it must be
case that 
, otherwise, following a veto, C will make the tough
offer again in the final period (this was proven above). But if the probability
of a breakdown is greater than .6, then the moderate type accepts the initial
offer, so that by Bayes Rule, 
following a veto, and C
will indeed make the accommodating offer in the second round.
There remains an additional incentive compatibility constraint to examine, however. Congress must find it more appealing to make a tough offer followed by an accommodating offer (conditional on a veto and no break down), rather than make an initial accommodating offer that would be surely accepted. This requires that
or
and in the example 
.
We can now indicate a haggling
equilibrium in the two period, two type sequential veto bargaining model with
the ideal points indicated earlier: If 
and , then C offers 
and 
, presidential type m accepts both and in both periods, presidential type e accepts offer and vetoes offer in both periods, and C’s
belief that the president is the extreme type following a veto is .
This example indicates how haggling, vetoes, and sequences of bills arise during veto bargaining. However, a somewhat more general model allowing a continuum of presidential ideal points, rather than simply two, yields richer and more interesting results:
Prediction 8 (SVB: basic dynamics): In sequential veto bargaining, Congress makes concessions in re-passed bills; there is a positive probability the president accepts each bill; and there is a positive probability no offer is accepted even if bargaining does not break down. Moreover, in the first period, some types of presidents are willing to strategically veto, that is, veto a bill they prefer to the status quo.
The possibility of “strategic vetoes” is particularly interesting. Here, a president vetoes an initial bill that he actually prefers to the status quo, in order to build a policy reputation that will extract an even more favorable bill in the next period.
Cameron (2000) explores the
comparative statics of this version of the SVB model in detail. Not
surprisingly, many of the model’s empirical predictions are identical to the
simple one-shot model, for example, increased differences between proposer and
receiver lead to increased veto rates.
However, a novel set of predictions involves the probability of a break
down in bargaining (denoted q in Cameron 2000 rather than
). Cameron argues for a link between legislative significance
and break down probabilities. In this view, less important bills are “brittle”
while important ones are more robust. The idea is that, because enactment of
any given unimportant bill is unlikely, such a bill is unlikely to return to
the legislative agenda if it is vetoed. Conversely, more important bills,
propelled by powerful advocates, are quite likely to retain their place on the
agenda even if they receive a check. Cameron shows this differential fragility
affects the dynamics of veto bargaining. In particular, bargaining is much
tougher for more important bills. Hence, in the model with a continuum of
types, we get the following:
Prediction 9 (SVB: effects of legislative significance): Given disagreement between president and Congress, more important bills are more likely to be vetoed than less important ones; are more likely to be re-passed if vetoed; are likely to incorporate smaller legislative concessions; and are more likely to be vetoed a second time.
Cameron (2000) also considers veto over-rides in conjunction with a model of sequential veto bargaining. For the most part, the dynamics of bargaining remain the same. A novel prediction is the following:
Prediction 10 (SVB: over-rides and re-passed bills): Congress is more likely to attempt an over-ride on re-passed bills than initially passed ones.
Driving the prediction is the concessions that follow a veto: re-passed bills are more likely to be geared for an over-ride attempt.
Finally, Cameron uses the model with a continuum of types to uncover a deadline effect in bargaining.
Prediction 11 (SVB and deadlines). The probability of vetoes for important legislation should fall at the end of a legislative session.
The rationale for this prediction turns on the “strategic vetoes,” discussed above. In the last period, the president has no incentive to build a reputation through strategic vetoes. Although Congress understands this and accordingly makes a tougher offer, its offers are not so much tougher as to offset the president’s weaker incentive to veto.
Bargaining over Multiple Bills
While the last section shows that incomplete information can
effect the dynamics of bargaining on a single issue, McCarty (1997) considers
how informational and reputational incentives alter the bargaining across multiple issues over
time. He considers
a model of veto bargaining with incomplete information where P and C
bargain over a series of policies with status quo points 
and 
. In each of the two
periods, C proposes 
and the president
decides whether to accept or reject it.
Thus, bargaining over each policy is modeled as one-shot such that if P
vetoes the status quo 
is the policy
outcome. Since the president’s ideal
point is assumed to be constant across policies, the outcome on policy 1 may
provide information to C prior to her making an offer on policy 2.[10] Since in the last period, the game is
identical to the one-shot incomplete information game described above, type m does better on the second
policy by having C believe that he is the extreme type if preferences
are such as those given in panel a or b.
Thus, given those preference configurations, m may be willing to
use his first period veto to build a reputation as the extreme type in order
get a better outcome on policy 2. This
involves rejecting bills that he, but not type e, prefers to . Thus, reputational
incentives increase the likelihood of a veto on policy 1.
Given that C understands these incentives, she may be willing to be sufficiently accommodating on the first policy to discourage type m from vetoing on reputational grounds. Thus, McCarty’s model predicts a “honeymoon” pattern of accommodating policies early in the president’s term followed by less accommodating policies toward the end when reputational incentives are diminished. However, he notes that since the existence of reputational incentives depends on preference configurations such as those in panel a and b, this honeymoon effect is unlikely when the expected difference P and C is small such as during unified governments.
Prediction 12 (Multiple bills: the honeymoon effect). When the expected difference between P and C is sufficiently large, policy enactments should show a declining accommodation to the president’s preferences over the course of his administration.
Blame Game Vetoes
A recent model argues that vetoes are less a product of legislative uncertainty than of electoral politics. Groseclose and McCarty (2001) examines a model in which the legislative agenda setter uses its proposal power to signal that the president has policy views that are out of step with the voters.[11] In this “blame game” model, vetoes occur when the agenda setter receives a larger payoff from signaling that the president has extreme preferences than she does from enacting new policy. Thus, in this model, the electorate’s uncertainty about the president is critical, not the uncertainty of legislators.
To illustrate a
simple version of this model, consider a new actor V, the voter. We assume V also has linear
preferences and an ideal point v.
Following the notation of the last section, V believes the
president is type e with probability p and type m
otherwise. We focus on the case where 
. We assume the voter evaluates the president
based on the expected distance between the president’s ideal point and her own
ideal point. Therefore, the voters evaluation is just
An important feature
of this model is that P and C care how much expected utility V
gets from the president’s position. The
most interesting case is one of conflict, in which the president gets greater
utility when the voter believes he is a moderate and Congress gets greater
utility when the voter believes the president is an extremist. Such a case
would plausibly arise when Congress and the presidency are controlled by
different political parties or factions, especially when those parties are
highly polarized ideologically, and voters are generally more moderate. In such
a case, C and P trade gains from enacting policy with gains from
political posturing. More specifically, the president would like to take
actions that lead the public to lower p while the legislature
would like to take actions that lead the public to increase 
. We allow C and P to value these trade-offs
differently by letting 
and 
be the respective
weights each place on policy. Therefore,
the utility functions for C and P become:
An important assumption of this model is that while V is relatively uninformed about P’s preferences, C is fully informed. Therefore, C may be able to credibly communicate its information about p through its choice of bill. Similarly, the president’s decision whether to veto particular proposals may also provide information to voters about his preferences.
A particularly interesting equilibrium is one in which C proposes an acceptable bill when P is moderate and submits a bill that will be rejected when the president is extreme. McCarty (2002) shows that such an equilibrium is the only one in which vetoes occur and it exists if and only if the following two conditions hold:
These conditions produce a
number of predictions about the occurrence of vetoes.[12] First, note that cannot be satisfied if 
or 
. Thus, voter
uncertainty about the president’s preferences is crucial. Without this uncertainty, orchestrating a
veto has no signaling value to C so she might as well make acceptable
proposals to both types.
Prediction 13 (Blame game: voter uncertainty): Voter uncertainty about the president’s preferences is necessary for equilibrium vetoes.
Next, note that both and are easier to satisfy when p is lower. Since the ex ante evaluation of the president is decreasing in p (the probability he is extreme), the model suggests that vetoes will occur more likely when the public believes the president is moderate (that is, believes the president is ideologically proximate). Intuitively, Congress finds the blame game most attractive when it has negative information about the president’s policy preferences that is inconsistent with the voter’s beliefs.
Prediction 14 (Blame game: voter beliefs): Blame game vetoes are more likely to occur when the public believes the president’s policy preferences are similar to its own.
The next three prediction are based
on C and P’s willingness to trade policy gains for political
gains. Figure 8 illustrates how each of
the conditions are affected by the policy weights and . The area under the
higher solid line represents the combinations of and that satisfy . Alternatively, the area above the lower
dashed line are those satisfying . The blame game equilibrium described above
exists in the intersection of these regions.
First, note that condition can be met only when 
, suggesting that the president must put relatively more
weight on the policy outcome than does Congress. If this were not the case, C would
prefer to achieve policy gains by passing mutually attractive bills rather than
seek purely electoral advantage by passing bills the president will reject.
However, condition puts an upper bound on the
difference in policy weights. If is too much larger than , C loses the ability to signal credibly through its
proposals.
Prediction 15 (Blame game: policy salience): Blame game vetoes will occur on issues that the president cares relatively more about than does Congress.
Assuming that the policy weights are uniformly lower during election years, the model generates the following prediction:
Prediction 16 (Blame game: electoral politics): Blame game vetoes will be more likely during election years.
One final prediction emerges from the fact that only extreme
types ever veto in the blame game model.
Since only type e vetoes, every veto is followed by a reduction
on support from to 
.
Prediction 17 (Blame game: vetoes and public approval): Vetoes lead to lower public support for the president.
Support for this prediction is found in Groseclose and McCarty (1999). Eric Magar develops some similar models where both executives and legislators care about position-taking in that they derive utility based not just on the outcome but from the actions that they tale in the process (2001). This modification generates equilibria with non-outcome consequential “publicity stunts” such as vetoing a bill certain to be overridden or passing a bill certain to fail. Thus, otherwise anomalous behavior such as successful veto overrides can be sustained in equilibrium. An important distinction is that Magar’s action contingent preferences are exogenous rather than endogenous as in Groseclose and McCarty. In particular, it is not clear why the voter in the Magar model would reward purely symbolic actions.
6. Empirical Applications
Although this chapter is primarily theoretical in orientation, we would be remiss not to review, if only cursorily, the very substantial body of empirical work that has used or tested the models we have reviewed. In some cases, we will note obvious gaps in the literature.
Methodological Issues
A central issue concerns the dependent variable, in particular, whether the analyst studies process measures related to bargaining (vetoes, over-ride attempts, threats, enactments, presidential popularity), or policy directly. Policy is often the measure of greatest interest but process measures are far easier to observe and measure. As indicated above, models with incomplete information often generate crisp propositions about process measures, and these can be used to test the models.
Regardless of the dependent variable, a central methodological issue arises from the three distinctive regimes that occur in many veto models, depending on the relative positions of the players’ ideal points and the status quo. As discussed above, in the “accommodating” regime the proposer offers her ideal point. In the “compromising” regime, she offers a proposal the responds to the receiver’s ideal point, with a unit move in the latter forcing a unit move in the former. In the third regime, the “recalcitrant” regime, a successful proposal is not possible so no offer is made. Thus, the comparative statics of both policy and process measures (e.g., vetoes) depend on which regime generated which observation. But associating observations with regimes can be problematic, because of the difficulty of measuring ideal points and status quos. Analysts have tackled this problem in two different ways.
The first method relies upon research design, using a priori grounds to associate observations with regimes. For example, increasing the distance between the ideal points of the proposer and receiver makes the accommodating regime less likely and the compromising or recalcitrant regime more likely (ceteris paribus). Hence, increased distances should increase the probability of a veto, given an offer and a degree of incomplete information. Most of the empirical predictions in this chapter take this form, and most of the empirical work has this flavor.
The second approach employs endogenous regime switching models to estimate simultaneously the probability that a given observation belongs to a regime (using appropriate indicators), and the behavior of the observations associated with each regime.
While conceptually appealing, this approach has been little
used, due to the difficulties of measurement and estimation (see however
Spiller and Gely 1992 and McCarty and
Not surprisingly, in light of the importance of regime switching, measurement issues often become central in empirical studies of veto bargaining. Typical problems include determining or finessing the location of the status quo, and placing proposers and receivers on common preference scales. There are no general solutions here: the analyst must tailor her response to each situation, and sometimes display considerable ingenuity (see e.g., Bailey and Chang 2001).
Experimental Studies
Laboratory experiments often afford the cleanest setting for testing game theoretic models of social interactions. For example, one can definitively address regime and measurement issues. Thus, one might expect to find a well-developed experimental literature on veto models. Unfortunately, this is not the case.
Within Economics, there is a vast literature on the “ultimatum game,” which strongly resembles the “compromising” regime in veto games. In the ultimatum game, a proposer offers a receiver a division x of a pie, retaining 1- x for herself; if the receiver rejects the proposal, both receive zero. Camerer (2003) and Roth (1995) elegantly review findings from this literature. Typical result are: 1) proposers do not make as “tough” an offer as theory predicts, and 2) choosers sometimes reject “stingy” offers that theory predicts they ought accept. The explanation for these departures from the theoretical predictions remains a subject of controversy.
Unfortunately, the ultimatum game is not isomorphic even to the one shot veto game, since the ultimatum game lacks two of the relevant regimes as well as comparative statics on the location of the status quo in the compromise regime. Veto games with repeated play, reputation, threats, and third party audiences are even farther removed from the ultimatum game. To the best of our knowledge, political scientists have conducted little or no experimental work on veto games, especially those with repeat play, reputation, and third party audiences. This is an obvious area for research.
Studies on Observational Data
Purely empirical studies of the veto abound, many of which are reviewed in Cameron (2000). More recent examples not referenced there include additional studies of veto probabilities for individual bills (Gilmour 2002, Sinclair 2002), veto threats (Deen and Arnold 2002, Jarvis 2002, Conley 2002, Marshal 2003), and over-ride politics (Conley 2000 and 2003, Wilkins and Young 2002, Manning 2003, Whittaker 2003). Comparative politics scholars increasingly draw on veto models to interpret case study materials from a variety of countries (see e.g., Lehoucq and Molina 2002 and Remington 2001). Rarer however are studies in which systematic observational data confront formally derived hypotheses from game theoretic models of the veto. We focus on these studies below.
Complete Information Model
The complete information model examines the consequences of veto power rather than vetoes. Tests of the model relate changes in preferences to changes in policy. For example, Kiewiet and McCubbins (1988) examines appropriations politics. Taking into account the normal reversion points in the appropriations process, Kiewiet and McCubbins argue that the veto gives the president strong power when he wants to cut budgets but much less power when he wants to increase them. Their statistical analysis of appropriations data provides support their argument. Krehbiel (1998) and Brady and Volden (1998) embed complete information veto models in larger models of law making under the separation of powers. Both find a variety of systematic evidence supporting these “gridlock” models. Cameron (2000 pp. 169-176) and Howell et al (2000) argue that patterns in the legislative productivity of Congress are compatible with predictions of a complete information veto model.
Veto Threats
Cameron (2000 pp. 178-202) tests many predictions from the Mathews model of veto threats, as does Cameron et al (2000), using data on threats from Truman to Clinton. The evidence they muster strongly supports the model. Evans and Ng (2003) use more extensive systematic evidence from the Clinton and George W. Bush administrations to test the Mathews model, and also find strong support. However, they also find evidence suggestive of a blame-game dynamic in veto threats (see also Conley 2001).
Sequential Veto Bargaining and Bargaining Over Multiple Bills
Cameron (2000) uses the SVB model to explain many patterns in the use of the veto in the post-war era. In addition, he tests hypotheses on concessions and the deadline effect. He finds very substantial empirical support for the model. The distinction this model makes between more important and less important legislation has not been exploited as fully in empirical work as one could imagine.
McCarty (1997) examines the “honeymoon”
prediction generated by the multiple bills model. Rather that use data on
actual bill locations, he uses data on average presidential support scores
which would tend to decline as legislative proposals move away from the
president’s expected ideal point.
Consistent with his prediction, he finds that presidential support
scores decline over time during divided, but not unified, government. McCarty and
Blame Game Vetoes
One of the principal predictions of the blame game model is
that presidential popularity should fall after a blame game veto. Groseclose
and McCarty (2001) test this prediction and find support in presidential job
approval. McCarty (2002) marshals a variety of evidence from the early
Republic, testing the blame game model and in some instances contrasting it
with predictions of the simple incomplete information model. He finds support
for the blame game model, especially relative to the simple incomplete
information model. Magar
applies his closely related model of “stunt” vetoes to data from several Latin
American countries, especially
Summary
A substantial empirical literature examines the presidential veto. Much of this literature investigates ad hoc hypotheses unsupported by theory, or repeatedly replicates simple and well-known patterns predicted by almost every model. A smaller number of studies attempt to test formal models of veto bargaining in a methodologically sophisticated way against appropriate data. However, those studies that have attempted this task have found repeated and substantial support for the models.
7. Conclusion
Veto bargaining has developed into a successful social scientific endeavor. This literature contains a rich set of explicit models with generally clear empirical predictions. Its large set of claims, sometimes complementary and sometimes competing, have proven a rich source of hypotheses for empirical research, research that has undoubtedly increased our knowledge of the veto power and its role in executive-legislative relations.
Despite this success, there remains much to be gained from pushing forward on the theoretical and empirical fronts. On the theoretical side, current models are somewhat limited by their simple informational and preference structures. The extent to which equilibrium veto bargaining is substantially different in a world with multi-dimensional preferences and signaling is still an open question. The incorporation of electoral politics and public opinion is also rudimentary. For example, the Groseclose-McCarty model only allows voters to learn about presidential preferences, but not congressional ones, and is also limited to preferences along a single dimension.
Open
empirical questions abound as well. Much
of the empirical literature has naturally centered around
data from the post-World War II United States national government. But with dozens of presidential democracies
and 50
8. Literature Cited
Bailey M, Chang K. 2001. Comparing presidents,
senators, and justices: inter-institutional preference estimation. J. Law Econ. Org. 17(2): 477-506
Brady D, Volden
C. 1998. Revolving Gridlock.
Camerer C. 2003. Behavioral Game Theory: Experiments in
Strategic Interaction.
Cameron
CM. 2000. Veto Bargaining:
The Politics of Negative Power.
Cameron CM, Lapinski JS, Riemann CR. 2000. Testing formal theories of political rhetoric. J. of Pol 62:187-205
Conley RS. 2000. Divided government and democratic presidents: Truman and
Conley RS. 2001. President Clinton and the Republican
Congress, 1995-2000: vetoes, veto threats, and legislative strategy. Presented at the Ann. Meet.
Am. Polit. Sci. Assoc. Aug
30 –Sep2, 2001.
Conley RS. 2002a. Presidential Influence and Minority Party Liaison on Veto
Overrides. Amer. Pol. Res. 30:34-65.
Conley RS. 2003. A revisionist view of George Bush and
Congress, 1989:
presidential support, ‘veto strength,’ and the Democratic agenda. Wor. pap.: Department of Political
Science.
Deen RE,
Evans
CL, Ng S. 2003. The institutional context of veto bargaining. Presented at the Ann. Meet.
Gilmour JB. 1995. Strategic Disagreement:
Stalemate in American Politics.
Gilmour
JB. 2001. Sequential veto bargaining and blame game politics as explanations
of presidential vetoes. Presented at the Ann. Meet. of the
Gilmour JB. 2002. Institutional and individual influences on the president’s veto. J. Polit. 64(1):198-218
Howell
et al. 2000. Divided government and the legislative
productivity of Congress, 1945-1994. Leg.
Stud. Q. 25(2):285-312.
Groseclose T , McCarty N. 2000. The politics of blame: bargaining before an audience.” Amer. J. Polit. Sci. 45(1):100-119
Jarvis M. 2002. Eisenhower’s veto threats: full of nothing, signifying sound
and fury. Presented at the Ann. Meet. Am. Polit. Sci. Assoc. Boston. Aug. 28 – Sep. 2.
Krehbiel
K. 1998. Pivotal Politics: A Theory of
Lehoucq FE, Molina
Magar E. 2001. Bully Pulpits: Posturing, Bargaining, and Polarization in the Legislative Process of the Americas. PhD Dissertation, University of California San Diego
Magar E. 2003a. A model of executive vetoes
as electoral stunts with testable predictions. Work.
pap., Departamento de Ciencia Política, Instituto Technólogico Autónomo de México.
Magar E. 2003a. Electoral stunts in comparative prespective:
executive vetoes in U.S. state governments, 1979-1999. Work. pap., Departamento
de Ciencia Política, Instituto Technólogico Autónomo de México.
Marshal BW. 2003.
Staring Down the Barrel of a Veto Pen:
Veto Threats and Presidential Influence in Congress. Presented
at the Ann. Meeting of the
Manning EW. 2003. Governors,
Legislatures and Veto Overrides: A State Level Test of Pivotal Politics. Presented at the Ann. Meeting of the
Matthews SA. 1989. Veto threats: rhetoric in a bargaining game. Q. J. Econ. 104:347-369.
McCarty N. 1997. Presidential reputation and the veto. Econ. & Polit. 9:1-27
McCarty
N. 2002. Vetoes in the early republic. Work. pap.,
McCarty N,
Moraski BJ, Shipan CR. 1999. The politics of Supreme Court nominations: a theory of institutional constraints and choices. Amer. J. Polit. Sci. 43(4):1069-1095.
Primo DM. 2002. Rethinking political
bargaining: policymaking with a single proposer. J. Law Econ. Org.
18(2):411-437.
Remington
T. 2001. The Russian Parliament: Institutional Evolution in a Transitional
Regime, 1989-1999.
Romer T, Rosenthal H. 1978. Political resource allocation, controlled agendas, and the status quo. Public Choice 33(1):27-44.
Roth AE. 1995. Bargaining experiments. In The Handbook of Experimental Economics, ed. J Kagel, A Roth, 253-348. Princeton: Princeton U. Press.
Sinclair B. 2002. The
President in the Legislative Process: Preferences, Strategy
and Outcomes. Presented at the Ann. Meet. Am. Polit. Sci. Assoc. Boston. Aug. 28 – Sep. 2.
Spiller PT, Gely
R. 1992.
Congressional control or judicial independence:
the determinants of U.S. Supreme Court labor-relations decisions,
1949-1988. Rand J. Econ.
23:463-492.
Wilkins VM, Young G. 2002. The influence of governors
on veto override attempts: a test of pivotal politics. Leg. Stud. Q. 27:557-75.
Whittaker M. 2003.
Presidential Influence
and Vote Switching in the Senate. Presented at the
Ann. Meeting of the
9. Appendix
Proposition 1: The subgame perfect equilibrium to the complete information veto game is:
President: Accept
any bill such that either 
or 
.
Override Pivot: Override
any veto such that .
Congress: Make the following proposals
Case 1: 
.
If
, 
If 
, make no proposal.
If 
,
Case 2: 
If
, 
If 
, make no proposal.
If 
,
Case 3: 
,
Case 4: 
,
Incomplete Information Models
We wish to establish the critical
values of given in equations -. Thus, we consider only the preference
configurations in Figure 5 i.e. 
. Other configurations
are quite simple to analyze and are left to the reader.
Let 
be the sets of bills
that each type 
is willing to accept over the status quo. Similar to above, these sets are 
if 
and 
otherwise. Notice that for any q, president m
is willing to accept a higher bill that is e. Just for simplicity, let 
so that 
--
any bill that e accepts m will accept, but the
converse is not true. Therefore, C
faces a tradeoff. It can propose 
which both types
accept, or can propose 
which e will veto.
Given C’s beliefs the latter strategy results in a veto with probability p.
Case 1: 
Assuming that C has the
linear utility function presented in the last section, her payoff from 
are 
and her payoffs from 
are 
. If
, C will propose and a veto may occur.
Case 2: 
Her payoff from is . Her payoffs from 
are 
. Therefore, C
will take the risky strategy when 
. Note that the
critical value of p
is lower than in case 1 making a veto less likely for any given set of beliefs.
Case 3: 
In this case, neither president will veto . So C
maximizes her utility by proposing her ideal point, and no vetoes will occur.
, so the President is infinitely patient, there may be
additional equilibria. But this is simply a technical curiosity (see Proposition
4 in Primo 2002).
.