Running title: “Equilibrium Party Government”
Equilibrium Party Government∗
John W. Patty
Department of Government
The Institute for Quantitative Social Science
Harvard University
March 5, 2008
Abstract
In this paper, I present an equilibrium model of party government within a two-party
legislature. The theory is predicated upon members of the majority party having potentially
conflicting individual and collective interests. In response to this potential conflict, the
members of the majority party endogenously choose a degree of control to grant to their
leadership. The equilibrium level of party strength is decreasing in the size of the majority
party and increasing in the strength of opposition among members of the minority party. The
theory implies that the average performance of W-Nominate estimates of majority party
members ideal points will be a decreasing function of the size of the majority party while the
performance of these estimates for members of the minority party will not be affected by the
size of the majority party. Using data from the U.S. House and Senate between 1866 and
2004, the theory’s predictions are largely consistent with roll call voting in both chambers.
∗
This paper has benefited enormously from discussions with John Aldrich, Christopher Berry, Ethan Bueno de
Mesquita, Barry Burden, Ernesto Dal Bo, Sean Gailmard, Will Howell, Maggie Penn, Keith Poole, David Rohde,
Eric Schickler, Jasjeet Sekhon, Jim Snyder, Ken Shepsle, Craig Volden, and Alan Wiseman, as well as the comments
seminar audiences at UC-Berkeley, University of Chicago, Duke University, and Harvard. Thanks are also due to
Keith Poole and Howard Rosenthal for making their data available. As always, the author retains sole ownership of all
faults, omissions, and errors contained herein.
1
Running title: “Equilibrium Party Government”
“. . .the larger your majority, the harder it is to maintain your unity.”
- Steny Hoyer (D, MD) (quoted in Poole 2004)
1 Introduction
Party leaders in both chambers of the United States Congress are confronted by a decentralized
party system. For example, since nominations are managed at the state level and even
long-serving incumbents may face serious reelection challenges from within their party, a party
leader in Congress faces significant limits on his or her ability to exert direct electoral influence
over the rank-and-file members of his or her party (Jacobson 1987, Jankowski 1993, Gimpel
1996, Schickler 2002). The lack of direct electoral control, combined with idiosyncratic and
varying constituency interests, presents a dilemma to all members of either party in either
chamber: in pursuit of a legislative agenda, each member must recognize that no other member’s
vote can be taken for granted. In particular, even though most members of Congress have multiple
goals, most members think first about securing their own reelection, with the other motivations at
best tempering the general rule of keeping in step with the interests of one’s own constituents
(Fenno 1973, Mayhew 1974, Canes-Wrone et al. 2002).
As noted by Cox and McCubbins 1993; 2005 and others, enacting a legislative agenda is a
collective action problem since, on most days, any one member can vote based solely on his or
her district’s idiosyncratic interests without substantially altering the fortunes of his or her party’s
legislative program. However, if many or all members behave in this way, the prospects for
enacting the party’s agenda decline substantially. To achieve a coherent legislative program,
members of Congress must bind themselves together in some way while remaining cognizant of
their own (reelection) incentives to defect when their own district’s interests come into conflict.
In this paper, I develop a theory of equilibrium party government in which strategic party
members democratically grant their party leaders the power to punish those who subsequently
defect from the party line in their choice of roll call votes. The results relate a simple, direct, and
2
Running title: “Equilibrium Party Government”
objective measure of party strength – the size of the majority party – to the members’ vote
choices. The main argument of the paper is intuitive: when the majority party is large, its
members have less of an incentive to bind themselves together on roll call votes. In simple terms,
when the majority party holds significantly more than a simple majority of the seats, any one
member’s vote is less likely to be pivotal and, accordingly, the members of the majority party care
less about how their compatriots vote on legislation. According to the theory, members of the
majority party recognize that accomplishing their legislative goals is a social dilemma and
democratically choose a “performance bond” that will be forfeited by any party member who
subsequently votes against the party’s legislation. In equilibrium, this bond is set so that no
individual member is likely to be sufficently tempted by his or her own reelection motivations to
“defect” from the party’s legislative program. The key conclusion of the theory results from the
simple fact that the number of defections that are required to sink the legislative program of a
small majority party is smaller than the number of defections required when the party holds a
larger majority of the seats.1
Focusing on the size of the majority party as a determinant of majority party strength has three
virtues. First, the conclusions presented here are consistent with the notion that members from the
same party tend to share the same preferences and, accordingly, simple correlation between
co-partisans’ behavior is insufficient to establish that parties-in-Congress play any true causal role
in determining policy outcomes. 2 Second, the seat shares of the two parties represents an
objective and essentially exogenous feature of each chamber of Congress. Finally, by
1
The theory in this paper is directly in line with – and in some sense can be viewed as an extension of – the strategic
party government framework examined very recently by Lebo et al. 2007. Lebo, et al. provide strong evidence in favor
of the presumption in this paper that party discipline, as conceptualized in both their paper and below in this paper,
is generally electorally costly, thereby establishing the broad strokes of both the individual and collective incentives
examined in this paper.
2
For example, as Krehbiel 1999 cogently argues, using roll call votes to validate or refute the existence of party
power is difficult for a number of reasons. For example, there is rarely an effective way to estimate the counter-factual
hypothesis of how a member would have voted in a party-free legislature (for some attempts to do this, Jenkins 2000,
Nokken 2000, and Nokken and Poole 2004). In addition, each chamber of Congress deals with a limited agenda in
any session, does not record all of its votes, and records its roll call votes under a wide array of procedures. For recent
discussions of these issues, see Hug 2006, and Roberts 2007.
3
Running title: “Equilibrium Party Government”
incorporating a feature of Congress that varies through time, the theory generates testable
implications for W-Nominate estimates. Specifically, when the majority party is smaller, the
W-Nominate estimates for members of the majority party will tend to perform worse among
members of the majority party when the majority party holds a large share of seats and will tend
to perform best when the largest party holds a razor-thin majority.
Of course, any useful model must be a stylization of reality; the theory presented here is no
exception. There are many factors other than the relative share of seats held by the two parties
that affect the ties between legislators’ behaviors and partisan affiliations. For example, intra- and
inter-party heterogeneity of policy preferences, electoral dynamics, and exogenous policy shifts
all undoubtedly play into members’ calculations about the strength of partisanship in determining
their individual vote choice. Accounting for all of these factors is beyond the scope of this paper.
In order to provide a substantive motivation for the theory, it is useful to juxtapose one era (the
1920s and 1930s) in which in which members’ partisanships are generally not considered to have
been the most important determinant of legislative behavior with another (the 1890s) in which the
role of parties-in-Congress has received considerable scholarly attention.
Bigger Does Not Mean Stronger.
Through the 1920s and 1930s, the House of Representatives
was generally characterized by large majority parties. Through the 1920s, the Republicans held
solid majority status in both chambers and, far from reinstating the strong central authority of the
Cannon era, their members largely relegated their formal party organization to the background.
Similarly, when the Democrats held overwhelming majorities in the House through the 1930s, not
only did they not return to the “King Caucus” form of party control utilized during the latter
1910s, they essentially splintered the institutional foundations of partisan control. As is well
known, by the late 1930s, the Rules Committee was effectively and formally independent of the
Speaker. During this period and the twenty-five years following it, the Democratic party
leadership managed the legislative process through bill-specific negotiations and coalition
building, rather than through the exertion of centralized control. Specifically, and in accordance
4
Running title: “Equilibrium Party Government”
with the theory presented below, “the rewards and sanctions which the rules placed in the hands
of party leaders were reduced.”3 In addition, in considering this era, it is useful to recall David
Brady’s description of party discipline in the 55th and 56th Houses (1897-1901).
“[T]he Republicans were in general more cohesive across the issues in the
Fifty-sixth House than they were in the Fifty-fifth. . . . The increased cohesiveness of
the Republicans in the Fifty-sixth House was largely the result of their decreased
majority. The Republican victory in 1896 was so overwhelming that the
congressional party could afford less cohesion and still pass all the legislation the
leadership desired. The decreased Republican majority in the Fifty-sixth House
meant that in order to pass desired legislation the congressional party had to be more
cohesive.” (Brady 1973, p.64)
Theorizing About Parties-In-Congress.
This paper’s theory is similar to both conditional
party government (Rohde 1991, Aldrich and Rohde 1998) and the cartel theory of party
government (Cox and McCubbins 1993; 2005). In both of those theories, as well as that presented
here, members of the same party are presumed to have similar policy preferences. The conditional
party government approach posits a linkage between the heterogeneity of majority party
members’ preferences and their incentive to grant procedural controls to its leaders. While the
results presented here indicate a difficulty with inferring heterogeneity of legislators’ underlying
policy preferences from the observed heterogeneity of their voting behavior, the logic of this
paper’s theory is compatible with that of conditional party government.
3
Cooper and Brady 1981, p.417. The reader may question whether the independence of the Rules Committee during this time period was driven by the heterogeneity, rather than the size, of the Democratic caucus in both chambers.
This objection clarifies one of the strengths of the theory and evidence presented below. In particular, the presumption
of homogeneous, instrumentally-motivated legislators generates a theoretical prediction of increased observed heterogeneity of voting behavior within larger majority parties. In other words, the theory offered here is consistent with
the machinations of the New Deal Congressional Democrats without requiring an appeal to considerations such as an
increased diversity of intraparty interests. In fact, a strong interpretation of the results here might lead an analyst to
pause before interpreting heterogeneity of within-party roll call behavior as being informative at all about (unobserved)
district heterogeneity.
5
Running title: “Equilibrium Party Government”
The link between this paper’s theory and the cartel theory is similarly clear: both theories
explicitly view the majority party leadership as facing a collective action problem. The cartel
theory differs from that presented here by more explicitly distinguishing between votes on
procedure and policy: members of the majority party are form a “cartel” in an attempt to maintain
monopolistic agenda control. The theory of equilibrium party government presented here
examines the degree to which members of the majority party will agree to bind themselves
together in pursuit of the legislative agenda. When the equilibrium level of party government as
defined below is high, the expected rate of defection from the party leadership’s favored position
is low. Conversely, when the equilibrium level of party government is low, the majority party
cartel is weak in the sense that its members are less likely to act in concert on any given roll call
vote. In the context of Brady’s description of the 55th and 56th Congresses, above, one partial
interpretation of the results presented below is as a recognition that instrumentally-minded leaders
of the majority party (i.e., those who seek to not be “rolled” on the floor) will tend to pursue lower
levels of intraparty cohesion when they hold a larger majority of the seats.
The theory presented here is also complementary to the work of Volden and Bergman 2006, who
focus on the Senate, Ashworth and Bueno de Mesquita 2004, who compare presidential and
parliamentary systems, and Iaryczower 2004, who utilizes a principal-agent framework. While a
complete comparison of these important contributions with the theory presented here is beyond
the scope of the paper, one advantage of the approach taken in this paper is that the focus of the
theory is on a collective democratic decision by members of the majority party to post a bond
before a vote with the knowledge that some or all of the members are ultimately free to make their
own vote choices. This paper accordingly focuses its attention on the fundamental tension
between the collective achievement of legislative outcomes through roll call votes and the
inevitability of individual members’ having electoral and/or personal motivations to vote against
their party’s agenda. In addition, the paper generates and utilizes a new empirical prediction about
the predictive performance of W-Nominate scores.4
4
This paper’s point is a small piece of a much larger puzzle – discussed in slightly more detail in the conclusion of
6
Running title: “Equilibrium Party Government”
Before continuing, it is valuable to consider why a formal model is a worthwhile component of
this research project. The formal theory offers several predictions, but the most important
justification for the development of a formal model in this setting is that, in addition to providing
a rigorous and transparent foundation for the empirical predictions (Krehbiel 1999), the formal
theory provides a normative and practical justification for describing the behavior as being in
“equilibrium.” Specifically, it is demonstrated formally that there is a majority-rule equilibrium
(i.e., core) in the intra-party determination of the majority party’s strength. Accordingly, the
theory offered here offers an intuitive prediction when one considers what a majority party leader
would want to do, but the prediction is not based on the implicit assumption a majority party
“leader” even exists. In this way, the theory offers an explicit derivation of a “strong” legislative
party that is nonetheless consistent with majoritarianism (Krehbiel 1991; 1999, Crombez et al.
2006, Patty 2007b).
The remainder of the paper is structured as follows. In Section 2, I present an equilibrium model
of “party government” within a legislature. The most interesting prediction of the model is that
the strength of the majority party leadership in determining its members’ vote choices will be a
decreasing function of the majority party’s seat share. In Section 3, I present a novel means of
testing the model that avoids some of the endogeneity problems associated with measures such as
party unity scores and distributions of legislators’ estimated ideal points. Instead of looking at the
estimates of legislators’ preferences themselves, this paper focuses on the statistical performance
of our estimates of members’ preferences. In Section 4, I examine the effect of the majority
party’s seat share on the predictive power of W-Nominate estimates in the House & Senate from
1866 to 2004.5
the paper – about the structure and workings of these estimates relative to the actual workings of Congress.
5
I consider only the post Civil War era in order to focus on a period with a mature two party system.
7
Running title: “Equilibrium Party Government”
2 Theory
In this section, a model of equilibrium party government is offered. The model’s depiction of
party government is sparse: it considers only the degree to which party control is exercised on
individual members’ roll call decisions. This control is exercised through a payoff penalty for
voting against the party-leadership-supported alternative. The size of this penalty is chosen
democratically by the majority party caucus at the beginning of the game, prior to the revelation
of the member’s non-party-based preferences over the alternatives being voted upon. The
legislature consists of a set of n legislators (where n is assumed to be odd), denoted by N, and is
divided into two parties, denoted by two sets M and m, with M ∩ m = ∅ and M ∪ m = N. The
sizes of the two parties are denoted by nM and nm , respectively, with nM > nm . Thus, M is the
majority party. The notation D ⊂ 2 N denotes the set of decisive coalitions in the legislature.
Though not necessary for the substantive conclusions of the model, it is assumed throughout that
D represents majority rule: it contains all coalitions with strictly more than
n
2
legislators.
The vote in question is between two alternatives: x and q, with x representing the majority party
leadership’s proposal and q representing the status quo. 6 The vote choice of member i is denoted
by ai , with ai = 1 if member i votes in favor of x and ai = 0 otherwise. An arbitrary vector of
vote choices is denoted by a = {ai }i∈N .7 For any member i and vote vector a, a−i represents the
vector of vote choices for all members other than i. Finally, if x receives the vote from each
member of some decisive coalition D ∈ D (i.e., if there exists D ∈ D such that a i = 1 for all
i ∈ D), it passes. Otherwise, the proposal fails and the status quo, q, is the final policy outcome.
6
For the theoretical model, I consider only a single vote. There are typically hundreds of recorded votes in any
session of Congress, the vote modeled here can be thought of as being the “expected roll call” (or perhaps a “representative roll call”) for the upcoming session. Extending the model to allow for many votes within this framework would
not change the results in any interesting way. One interesting extension would be to explicitly model the set of bills that
will be brought up for a vote. Such a model, which would essentially incorporate an explicit “gate keeping” stage into
the decision making of the majority party caucus, would be much more complicated. Furthermore, the predictions of
such a model would rely on a primitive that we currently have no way to estimate. Specifically, empirically evaluating
such a model would require that one construct the set of potential bills that could have been brought forward in each
Congress.
7
That is, a represents a vector of n 0s and 1s.
8
Running title: “Equilibrium Party Government”
The Tension between Individual and Collective Interests.
The theory is based on legislators
having two potentially conflicting motivations behind their vote choice. In particular, members
care both about the outcome of the vote and about their own vote choice. These motivations
conflict when the legislator simultaneously wants the bill to pass while he or she votes against it
or when he or she wants the bill to fail but nonetheless wants to vote in favor of it. 8 Formally,
each member i ∈ N is assumed to receive an member-specific payoff from the final policy
outcome, x or q. This component of legislator i’s payoff is denoted by v i if the policy outcome is
x, and 0 if the status quo q is retained. In addition, each member i ∈ N is also assumed to care
about his or her vote choice (i.e., whether the member votes in favor of, or against, x) Member i’s
individual benefit or cost from voting for x is assumed for simplicity to be determined
exogenously and, furthermore, is unknown until immediately prior to the vote. In the real world,
members often have strict preferences over the votes they cast for “position-taking” or signaling
reasons. Regardless of the source or sources, the key for the purpose of this paper is that these
benefits or costs are tied to the individual vote cast by the legislator, rather than the collectively
chosen policy. This leads to the possibility of individual legislators free-riding on the votes of
their fellow partisans in the legislature.
The payoff received by i from voting for the proposal, x, is denoted by u i ∈ R, while i’s payoff
from voting against the proposal is normalized to equal zero. Thus, if u i > 0, voting in favor of x
is in accord with legislator i’s individual interests, while u i < 0 represents a situation in which it
is costly for legislator i to cast a vote in favor of x. It is assumed that legislator i’s benefit or cost
from voting for x, ui , is observed by legislator i after the selection of majority party strength
(discussed below) and distributed according to a continuously differentiable density function,
8
Notable examples of such cases would include pay raises for legislators, civil rights legislation, or increases in the
debt ceiling.
9
Running title: “Equilibrium Party Government”
fi : R → R+ .9 The payoff function for legislator i ∈ N is written as follows:
⎧
⎪
⎪
0
⎪
⎪
⎪
⎪
⎪
⎨ vi
Ui =
⎪
⎪
ui
⎪
⎪
⎪
⎪
⎪
⎩ v +u
i
i
if i votes against x and x is defeated.
if i votes against x and x defeats q.
(1)
if i votes in favor of x and x is defeated.
if i votes in favor of x and x defeats q.
The distribution functions of u i for all legislators i ∈ N, (i.e., f ≡ {fi }i∈N ) are common
knowledge between the members and the cumulative distribution function for any member i is
denoted by Fi , with F ≡ {Fi }i∈N . In addition, each legislator i knows his or her policy payoff
from x, denoted by vi ∈ R, with certainty.10 For simplicity, the policy payoff from the proposal
passing is assumed to be identical for all members of the same party and, furthermore, positive for
members of the majority party and negative for members of the minority party. Thus,
vi = vM > 0 for i ∈ M and vi = vm < 0 for i ∈ m.11
Party Strength As a “Performance Bond.” The members of the majority party, M ⊆ N,
choose a level of party strength, p ≥ 0. In this model, the endowment of the majority party
leadership with “strength” is represented as the posting of a performance bond by the members of
the majority party. In particular, given a majority party strength, p, any majority party member
will vote for the proposal whenever ui ≥ −p – as if, conditional upon not voting for the party’s
proposal, the member would forfeit resources (e.g., electoral support, stature within the party,
The key assumption here is that u i , i’s individual payoff from voting for the proposal, is not observed until after
the the selection of majority party strength. In particular, it is irrelevant whether u i is privately or publicly observed.
The fact that the distributions of these individual payoffs are common knowledge is a technical necessity but also
descriptively accurate, as it reflects the fact that members are generally aware of each others’ constituencies, the issues
on which they each won election, etc.
10
The results would remain unchanged if one assumed that v i represents legislator i’s expectation about the policy
payoff he or she would receive from passage of x.
11
The assumption that members of the majority (or minority) party all have the same collective policy preferences,
given vM (resp., vm ) is made for presentation purposes. Heterogeneity of members’ collective payoffs is straightforward to incorporate within the model and is discussed in the appendix. As discussed earlier, direct estimation of
heterogeneity of legislators’ policy preferences is difficult at best. Accordingly, any predictions based on preference
heterogeneity are difficult to test.
9
10
Running title: “Equilibrium Party Government”
future committee assignments, or some other perk) equal to p. Thus, a member whose vote choice
is determined by the majority party’s strength does not “enjoy” the party strength, per se. Rather,
the ex ante posting of a forfeitable bond commits each member to voting the party line in some
circumstances where otherwise he or she would not find it in his or her interest to do so.
In equilibrium, the performance bond affects the probability with which any given member will
forgo potential future non-party-based benefits that he or she would have derived from voting
against the party line. Since the bond occasionally forces the member to vote in a way that is
counter to his or her individual interests and larger bonds increase both the frequency and severity
of such occurrences, larger bonds – i.e., higher levels of majority party strength – are more costly
to each member of the majority party than are smaller ones. 12 I discuss some possible real-world
analogues for this performance bond in more detail in Section 5.
The Voting Decision. For any member i in this framework, the fundamental tension occurs
when that member’s individual and collective interests are in conflict: u i < 0 < vi or vi < 0 < ui .
Considering the case of ui < 0 < vi (the other case is symmetric), the member wants to vote
against the proposal but also wants the proposal to pass. This is the crux of the majority party’s
potential collective action problem. For any member i ∈ N and vote vector a −i ∈ {0, 1}n−1,
define the following indicator for whether i’s vote can be pivotal (or decisive):
⎧
⎪
⎪
0
⎪
⎪
⎨
πi (a−i ) =
0
⎪
⎪
⎪
⎪
⎩ 1
if the bill will pass even if i votes against the bill.
if the bill will fail even if i votes for the bill.
if the bill will pass if and only if i votes for the bill.
The πi (a−i ) notation allows us to consider an individual member’s vote decision in some detail.
Any member of the minority party, i ∈ m, and conditional upon the other legislator’s votes, a −i , i
12
As discussed below, the equilibrium level of majority party strength is determined democratically within the majority party caucus and it is assumed that all members are bound by the democratic decision of the caucus. Extending
the model to allow for endogenous membership within the majority party caucus is beyond the scope of this paper and
left for future research.
11
Running title: “Equilibrium Party Government”
should vote in favor of x if and only if 13
ui + πi (a−i )vm > 0.
(2)
The logic of Equation 2 is as follows. When π i (a−i ) = 1, i should vote for the proposal x only if
ui ≥ −vm : i.e., when the member’s individual interests outweigh his or her collective interests.
On the other hand, when 0 < ui < −vm , member i should vote against the proposal and sacrifice
his or her individual payoff. There is no tension between individual and collective payoffs when
πi (a−i ) = 0: since the member’s vote choice does not affect whether the bill passes or not in this
case, his or her optimal vote choice depends only on the member’s individual vote-based payoff,
ui . If ui > 0, the member should vote for x. Otherwise, the member should vote for q.
For a member of the majority party, the analogous calculation involves the performance bond held
by the majority party leadership, p. Specifically, a member of the majority party, i ∈ M, should
vote in favor of the proposal, x, only if
ui + p + πi (a−i )vM ≥ 0.
(3)
The logic of Equation 3 is analogous to that for Equation 2, except that the majority party
strength, p, is added to ui – for a member of the majority party, voting against the proposal
sacrifices both his or her individual payoff for voting in favor of the proposal, u i , and the
performance bond, p. Thus, whenever ui < 0 and Equation 3 holds, then member i should vote
for the proposal in order to avoid the forfeiture of his or her bond. It is exactly such situations in
which “party government” causally affects individual behavior.
Endogenous Majority Party Strength.
We are now in a position to define the equilibrium
level of party strength, p∗ , in a setting where the majority party membership chooses the party
13
It is assumed, without loss of generality, that otherwise indifferent members of the minority party vote against the
proposal and (in Equation 3) that otherwise indifferent members of the majority party vote in favor of the proposal.
12
Running title: “Equilibrium Party Government”
strength prior to members observing their individual benefit or cost from voting in favor of the
party proposal (i.e., ui ). The presumption that the majority party democratically chooses its level
of intraparty strength prior to the consideration of legislation is central to the theory and can be
justified by the pre-Congress organizational meetings of the party caucuses in each chamber.
During these meetings, caucus officials (e.g., party leaders, whips, a nominee for Speaker on the
House) are elected and the details of caucus operations for the upcoming Congress are worked
out. These details include such aspects as the “binding caucus” rule of the Democratic Caucuses.
With this timing in hand, the derivation of equilibrium party strength is performed under the
assumption that all members will ultimately vote as if they are not pivotal (i.e., as if
πi (a−i ) = 0).14
Nevertheless, since the goal of majority party strength is to bind the party membership together in
order to maximize the probability that preferable policies are implemented, the optimal majority
party strength depends upon the probability that any member’s vote choice will be pivotal. Before
presenting the model’s results, the logic underlying them can be described in terms of being
pivotal in the following way: when a member i is very likely to be pivotal, other members have an
increased interest (through their concern about whether the proposal passes or not) in i’s vote
choice. Accordingly, in such situations, majority party members are more willing to bind
themselves together through the granting of a high level of party strength, p. Intuitively, any
member is more likely to be pivotal when the numbers of supporters and opponents of the bill are
both close to half of the legislature. Finally, if one presumes that members’ partisanships are
somewhat correlated with the policies they wish to see enacted, then all members of the majority
party will be more willing to bind themselves together through the exercise of majority party
strength.
14
This choice represents a close approximation of a truly strategic calculation. Indeed the approximation is very
close in large legislatures (McKelvey and Patty 2006). A practical justification is that the inclusion of pivot probabilities in the individual members’ ex ante preferences over majority party strength leads to a dramatic increase in notation
with no added intuition and no change in the substantive results. Finally, a key consideration here is not whether any
individual votes solely based on u i , but whether they believe other members will behave in this manner.
13
Running title: “Equilibrium Party Government”
Before presenting the theoretical results, it is necessary to define four functions. First, for any
member i ∈ N and party strength p, the probability that i votes for x, given majority party
strength p, is denoted by φi (p). Following Equations 2 and 3, this is defined as follows:
⎧
⎪
⎨ 1 − Fi (−p)
φi(p) ≡
⎪
⎩ 1 − Fi (0)
if i ∈ M
(4)
if i ∈ m
In words, φi (p) is simply the probability that member i’s individual interests (i.e., u i ) will be such
that he or she will vote for x. Equation 4 thus has two cases: one for members of the majority
party and one for members of the minority party. Consistent with Equation 2 and 3, p affects the
voting behavior only of members of the majority party. Furthermore, since F i is a cumulative
distribution function and thus weakly increasing for all i ∈ N, it follows from Equation 4 that
φi (p) is a weakly increasing function for all members of the majority party (i.e., i ∈ M) and φ i (p)
is a constant function for members of the minority party (i.e., i ∈ m). In words, a higher level of
majority party strength leads to a higher probability that any given member of the majority party
will vote for the bill, while majority party strength does not affect the voting behavior of members
of the minority party. Using the φ notation, the ex ante probability that x will pass, given p and F ,
is denoted by RF (p) and defined as
RF (p) ≡
D∈D
φi (p)
(1 − φj (p)) .
(5)
j∈D
i∈D
Equation 5 represents the probability of the members of at least one decisive coalition D ∈ D
voting in favor of the proposal, x. Now, given p, v M , and f , the net expected utility of majority
party member i ∈ M from party strength p (relative to p = 0) is
Vi (p, vM , f ) = (RF (p) − RF (0)) vM +
0
−p
sfi (s)ds.
Our main result – that majority party members have single-peaked preferences with respect to
14
(6)
Running title: “Equilibrium Party Government”
party strength – presumes the simultaneous satisfaction of two conditions. The first condition is
that the probability of passage, RF , is a concave function of p ≥ 0.
Condition 1 For all p ≥ 0, RF is a concave function of p.
Substantively, this condition is equivalent to assuming that there are decreasing marginal returns
to increased levels of majority party strength in terms of success enacting the majority party’s
legislative agenda. The condition is generally satisfied whenever members of the majority party
are more likely to support the majority party’s legislative agenda even when the majority party is
powerless (i.e., p = 0) and members’ individual payoffs are normally distributed with mean
greater than or equal to zero. For example, Condition 1 is consistent with settings in which
“most” members of the majority party are faithful followers “most” of the time. In such a setting,
majority party strength operates essentially as insurance against occasional situations in which
several members’ individual goals happen to oppose the majority party’s legislative program.
The second condition requires that, for each member i ∈ N, the distribution of i’s individual
vote-based payoffs, fi (p), is a weakly increasing function for p < 0.
Condition 2 For each i ∈ M, fi (p) is a non-decreasing function for all p ≤ 0.
Formally speaking, Condition 2 is satisfied by many distributions; for example, all symmetric
unimodal distributions (such as the Normal) with nonnegative mean satisfy it. Substantively, this
condition is consistent with situations in which members’ individual, vote-based payoffs are
typically small in magnitude and the probability of a large negative payoff shock from a given roll
call vote is smaller than the probability of negative payoff shock closer to zero. This condition is
empirically plausible, given the relative rarity of high external (i.e., electoral) visibility for any
given roll call vote.
Theorem 1 provides an existence result regarding an equilibrium level of majority party strength.
The proof is simple and relegated to the appendix. Theorem 1 implies that majority party
members’ utility functions are single-peaked with respect to majority party strength, p, and,
15
Running title: “Equilibrium Party Government”
accordingly, since p is unidimensional, the median voter theorem (Black 1948) implies that there
exists a Condorcet winner within majority party strengths p ≥ 0 among the majority party
membership.15
Theorem 1 Suppose that Conditions 1 and 2 are satisfied. Then
1. Vi (p, vM , f ) is a concave function of p for all v M > 0,
2. there exists a Condorcet winner within p ≥ 0 among the majority party membership (i.e.,
some p∗ ≥ 0 such that a majority of the members of M prefer p ∗ to any other p ≥ 0).
Before identifying the Condorcet winner among majority party strengths, it is useful to consider
the implications and meaning of Theorem 1. The first conclusion, that V i (p, vM , f ) is a concave
function of p for all vM > 0, essentially implies that each member of the majority party has an
“ideal” level of party strength and, furthermore, his or her induced preferences over party strength
are single-peaked. Since party strength is unidimensional, the median voter theorem (Black 1948)
applies to the determination of majority party strength in this setting. Accordingly, the second
conclusion of the theorem is that there exists a Condorcet winner among the set of possible party
strengths.
Who Determines Majority Party Strength?
It follows from the median voter theorem that the
Condorcet winner, p∗ , is any median of the majority party’s members’ most-preferred levels of
party strength, as defined by Equation 10. Proposition 1 gives us a sufficient condition for the
simple identification of the median member of the majority party with respect to preferences over
party strength. In words, the proposition identifies the member who, in equilibrium, decides the
majority party strength, p∗ . The following definition makes it possible to state the proposition in a
succinct fashion. (The proof of Proposition 1 is contained in the appendix.)
15
It is important to note that this is a Condorcet winner among the majority party membership. For obvious reasons,
I exclude minority party members from the collective choice of majority party strength.
16
Running title: “Equilibrium Party Government”
Definition 1 For any two probability density functions f j : R → R and fj : R → R, with
corresponding cumulative distribution functions F i and Fj , fi is said to 2nd-order stochastically
dominate fj (written as fi 2 fj ) if, for all real numbers t ∈ R,
t
−∞
(1 − Fi (s))ds ≤
t
−∞
(1 − Fj (s))ds.
(7)
Proposition 1 Suppose that Conditions 1 and 2 are satisfied and there exists a complete ordering
of M, o : M → {1, 2, . . . , nM }, such that o(i) > o(j) implies that f i 2nd-order stochastically
dominates fj . Then the equilibrium level of party government, p ∗ , is equal to the most preferred
level of party strength of a median member of o.
If one conceives of member i’s individual payoffs, u i , as being negative whenever the member’s
reelection chances will be hurt by voting for the proposal, x, the proposition states that the
equilibrium level of party government is determined by the median member of the majority party,
where the median is with respect to the probability of facing external pressures to vote against the
party platform. In a very stylized and direct way, Proposition 1 links the majority
party-in-congress with the majority party-in-the-electorate. In other words, Proposition 1 links
the upper bound of majority party strength with the reelection concerns of its members. Under
this interpretation, the level of influence granted to the party leadership over its members’ voting
decisions is necessarily constrained by its members’ reelection motivations. 16
2.1 Comparative Statics
While there are many different theoretical comparative statics that one can investigate in this
framework, two are of primary interest to us: the effect of the minority party’s voting behavior,
φm , and the effect of the size of the majority party, nM . Broadly speaking, these two parameters
affect the optimal level of party strength, p∗ , in the following ways:
16
Proposition 1 represents an important link between this paper and the work of Lebo et al. 2007.
17
Running title: “Equilibrium Party Government”
1. Larger majority party seat shares decrease the equilibrium level of party strength.
2. Higher levels of minority party support for the majority party leadership’s favored position
decrease the equilibrium level of party strength.
Both of these comparative statics rely on the same underlying dynamic: given that majority party
strength is costly, it follows that when the majority party leadership’s preferred policy becomes
more likely to pass at a given level of party strength, p, then the equilibrium level of party strength
will decrease. This is satisfied by either less fervent opposition by the minority party or a smaller
minority party seat share. Each of the comparative statics flows from the same reality – higher
levels of majority party strength are adopted as a function of the likelihood that a member’s vote
will be pivotal in the passage of the proposal. When the majority party holds a slim majority of
seats, then its members must be more unified (in terms of the percentage voting in favor of the
proposal) in order to overcome any given level of minority party opposition. Similarly, for any
given size of the majority party, its members need to be more unified when the minority party’s
members are less likely to defect and vote for the majority party’s proposal.
In order to focus attention on a substantive and testable prediction of the model, the remainder of
the paper presumes that fi = fj = fM for all i ∈ M and fk = fh = hm for all i ∈ m. Figure 1
displays the effect of majority party size and minority party opposition on the equilibrium
probability of any given member of the majority party voting for his or her party’s proposal. 17
[Figure 1 Here.]
3 Numerical Results
As alluded to earlier, direct measures of the “strength of party government,” are difficult to
construct from available primary data sources. Turning to secondary data sources, the paper’s
theory has implications for the statistical performance of the W-Nominate estimator (Poole and
17
The figures were generated within a 100-member legislature.
18
Running title: “Equilibrium Party Government”
Rosenthal 1997). W-Nominate assumes that legislators make their vote decisions in accordance
with preferences over an underlying policy space in which legislative proposals are embedded.
Based on this assumption, W-Nominate produces an estimated ideal point for each legislator. The
estimator is accordingly “party-free,” in the sense that it produces estimates for a model of vote
choice in which the partisanship of a member plays no role. 18 According to the theory developed
above, the degree to which a majority party member’s vote choices will be determined by his or
her own policy preferences depends on the seat share held by the majority party. In this section, I
show that this dependence leads to a predicted correlation between the performance of the
W-Nominate estimates and the majority party’s seat share. Before demonstrating this, however, I
provide some more intuition for this prediction.
Estimating Legislators’ Preferences from Roll Call Votes in a Legislature with Strong
Parties. Suppose for a moment that the majority party leadership position was completely
determinative of its members’ vote choices (i.e., p = ∞). In such a world, any roll-call-based
estimator of members’ preferences could not distinguish between any majority party member: in
other words, the estimated ideal points of all members in the majority party would be identical.
Furthermore, this “estimated ideal point of the majority party” would (ex post, or within sample)
correctly predict the vote choice of each of the majority party’s members on every recorded
vote.19 At the other extreme – when the majority party has no influence on its members’ vote
decisions (i.e., p = 0) – the estimated ideal points will be based upon behavior actually
determined by the members’ underlying preferences and, accordingly, accurate to the degree that
the space of underlying preferences is sufficiently rich to capture legislators’ true preferences.
Paradoxically, when one’s party membership plays a larger role in determining how one votes, an
18
Of course, many estimators have been designed to accomplish goals similar to those of W-Nominate. However,
the empirical estimates generated by these estimators are in general highly correlated. For more on this, see Burden
et al. 2000.
19
This follows from the fact that the coding of whether an individual should vote “yea” or “nay” on a particular roll
call is chosen so as to maximize the number of roll calls correctly predicted – since the majority party holds a majority
of the seats, this would always be in accordance with how the majority party membership voted.
19
Running title: “Equilibrium Party Government”
estimator that does not condition on legislators’ party memberships will perform better within
sample than in a party-free world.20 This intuition drives the predicted effect (within this model)
of the majority party’s seat share on the within sample performance of W-Nominate estimates of
majority party members’ ideal points. When the majority party holds a larger share of the
legislative seats, the equilibrium level of party strength is lower and, therefore, the within sample
performance of the W-Nominate estimates is also lower.
The within sample performance of the W-Nominate estimates can be measured in a number of
ways, all of which are highly correlated with one another.21 In this paper, I use the geometric
mean probability (GMP) of the estimates. 22 Formally, the GMP for member i is the exponential
of the average of the log-likelihood of the observed vote choices by i. Put loosely, the GMP for a
member is similar to a weighted measure of how many of that member’s votes were predicted
correctly by his or her estimated ideal point. The “weighted” aspect is captured by the fact that
the W-Nominate estimates of ideal points (and roll call locations) assigns a probability of voting
“yea” to each member for each roll call. The GMP is more responsive to votes on which a
member was predicted to vote “yea” with a probability close to either 0 or 1: if such a roll call
vote was correctly predicted, the members’ average GMP is increased by a (relatively) large
amount, whereas it is decreased by a similarly large amount if the members’ predicted vote was
incorrect.23
The predicted effect of majority seat share on GMP (for both majority and minority party
members) is displayed in Figure 2. In both graphs, the vertical axis measures the GMP of the
20
Partly, this is because members’ party memberships generally do not change during a Congress. While this
constraint – no party movement – is obviously not 100% true in reality (members do occasionally change their partisan
affiliation during a Congress), it is imposed by the construction of the roll call data, in which any member who
(publicly) changed his or her party affiliation is assigned a new identity (a.k.a., ICPSR identification number) as of his
or her party switch.
21
For example, Poole and Rosenthal 1997 use several measures, including the log-likelihood of the estimates, the
percent of votes correctly predicted, the average proportional reduction in error (APRE), and the geometric mean
probability.
22
The choice of GMP is somewhat arbitrary, based primarily on the fact that it is easily obtained from the output of
the W-Nominate software and the empirical estimates reported by Poole and Rosenthal.
23
The GMP is bounded between 0 and 1. Additionally, W-Nominate does not predict members’ abstention decisions: accordingly, a member’s GMP is not affected by roll call votes on which he or she did not cast a vote.
20
Running title: “Equilibrium Party Government”
W-Nominate estimates generated from a simulated 100 member legislature and the horizontal
axis represents the number of seats held by the majority party. The data plotted in the top graph
were generated by simulating 500 votes in a 100-seat legislature with varying seat shares for the
majority party in which the seat-share-specific equilibrium level of party strength was applied for
each majority party seat share. As discussed earlier, the graph demonstrates that the predicted
average GMP for majority party members will be negatively correlated with the majority party’s
seat share. Furthermore, since the minority party leadership is assumed to not exert party pressure,
the average GMP for minority party members does not vary with the size of the majority party.
[Figure 2 Here.]
The bottom graph displays the effect of the majority party’s seat share with a fixed level of party
strength. Since the average GMP does not vary with seat share, this graph demonstrates that the
majority party’s seat share, per se, does not affect the statistical performance of the W-Nominate
estimates. The predicted effect of majority party size on the average performance of W-Nominate
estimates within the majority party is based on the seat share’s effect on the endogenous variation
of equilibrium party strength.
4 Data Analysis
In this section, the theory’s predictions about the average GMP within the majority and minority
parties of the House and Senate are compared with the corresponding data for the U.S. Congress
since 1866. The data for the House are displayed in Figure 3, while Figure 4 displays the
analogous data for the Senate. Both graphs in each Figure include the predicted values of average
GMP from an ordinary least squares (OLS) regression of the appropriate party-chamber average
GMP on the majority party’s seat share. For the majority party in both chambers, the negative
relationship between average GMP and majority party’s seat share is clear. For the minority party
in the House, the effect of majority party seat share on average GMP is slightly positive, but the
effect is not statistically significant. For the Senate, the effect of the majority party’s seat share on
21
Running title: “Equilibrium Party Government”
the minority party’s average GMP is positive (and statistically significant). This result for the
Senate is at odds with the (assumption) that the voting behavior of the minority party is
unresponsive to p. Because the Senate is not a majoritarian body for many of its decisions, future
work should extend the numerical analysis in this paper to explicitly account for
supermajoritarian rules. When the majority party holds less than 60 seats in the Senate, there may
exist circumstances in which the minority party has an incentive bind itself together as well (e.g.,
cloture votes).
[Figures 3 and 4 Here.]
Regression Analysis & Institutional Details. Beyond the evidence of Figures 3 and 4, I now
present a more systematic regression analysis. Considering the 40th-107th Congresses
(inclusive), the mean GMP for the majority party, and the mean GMP for minority party for each
Congress and each chamber is the dependent variable in a separate OLS regression (i.e., there are
4 regressions). The independent variables present in all four analyses are: the majority party’s
seat share,24 the number of years elapsed since 1866, and an indicator for Republican party
having a majority of the seats. In addition to these independent variables, several
chamber-specific variables, described below, were included as well. (The results for the common
independent variables are not substantively or statistically altered by dropping these
chamber-specific variables from the analysis.)
House-Specific Variables. In the House of Representatives, an indicator variable for the 81st
and 89th Congresses are included to measure the impact of the “21-day rule,” which largely
eliminated the ability of the Rules Committee to keep the floor from voting on measures that had
been reported. These Congresses are particularly important from the standpoint of the conditional
party government hypothesis, since the fight over the 21-day rule (as with the fight over
24
In order to make the coefficients more easily interpreted, the majority party’s seat share is expressed in net terms:
this is the majority party’s seat share minus 0.5. In the 65th and 72nd Congresses, this net share was slightly negative due to the presence of independent members (the GOP held 216 seats in the 65th Congress and the Democrats
controlled 217 seats in the 72nd).
22
Running title: “Equilibrium Party Government”
enlargement of the Rules committee in the 87th and 88th Congresses) was both intra- and
inter-party.
Senate-Specific Variables. In the analysis of the Senate, two chamber-specific indicator
variables were added. The first of these indicates the subset of Congresses elected after
ratification of the 17th Amendment. 25 The second of these variables indicates the subset of
Congresses during which the requirement for cloture has been 60 votes. 26
4.1 Empirical Results
The results of the regressions are reported in Table 1.27 In both chambers, the majority party’s
seat share is significantly and negatively correlated with the mean GMP of the W-Nominate
scores for the majority party. In the House, Congresses under Republican control have been
associated with a significantly higher mean GMP for the majority party. The estimated effect of
control by the GOP – though it is not significant at the 5% level – is also positive in the Senate.
Thus, the effect of the size of the majority party on the mean GMP of its members is as predicted
in both the House and the Senate. Thus, in line with an increasing number of scholars, 28 the third
column of results in Table 1 provides evidence of majority party power in the Senate.
[Table 1 Here.]
Turning to the chamber-specific variables, the estimated effect of the twenty-one day rule is
positive and significant. At first this may seem surprising: the twenty-one day rule reduced the
power of the Rules Committee, which is typically thought of as an arm of the majority party
25
The 17th Amendment was ratified in 1913. Thus, the first elections held after its ratifications were held in 1914.
This variable is one for all Congresses including and following the 63rd and zero for all others.
26
This change occurred in 1975. This indicator variable is one for all Congresses including and following the 93rd
and zero for all others.
27
Perhaps unsurprisingly, Figures 3 and 4 provide visual evidence of heteroscedasticity in both chambers. Accordingly, the regressions reported in Table 1 were replicated with heteroscedasticity consistent standard errors. The
results are statistically indistinguishable from those reported in Table 1. Sepcifically, the HC3 correction of the HuberWhite was used, as is recommended when the number of observations is less than 250 (Long and Ervin 2000). It is
implemented in Stata via the hc3 option to the regress command.
28
Consider, among others, Campbell et al. 2002, Cox and McCubbins 2005, Crespin and Monroe 2005, Gailmard
and Jenkins 2007, Volden and Bergman 2006, Schickler and Wawro 2006, and Woon 2008.
23
Running title: “Equilibrium Party Government”
leadership. However, the 21-day rule was supported by much of the majority (Democratic) party
leadership as an outlet to circumvent the conservative coalition that controlled the Rules
Committee (Jones 1968, Schickler 2000). Thus, securing its approval (over the objections of the
majority of the minority party’s membership) is interpretable as a victory for party government.
The logic cuts both ways, of course: one should hesitate before pushing this line of argument too
far: one could just as reasonably inquire as to why a strong “party government” could not muster
the resources to oust “Judge” Howard Smith from the Rules Committee or successfully defend
the 21-day rule in the 82nd and 90th Congresses. The fact that the estimated effect is positive is
interesting in the sense that, if it is easier to secure a vote on one’s favored measure, the majority
party’s membership’s incentive to provide their leaders with influence on roll call voting decisions
is greater, which would appear in this type of regression as having a positive impact on the mean
GMP of the majority party.
The results for the Senate’s chamber-specific variables are interesting as well: both the reduction
of the cloture requirement and the ratification of the 17th Amendment led to decreased mean
majority party GMP. The effect of reducing the cloture requirement is consistent with the theory –
by reducing cloture, the majority party membership effectively increases its net seat share. Put
another way, after the cloture requirement is lowered the majority party leadership can secure the
same success rate on cloture votes with a lower level of party strength. Accordingly, fewer
majority party members will be forced to vote the party line after the cloture requirement is
reduced. One plausible effect of the 17th Amendment, which formally eliminated the selection of
a state’s Senators by its state legislature, is an increase in the variance of the idiosyncratic,
vote-specific payoff shocks experienced by the Senators, as the successful pursuit of the
reelection motive became one more closely associated with mass publics and less with the
insiders’ confines of the statehouse. It may also have increased the career concerns for Senators in
another way: Senators could, through the development of their own reelection constituency,
increase the security of their future employment as a Senator, thereby increasing the expected
24
Running title: “Equilibrium Party Government”
payoff of developing expertise and/or stature within the Senate, both of which would potentially
be at odds with deference to Senate party leaders.
These conjectures about the effect of the reduction of the cloture requirement and the ratification
of the 17th Amendment can be subjected a simple “sanity check” by examining their effects on
the mean GMP for the members of the minority party: if the 17th Amendment affected mean
GMP of the majority party because of its effect on the distribution of the members’ vote-specific
idiosyncratic payoff shocks, then the ratification of the 17th Amendment should have also
reduced the mean GMP for members of the minority party. 29 The results of the analogous
regression for the minority party’s mean GMP are presented as the fourth column of results in
Table 1. The reduction in the cloture requirement has not significantly affected the mean GMP of
the minority party, but the 17th Amendment did so in the same direction as it did for the majority
party: the ratification of the 17th Amendment reduced the mean GMP of both parties.
Interestingly, the estimated size of the effect is similar in the two parties. This is consistent with
the hypothesis that the 17th Amendment’s Constitutional commitment to direct election of
Senators increased the idiosyncratic determinants of vote choice on the Senate floor. Overall, the
results are similar to the recent findings of Gailmard and Jenkins 2008, who more directly
examine the effect of the 17th Amendment on the voting behavior of Senators. They find that the
17th Amendment led to moderation in the roll call behavior of Senators from moderate states and,
most relevant to the argument forwarded here, an increase in the occurrence of divergent voting
by Senators from the same state on the same roll call.
5 Congressional Parties & Performance Bonds
The notion of a performance bond as applied in this paper can be viewed simply as an illustrative
metaphor primarily intended to distinguish this paper’s conception of party strength from models
29
Though not necessarily by the same amount, as the minority party’s membership’s incentives to yield their leaders
power to determine their subsequent vote choices generally differ from those of the majority party.
25
Running title: “Equilibrium Party Government”
in which legislators are paid to change their vote. Nevertheless, one can also argue that the
metaphor is also descriptively realistic. When exploring for analogues of the performance bond
within Congressional parties, it should be noted that a performance bond does not necessarily
have to be literally “taken away” from the member (e.g., few employees are paid in advance).
Specifically, it is important to note that expected future rewards under the control of party leaders
(e.g., support during a future primary or general election campaign, recognition on the floor,
inclusion of provisions in special rules about which the member is typically interested, etc.) can
serve the same purpose.
While the scholarly literature is replete with references to a variety of inducements possessed by
party leaders for the rewarding and/or punishing of rank-and-file party members, 30 the possible
ways by which party leaders/elites may punish defectors might be broken into three categories
that can be described as “institutional,” “policy,” and “electoral” in nature. Examples of these
might include the following. 31
1. Institutional Prerogatives. While the formal rules of both chambers are largely silent on
the role of legislative parties, there are a few notable exceptions. For example, in the House
of Representatives, Clause 5 of Rule X states (in part) that “[m]embership on a standing
committee during the course of a Congress shall be contingent on continuing membership
in the party caucus or conference that nominated the Member.” A large literature has
established that committee assignments are valuable to members in pursuing both policy
and reelection goals. Accordingly, the explicit role given to the party caucuses by Rule X
represents a formal instance of the performance bond: deviation from the party’s platform
(as in the “binding caucus” rules of the House Caucuses) can be punished by the forfeiture
of an asset valued by the member in question. Furthermore, there is evidence that the
operation of the committee assignment process within party caucuses affects “party
30
Some recent examples include Snyder and Groseclose 2000, Burden and Frisby 2004, and Forgette 2004.
For reasons of space, the list is not exhaustive. The tripartite division is roughly analogous to the “three goals”
description of member’s motivations famously offered by Fenno. 1977.
31
26
Running title: “Equilibrium Party Government”
loyalty” (e.g., Crook and Hibbing 1985, Wright 2000).
2. Policy Influence. There is evidence that members – of either party – with higher party
loyalty are more likely to be assigned to conference committees (McQuillan and Ortega
1992). Such assignments are desired by members, since the conference negotiations
typically represent the final opportunity to make changes to legislation and the changes are
nearly guaranteed acceptance in both chambers. The assignments to conference committees
are directly controlled by the Speaker of the House (Rule I, clause 11), who typically makes
appointments of members of the minority party only after consultation with the Minority
Leader. Furthermore, the Speaker has broad discretion in making appointments to
conference committees and may specify the issues on which individual members are to
confer.32
3. Electoral Support. The possibility of withholding expected future support is observed
within the empirical workings of campaign finance, where individual members often
explicitly provide resources to their party leaders (e.g., Heberlig et al. 2006, Heberlig and
Larson 2007). For example, in the 2006 election cycle, the three main campaign organs of
the Republican party received over $30 million from Republican candidates and their
political action committees, while the analogous 3 Democratic organizations received over
$40 million in contributions from Democratic candidates and their PACs. 33 Furthermore,
members’ campaigns represented 16 of the top 20 donors to the Democratic Party, and 17
of the top 20 donors to the Republican Party in the 2006 election cycle.
Finally, it should be noted that – in equilibrium – the use of these levers may be quite rare.
Furthermore, such rarity is by design – when the intraparty cohesion that is pursued through their
presence is achieved, one will not observe members being ousted from committees, passed over
On the Speaker’s discretion in appointments, see House Rules and Manual §637, and on the Speaker’s right to
specify issues to conferees, see House Rules and Manual §536. In addition, see Chapter 13 of Brown and Johnson
2003.
33
The precise amounts, as reported by the Center for Responsive Politics (http://www.opensecrets.org), are
$33,577,915 for the GOP and $40,233,445 for the Democrats.
32
27
Running title: “Equilibrium Party Government”
in the appointments of conferees, or having electoral support withheld. Nevertheless, the
experiences of some senior Republican members in the early 20th century and southern
Democrats in the early 1970s are consistent with the use of some or all of such levers against
less-than-faithful legislators. More recently and directly on point is the experience of then-Rep.
James Traficant (D, OH) in the 107th Congress (2001-02), whom the House Democratic Caucus
refused to appoint to any committees as punishment for his voting in favor of Rep. Dennis Hastert
(R, IL) for Speaker of the House.
6 Conclusion
The influence of members’ partisanships on legislative policymaking is an important and active
topic of research. To this end, I have presented a formal theory of equilibrium party government
by the majority party in which majority party members “bind themselves together” in pursuit of
common policy goals, aware that day-to-day influences on their future voting behavior create the
potential for collective action failures in attempting to enact their preferred collective policy
goals. By incorporating the collective preferences into their individual grants of power to their
leadership, majority party members can increase their expected payoffs.
This paper extends an active research agenda on the determinants of partisan-appearing behavior
in legislative settings, including the role of procedural details, members’ pursuits of reelection,
and the combination of the two. 34 In this paper, variation in external and procedural factors is
purposefully ignored: the focus is on the easily measurable variation in the size of the majority
party in a two-party legislature. Ultimately, the theory should be extended to explicitly include
choices about procedures and variation in the members’ electoral situations.
The two-party theory presented here implies that – for members of the majority party – the
predictive power of a party-free measure of legislators’ preferences, W-Nominate, will be
34
Among others, consider Roberts and Smith 2003, Bernhard and Sala 2006, Bovitz and Carson 2006, and Cox and
Katz 2007, Carey 2007, and Lebo et al. 2007.
28
Running title: “Equilibrium Party Government”
decreasing in the size of the majority party, whereas the performance of these estimates for
minority party members will not depend on the size of the majority party. The average
performances of the W-Nominate estimates since the Civil War within both parties’ memberships
support the theory’s predictions. In both chambers, majority party members’ votes are predicted
less accurately when their party’s seat share is larger. The average performance of the estimates
for minority party House members is unaffected by their share of seats, while the average
performance of these estimates for members of the minority party in the Senate is positively
affected by their seat share.
Sure, the House. . . but the Senate?
The finding for the majority party within the Senate is
probably the most surprising. According to the traditional picture of the Senate, every member
may potentially affect what is voted upon through various dilatory tactics. Accordingly, any
Senator’s voting behavior should be less susceptible to “party influence” than his or her
counterparts in the House. The theory presented here, however, offers an intuitive rationale for the
apparent influence of the majority party’s seat share on the predictability of the majority party
members’ voting behaviors. By recognizing the potential conflict between their collective policy
objectives and individual electoral interests, both Senators and Representatives may gain from the
exertion of a reasonable degree of majority party influence on their voting behavior. This paper’s
results fit nicely with other recent findings, particularly those of Gailmard and Jenkins 2007;
2008. Specifically, this paper’s results provide further evidence that Gailmard and Jenkins are
correct in suggesting that “there is reason to be sanguine about Senate majority party power.” 35
Institutional Details. The empirical results also indicate significant effects of several key
institutional features of the chambers. The access to the floor of the House provided by the 21-day
rule in the 81st and 89th Congresses increased the average performance of W-Nominate estimates
within the majority party (i.e., Democratic) membership – but not the average performance for
35
Gailmard and Jenkins 2007, p.699
29
Running title: “Equilibrium Party Government”
those of the minority party (i.e., Republican) members. Within the Senate, the results indicate that
the passage of the 17th Amendment, which loosened state party leaders’ direct control over their
state’s Senators, also reduced the average performance of the W-Nominate estimates within both
parties. The reduction in the Senate’s cloture requirement from two-thirds to three-fifths reduced
the average performance of the W-Nominate estimates within the majority party, but not the
minority party. This finding deserves more study, since, following the “pivotal politics” logic of
Krehbiel 1998, one could interpret the reduction in the cloture requirement as an increase in the
effective size of the majority party.36 This intuition suggest that the equilibrium level of party
strength (and average performance of W-Nominate among the majority party) would decline after
cloture is introduced, which is consistent with the empirical results. A richer model of procedures
should be deployed within this type of setting. Given the variety of procedures (concerning both
agenda-setting and voting, per se), the seeming ubiquity of partisan division, and the potential
electoral ramifications of individual legislators’ recorded vote choices, one might wonder how the
contextual and procedural details of each roll call vote, which vary widely both within and across
Congresses affect the proper interpretation of the relationship between vote-based estimates and
Congressional politics as a whole. The theory and results presented in this paper indicate that at
least one detail of the Congressional landscape – the partisan balance within either chamber – is
an important component of this relationship.
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A Technical details and Proofs
A.1
Proof of Theorem 1
Applying Leibnitz’s rule, the first derivative of V i with respect to p is
∂Vi (p, vM , f )
∂RF (p)
=
vM − pfi (−p).
∂p
∂p
Applying Lemma 1 of Patty 2007a and recalling that δ i (p) denotes the pivot probability of
legislator i given party strength p, Equation 8 can be rewritten as
∂Vi (p, vM , f )
=
∂p
∂φj (p)
δj (p)
∂p
j∈N
36
vM − pfi (−p),
(8)
Running title: “Equilibrium Party Government”
i (p)
which, after noting that ∂φ∂p
= 0 for all i ∈ m, and that
to
∂Vi (p, vM , f )
=
∂p
∂φj (p)
∂p
= fj (−p) for any j ∈ M, reduces
δj (p)fj (−p) vM − pfi (−p).
(9)
j∈M
Thus, setting Equation 9 to zero, an (interior) level of party strength that maximizes the expected
payoff of majority party member i ∈ M, pi∗ , must satisfy
δj (pi∗ )fj (−pi∗ ) vM − pi∗ fi (−pi∗ ) = 0
(10)
j∈M
Theorem 1. Suppose that Conditions 1 and 2 are satisfied. Then
1. Vi (p, vM , f ) is a concave function of p for all v M > 0 and
2. there exists a Condorcet winner within p ≥ 0 among the majority party membership (i.e.,
some p∗ ≥ 0 such that a majority of the members of M prefer p ∗ to any other p ≥ 0).
Proof : Conclusion 2 immediately follows from Conclusion 1. Accordingly, only Conclusion 1 is
demonstrated here.
The second derivative of majority party member i’s value from party strength p, given v M and f ,
is
∂ 2 Vi (p, vM , f )
=
∂p2
Note that
∂ 2 φj (p)
∂p2
=−
∂ 2 Vi (p, vM , f )
=
∂p2
∂δj (p) ∂φj (p)
∂ 2 φj (p)
+ δj (p)
∂p
∂p
∂p2
j∈M
∂fj (−p)
∂p
vM − fi (−p) + p
∂fi (−p)
.
∂p
(11)
for any j ∈ M. Accordingly, Equation 11 reduces to
∂δj (p)
∂fj (−p)
fj (−p) − δj (p)
∂p
∂p
j∈M
Satisfaction of Condition 1 implies that
Condition 2 implies that
∂fi (−p)
∂p
j∈M
∂δj (p)
fj (−p)
∂p
vM − fi (−p) + p
− δj (p)
∂fj (−p)
∂p
∂fi (−p)
.
∂p
(12)
≤ 0, satisfaction of
≥ 0, the fact that fi is a probability density function implies that
37
Running title: “Equilibrium Party Government”
fi (−p) ≥ 0, while p ≥ 0 and vM > 0 by hypothesis. Accordingly, each of the three terms in (12)
is less than or equal to zero, implying that
A.2
∂ 2 Vi (p,vM ,f )
∂p2
≤ 0, as was to be shown.
Proof of Proposition 1
The proof of Proposition 1 uses monotone comparative statics. 37 This approach is significantly
attractive because it generally requires few, if any, functional form assumptions. In this setting,
this means that little needs to be assumed about the distributions of legislators’ individual payoffs,
f = {fi }i∈N . In order to apply monotone comparative statics, it is useful to use Equation 6 to
define the following function:
G(p, i) ≡ Vi (p, vM , f ) = (RF (p) − RF (0)) vM +
0
−p
sfi (s)ds.
(13)
This definition treats i as a parameter of an optimization problem and allows us to deduce facts
about induced preferences over party strength within the majority party. With this function in
hand, it is now possible to define a very powerful property, known as the single crossing
condition.
Definition 2 The function G satisfies the single crossing condition (SCC) if for all p > p̃ and
i > j, G(p; j) − G(p̃; j) ≥ 0 implies G(p; i) − G(p̃; i) ≥ 0, and G(p; j) − G(p̃; j) > 0 implies
G(p; i) − G(p̃; i) > 0.
Before formally stating the next result, for any probability density function f i and any closed
interval I ⊆ R such that I fi (t)dt > 0, define fi |I as follows:
⎧
⎪
⎨ 0
fi (x)|I ≡
⎪
⎩ Ê fi (x)
I
fi (t)dt
37
for all x ∈ I
for all x ∈ I
See Ashworth and Bueno de Mesquita 2006 for more details on this powerful technique and its potential in
political science.
38
Running title: “Equilibrium Party Government”
Thus, for any closed interval I ⊆ R such that I fi (t)dt > 0, fi |I simply denote the conditional
distribution induced by f i on I. Using this notation, note the following well-known facts:
Fact 1 For any two probability density functions f i and fj with the same support (i.e.,
fi (t) > 0 ⇔ fj (t))
2
2
fi fj ⇒ fi |I fj |I for all closed intervals I such that
2
fi fj ⇒
tfi (t)dt ≥
tfj (t)dt.
R
I
fi (t)dt > 0, and
R
Lemma 1 If there exists an ordering of M, o : M → {1, 2, . . . , nm }, such that o(i) > o(j)
implies that fi 2nd-order stochastically dominates f j , then G satisfies the SCC.
Proof : Suppose without loss of generality that o(i) = i for all i ∈ M and, as stated in the
hypothesis of the lemma, that i > j implies that F i 2nd-order stochastically dominates F j . Then,
for i > j and p > p̃ ≥ 0,38 Equation 13 implies
G(p, i) − G(p̃, i) ≥ 0
⇒ (RF (p) − RF (p̃)) vM +
−p̃
−p
sfi (s)ds ≥ 0.
(14)
It follows from Equation 14 that G satisfies SCC if,
(RF (p) − RF (p̃)) vM +
−p̃
−p
sfj (s)ds ≥ 0
−p̃
−p
⇒
(RF (p) − RF (p̃)) vM +
sfj (s)ds ≥ 0 ⇒
−p̃
−p
−p̃
−p
sfi (s)ds ≥ 0
sfi (s)ds ≥ 0.
The hypothesis that fi 2 fj , along with the two conclusions of Fact 1 jointly imply that
−p̃
−p̃
sf
(s)ds
≥
sfj (s)ds, so that Equation 15 must hold.
i
−p
−p
38
Recall that majority party strength is restricted to be nonnegative.
39
(15)
Running title: “Equilibrium Party Government”
Proposition 1 Suppose that Conditions 1 and 2 are satisfied and there exists a complete ordering
of M, o : M → {1, 2, . . . , nM }, such that o(i) > o(j) implies that f i 2nd-order stochastically
dominates fj . Then the equilibrium level of party government, p ∗ , is equal to the most preferred
level of party strength of a median member of o.
Proof : Follows immediately from Lemma 1, above, and Theorem 4 in Milgrom and Shannon
1994.
A.3
Incorporating Heterogeneous Policy Preferences
It is simple to check that vM in Equations 8-12 can be replaced by vi without changing any of the
derivations. Following such an exercise, Vi (p, vm , f ) would be rewritten as the more general
Vi (p, v, f ), where v ≡ {vj }j∈N , and Theorem 1 would be stated as follows
Theorem 1 Suppose that Conditions 1 and 2 are satisfied. Then
1. Vi (p, v, f ) is a concave function of p for all vi > 0,
2. the solution to Equation 10, p i∗ , maximizes Vi (p, v, f ), and
3. there exists a Condorcet winner within p ≥ 0 among the majority party membership (i.e.,
some p∗ ≥ 0 such that a majority of the members of M prefer p∗ to any other p ≥ 0).
40
Running title: “Equilibrium Party Government”
Probability of Majority Party Member Voting With Party
1
0.9
Strong Minority Opposition
0.8
0.7
0.6
Weak Minority Opposition
60
70
80
90
100
Seats Held by Majority Party (100 Total Seats)
Probability of Majority Party Member Voting With Party
1
Small Majority Party Seat Share (55 Seats)
0.9
0.8
0.7
Large Majority Party Seat Share (70 Seats)
0.6
0.1
0.2
0.3
0.4
Probability of Minority Party Member Voting With Majority Party
Figure 1: Theoretical Comparative Statics of Majority Party Voting
41
0.5
Running title: “Equilibrium Party Government”
1
Average Geometric Mean Probability
0.9
Majority Party
0.8
0.7
Minority Party
0.6
55
60
65
70
75
Majority Party Seat Share (100 Total Seats)
1
Average Geometric Mean Probability
0.9
0.8
Majority Party
0.7
Minority Party
0.6
55
60
65
70
Majority Party Seat Share (100 Total Seats)
Figure 2: Predicted Effect of Majority Party Size on GMP
42
75
.9
.85
.8
.75
.7
.65
.65
.7
.75
.8
.85
.9
Running title: “Equilibrium Party Government”
.5
.6
.7
Majority Seat Share
Majority Party Avg. GMP
.8
.5
Fitted values
.6
.7
Majority Seat Share
Minority Party Avg. GMP
.8
Fitted values
.85
.8
.75
.7
.65
.6
.6
.65
.7
.75
.8
.85
Figure 3: Majority Party Size and Mean GMP: House of Representatives since 1866
.5
.6
.7
.8
Majority Seat Share
Majority Party Avg. GMP
.9
.5
Fitted values
.6
.7
.8
Majority Seat Share
Minority Party Avg. GMP
Fitted values
Figure 4: Majority Party Size and Mean GMP: Senate since 1866
43
.9
Running title: “Equilibrium Party Government”
Table 1: Determinants of Geometric Mean Probability: OLS Regression
House
House
Senate
Senate
Variable
Majority
Minority
Majority
Minority
∗∗
∗∗
Net Majority Seat Share
-0.193
0.003
-0.307
0.118∗
Republican Control
Year - 1866
21-Day Rule
(0.069)
(0.062)
(0.056)
(0.054)
0.038∗∗
0.019∗
0.019†
-0.013
(0.011)
(0.009)
(0.011)
(0.010)
0.000∗∗
0.000∗∗
0.001∗∗
(0.000)
(0.000)
(0.000)
(0.000)
0.037∗∗
0.005
.
.
(0.010)
(0.025)
.
.
Post 17th Amendment
3/5ths Cloture
Intercept
N
R2
F (4,63)
F (5,62)
Significance level : † : 10%
Standard Errors in Parentheses.
.
.
0.000
-0.070 ∗∗
-0.059∗∗
(0.019)
(0.018)
-0.040∗
0.010
(0.018)
(0.017)
0.766∗∗
0.704∗∗
0.769∗∗
0.744∗∗
(0.024)
(0.013)
(0.018)
(0.017)
68
0.307
11.644
.
68
0.312
7.134
.
68
0.482
.
11.533
68
0.346
.
6.559
∗ : 5%
∗∗ : 1%
44