Presidential Pork: Executive Veto Power and
Distributive Politics
Nolan McCarty
Department of Political Science
Columbia University
June, 1998
Version 2.1
Abstract
Most previous studies of the president’s role in the legislative process and the
implications of veto power can be placed into two categories. The first is the application
of the spatial model of agenda control. These models, which assume that the legislature
has a monopoly over the legislative agenda, have typically predicted a limited role for the
president in the process. The second research agenda views the veto as an institution
designed to limit the distributive politics of the legislative branch. This approach
generally assumes that the president uses his veto power to maximize the welfare of his
entire constituency.
In this paper, we relax the assumption of the universalistic president and allow the
executive to have preferences over the distribution of expenditure across legislative
districts. Such preferences are likely for a variety of reasons including partisanship as
well as the maintenance of electoral and legislative coalitions. The formal model we
develop explores the extent to which the president can alter the distribution of federal
expenditures to further his partisan, electoral, and legislative goals as well as how his
distributional preferences affect aggregate levels of distributive spending.
I. Introduction
A major, but largely open, question in the study of American political institutions
is the extent and nature of presidential influence in the legislative process. Scholars are
engaged in considerable debate both as to how much legislative power the president can
assert and the processes and mechanisms by which it comes about.1 This debate also has
attracted the attention of many rational choice institutionalists who are interested in the
ways in which different institutional frameworks influence the strategic interaction of
political actors involved in the policymaking process. The role of the executive in the
legislative process provides a reasonably transparent institutional structure so that it is
relatively ideal for the tools of rational choice. When the institutional constraints
imposed on political actors are well understood, the analyst can let the constraints do
most of the work in providing analytical and empirical predictions. The analyst can
(within reason) remain fairly agnostic about the preferences and goals of the agents of the
model. Typically, in legislative models, the reelection motive is sufficient to derive
plausible predictions. For example, in models of the budgetary process, legislators often
are assumed to behave so as to maximize net expenditure within their own electoral
districts. Such an assumption has a great deal of analytical power. Since it is easy to
accept the link between budgetary largess and the reelection of the incumbent, the analyst
is free to proceed to more interesting questions such as those regarding the collective
ability of legislative bodies to control spending.
When the role of the president in distributive politics has been studied, the
reelection motive has been applied in exactly the same fashion: the president will seek to
1
maximize the net benefits going to his electoral district. Since his electoral district is the
entire nation, the president is typically viewed as a counterweight to the distributive
politics of the legislature (Carter and Schap 1987; Dearden and Husted 1990; Fitts and
Inman, 1992; Inman, 1993; Lohmann and O’Halloran 1994). It is assumed that the
president uses his veto power (or delegated proposal powers) to maximize the welfare of
his entire constituency. In this literature, institutions such as the executive veto are
designed to thwart the tendencies of a legislature that is biased towards the over-provision
of particularistic benefits to its members, at the expense of more general interests. Based
on this assumption of presidential universalism, this literature has put forward strong
normative arguments for increasing executive power in the legislative process. Among
these proposals are the line item veto and other reforms which move budgetary decisionmaking from the legislative branch to the executive branch.2
Yet there are reasons to be suspicious of presidential universalism when applied to
budgetary politics. It is not obvious that the simple strategy of insuring budgetary
efficiency accords as nicely with his reelection (or even history book) incentives as do
other possible strategies. There are many reasons why the president may depart from
welfare maximization of his entire constituency. The first is electoral politics. While
much of the previous literature assumes that the president is an agent of his entire
constituency, his electoral constituency is likely to be more important in determining his
preferences over appropriation outcomes. In principal, the president may try either to
reward regions that provided support in his election or to direct resources to strategic
“swing” regions to enhance his reelection prospects (or those of his party).3,4 Consistent
with this view, Grier, McDonald, and Tollison (1995) find that the president’s decision to
2
veto a bill can be predicted by the votes of senators from electorally important states.
Mebane and Wawro (1996) also find support that the president specifically targets
spending toward areas that are important for his re-election. These results suggest that
the president may use the veto and other perquisites of his office to favor some districts
over others.
A second source of particularistic preferences of the president is the desire to
direct distributive benefits to certain legislators in order to further his legislative agenda.
It has long been recognized that the president often promotes his agenda by influencing
individual legislators or “buying votes.”5 However, discussions of presidential favor
giving are usually limited to the president’s campaigning for members of Congress or
Rose Garden photo opportunities. The role of the president in allocating spending across
districts has not received as much attention.
Finally, the president may participate in distributive politics with partisan
motivations. As the leader of his party, the president may feel pressure to attempt to
favor legislative districts controlled by members of his own party. Levitt and Snyder
(1995) find that districts represented by Democratic representatives faired much better in
terms of federal spending during the Carter administration than they did during the
Reagan years.
The problems associated with mischaracterizing presidential motives might well
be minimal if in fact the institutional constraints are well specified. However, many
rational choice models of the presidency have tended to use highly stylized
representations of the legislative process which may in fact confound the problems
alluded to above. In most treatments, the legislature is modeled as a monopoly agenda
3
setter who proposes legislation subject to an executive veto (Hammond and Miller 1987;
Ingberman and Yao 1991; Kiewiet and McCubbins, 1988). These models and others in
the literature on agenda control have typically predicted only a limited role for the
president in the process. Veto power in these models, to the extent that it influences
legislative output at all, only permits the president to insure that policies he desires less
than the previous status quo are not enacted. When applied to the budgetary process,
Kiewiet and McCubbins (1988) argue that the effects of the veto on the overall budget are
asymmetric. If the reversionary appropriations are lower than the desired budget of the
legislature and the president, the effect of veto power will be to lower spending if the
president prefers a lower budget than the legislature. Alternatively, it has no effect when
the president prefers a larger budget than the legislature. By demonstrating the inability
of the president to increase budgetary items, these theoretical results and the empirical
support provided by Kiewiet and McCubbins are inconsistent with a large role of the
executive in the budgetary process.6 Even models of asymmetric information, which
allow the president to achieve outcomes that he prefers to the status quo (Cameron and
Elmes 1995; McCarty, 1997; Matthews, 1989), have not gone very far in establishing the
theoretical basis for a large role for the president in legislative decision-making.
If there is common implication of these behavioral and institutional assumptions,
it is that they both predict that the net effect of executive veto power is to lower
expenditure. The behavioral assumption suggests that the executive will always prefer
lower budgets, while the agenda control assumption produces lower spending as veto
power will be ineffective in increasing it, except in rare circumstances.7
4
In this paper, we attempt to address the shortcomings of both sets of assumptions
that have underlain previous analyses. While the results of our model generally concur
that veto power will generally lower overall spending, the actual logic differs
substantially and our model delivers a number of new predictions.
The model differs from previous work in two fundamental ways. First, we allow
the president to have preferences over the distribution of new benefits across districts.
We resist specifying a specific source (electoral, legislative, or partisan) of these
preferences and assume only that the president wishes to maximize the net spending in a
subset of districts, or coalition.8
Secondly, our model differs in the way it approaches the legislative bargaining
process. Whereas the agenda control literature assumes that the legislature makes a
single take-it-leave offer to the president to alter an exogenous status quo or reversion, we
relax this assumption by employing a sequential choice model (Baron 1994) of the
legislative process and inter-branch bargaining. The sequential choice model developed
here is an infinitely repeated, non-cooperative game that focuses on the effects of
presidential veto power on legislative proposals and voting. While the sequential choice
model does preserve the legislative monopoly over agenda control, it does allow the
bargaining to take place over time rather than a single shot. In the dynamic model, the
agents no longer bargain in the shadow of an exogenous status quo but rather of
endogenous expectations of future legislative decisions and presidential vetoes. These
equilibrium expectations about proposals subsequent to presidential vetoes work to give
the president a greater degree of leverage than in a single shot game. Another assumption
of the agenda control model that we relax is that legislative proposals are generated from
5
a single proposer, generally the median legislator. This assumption is often defended on
grounds that the legislative decision-making process will generate median voter
outcomes. However, in a purely distributive setting such as the one we pursue, median
voter theorems carry little weight as the set of feasible allocations is multidimensional. In
the sequential choice model, these problems are dealt with by assuming that proposals are
made sequentially according to a recognition rule. If the recognition rule contains some
randomness, there will be uncertainty about which majority legislative coalitions will
form subsequent to a presidential veto. This uncertainty gives the president a degree of
leverage over the proposals of the current legislative majority.
The paper proceeds as follows. In Section II, we develop a sequential choice
model of distributive politics based on the work of Baron and Ferejohn (1988) and Baron
(1991). In this game, each legislator tries to maximize the amount of net benefits
appropriated to his or her district while the president uses his veto power to direct as
many resources as possible to his coalition. This model allows a comparison of the polar
cases of no executive veto and an universalist executive who wields the veto to maximize
social welfare. In section III, we allow for particularistic preferences on the part of the
president where we investigate the effects of the executive veto on the level of spending.
These results establish a link between the form of the veto institution, the president’s
objectives, and the level of government spending. Specifically, we find that the size
government is decreasing in both the number of votes required for override and the size
of the president’s coalition. In Sections V and VI, we explore two extensions of the basic
model. First, we discuss how executive veto institutions fare versus supermajoritarian
procedures. Then we explore what role political parties might have on the basic model.
6
Section VII concludes and draws implications for application to other institutional
arrangements and institutional design as well as the agenda for future theoretical and
empirical research.
II. A Model of Distributive Politics and the Veto
To focus on the role of executive veto power in altering the dynamics and
outcomes of legislation on spending bills, we consider an appropriations bill to distribute
the benefits of a project with a value B among N districts. The tax cost of the project T
will be distributed evenly among all districts so that each must pay T/N.9 An important
parameter in the analysis is the benefit-cost ratio R ≡ BT . Programs for which R ≥ 1 will be
referred to as efficient while those for which R < 1 will be referred to as inefficient as the
benefits fail to exceed the costs. Our evaluation of executive veto institutions will be
based on their ability to restrict the passage of inefficient programs. Therefore, we will
be concerned with the programs with the smallest R that are able to pass through the
legislative process. We will refer to this critical value as the minimally efficient benefit
cost ratio, and we denote it as R*.10 Finally, we assume that the allocation of the benefits
will be determined by majority rule subject to an executive veto and supermajority
override.
Let a proposal by legislator O at time t and a history of play h be denoted as
<
A
x th = x1th , x 2 th ,K , x Nth where x ith is the benefit share going to district i under proposal
7
N
x th . Obviously, we require that ∑ x ith ≤ B. In equilibrium this constraint will always
i =1
bind.
Rather than arbitrarily limit the opportunities for legislative consideration of this
project, following Baron (1991), we assume that the legislature may consider the passage
of the project for an infinite number of sessions.11 If the project does not pass in a given
session, it may be taken up again in the future. Each legislator discounts future payoffs
2
7
by δ so that legislator i’s payoffs are δ t u x ith − NT where t is the time period in which an
agreement passes, O is the proposer at time t, and u(⋅) is a utility function over net
spending. To capture any effects of risk aversion while still taking advantage of the
tractability afforded by linearity, we assume that
1 6 %&'λr r
ur =
if r ≥ 0
[1]
if r < 0
where λ < 1. Therefore, the marginal utility of spending is greatest when the district is
receiving negative net benefits. This (weakly) decreasing marginal utility insures that u(⋅)
is concave.12 If the appropriation never passes, the payoff for each legislator is u(0) = 0.13
In order to investigate the role of the executive, we must consider the preferences
of the president over the distribution of expenditure. We assume that he wishes to
maximize the utility of a subset of m districts, or his coalition.14 Assuming that the
districts are indexed so that i = 1,...,m are members of the president’s coalition and
district i = m + 1,..,N are those not represented in the coalition. Thus, the president
∑ δ u2 x
m
wishes to maximize
t
i =1
ith
7
− NT . The concavity of u(⋅) also suggests that the
8
president cares about the distribution of spending within his coalition as the president’s
utility can be raised by taking a dollar from a coalition district receiving positive net
benefits and giving it to one receiving negative net benefits.
We treat the choice of the coalition as exogenous in order to focus most of the
attention on the implications of particularistic preferences regardless of their source. We
prefer not to link the analysis too strongly to any particular supergame that would
generate such preferences.
As shown by Baron (1991), the possibilities for passage of the project and the
distributional consequences are affected by the choice of legislative rules and recognition
procedures.15 In our analysis, however, we consider the case of legislative bargaining
under the closed rule with uniform random recognition as proposed by Baron. Under a
closed rule with uniform random recognition, proposer O is chosen with uniform
probability
1
N
in each period.16 She subsequently makes a proposal x th . The legislature
votes on this proposal and decides by majority rule so that when N is odd n ≡ (N+1)/2
votes are needed for passage while if N is even n ≡ (N+2)/2 are required.17 The proposal
is then submitted to the president for his signature or veto. If he signs it, the
appropriations are made according to x, each district is assessed taxes T/N, and the game
ends. If he vetoes it, the legislature may override his veto with k > n votes.18 In the event
that the legislature is unable to override the veto, the session ends and each legislator
discounts the future at a rate of δ.19 An important consideration for deciding whether to
vote for the current proposal is the utility of defeating it and continuing to the next period.
Let vith be the expected utility player i receives for defeating a proposal at time t with
9
history h. We will refer to this expected utility of the future as the continuation value.
These values will be determined in equilibrium.
Following Baron and Ferejohn (1988), we only consider stationary and symmetric
strategies. Stationary strategies are those that are time and history independent.20 In this
context, stationarity implies that proposals will only be a function of the identity of the
proposer as well as the basic parameters m, k, N, and δ. Symmetry is imposed so that
proposers treat all legislators of the same type identically. Since the only ex ante
differentiation of legislators in this model is based on membership in the president’s
coalition, the stationarity and symmetry assumptions suggest that strategies will depend
only on whether the proposer is a member of the president’s coalition. Thus, the
continuation values, vi , and optimal proposals of each legislator depend only on her
coalition status. Let vi = vp for members of the presidential coalition members and vi = v
for non-members. The stationarity assumption also implies that these are also the ex ante
expected utilities of the game.21 Much of the analysis will concern the relationship of vp
to v.22 In order to examine the role of the president, we must consider his continuation
value as it will determine his veto strategies. Stationarity and symmetry imply that the
president’s continuation value is mvp.
Now consider the decision of each legislator to vote for a given proposal given her
expectations about the future. Certainly, a legislator will only vote for proposals that
provide her district at least as much utility as can be gained by having the bill defeated
and reconsidered in the next period. Due to discounting, the utility of defeating the
current bill is δvi while the utility of accepting the current proposal is u(xi -
T
N
). Thus,
10
member i will vote for the proposal if and only if xi ≥ δvi +
T
N
if vi < 0 or xi ≥ δvi/λ+
T
N
if
vi ≥ 0.23 The decision rule for a coalition member is analogous.
The president’s veto decision rule can be derived along similar lines by recalling
∑ u1 x
m
that the president’s utility from the proposal x is
i =1
i
6
− NT so that the president will
accept the proposal if and only if this value exceeds δmvP.
Having specified the voting strategies for all legislators and the veto strategies of
the president, we turn to the strategies of the proposers. Proposers must choose whether
or not to make any proposal, and if so, how to allocate funds across districts. We begin
by analyzing those proposers who are not part of the president’s coalition. Their problem
is to make a proposal capable of generating a coalition sufficient to pass a bill while
keeping as much of the program’s benefits as possible for herself. Let zi +
T
N
be the
retained benefits so that after taxes the net benefits to the proposer are zi. By symmetry,
zi = z for all non-coalition members. To maximize z, she must choose the winning
coalition that commands the smallest share of the benefits. Conditional on making a
proposal, there are two types of strategy that the proposer might employ. Either the bill
must be one that can satisfy the president and a simple majority of n members, or it must
satisfy a supermajority of k members. For simplicity, we refer to “n + the president” as
the majority strategy and a coalition of k members as the override strategy.
Let π(R,m,k,N,δ) be the probability that a non-coalition proposer chooses to
pursue the override strategy. An override coalition is easy to construct. Assuming that vi
≥ 0, the proposer would offer δvi /λ +
T
N
to k-1 legislators with the lowest reservation
values and keep the remaining benefits for her own district.24 The majority strategy can
11
be implemented by offering δvi/λ +
T
N
to the n-1 other legislators and insuring that at least
δmv P λ + m NT goes to members of the president’s coalition. It follows that the
“cheapest” way to implement this strategy is to offer δvP/λ +
T
N
to each member of the
president’s coalition and if m < n build the rest of the majority by offering δv/λ +
T
N
to n-
m-1 non-coalition members.25 The case of vi < 0 is exactly analogous -- we need only
replace λ with 1 in each of the preceding expressions. Having analyzed the optimal
construction of a coalition, we consider whether or not a proposal will be actually be
made. If no proposal is made, the game continues to the next session which has a value
of v to the proposer. Therefore, no proposal will be made when u(z) < δv.
The situation faced by a proposer in the president’s coalition is quite similar but
contains an additional wrinkle. Such a proposer must also choose between a majority
coalition and an override coalition.26 Let πP(R,m,k,N,δ) be the probability that a noncoalition proposer chooses to pursue the override strategy which would be implemented
exactly as above: she would offer δvi/λ +
T
N
to k-1 legislators and keep zp +
T
N
for her
district.
A slight complication arises in the case of the majority coalition. To ensure that the
president accepts, a coalition proposer (say from district 1) would have to make a proposal
∑ u1 x
m
such that u(zp) +
i=2
i
6
− NT ≥ δmv P . Unlike the non-coalition proposer, in order to satisfy
the president, the coalition proposer may offer benefits either more than sufficient or less
than sufficient to receive a vote from that district. Doing so helps to satisfy the veto
constraint if it goes to districts that are receiving negative net benefits. Thus, we can think
12
of her problem as one of including j < m-1 presidential coalition members and randomly
allocating $c to districts with negative net benefits.27 Therefore, the constraint may be
1
6
1
6
written as λz P + c ≥ m − j δv P + m − j − 1
T
N
. Thus, unlike the non-coalition proposer who
must only choose between a majority and override proposal, the coalition proposer has a
greater degree of latitude in choosing exactly how to form a majority coalition.
Note that when j < n increasing j has the effect of replacing one non-coalition
member with a member of the coalition. This decreases the proposer’s utility by δvP - δv
and increases the utility of one coalition member by δvp +
increases by δv +
T 28
N
.
T
N
so that the president’s utility
If j > n-1, reducing j by one has the effect of decreasing the utility of
one coalition member by δvP +
T
N
. This change also increases the proposer’s utility by an
equal amount. Thus, it is a dominated strategy to choose j > n-1 as it lowers the proposer’s
utility without increasing the president’s. A coalition proposer will not make a proposal if
u(zP) < δvP.
For this sequential choice model, a symmetric, stationary Nash equilibrium will
constitute values of zP, z, v, vP, π, and πP that are consistent with each player maximizing
her utility given the strategies of other players.
Benchmark Cases
Having laid out the model, we turn to deriving some results for two important
benchmark cases: the case of no executive veto and the case of a universalistic president.
13
A. No Executive Veto
The easiest way to proceed in the case of no executive veto is notice that it is
identical to the model presented above where m = 0 so that all legislators are noncoalition members. We need only be concerned with computing equilibrium values of z
and v.29 We will begin with the case of v ≥ 0. Since selected proposer must build a
majority, she will allocate δv/λ +
T
N
to n-1 other legislators so that
1 6
z = B − δ n − 1 v λ − n NT
[2]
The proposer and n - 1 other legislators vote for the proposal, and it passes. To
complete the solution for the symmetric, stationary Nash equilibrium, we must solve for
v. The utility of continuing to the next round is based on a 1/N probability of being the
proposer and receiving utility of λz, a (n-1)/N probability of receiving δv/λ +
(N-n)/N probability of being left out and paying
v=
1 6
1
T
N
λz + n − 1 δ v λ − N − n
N
6
T
N
, and a
. Thus, v can be written as
T
N
[3]
Solving [2] and [3] for z and v yields
z
*
N − δ1 n − 16 − δ1 n − 16 1 6 =
N + δ1λ − 161n − 16 B − N + δ1λ − 161n − 16 T
n
N
N − n λ −1
N
[4]
and
v* =
λ2 B − λT
N + λ −1 n −1 δ
1 61 6
[5]
14
Equations [4] and [5] describe the equilibrium allocations of costs and benefits
conditional on a proposal being made. Note that for a program where the benefits equal
the costs i.e. B = T, z* > 0. In fact, z* > 0 for programs with B < T so that inefficient
programs may be proposed. However, v* < 0 when B ≤ T, so we must recompute v* and
z* under the assumption than v < 0. In fact, since we are primarily concerned with the
case of inefficiency, we will devote ourselves to this case throughout. When v < 0,
equations [2] - [5] become
1 6
z = B − δ n − 1 v − n NT
v=
z* =
1 6 1
λz + n − 1 δ v − N − n
N
6
[6]
T
N
[7]
N − δ1n − 16 B − n − δ1n − 16 T
N + δ1λ − 161n − 16 N + δ1λ − 161n − 16
[8]
2 1 6 7T
N + δ1 λ − 161 n − 16
[9]
and
v* =
λB − 1 + λ − 1
n
N
However, we need to consider whether it is optimal for the proposer to make any
proposal at all. It turns out that there are a continuum of stationary, symmetric Nash
equilibria such that a proposal is made if and only if z* ≥ ξ where 0 ≥ ξ ≥ δv. We will
follow Baron (1989) and analyze only those where a proposal is made if z* ≥ 0. From
equations [8] and [9], a proposal will be made and passed if and only if
1 6
1 6
n − δ n −1
B
≥ R* =
T
N − δ n −1
[10]
15
The ratio R* defines from each equilibrium a critical ratio of benefits to costs which must
be exceeded in order for the program to be passed. As R* is bounded above by
n
N
< 1, we
can see that some inefficient programs will be passed in addition to all of the efficient
programs. Since many programs whose costs exceed their benefits will be passed,
equation [10] shows that legislators will rationally vote for programs in which they
receive negative net benefits. This occurs as they rationally anticipate the possibility of
receiving a worse distribution of net benefits in future periods. Given these rational
expectations, they will vote for a bill that makes them worse off than they would be if the
bill did not pass. One of the interesting implications of this result has to do with the
effect of the discount factor on the size of the minimally efficient program. It is easy to
see that the size of the minimally efficient program is decreasing in δ. The logic is
straightforward. The more that legislators fear bad future outcomes, the more likely they
are to accept bad current ones.
Equation [10] also has implications for the size of government when no executive
veto is available. Given a fixed menu of possible government projects, more projects will
pass as this ratio diminishes. This will lead to the government spending more than the
optimal level, as projects unjustified on cost-benefit grounds will be enacted. This is a
key result of Baron (1991).30 This tendency of majority rule to lead to inefficiently large
government is a very robust theoretical result. An overspending result is generated also
in models by Tullock (1959), Weingast, Shepsle, and Johnsen (1981), and others. These
results occur because the majority does not internalize the costs that it imposes on the
minority. The wrinkle of the sequential choice model is that both the minority and the
majority (except the proposer) are made worse off by some of the proposals that pass.
16
B. Universalisitic Presidents
One of the arguments that is prominent in the literature on the executive’s role in
budgetary politics is that it can serve as a mechanism to limit the inefficient legislative
logrolls and thus the size of government (Inman 1993). These analyses typically assume
that the president is a universalist; that is, he serves to maximize the net benefits of all
districts. Given these objectives, an executive can use the veto to prevent excessive
spending.
This argument may be made explicit in the current model as it corresponds to m =
N. Again so that we may compute the critical benefit cost ratio, we will focus on the case
of vP < 0. Since all members are in the president’s coalition, the coalition’s utility must
exceed δNvP. This requires the proposer to pay out at least δNvP + T. Note, however,
that an override coalition can be constructed for δkvP + k NT which is always less costly so
that the majority strategy will not be pursued and πP = 1. The proposer’s net benefits can
be written as
1 6
z P = B − δ k − 1 v P − k NT
[11]
and the continuation values as
vP =
1 6
1
λz P + k − 1 δv P − N − k
N
6
T
N
[12]
which implies that
z*P =
N − δ1k − 16 B − k − δ1k − 16 T
N + δ1λ − 161k − 16 N + δ1λ − 161k − 16
[13]
and
17
v *P =
2 1 6 7T
N + δ1λ − 161 n − k 6
λB − 1 + λ − 1
k
N
[14]
Again, we focus on the equilibrium where a proposal is made if and only if zP ≥0.
Therefore, now a proposal will only be made in the equilibrium if R >
1 6 . Since k >
1 6
k − δ k −1
N − δ k −1
n, this critical value must be higher than the one for no veto. The executive veto
eliminates some of the inefficient programs that would be enacted in its absence.
Furthermore, the effectiveness of the veto in limiting spending is increasing as the
number of votes required for override. The lowest possible benefit/cost ratio approaches
unity as k goes to N. This analysis again suggests a normative rationale for stronger veto
provisions. Intuitively, the veto power increases the efficiency of the level of government
expenditure because, as the president cares about the payoffs to each district, all benefits
must be shared more equitably. As the benefits get spread over more districts, it becomes
reasonably less attractive to implement costly programs. However, if the president
wishes to use the veto to favor particular districts, it will turn out that benefits may not be
spread more equitably as veto power increases via an increase in k. In turn this effect will
tend to undermine the beneficial effects of the veto.
III. Particularistic Presidents
To analyze the effect of a president with non-universalistic preferences, we now
consider the model for the case where 0 < m < N. As an example to motivate the more
general results, we focus of the case where k > N so that the president has an absolute
18
veto. Since overrides are not possible, π = πP = 0. We will derive all of our expressions
for the case of vp < 0 and v < 0 as these are the relevant cases for checking the limits on
1
inefficiency. Since a majority coalition is the only feasible route, at least m δv P + NT
6
must go to the president’s coalition. As discussed above, this implies that non-coalition
proposers must allocate δv P + NT to each member of the coalition and build the remaining
majority from non-members. Thus,
%KB − δmv − δ1n − m − 16v − n
z=&
K'B − δmv − 1m + 16
P
if m < n
T
N
[15]
if m ≥ n
T
N
P
To avoid a veto, the coalition proposers will choose to allocate enough benefits to
j coalition districts and allocate c more dollars to avoid a veto so that
1
6
z P = B − c − δjv P − δ n − j − 1 v − n NT
[16]
and
1
6
1
6
λz P + c ≥ m − j δ v P + m − j − 1
T
N
[17]
where j < min{n-1,m-1}.
We can now compute the continuation values which are expectations over the
utilities of being the proposer, being in the winning coalition, and being left out of the
winning coalition. Working out these expected utilities, it can be shown that
19
vP
%KN
=&
K'N
1
6
−1
λz P + c + a1δv P − N − a 1 − 1
−1
z P + c + a 1δv P − N − a1 − 1
1
6
T
N
T
N
if z P > 0
[18]
otherwise
and
%KN
v=&
'KN
1
6
−1
λz + a 2 δv − N − a 2 − 1
−1
z + a 2 δv − N − a 2 − 1
1
6
T
N
T
N
if z > 0
[19]
otherwise
where a1 and a2 are probabilities of receiving benefits and
a1 = N + j − m
a2
%Km n − j − 1 + n − m − 1 if m < n
K N−m =&
KKm n − j − 1
if m ≥ n
' N−m
The resulting systems of equations can be solved in terms of z, zP ,v, vP, and c. Given a
solution, j* can be chosen to maximize zP. Since the continuation values in a stationary
game are identical to the expected payoffs for the game, the values of v and vP reflect the
distribution of net benefits across presidential coalition members and non-members.
Because we are interested primarily in the extent of the inefficiency and because the
expressions are simpler, Proposition 1 presents the continuation values for the lowest
possible program that passes.
20
Proposition 1: The minimally efficient benefit-cost ratios for the absolute veto game are
R* =
1
6
1
6
67
n N − m − δN n − m
N N − m−δ n− m
2
1
if m < n and R * =
m
if m > n.
N
The continuation values of the game at R* are:
1
6
1
If m < n, v P = 0 and v =
− N−n T
N N − m−δ n− m
If m ≥ n, v P = 0 and v =
− mT
.
N N−δ n−m
2
2
1
67
67
Proof: See appendix
A few comments are in order. First, in the case of the absolute veto, there is a
premium to members of the president’s coalition as vP > v. The logic of this premium is
quite straightforward. First, the president’s veto power increases the probability that
coalition members receive benefits. Secondly, the net benefits of a proposer from the
president’s coalition are larger since it is less costly for them to satisfy the president’s
demands. It is easy to show that such a premium exists for all values of B and T, not just
for the lowest program that can be adopted.
The main result of Proposition 1 concerns the ability of inefficient programs to
pass. Comparing R* from proposition 1 with equation [10], we find that the absolute veto
is more efficient than pure majority voting for all values of m. The president’s desire to
favor some districts over others does not undermine the effects of the veto. The intuition
is clear. Under pure majority rule, all members expect to get negative benefits from an
inefficient program. Therefore, the primary consequence of using the veto to favor some
21
districts is to block inefficient programs. However, this effect is clearly stronger when
the president wants to favor more districts.
For a more general set of results, we relax the assumption that k > N and consider
the role of the veto override. Now proposers must determine whether to pursue a
majority or an override coalition. Note that when m is much larger than k, this decision is
irrelevant. The proposer will always build an override coalition. Thus, the outcome is
identical to the case of a universalistic president which was discussed above.
Alternatively, when m is reasonably small, the proposer will always choose to satisfy the
president and a simple majority. In this case, the results are identical to the case of an
absolute veto.
In general, however, it will not be an equilibrium for the proposer to choose either
type of bill with certainty. If the proposer has a clear preference for the override proposal,
this will tend to drive down the continuation values of the presidential coalition.
Alternatively, if the proposer prefers a proposal acceptable to the presidential coalition,
the continuation values of the non-coalition members will diminish. So in equilibrium,
this “bidding process” ends only when the proposer is indifferent between proposing to
the president coalition or to a size k coalition. Given this indifference, each proposer will
play a mixed strategy so that π and πP may be strictly between 0 and 1.31
The solution to this more general model involves a number of cases that depend
on the values of m, k, and n. For each of the cases, the solution of a system of equations
in terms of vP ,v, zP , z, π, πP, c, and j will constitute a symmetric, stationary Nash
equilibrium. The systems of equations that generate a solution to this game are relegated
to the appendix. In each case, the conditions include expressions for the equilibrium
22
proposals and the expected utilities of each legislator. In the case of mixed strategy
equilibria, an additional condition is imposed by the required indifference condition on
the proposer. The equilibrium expressions involved in the case of a qualified veto and a
non-universal coalition turn out to be very complicated and not very informative. We
turn instead to a numerical example to demonstrate the effects both presidential coalition
size and override rules on the size of budgets. Figure 1 plots the critical level of benefits
for a 400-member legislature required to pass a program that costs $10,000 as a function
of m and k.
Insert Figure 1 About Here
The logic behind these results is straightforward as two effects are combined. The
enhanced veto power increases the president’s ability to shield his coalition from
inefficient programs; while at the same time, it gives proposers an incentive to build
override coalitions to the defeat the presidential veto. This spreads the benefits across a
greater number of districts and lowers the benefit of an inefficient program to the
proposer. This results conforms to the conventional wisdom that executive veto power
may well place a break on distributive spending. Yet, the result depends neither on
universalistic preferences or the placement of an exogenous reversion. Any constraint on
the proposer’s ability to play each district against another in the formation of a coalition
will inhibit inefficient spending. Particularistic presidents are not sufficient to eliminate
the beneficial effect of veto power.
We also can see the effect of the president’s coalition size. Increasing m will
force proposers to spread the benefits across more districts so as to lower the amount that
23
they may retain for themselves. Larger presidential coalitions also lessen the ability and
desire of the president to redistribute. Both of these influences tend to lower the critical
benefit-cost ratio.
IV. Supermajoritarianism and the Executive Veto
While it appears that the executive veto is an effective institution in terms of
stymieing legislative logrolls, it actually fairs relatively poorly in comparison to
alternative supermajoritarian procedures. Recall the result pertaining to the absence of an
executive veto power where R* =
1 6
1 6
n − δ n −1
. Note that efficiency (R* = 1) can be
N − δ n −1
obtained by increasing n from (N+1)/2 to N (i.e. moving from majority rule to
unanimity).32 Furthermore, setting n = k sets R* to the same value as for the case of an
executive veto with a k vote override when the president chooses m = N. Given the
results of the previous section, it is easily shown that in terms of efficiency this k-majority
rule dominates a k-veto institution. Furthermore, supermajoritarianism does not lead to
the inequitable distribution of resources induced by the veto. These results suggest that
budgetary reforms of internal legislative procedures may well dominate those that involve
enhancements of executive power.
24
V.
Partisanship and Divided Government
To this point, we have discussed the role of the president’s coalition in rather
abstract terms. However, empirically it would seem most plausible that the president’s
coalition would generally coincide with membership in his party. If we adopt such a
view, our previous results would suggest testable connections between distributive
spending and the size of the president’s party in the legislature. Periods of small
presidential parties (such as divided government) should be associated with more
distributive spending than periods when the president’s party is stronger (unified
government). This prediction, however, is tentatively based on a dubious assumption.
To this point, we have assumed that the recognition probabilities are uniform and do not
depend on a legislator’s status in the president’s coalition. However, if the president’s
coalition is partisan, the ability of the majority party to exert disproportionate control of
the legislative agenda may lead to recognition probabilities that are a function of a
member’s status vis a vis the president. Suppose there were divided government and the
minority (president’s) party were recognized to make proposals with probability zero.
This may inhibit the president’s ability to redirect benefits to his party members and thus
upset the prediction that divided governments engage in more distributive spending.
Again, such logic turns out to be false.
To explore the possible impact of partisan differences in recognition probabilities,
let q/m be the probability that a member of the president’s party is recognized and (1q)/(N-m) be the probability that an opposition party member. An interpretation of these
25
probabilities is that the president’s party is chosen to make a proposal with probability q
while each member has an uniform probability of being chosen as the actual proposer.
Our previous results for uniform recognition represent the case of q = m/N. This is
the relevant benchmark for a weak party system. We will consider the case of a strong
party system where q = 1 if m ≥ n and q = 0 if m < n. For simplicity, Proposition 3
focuses only on the case of an absolute veto.
Proposition 2: In the case of an absolute veto, the following conditions hold:
1. If q = 0 and m < n, then
i) R* =
n
N
1N − m6 − δ1n − m − 16
N − m − δ1 n − m − 16
ii) At R*, vP = 0 and v = −
1N − n6T
N N − mδ1 n − m − 16
2. If q = 1 and m ≥ n
i) R * =
m
N
ii) At R* , vP = 0 and v = −
T
N
3. In both cases, R* is lower than that for both strong and weak party legislatures without
a veto.
4. R* in strong party legislatures with the veto is slightly greater than or equal to R* in
weak party legislatures with the veto.
proof: see appendix.
26
In case 1, while the veto power without proposal power may not allow the
president’s party to share in the positive benefits of an efficient program, the negative
power of the veto prevents the president’s party from having to share in the costs of an
inefficient program. This also serves to limit the inefficiency of passed programs. Thus,
even when the president’s party has no proposal power, the presidential veto might
constrain the distributive choices of the legislature.
Turning to the case of the president’s party as a majority, one might suspect that
the veto may help majority further exploit the minority and increase distributive spending.
Proposition 2 shows not to be the case as the primary role that the veto plays is to prevent
the majority from exploiting each other.
Proposition 2.4 also underscores that veto powers are more important than the
allocation of proposal powers for inefficient programs. In the case of m > n, the critical
value R* is identical across the cases. When m < n, the strong party legislature performs
better, but the effect is quite small. In the case of m = 180, N = 400, and δ = .9, the
difference between strong and weak-party legislatures is a trivial .003.
Thus, the inclusion of a strong partisan legislature does not contradict the
implication of a correlation between divided government and distributive spending.
McCubbins (1991) presents evidence of such a correlation for appropriations to 69
federal agencies from 1948-1985 while Lohmann and O’Halloran (1994) find a
correlation with trade protection --a quintessential distributive policy-- and divided
government.
27
VI. Conclusions
In this paper, we have presented a model of the influence of the executive veto on
legislative spending decisions. In contrast to previous work, we have focused not only on
how the veto may affect the overall level of spending but also on the distribution of
spending across political jurisdictions. Our results indicate that the executive veto may
have quite large effects on the distribution of spending when the executive chooses to
favor small coalitions. Further, we show that the concentration of benefits to members of
the coalition does indeed serve to limit spending rather than increase it. For this reason,
increasing the power of the executive regardless of their parochial or political interests
may move distributive spending towards the efficient level.
The model has many normative implications for the design of legislative
institutions and electoral institutions. In terms of the institutional design of legislative
processes, it argues strongly for executive veto provisions in terms of efficiency but
shows that such institutions will have large distributive effects. Such control over the
distribution of spending may give the executive a large bargaining advantage in other
policy areas. This effect will certainly tend to inhibit reforms such as the number of votes
needed to override. However, reforms of electoral institutions may have the same
desirable effects without the distributional consequences. For example, the Electoral
College system may encourage presidential parochialism as votes in some legislative
jurisdictions are more important than in others.33 The presidential primary system tends
to place weight on early and winner-take-all contests. The logic of the preceding model
28
suggests that unweighted electoral schemes or national primaries may minimize the
incentive to favor one district over another.
A number of testable hypotheses emerge from this model. The first is that we
might expect the president to use the veto to favor electorally important districts of
legislative allies. Grier, McDonald, and Tollison (1995) and Mebane and Wawro (1996)
have supported the hypothesis that the president uses the veto to favor election
constituencies. In addition to these hypotheses, the model predicts that patterns of
spending across states should reflect electoral and/or legislative support for the president.
Finally, the results suggest a relationship between the size of the president’s coalition and
the size of government.
Again, if one uses political party as a proxy for the president’s coalition, the
model suggests that government should grow faster during periods of divided government
because the president’s coalition is smaller. This implication could also be tested on state
level data. With state level data, one not only has cross sectional variation in divided
versus unified governments but also variation in the types of executive veto institutions,
including the line item veto which we do not consider here.
Finally, the model might be able to explain differences between presidents in their
first term versus those in the second term. Since the second-termer has somewhat less
proximate electoral concerns, he may have less parochial preferences and may attempt to
maximize the utility of a greater set of districts. In turn, the model implies that fewer
inefficient projects would pass, leading to lowered government spending in the second
term relative to the first.34
29
In addition to explaining patterns of spending in jurisdictions that have executive
veto institutions, the present model can also be easily applied to a number of other
legislative settings where certain actors have veto rights such as the nations in the
European Community (Tsbellis 1994) or representatives of political minorities. The
fundamental implication for institutional design in these settings is to insure that a
sufficient number of legislators possess veto power to prevent those who do have it from
causing excessive redistribution to themselves.
Straightforward extensions of the model could analyze the effects of different
legislative actors having vetoes subject to different qualifications as well as the
interaction between proposal powers and veto powers. For example, one could determine
the relative values of certain veto powers and recognition rules from the perspective of
legislators. From these results, a broad set of implications about of legislative institutions
might emerge.
30
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34
Endnotes
1
A complete review of this literature would take us far afield. Prominent book length
studies specifically focused on these questions include Edwards (1980), Bond and
Fleisher (1990), and Cameron (1997).
2
However, even when the president desires lower budgets than Congress, Carter and
Schap (1987) and Dearden and Husted (1990) demonstrate theoretically that line item
vetoes do not necessarily lower expenditure below that associated with an all or nothing
veto. This may explain weak and negative empirical results about the effect of line item
vetoes in reducing expenditure in the states (Alm and Evers 1991; Holtz-Eakin 1988).
3
An exception to this statement is Lohmann and O’Halloran (1992) who consider the
effects of delegation to the president who prefers to distribute favors to members of his
own party.
4
See Brams (1978) for discussions of the strategies the president may employ to win the
Electoral College.
5
For theoretical treatments of vote buying, see Groseclose (1996), Groseclose and
Snyder (1996), and Snyder (1991).
6
Perhaps more troubling is that the extent that the president can alter budgetary
outcomes at all in the Kiewiet and McCubbins model depends crucially on an assumption
about the reversion policy enacted after a veto. They assume that the relevant reversion is
the previous years spending level, which would be established in a continuing resolution.
If the relevant reversion were the statutory reversion of $0, the Kiewiet and McCubbins
model would predict that the budgetary outcome would only reflect legislative
35
preferences. We will argue below that the norm of continuing resolutions at previous
spending levels is not a necessary condition for the executive to have influence over
budgetary outcomes.
7
There are conditions in the Kiewiet and McCubbins model which imply that the veto
power limits the Congress’s ability to cut spending. This occurs when Congress wishes
to cut spending below the previous year’s nominal level, and the president does not agree
to the extent of the cuts. Due to inflation (which turns nominal freezes into real cuts) and
the political climate for larger government, this scenario was rare in the years studied by
Kiewiet and McCubbins. In the current climate, the situation where the veto helps
maintain spending levels is more plausible.
8
To keep things a bit general we do not specify the process by which the president
determines which districts are to be supported.
9
A roughly symmetric analysis could be conducted assuming that the benefits accrue to
every district and the costs were allocated via the political process.
10
There is an alternative way of modeling the set of legislative opportunities. One might
model the benefits and costs as B(s) and T(s) where s the project’s scale which is also
determined within the legislative process. We could then evaluate legislative institutions
based on the benefit cost ratio at the equilibrium value of s. Such an approach would
deliver qualitatively similar results to the approach taken here.
11
The results will not be qualitatively affected by assuming that the process infinite.
12
Gilligan and Krehbiel (1995) also use a similar utility function in the context of a
sequential choice model.
36
13
Thus, we are essentially assuming zero-based budgeting. While other baselines could
be easily incorporated, this one is the most interesting one for our purposes since previous
analyses of the veto power only find an impact in cases of non-zero baselines such as
continuing resolutions.
14
We will use the term president to refer to this player, although the model may be
directly applied to any executive with veto power.
15
In fact, given that the model is an N-dimensional voting game, the mere existence of a
solution will depend on there being at least minimal legislative structure to overcome the
well known voting cycle problem.
16
A few words are in order about the use of random recognition rules as a modeling
device. While random recognition does not mimic any actual procedures of any know
legislature, it turns out to be a useful device for capturing the inherent uncertainty that
legislators face in building distributive coalitions. Random recognition is a way of
modeling the fact that legislators do not know exactly which coalitions will form in the
future if the current coalition fails to pass the legislation. More troubling is the
assumption of uniformity which we relax in Section V.
17
In most legislatures including the U.S. Congress, a motion fails on a tie vote.
Supermajoritarian institutions can be easily be accommodated by redefining n.
18
Note that an override rule of k ≤ n is superfluous as any group of legislators large
enough to pass the bill is also large enough to override the veto. We will also consider
the case of an absolute veto where no override is possible. This is equivalent to the
assumption that k > N.
37
19
Baron and Ferejohn (1989a,b) interpret δ not only as the discounting of future costs
and benefits but also the probability that the legislator is returned to office while
McKelvey and Riezman (1992) endogenize δ as a reelection probability based on the
legislator’s success in obtaining benefits for her district. We are more inclined to treat δ
exclusively as a time discount since appropriations must pass every year. Therefore, the
probability that a member leaves office during the allocation process is not very relevant
to decision making. Since our perspective implicitly treats legislative periods as shorter
in duration, it implies that the discount factors should be correspondingly higher.
20
Baron and Ferejohn (1989a) show that any division can be supported in non-stationary
equilibria using infinitely nested punishment strategies. The intuition for this result is
straightforward. Any proposer who deviates from the prescribed distribution of benefits
will be “zeroed out” by the next proposer who would be punished if she failed to do so.
Because of the infinite number of periods, proposers will always find it rational to carry
out the punishment and so that the original proposer will not deviate. Such strategies can
only be implemented if proposers can recall the entire (infinite) history of play so as to
ascertain which members are to be zeroed out. Baron and Kalai (1993) argue that this is
an attractive restriction of the strategy space due to the fact that it requires the fewest
computations by the agents in the model.
21
Stationarity implies that the utility of proceeding from time 0 to time 1 (i.e. beginning
the game) must be the same as proceeding from time 1 to time 2 (i.e. defeating proposal
1).
38
22
We will also take advantage of symmetry to suppress the superscript Oand stationarity
to suppress the subscripts t and h on x th and x ith .
23
It is interesting to note that δv can be thought of as the expected utility of the status
quo prevailing on the current vote. However, unlike the status quo in most agenda
control models, δv is not exogenous, but derived from rational expectations of future
legislative outcomes.
24
1 6
This expression uses the fact that u −1 δv i =
δv i
when vi ≥ 0. We assume that the
λ
proposer randomizes over legislators who have the same continuation value. It can be
shown that this assumption is supported by a mixed strategy equilibrium where the
proposer chooses among legislators with the same probability (Harrington, 1990). If the
proposer chose any legislator with a higher probability, the other legislators would bid
down the price of support and the proposer would no longer be indifferent.
25
There is a bit of an indeterminacy when m > n. For example, a majority coalition
could be built equally cheaply by offering
m
N
(δv P + NT ) to n members of the president’s
coalition. However, this indeterminacy will not effect any of the results stressed in this
analysis.
26
Thus we are assuming that a member of the president’s coalition may defect and make
proposals that the president would prefer to veto.
27
Once again randomization can be rigorously justified as the mixed strategy
equilibrium.
28
We soon shall see that vp ≥ v.
39
29
The override strategy is dominated so that π = 0.
30
It should be noted that Baron (1991) finds that the legislative inefficiency is smaller
under an open rule where proposals may be amended and Krehbiel (1992) finds
empirically that open rules are more likely for distributive legislation. While we do not
consider the effect of the executive veto on appropriations under open rule, we plan in
future research to relate the executive veto to the choice of legislative rules.
31
It is important to note that these probabilities should not be interpreted as the
probability of a veto occurring. If the president knows that his veto will be overridden, he
will have no incentive to execute it. In fact, vetoes never occur in equilibrium.
Therefore, the model should not be viewed as a model of vetoes per se but rather as a
model of the effect that the existence of veto institutions has on the distribution and level
of expenditure. The only empirical content of π and πP is that they determine the
probability distribution of winning coalition sizes.
32
This observation is made to illustrate a point rather than to be prescriptive. Clearly,
there may be quite large obstacles and costs (outside the model) that prevent the
implementation of unanimity requirements. Buchanan and Tullock (1962) have also
made the efficiency argument for unanimous voting rules. A distributive argument in
favor of unanimity can be found in Harrington (1990).
33
See Colantoni, Levesque, and Ordeshook (1975) and Brams (1978) for analyses of the
effect that the Electoral College has on the allocation of campaign resources.
34
While we think that a change in the incentives for the size of the president’s coalition
is the most natural way to model the lame duck president, an alternative would be to give
40
the second-term president a lower discount factor because of the reduced importance of
the future. While a complete analysis of a model where the president has a lower
discount factor than the legislators is beyond the scope of this paper, our intuition is that
the implication would be the same as that of a larger coalition. As in the case of the
individual legislator, a lower discount factor suggests that fears of future inefficient
programs do not sufficiently intimidate the president into accepting a current one. This
also eliminates inefficient programs.
41
Appendix
Proof of Proposition 1: The minimally efficient benefit-cost ratio R* must solve zP = 0
and equations [15]-[19] in the text.
Case 1: m < n
Given zP = 0, [17] may be rewritten as
1
6
1
6
c ≥ m − j δv P + m − j − 1
T
N
Either this condition must bind or c = 0. Otherwise a coalition proposer could keep more
benefits. If c = 0, then we claim j* = m-1. If not then, the condition implies that
vP < −
m − j−1
m − j−1
whereas equation [18] would imply v P = −
which is a
δ m− j
N − δN + δ m − j
1
6
1
6
contradiction since N > δN. Since either the veto constraint must bind or j* = m-1,
equation [18] becomes vP = δvP which implies that vP = 0 at the minimally efficient
proposal. Substituting vP = 0 into [15], we find that [15] and [16] imply that z = δv.
Substitution into [19] yields v = −
1N − a − 16T . Substituting z , v , and v into [16]
1N − δa − δ6N
2
P
P
2
gives us
R* =
1
6 1
61
6
n N − δa 2 − δ − δ n − j − 1 N − a 2 − 1
N − δa 2 − δ
It is easy to check that this is a decreasing function of j so that the minimum is obtained
when j = m -1. This substitution and some re-arranging delivers
R* =
1
6
1
6
67
n N − m − δN n − m
N N − m−δ n− m
2
1
which leads to v =
1
6
1
− N−n T
.
N N − m−δ n− m
2
67
Case 2: m > n. Now at zP = 0, we can show using arguments similar to above equation
that [17] must be a binding constraint with c > 0. As above this leads to vP = 0. We now
claim that at the minimally efficient program j* = n-1. Suppose not. Then the coalition
proposer could lower c by T/N by replacing one non-coalition member with a coalition
member and still satisfy the veto constraint. This costs δvP - δv = -δv. Since v > -T/N (a
member cannot do worse than always pay the tax without getting any benefits), this
deviation pays for the proposer. Thus, at the minimally efficient program, j* = n-1.
Given these results [16] and [17] imply that B − m NT = 0 so that R * =
m
. However, note
N
that from inspection of [15] and [19], a non-coalition proposer would not make this
proposal as it implies z = v = − NT so that z < δv. So at this critical value only coalition
proposers make the proposal and non-coalition make no proposal. Thus, in periods where
a non-coalition member is chosen every members payoff is the discounted continuation
value. This implies that v = −
QED
mT
.
N N−δ N−m
1
6
The Qualified Veto with a Particularistic President
In the model, there are 8 possible that cases must be dealt with:
Case1: m < n, π = 0
Case1b: m > n, π = 0
Case 2: m < N-k, 1> π > 0
Case 3: n > m > N-k, 1> π > 0
Case 4: m > n , 1> π > 0
Case 5: m > n, π = 1
Case 6: m > n, π = 1, 1> πP > 0
Case 7: m > n, π = 1, πP =1
The expressions for vp, v, zp , and z can be written as
1
67
2
v = N 2 z + δa v − 1 N − a − 16 7
z = B − δa v − δa v − 1a + a + 16
z = B − δa v − δa v − 1a + a + 16
v P = N −1 z P + δa1v P − N − a1 − 1
−1
2
P
3
5
P
4
6
3
5
(i)
T
N
2
P
T
N
4
6
(ii)
T
N
(iii)
T
N
(iv)
The terms a1- a6 will vary across cases and are thus given in Table 1.
Insert Table 1 About Here
In cases of pure strategy equilibria equations i)-iv) represent four linear equations with
four unknowns. In the cases of mixed strategy equilibria there is an additional unknown,
either π or πP, which requires an additional equation. The condition that proposers who
mix must be indifferent leads to an additional equation of the following general form
αv P − β v − γ
T
N
=0
(vi)
where α, β, and γ are all non-negative functions of the model’s parameters. Table 2 gives
the values of α, β, and γ for each of the cases of mixed strategy equilibria.
Insert Table 2 About Here
A set of GAUSS programs is available from the author to compute the equilibria
numerically.
Proof of Proposition 2:
1) If m < n and q = 0, the only proposers are non-coalition proposers who must allocate
1
6
m δv P + NT to the president’s coalition to avoid a veto. Thus, each coalition member
will receive benefits with probability one so that vP = δvP so that vP = 0. This implies
1
6
z = B − δ n − m − 1 v − n NT and v =
1
6 1
z + n − m − 1 δv − N − n
N−m
efficient program is the one where z = 0, we have v = −
!
B− n−
1
61
6 "#
6$
δ n − m−1 N − n T
= 0. This leads to R *
N − m− δ n − m−1 N
1
6
T
N
. Since the minimally
1N − n6T
and
N N − m − δ1 n − m − 16
1N − m6 − δ1n − m − 16 .
=
N − m − δ1 n − m − 16
n
N
2) If m > n and q =1, a non-coalition member can never be a proposer. Therefore,
v=
1n − j − 16δv − 1N − m − n + j + 16
N−m
T
N
. Using an identical argument to the one
pursued in part 2 of Proposition 1, we can establish that j* = n-1 and the veto
constraint binds with c > 0. Since j* = n-1, v = -T/N. The continuation value for a
member of the president’s coalition is v P =
1
6
1
6
since zP = 0 and c = m − j δv P + m − j − 1
1
6
z P + c + jδ v P + m − j − 1
m
T
N
T
N
. However,
at the minimally efficient program, this
reduces to vP = 0. Finally, inserting vP = 0 and j* = n-1 to [15], we get B − m NT = 0 so
that R * =
m
.
N
3) and 4) by inspection.
QED
Table 1
Parameters of Nash Equilibrium System
a1
a2
m
Case 1
Case 1b
Case 2
N+j-m
N+j-m
j + (N-m)(1-π)
( )+ n − m − 1
n − j −1
N−m
m(nN−−jm−1 )
m
Case 3
((
j + (N − m ) π
( )+ π(k − 1) + (1 − π)(n − m − 1)
n − j −1
N−m
m
m+k−N
m
) + 1 − π)
( )+ π(N − m − 1) + (1 − π)(n − m − 1)
n − j −1
N−m
a3
j
j
j
j
a4
n-j-1
n-j-1
n-j-1
n-j-1
a5
m
m
(1 − π)m
π(m + k − N ) + (1 − π )m
a6
n-m-1
0
π(k − 1) + (1 − π )(n − m − 1)
π(N − m − 1) + (1 − π )(n − m − 1)
Case 4
a1
((
j + (N − m ) π
m+k−N
m
Case 5
)+ 1 − π )
(
j + (N − m ) m +mk − N
Case6
)
Case 7
(
(N − m )(
m+k − N
m
a2
a3
m
( )+ π(N − m − 1)
n − j −1
N−m
j
m
( )+ N − m − 1
n − j −1
N−m
j
)
πP (m + k − N − 1) + 1 − πp j +
)
n − j−1
m π P + (1 − πP ) N − m  + N − m − 1


πP (m + k − n − 1) + (1 − π P )j
n −1
n
n −1
n
(m − 1) n − 1
n
a4
n-j-1
n-j-1
πP (N − m ) + (1 − π P )(n − j − 1)
(N − m ) n − 1
n
a5
π(m + k − N ) + (1 + π )m
m+k-N
N-m-1
a6
π(n-m-1)
N-m-1
m+k-N
m
n −1
n
(N − m − 1) n − 1
n
Table 2
Parameters for Indifference Conditions
Case 2
Case 3
Case 4
Case 6
α
m
N-k
N-k
N+j-m-k+1
γ
(k-n)/δ
(k-n)/δ
(k-m-1)/δ
(k-n)/δ
β
m+k-n
N-n
N-m-1
N+j-m-n+1
Figure 1
Benefit Level
Critical Benefit Levels
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
k=250
k=300
k=350
400
k=400
370
340
310
280
250
220
190
160
130
100
70
40
10
Coalition Size