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 =