Uncovering Evidence of Conditional Party Government:
Reassessing Majority Party Influence in Congress and State Legislatures
William T. Bianco
Dept. of Political Science
Penn State University
Itai Sened
Dept. of Political Science
Washington University in St. Louis
September 2004
Abstract
This paper aims at resolving the debate over the measurement of majority party influence
in contemporary American legislatures. Our use of new analytic techniques (a gridsearch program for characterizing the uncovered set) enables us to begin with a better
model of legislative proceedings – to abandon simple one-dimensional spatial models in
favor of more realistic two-dimensional versions. Our conclusions are based on the
analysis of real-world data rather than arguments about the relative merits of different
theoretic assumptions. Our analysis confirms that when legislators’ preferences are
polarized, outcomes will generally be closer to the majority party’s wishes, even if the
majority party leadership does nothing to influence the legislative process. However, our
analysis also shows that at the margin of the majority party’s natural advantage, agendasetting by the majority party remains an efficacious strategy.
This paper takes aim at a critical issue in the debate over majority party influence
in American legislatures: what phenomena constitute evidence of conditional party
government? The theory (Aldrich and Rohde 1998, 1999, 2001) states that when party
caucuses are polarized, (similar policy goals within each caucus, disagreement across
caucuses), majority party leaders work to create outcomes in line with the caucus
consensus. Thus, a situation where legislative outcomes favor the majority party is seen
as evidence of conditional party government in action. However, using a onedimensional spatial model, Krehbiel (1999, 2000) shows that as preferences become
polarized, the expected outcome of legislative action shifts towards the majority party,
implying that the same observation (outcomes favoring the majority party) is consistent
with two states of the world: one where conditional party government exists, and one
where party leaders are inactive.
Our analysis begins with this anomaly: two canonical and opposing hypotheses
about the contemporary Congress make the same prediction about legislative outcomes.
The dispute embodies a fundamental question about the factors driving legislative
outcomes. Do parties matter? That is, do legislative outcomes reflect preferences
aggregated through exogenous institutions, or can the majority party structure the
legislative process in its favor? Put another way, the disagreement is over the validity of
Mayhew’s generation-old claim that “…no theoretical treatment of the United States
Congress that posits parties as analytic units will go very far (1974, 27).”
Our analysis brings new analytic techniques to this debate. We begin with the
truism that results derived from one-dimensional spatial models often do not generalize to
multi-dimensional versions. Moreover, research suggests that an adequate description of
congressional proceedings requires at least two dimensions (Poole and Rosenthal 1997).
1
The core of our work is a multi-dimensional analysis of the conditional party government
story. To what extent can majority party leaders use power over the agenda to influence
the results of legislative action? Under what conditions is this influence observable?
That we can offer this extension is notable in itself. The continued use of onedimensional spatial models despite well-characterized limitations reflects the fact that up
to now, no solution concept existed for multi-dimensional spatial games that matched the
intuitive plausibility or predictive power of the median voter’s ideal point in onedimension models (Bianco et al 2004b). This situation led the authors of one seminal
paper to “… wonder whether some unidentified theory is waiting to be discovered and
used (Fiorina and Plott 1978: 590).” Arguably the most attractive solution concept, the
uncovered set, proved impossible to implement except for a few special cases (AustenSmith and Banks 2001). Thus, absent restrictions such as a fixed status quo or exogenous
institutions, predicting outcomes in multi-dimensional spatial games has proved a
difficult task. Our analysis resolves this problem with a new technique for estimating
uncovered sets in multi-dimensional spatial games (Bianco et al 2004a).
Our analysis also moves the debate over conditional party government from a
comparison of assumptions and purely abstract models to a discussion framed in terms of
preferences and feasible outcomes in real-world legislatures. Using two-dimensional
preference data from the U. S. House and state legislatures, our analysis shows that in a
more realistic model of the legislative process, observability concerns plague the
measurement of party influence. However, within this result, we identify an opportunity
for majority party leaders to exercise real and observable influence over legislative
outcomes. In all of the real-world legislatures we analyze, the set of feasible or enactable
outcomes is much larger than in Krehbiel’s single-dimension game.1 This result implies
2
that a critical necessary condition for conditional party government is met in polarized
real-world legislatures: majority party leaders can make themselves and their caucus
better off by selecting one uncovered set outcome and devising agendas that yield this
outcome from floor proceedings. Finally, we show that Aldrich and Battista’s (2002)
findings about the electoral roots of legislative polarization do not hold when we move to
a more realistic multi-dimensional specification of legislators’ preferences.
The Uncovered Set, Parties, and Legislative Outcomes
This section describes the logic of conditional party government: its expectations
of where party influence comes from, how it is exercised, and where it might be
observed. We detail Krehbiel’s concerns about the observability of party influence,
offering one-dimensional and two-dimensional versions of his argument, and suggesting
how concerns about observability are at best premature. First, however, we describe the
uncovered set, a piece of spatial modeling technology that is central to our analysis.
The Uncovered Set: Theoretic Rationale and Empirical Relevance
The essence of formal modeling is to develop abstract representations of realworld situations, and to use these models to predict real-world behavior and outcomes.
Such models facilitate critical tests between competing theories. In the case of
conditional party government, the technique of choice is spatial modeling, where
preferences and outcomes are specified as points in a one-dimensional or higher space.
Faced with a spatial model, the question is, how do preferences translate into
outcomes? In a one-dimension spatial model, the Median Voter Theorem states that the
expected outcome of majority-rule voting given an open agenda is the ideal point of the
median voter (the core or Condorcet winner).2 Thus, if we know the median voter’s ideal
point, we can predict the outcome of majority-rule voting in these games.
3
It is well-known that the median voter result does not generalize to spatial models
where multiple dimensions are used to describe preferences and outcomes, implying that
outcomes in these games are sensitive to agendas, voting rules and other constraints
(Shepsle 1979, 1986). The so-called Chaos Theorems, (McKelvey 1976 1979; Schofield
1978; McKelvey and Schofield 1987) state that majority-rule decision making,
unchecked by institutions, can go ‘from anywhere to anywhere,’ rendering the ultimate
outcome indeterminate. However, further work showed that if voters in these games
consider the ultimate consequences of their actions, rather than choosing myopically
between alternatives presented at each decision point, majority-rule voting will yield an
outcome in a small area, the uncovered set (Miller 1980, McKelvey 1986).
In essence, the uncovered set generalizes the Median Voter Theorem to multidimensional spatial models.3 Its significance lies in the potential to specify the set of
possible majority-rule outcomes in these games, and in the real-world situations these
games are intended to capture:
If one accepts…that candidates will not adopt a spatial strategy Y if there is another
available strategy X which is at least as good as Y against any strategy the opponent
might take, and is better against some of the opponent’s possible strategies, then one
can conclude that candidates will confine themselves to strategies in the uncovered
set (Cox 1987, 419).4
While Cox’s argument focuses on electoral politics, its logic applies equally to
legislatures: outcomes outside the uncovered set are unlikely to be offered or supported
by sophisticated decision-makers, who know that the proposals are cannot survive the
voting process. Additional work shows that regardless of what ‘status quo point’ a voting
process begins at, supporters of outcomes in the uncovered set can secure these outcomes
4
using relatively simple (two-step) agendas and, moreover, defend them against opponents
who propose outcomes outside the uncovered set (Shepsle and Weingast 1984).
Thus, if
we know which outcomes are in the uncovered set, we know what is possible in a
legislative setting – which outcomes might be the ultimate result of legislative action.
Formally, let N be the set of n voters or legislators. Assume n is odd. For any
agent, i ∈ N , preferences are defined by an ideal point ρ i . Let x, y, z be elements of the
set X of all possible outcomes. A point x beats another point y by majority rule if it is
closer than y to more than half of the ideal points (Throughout the paper, we assume that
preferences are Euclidian). A point x is covered by y if y beats x and any point that beats
y beats x. The uncovered set includes all points not covered by other points.
The attractiveness of the uncovered set as a solution concept lies in that if y
covers x, y dominates x as an outcome of a majority-rule voting game (McKelvey, 1986;
Ordeshook, 1986: 184-5): if y covers x, any outcome that ties y defeats or ties x and any
outcome that defeats y also defeats x. Therefore, strategic legislators should eliminate
covered points from voting agenda. Instead of promoting outcomes that are bound to be
defeated later in the game, sophisticated legislators should promote points in the
uncovered set that may survive the voting process.
Previous analysis has identified four properties of the uncovered set:5 the
uncovered set is never empty (McKelvey, 1986); if the core is nonempty, it coincides
with the uncovered set (Miller 1980, McKelvey 1986); the uncovered set is a subset of
the Pareto set (Miller 1980; Shepsle and Weingast 1984), and if Y is the smallest ball that
intersects all median hyperplanes, the uncovered set is contained within a ball of radius
4Y centered on Y (McKelvey 1986). These properties provide little insight into the
uncovered set’s size or location.6 As a result, deriving predictions in multi-dimensional
5
spatial models typically requires strong, often problematic assumptions, such as assuming
institutions restrict admissible proposals, that leaders can compel backbenchers to support
procedural restrictions, a fixed status quo, or strong assumptions about uncertainty.7
This paper utilizes a new a grid-search computational method (Bianco et al
2004a) for estimating the uncovered set for Euclidean preferences on a two-dimensional
space. The approach follows McKelvey (1986. 27): “…proposition 4.1 gives a potential
“brute force” method for computing [the uncovered set] up to any desired degree of
accuracy.” The technique treats the policy space as a set of discrete potential outcomes.
It starts with two-dimensional preference data, compares points across a coarse grid to
determine the uncovered set’s general location, then generates a more precise
specification set using a tighter grid.
The grid-search technique also allows us to determine whether the uncovered
set’s theoretic attractiveness is matched by an ability to predict real-world outcomes.
Predictive power is crucial to our analysis: if the uncovered set does not capture actual
outcomes, its size or location provides no insight into party influence or its observability.
Bianco et al (2004b) reanalyze data from canonical majority-rule experiments, showing
that the uncovered set is a very good predictor of experimental outcomes – depending on
the experiment, over 80 percent (often 100 percent) of outcomes are in the uncovered set.
Experiments using 5-player and 35-player groups (Bianco et al 2004c) provide additional
evidence of the uncovered set’s predictive power.8 And Bianco et al (2004a) also show
that the uncovered set is highly consistent with outcomes in the contemporary Congress.
The Uncovered Set and The Observability of Party Influence
The theory of conditional party government (Aldrich and Rohde, 1998, 2001;
Aldrich 1995) states that majority party influence stems from its leaders’ control of the
6
agenda, debate, and institutions. When parties are polarized, “the majority party acts as a
structuring coalition, stacking the deck in its own favor – both on the floor and in
committee – to create a kind of 'legislative cartel' that dominates the legislative agenda”
Cox and McCubbins (1993: 270; see also 2003). As a result, “… the greater the degree
of satisfaction of the condition in conditional party government, the farther policy
outcomes should be skewed from the center of the whole Congress toward the center of
opinion in the majority party” (Aldrich and Rohde 1998, 10-11).
Some evidence supports conditional party government. Aldrich and Rohde
(1998) find polarization in legislators’ ideal points in the contemporary House. Aldrich
and Battista (2000) explain this polarization in terms of electoral forces, finding a
positive relationship between the effective number of parties in a state and various
measures of legislative polarization. However, the key prediction of conditional party
government – that outcomes will favor the majority party – has never been tested.
Krehbiel (1999, 2000) argues that outcomes favoring the majority party are a
natural consequence of polarization, and thus imply nothing about majority party power:
“Parties are said to be strong exactly when, viewed through a simple spatial model, they
are superfluous” (Krehbiel 1999, 35). That is, when legislative parties are polarized,
outcomes will lie closer to majority party ideal points because the party contains a
majority of legislators, not because of anything party leaders do. This claim is derived
from a one-dimension spatial model with two parties, where all legislators are party
members (thus, the median floor legislator is a majority party member). The Median
Voter Theorem predicts that the outcome of voting in this game will be the median
voter’s ideal point. Therefore, as the party medians diverge towards opposite ends of the
dimension, the median voter – and expected outcomes – moves away from the center of
7
the distribution and towards the majority party. However, this effect is the result of
polarization coupled with majority rule; it does not require any actions by party leaders.
Figure one contains a nine-voter example of Krehbiel’s argument.
***Figure One Here***
The figure contains two one-dimensional spatial games where majority party ideal points
are denoted by diamonds and ideal points for the minority party are squares. The top
example depicts a situation where ideal points are not polarized. As the figure indicates,
the expected outcome is the median voter’s ideal point, located near the center of the plot.
In the bottom example, ideal points are clearly polarized –majority-party legislators are
on the left-hand side of the plot, with legislators from the minority on the right. Here
again, the expected outcome is the median legislator’s ideal point. However, with the
change in the distribution of ideal points, the median legislator’s ideal point (the expected
outcome) has shifted leftward. However, this shift is driven by the changes in legislators’
preferences, without any additional assumptions about actions taken by party leaders.
The concern about the observability of party influence is not a technical point.
Conditional party government and Krehbiel’s counter-hypothesis are based on very
different conceptions of the limits on majority party action. The implicit assumption
under conditional party government is that there are a wide range of enactable outcomes.
The task for party leaders is to decide which of these outcomes are most acceptable to
their caucus, and to select procedures that generate this outcome. In contrast, in
Krehbiel’s model, there is only one enactable outcome – the median voter’s ideal point.
Thus, the majority party is fundamentally constrained by floor preferences. If majority
party leaders propose a non-median outcome (or procedures that would lead to a nonmedian outcome), their proposal or agenda will not gain majority support.9
8
This debate provides an entry point for our analysis. Krehbiel’s findings are
based on a one-dimensional spatial model. As noted earlier, the median voter’s
dominance in these models does not generalize to more complicated higher-dimension
spatial models. Moreover, while it is not clear just how many dimensions are necessary
for a realistic depiction of modern-day congressional proceedings, considerable evidence
suggests that at least two are necessary (Smith 2000). Up to now, however, the problem
facing scholars interesting in analyzing more sophisticated models of legislative
proceedings is that there was no technique for estimating the set of expected outcomes in
a multi-dimensional setting that did not require additional arbitrary assumptions.
The Bianco et al (2004a) technique for estimating uncovered sets provides a
solution to this problem. As discussed earlier, the uncovered set is attractive both on
theoretic and empirical grounds. Moreover, data on its size and location in real-world
legislatures offer a resolution to concerns about the observability of party influence – and
a new scenario for the observable exercise of party influence. Consider figure two.
***Figure two Here***
Figure two summarizes four hypothetical configurations of ideal points and uncovered
sets in two dimensions for a series of nine-voter, polarized party examples.10 In each
plot, our assumption is that the uncovered set described feasible outcomes to the game,
just as the median voter’s ideal point does in one-dimensional models.
The top-left plot is a two-dimensional version of the one-dimensional scenario in
figure one: the uncovered set is small, and offset towards the majority party. These
conditions give rise to the same conclusion about party influence as in figure one: a focus
on ideal points and outcomes suggests that party leaders are powerful when in fact they
are not. Suppose legislators were allowed to offer, amend, and vote on a series of
9
proposals without intervention by majority party leaders, yielding a series of outcomes
that were randomly distributed inside the uncovered set. An observer examining these
outcomes without knowing anything else would conclude that they demonstrated
conditional party government at work: after all, the outcomes are closer to the majority
party than they are to the minority party. A look at the uncovered set destroys this
conclusion: the outcomes favor the majority party because the uncovered set, which
describes possible outcomes, is offset towards the majority party.
The top-right plot presents hypothetical uncovered sets that reveal a new
mechanism for majority party power. The uncovered set in this plot is relatively large
and offset towards the majority. This location implies that outcomes will always favor
majority party legislators to some extent regardless of what their leaders do – just as in
Krehbiel’s one-dimensional model. However, the larger size of the uncovered set (the
fact that many outcomes are enactable) creates a new opportunity for the exercise of
majority party power. Rather than allowing outcomes to be determined by unconstrained
floor action, majority party leaders can pick a point inside the uncovered set (presumably
one that is close to the ideal points of the members of their caucus), and use procedural
strategies that yield this outcome from floor consideration.11 One such outcome is
labeled in the plot as “X” – note that all majority party legislators prefer this outcome to
everything else in the uncovered set. Suppose that party leaders structured the legislative
process to yield this outcome. If an observer considered these outcomes, and knew where
the uncovered set was located, he or she would conclude that the distribution of
preferences conveyed a natural advantage to majority party legislators – but that majority
party power was being exercised at the margin of this advantage.
10
The bottom plots describe cases where the uncovered set is centrally located. In
the bottom-left plot, the uncovered set is small, while in the bottom-right it is large. The
interpretation is straightforward. An observer looking at actual outcomes in the bottomleft plot without knowing anything about the uncovered set would conclude, correctly,
that the majority party had little influence over outcomes. On the bottom-right, the
majority party has no natural advantage, but the size of the uncovered set offers an
opportunity to use procedural strategies that shift outcomes closer to the majority caucus.
In sum, in a one-dimensional spatial model of legislative action, if outcomes favor
the majority party, it is all but impossible to determine whether this result is due to
conditional party government or is the result of polarized preferences. In fact, in this
setting, it is hard to see how the majority party could influence outcomes at all, which is
exactly Krehbiel’s point. However, these results may not hold in more realistic spatial
models or in the real-world legislatures they depict. Our aim here is to derive uncovered
sets for a variety of real-world legislatures using two-dimensional preference data, and to
assess their size and location relative to the majority and minority parties, allowing a
direct resolution of the party influence debate.
More specifically, our focus will be on two measurements. The first is a
comparison of the average distance between outcomes in the uncovered set and the ideal
points of legislators in the majority and minority parties. For a given session of a
legislature (ex., the 106th U. S. House), let M be the set of legislators in the majority party
(m in number), N be the set of minority party legislators (n in number) and U the set of
outcomes in the uncovered set (u in number). Let Dij be the distance between legislator
i’s ideal point and an outcome j in the uncovered set. We will calculate Dm, the average
11
distance between the ideal points of legislators in the majority party and outcomes in the
uncovered set:
Dm = (Σ Dij)/(m*u)
for all legislators i in M and outcomes j in U
and Dn, the corresponding average distance measure for legislators in the minority party.
We will express the difference in these measures as a percentage:
100*(Dm –Dn)/Dn.
This measure varies from -100 to 100. If the uncovered set is equidistant from majority
and minority-party legislators, it will equal zero. If the uncovered set is closer to the
majority party on average, as per Krehbiel, the measure will be positive. For example, if
the average distance between majority party legislators and uncovered set outcomes is
half as large as the distance between these outcomes and minority party legislators, the
measure will equal 50. (Negative values imply the uncovered set is closer to the minority
party.) Difference-of-means tests will be used to assess the statistical significance of the
difference in average distance between the majority and minority parties.
Our second measurement focuses on the potential gains from agenda-setting
within the uncovered set. That is, to what extent can efforts to produce one particular
uncovered set outcome improve on the situation where leaders are inactive and all
uncovered set outcomes are equally possible? In general, it is not obvious which
outcome will be the focus of party leaders’ agenda-setting efforts. In real-world
legislatures, this calculation is a complex optimization involving the preferences of
caucus members, factional splits in the caucus, and the availability of side payments and
threats. Our analysis approximates this calculation as follows. Rather than considering
legislators’ utilities or payoffs, we focus on distance: to what extent can agenda-setting
12
within the uncovered set bring outcomes closer to the ideal points of majority party
legislators compared to the expected distance given no leadership action?12
We assess the potential for majority party agenda-setting as follows. For a given
legislature, we calculate the average majority party ideal point (average on dimension 1,
average on dimension 2).13 We label the result as the “consensus point,” and interpret it
as an approximation of the outcome that majority party leaders and caucus members
would like to see enacted if possible.14 Let Cj be the distance between the consensus
point and an outcome j in the uncovered set. We calculate the average distance between
the consensus point and all of the outcomes in the uncovered set, C, as follows:
C=
(Σ Cj)/u
for all j in U
This distance gives a baseline for how the majority caucus evaluates a situation where
their leaders are inactive and all uncovered set outcomes are equally likely – on average,
how far away are these outcomes from what caucus members would like to enact?
The next step is to determine how much party leaders can improve on this
baseline. First, we find outcome X, the uncovered set outcome that is closest to the
consensus point, and denote the distance between X and the consensus point as Cx. (An
example of outcome X is in the top-right plot in figure two.) Outcome X is the best that
party leaders can do in terms of using agenda-setting to satisfy their caucus – anything
closer to the consensus point is outside the uncovered set and unenactable.
Our analysis of the potential for agenda-setting in a given legislature will focus on
the difference between C and Cx. We will scale both distances by expressing them as a
percentage of the range of legislator ideal points on the x-axis. Doing so helps to
normalize the results across different legislatures and data sources. In addition, scaling
provides insight into the substantive significance of the two distances and the differences
13
between them.15 The theory of conditional party government would predict that a
conditional party government is more likely insofar as C is relatively large, indicating
that the set of possible outcomes (the uncovered set) is relatively large and contains many
outcomes that are far away from what members of the majority caucus would like to
enact. Moreover, the theory would predict that conditional party government is more
likely to exist insofar as Cx is smaller that C, implying that the potential gains from
agenda-setting are substantial.
Uncovered Sets and Conditional Party Government
This section reports the size and location of the uncovered set for a number of
different sessions of the U. S. House of Representatives and state legislatures. Regarding
our data, there is an ongoing and unresolved debate over the appropriate technique for
recovering legislators’ ideal points from observed behavior (votes).16 As our goal is to
analyze majority party influence rather than adjudicate among the various techniques –
and because there is no consensus about which is best – we use several datasets, with the
aim of showing that our results hold regardless of source:17
•
Constant-space ideal points calculated using NOMINATE (Poole and Rosenthal,
1997) for the 81st, 86th, 91st, 96th, 101st, and 106th U. S. House of Representatives.
•
Ideal points derived from a linear model for the same House sessions (Groseclose
and Snyder 2000).
•
Ideal points for the 106th House calculated with a Markov Chain Monte Carlo
technique (Jackman et al 2004).
•
Ideal points for ten state legislatures from the late 1990’s (Aldrich and Battista,
2002) calculated using NOMINATE.
Our analysis strategy is as follows. First, we present uncovered sets for the 106th U. S.
House calculated from three different sets of ideal points. While the distribution of ideal
points and the size and location of the uncovered set vary across these plots, all show the
14
same pattern: a substantial uncovered set that is closer to majority-party legislators
compared to those in the minority party. Our next step examines whether Krehbiel’s
conjecture about polarization and outcomes holds for more realistic spatial games. To do
this, we compare the average distance of uncovered sets to majority and minority party
legislators using the technique discussed earlier. Then, we analyze the potential for
agenda-setting inside these uncovered sets, again using the technique described earlier.
Finally, we reanalyze the electoral roots of legislative polarization.
The Observability of Majority Party Power
Our analysis provides strong support for the idea that when legislators are
polarized by party, the uncovered set is closer to the majority party than to the minority
party). Figure three gives three examples for the 106th U. S. House.
***Figure Three Here***
The top plot in figure three gives ideal points and the uncovered set for the 106th House
calculated using Poole-Rosenthal ideal points; the middle plot uses Groseclose-Snyder
estimates; the bottom uses Jackman-Rivers scores. In all three plots, idea points for
minority party Democrats are denoted as diamonds and located on the left-hand side,
while ideal points for majority party Republicans are squares on the right-hand side. The
shaded region is the uncovered set estimated using the grid-search procedure.
The plots show that the different ideal point estimation techniques yield different
results, both in terms of the preferences ascribed to each legislator and the uncovered sets
calculated from these ideal points.18 Even so, the uncovered sets are similar in two
important respects. First, they are not located in the center of the distributions of ideal
points. Rather, they are shifted towards ideal points from the majority party, consistent
with Krehbiel’s critique of conditional party government. In addition, the plots reveal
15
that the uncovered sets are fairly substantial in size, occupying about ten percent of the
Pareto Set. In other words, the intuition of the Median Voter Theorem, that only one
outcome is enactable, does not hold in more realistic spatial games. This finding is
consistent with our hypothesis about the potential gains from agenda-setting.
Figure four expands our analysis of the location of uncovered sets in real-world
legislatures by reporting the relative position of the uncovered set in eleven U. S. state
legislatures and six sessions of the U. S. House. (As noted earlier, we have two sets of
ideal points for five House sessions and three sets for one session. We include the single
data point from Jackman et al at the end of the Poole-Rosenthal series, denoted JR).
***Figure Four Here***
The number reported for each legislature is the ratio of the average distance between
majority party legislators and uncovered set outcomes and the average distance between
minority party legislators and uncovered set outcomes, expressed as a percentage. For
clarity, we present plots for different venues (state legislatures vs. the U. S. House) and
different methods of calculating ideal points (Heckman-Snyder vs. Poole-Rosenthal).
Percentage difference bars that are statistically significant at .05 or better are in dark
color; empty bars reflect lower significance levels.19
As the figure shows, with one exception, all of the legislatures in our analysis
have uncovered sets that are closer on average to majority party legislators than to
legislators in the minority party.20 Note that in both congressional plots, the offset of the
uncovered set increases over time, suggesting that at least part of the apparent increase in
party influence in the post-War House is due to the polarization of the party caucuses.
Figure five extends the analysis, showing that the position of the uncovered set
relative to the majority and minority parties is influenced by polarization: as the average
16
distance between majority and minority party legislators increases, the relative position of
the uncovered set moves closer to the majority party.
***Figure Five Here***
These findings about the location of uncovered sets in real-world legislatures
suggest that concerns over the observability of party influence are well-founded.
Regardless of whether preferences are specified using one dimension or two, when
legislators are polarized by party, the set of feasible outcomes favors – is closer to – the
majority party. Thus, an observer who considered actual outcomes relative to legislators’
ideal points without examining the uncovered set would conclude that the location of
these outcomes indicated a majority party cartel at work, when in fact party leaders were
inactive or powerless. In this sense, our analysis provides a partial confirmation of
Krehbiel’s conjecture concerning the observability of party influence.
Agenda-Setting and Majority-Party Influence
The fact that polarization gives the majority party a built-in advantage in terms of
legislative outcomes does not imply that conditional party government is impossible. As
noted earlier, when the uncovered set contains many outcomes, majority party leaders can
pick one and formulate an agenda that yields this outcome as the result of majority-rule
voting. Earlier, we described distance measures that characterized this potential. Figure
seven reports these measures for the three datasets in our analysis – again, we separate
results by estimation method and venue, and add the single Jackman et al data point at the
end of the Poole-Rosenthal series.21
***Figure Seven Here***
The results highlight the potential for agenda-setting: in all cases, the uncovered set
outcome that is closest to the majority party consensus is noticeably closer than the
17
average uncovered set outcome.22 For example, in the case of the 106th House using the
Groseclose-Snyder data, the average distance of uncovered set outcomes to the caucus
consensus point is abut 25 percent of the x-axis range.23 However, by using an agenda
strategy that yields the closest-possible uncovered set outcome, majority party leaders can
cut this distance in half: the distance between the majority consensus and this outcome is
only 13 percent of the x-axis range.24
In substantive terms, these results show that in real-world legislatures, by
choosing an appropriate agenda, party leaders can move legislative outcomes closer –
sometimes much closer – to the preferences of their caucus compared to the expected
results given leader inaction. Because these efforts involving movement within the
uncovered set (selecting one enactable outcome and devising an agenda that yields it),
this potential for majority party influence exists at the margin of whatever inherent
advantages are conveyed to the majority by the location of the uncovered set.
The charts also show that the potential gains from agenda-setting vary across
legislatures. For example, among the state legislatures, some states (e.g., Maine) have
uncovered sets that are close to the majority caucus to begin with (low C), while in others
the uncovered set lies farther away (e.g., Connecticut, where C is high). Similarly, in
some states agenda-setting provides relatively substantial gains over the situation where
leaders are inactive (e.g., Vermont; note the difference between C and Cx), while in other
states the gains are more modest (e.g., South Carolina, where C and Cx are similar).
These results suggest that the value of conditional party government is not the
same for all legislatures. Polarization may be a necessary condition for conditional party
government to operate, but it is not sufficient. Depending on the distribution of
legislators’ preferences (both the level of disagreement between the parties and the level
18
of agreement within the majority party), those in the majority caucus may decide that the
range of outcomes that are possible given an inactive leadership are sufficiently good that
the cost of empowering their leaders outweighs the gains – or that leaders with agenda
power cannot generate sufficiently better outcomes to justify giving them agenda power.
More generally, the data in figure seven only describe the potential gains from
agenda-setting. There is no assurance that the majority caucus will agree on the
implementation of the consensus point (or any point), or that party leaders will respond to
a caucus mandate by devising appropriate agenda strategies. What these results establish
is that in a realistic model of the legislative process, the potential exists for the majority
party to use its control over legislative procedures to make real improvements in
legislative outcomes – improvements that occur at the margin of whatever advantages
convey to the majority party because of polarization.
The Electoral Roots of Conditional Party Government
This paper has used new data to reassess the potential for conditional party
government in real-world legislatures. Compared to previous analyses built on onedimensional preference data, our use of two-dimensional data gives a very different
picture of how the majority party can shape legislative outcomes. This section extends
the analysis to results offered by proponents of conditional party government: we use our
two-dimensional data to reanalyze Aldrich and Battista’s (2002) hypotheses about the
electoral roots of legislative polarization and conditional party government.
Aldrich and Battista (2002) argue that external forces such as electoral
competition drive the polarization of legislative parties. A quote from Rosenthal (1998)
cited in their paper summarizes their expectations: “…as competition for control of
legislative bodies became more balanced and intense, partisanship assumed greater
19
salience both in those legislative bodies where it already mattered and in those where it
never mattered much at all” (1998, 184). Using data from eleven U. S. state legislatures
(chosen for their variation on competitiveness and polarization), they find a strong
positive correlation between the effective number of parties in a state and various
measures of legislative polarization, as measured using one-dimensional preference data.
Our reanalysis focuses on a critical assumption in the Aldrich-Battista paper: the
use of one-dimensional preference data. As noted earlier, if legislative deliberations
involve only one dimension, then conditional party government as described by Aldrich
and Rohde simply cannot operate. But if two or more dimensions are needed to describe
legislators’ preferences, then it is necessary to assess whether the relationship between
competitiveness and polarization still exists in this more realistic formulation?
Our analysis uses data provided by Aldrich and Battista for the eleven states in
their analysis. Our dependent variable, the average distance between the ideal points of
majority and minority party legislators, captures the legislative polarization and is the
two-dimensional analogue to the one-dimensional measures used by Aldrich and Battista.
Table one reports parameters for a regression with (two-dimensional) polarization as the
dependent variable and the effective number of parties as the independent variable.
***Table One Here***
Despite Aldrich and Battista’s finding that electoral competition is related to polarization
using one-dimensional preference data, our analysis finds no evidence of a relationship
given our two-dimensional data.25 However, additional analysis of the 2-D data (omitted
here) reveals a positive relationship between electoral competition and polarization
measured only on the first policy dimension. This finding, coupled with the AldrichBattista analysis, suggests that electoral competition is a partial explanation for
20
ideological polarization between parties in real-world legislatures – that is, competition
may cause polarization on some (but not all) ideological dimensions or policy domains.
If so, then other factors must be found that explain the general and sometimes quite
extreme levels of polarization observed in many of the legislature in our analysis.
Discussion
This paper has aimed at resolving the debate over majority party influence in
contemporary American legislatures. Our use of new analytic techniques enabled us to
begin with a better model of legislative proceedings – to abandon simple one-dimensional
spatial models in favor of more realistic two-dimensional versions. Our conclusions are
based on the analysis of real-world data rather than arguments about the relative merits of
different theoretic assumptions.
Our analysis confirms that when legislators’ preferences are polarized, outcomes
will generally be closer to the majority party’s wishes, even if the majority party
leadership does nothing to influence the process by which proposals are offered,
amended, and voted on. Put another way, even in a multi-dimensional model of
legislative proceedings, a single-minded focus on outcomes and preferences will tend to
overstate the majority party leadership’s influence over the legislative process.
However, our analysis also shows that at the margin of the majority party’s
natural advantage in a polarized legislature, agenda-setting remains an efficacious
strategy. Previous analyses of conditional party government, which framed the
legislative process in terms of a single policy dimension, assumed this possibility away,
for in these settings, party leaders’ only option is to accede to the preferences of the
median floor legislator. Our work analyzed party influence using a two-dimensional
framework, exploiting a new technique for determining enactable outcomes (the
21
uncovered set) given real-world preference data. For all of the legislatures analyzed here,
the potential exists for majority party leaders to use agenda-setting strategies to move
outcomes closer to the preferences of their caucus. The magnitude of these potential
gains varies across legislatures and data sources, but always exists.
Finally, our analysis of the sources of legislative polarization reveals a nuanced
picture of how electoral forces generate differences between party caucuses. While onedimensional preference data suggests a strong relationship between electoral competition
and polarization, our analysis of two-dimensional data shows that competition has no
impact on the distance between majority and minority parties. At best, it appears that
competition separates party caucuses on some but not all policy dimensions.
The limits of our findings bear emphasis. As noted earlier, the potential for party
influence varies across legislatures, most notably with the distribution of legislators’
preferences, which in turn shape the size and location of the uncovered set. Moreover,
our analysis has only considered the potential for party influence – we have not examined
whether majority party leaders actually implement (or try to implement) agenda-setting
strategies. Finally, our analysis says nothing about other mechanisms of majority party
influence, such as strategies involving committee jurisdictions or assignments.
Notwithstanding these caveats, this paper has shown that conditional party
government is more than a description of how real-world legislatures appear to operate.
Rather, the theory’s expectations of how the majority party shapes legislative
proceedings, as well as its claims about the potential gains from these strategies, are
consistent with over two generations of work on spatial models of legislative action and
supported by empirical analysis. With this rationale in hand, the next step is to begin the
systematic testing of hypotheses about majority party influence.
22
References
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112–35.
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in America. Chicago: University of Chicago Press.
Aldrich, John H. and James S. Battista. 2000. “Conditional Party Government in the
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23
Cox, Gary W. and Mathew D. McCubbins. 2003. Legislative Leviathan Revisited.
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24
McKelvey, Richard D. and Norman Schofield. 1987. “Generalized Symmetry Conditions
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25
Figure One.
Measuring Party Influence:
The Problem of Observability in One Dimension
Non-Polarized Parties
Floor Median
(Expected Outcome)
Majority Party
Median
Majority Party
Minority Party
Polarized Parties
Majority Party
Median
Floor Median
(Expected Outcome)
26
Figure Two.
Scenarios for Observing Party Influence
Uncovered Set Small
Uncovered Set Big
Offset To
Majority Party
Location of
Uncovered Set
Scenario 1: small, offset uncovered set =
minimal party influence.
Scenario 2: large, offset uncovered set =
potential party influence.
Centrally
Located
Scenario 3: small, central uncovered set =
minimal party influence.
Scenario 4: large, central uncovered set =
potential party influence.
Note: Majority party ideal points are diamonds, minority party are squares, uncovered sets are shaded circles.
Figure Three.
Uncovered Sets for 106th U. S. House
Poole - Rosenthal Data
Democrats (minority)
Republicans (majority)
Heckman - Snyder Data
Jackman - Rivers Data
Figure Four.
The Majority Party’s Built-in Advantage
State Legislatures
80
60
40
Offset of
20
Uncovered Set
(% closer to
0
majority party)
CT
GA
IA
LA
ME
MN
NH
RI
SC
VT
-20
-40
-60
U. S. House (Groseclose-Snyder)
40
30
Offset of
Uncovered Set
20
(% closer to
majority party)
10
0
81st
86th
91st
96th
101st
106th
U. S. House (Poole-Rosenthal)
40
30
Offset of
Uncovered Set
20
(% closer to
majority party)
10
0
81st
86th
91st
96th
101st
106th
106th (JR)
Figure Five.
Expected Outcomes and Polarization
State Legislatures
70
60
50
Location of
40
Uncovered Set
(% closer to majority) 30
20
10
0
1
1.2
1.4
1.6
1.8
Preference polarization (average distance between majority and minority legislators)
Congress (Heckman-Snyder)
45
40
35
30
Location of
25
Uncovered Set
(% closer to majority) 20
15
10
5
0
1.9
2.1
2.3
Preference polarization (average distance between majority and minority legislators)
Congress (Poole-Rosenthal)
40
30
Location of
Uncovered Set
20
(% closer to majority)
10
0
0.79
0.82
0.85
Preference polarization (average distance between majority and minority legislators)
0.88
Figure Six.
The Potential for Majority-Party Influence via
Movement within the Uncovered Set
U. S. State Legislatures (Aldrich-Battista Data)
70
60
50
Distance as pct. of
x-axis range
40
Ave. distance, uncovered set to
caucus (C)
30
Distance between closest uncovered
set outcome and caucus (Cx)
20
10
0
CT GA IA
LA ME MN NH
RI
SC VT
U. S. House (Groseclose-Snyder Data)
40
30
Distance as pct.
20
of x-axis range
10
0
81st
86th
91st
96th
101st
106th
U. S. House (Poole-Rosenthal Data)
16
14
12
10
Distance as pct. of
8
x-axis range
6
4
2
0
81st
86th
91st
96th
101st 106th 106th
(JR)
Table One. Electoral Competition and Legislative Polarization
Variable
Parameter
(std. error)
Effective Number of Parties
.37
(.40)
Constant
.63
(.75)
R2
.31
N
11
1
Informally, an outcome is enactable if there exists some admissible agenda such that (a) the outcome
will be the ultimate result when sophisticated legislators vote through the agenda using majority rule
and (b) the agenda itself will receive majority support when brought to the floor. All points in the
uncovered set are enactable; no covered points are enactable.
2
Formally, this result requires an open agenda and that legislators’ ideal points fully summarize their
motivations. Nonmedian outcomes could result given exogenous restrictions on amendments or
proposal power, supermajority requirements, or side payments (Austen-Smith and Banks 2001).
3
In a one-dimensional spatial model, the uncovered set is a single point – the median voter’s ideal
point. In a multidimensional game, the uncovered set is a relatively compact region within the space,
unless ideal points satisfy Plott symmetry conditions, in which case again it is a single point.
4
For similar arguments, see Calvert 1985; Grofman et al 1987; Shepsle and Weingast 1984, 1994;
McKelvey 1986; Miller 1980 Ordeshook and Schwartz 1987.
5
We define these properties for two-dimensional spaces.
6
Austen-Smith and Banks, 2001. For special cases, see DeDonder 2000, Epstein 1997, Hartley and
Kilgour 1987, Miller 1980, 2002, and Miller et al 1987.
7
Why are these assumptions problematic? Given that institutions are typically endogenous, for any
outcome they produce, a majority prefers some other outcome and has the votes to overturn the
institution to secure it. Uncertainty assumptions fall prey to a similar argument: given that the impact
of uncertainty is known, legislators or outside groups would have a considerable incentive to gather
the information needed to resolve the uncertainty. Contemporary accounts of caucus politics in the U.
S. Congress (Rohde 1989) suggest that the threats or rewards available leaders are not sufficient to
switch many votes. And finally, unpublished work by the authors shows that in real-world settings,
win sets are generally very large, suggesting that status quo assumptions have little predictive power.
8
One referee wondered whether decision-makers could trade votes to produce outcomes outside the
uncovered set as an equilibrium result. Such a phenomena would call into question the uncovered
set’s utility as a solution concept. The 5-player experiments allow a test of this possibility. Players
were able to make confidential communications to one or more of their opponents throughout the
game, allowing them to make deals and coordinate behavior. The transcripts show many examples of
deal-making. However, virtually none of the deals designed to yield outcomes outside the uncovered
set survived the voting process. This result supports the uncovered set’s predictive power, and
suggests that vote trades are feasible only if they are designed to produce uncovered set outcomes.
9
The only exception is if majority party leaders have a large supply of side-payments (or
punishments), enough to force a majority to support a non-median outcome, either in an up-or-down
vote or in votes to establish institutional constraints that lead to the enactment of such an outcome
10
The uncovered sets are hypothetical – actual 2-D uncovered sets are generally not circular.
11
The definition of the uncovered set implies that these strategies will receive majority support.
12
Regardless of what legislators’ utility functions look like, it seems safe to say that they prefer
outcomes that are closer to their ideal points those that are farther away.
13
This average ideal point represents the consensus in the majority party, and is used to simplify
calculation. Alternatives include the majority median on both dimensions or the majority party
uncovered set. Additional analysis suggests that all of these assumptions would yield similar results.
14
In general, given variation in majority party ideal points, no one uncovered set outcome will be
closest to all majority party legislators. The ideal points in figure two are arranged to produce this
result, but it is easy to devise examples where one outcome is closest to some legislators while a
different outcome is closest to others. Thus, any attempt to model the agenda-setting has to focus on
some aggregation or averaging of majority party ideal points.
15
While our focus here is on substantive significance, the agenda-setting results we present later are all
statistically significant (difference of proportion tests) at the usual significance levels.
16
A partial list of relevant papers would include Cox and Poole 2002, McCarty, Londregan 1999,
Poole and Rosenthal 2001, Groseclose and Snyder 2001; Jackman et al 2004, and the Summer 2001
issue of Political Analysis.
17
A concern is that some of these estimates may be contaminated. Suppose party leaders are able to
use threats, rewards, or side payments to force backbenchers to vote for leadership-sponsored
proposals that they would otherwise oppose. If this behavior occurs on enough proposals, it will
create or exacerbate polarization of ideal points, and shift the location of uncovered sets calculated
from these ideal points. If so, an uncovered set offset towards the majority party would itself be
evidence of conditional party government in action and party influence would again be unobservable.
With these concerns in mind, we replicated our analysis using data from Groseclose and Snyder
(2000), who estimate two sets of ideal points for the U. S. House, one based on all votes, and one
based only on lopsided votes (where the winning side received more than 65% of votes cast).
Lopsided votes are unlikely to have been the focus of leadership efforts – why offer rewards or
threaten punishment when the result is certain (King and Zeckhauser 2003)? Analysis of uncovered
sets calculated from lopsided data (available on request) yields results that are very similar to those
presented here, suggesting that contamination is not an issue for our findings.
18
It is not clear whether this variation is the result of differences in the estimation techniques,
auxiliary assumptions such as the salience of each dimension in legislators’ decisions, the exclusion of
certain votes, or stochastic influences (Jackman, personal communication).
19
As an example of how these percentages are calculated, consider the 106th House and the
Groseclose-Snyder data. The average distance between minority party ideal points and uncovered set
outcomes is 1.6; the corresponding measure for the majority party is ,98, and 100*(1.6-.98)/1.6 =
38.75, which is the percentage reported in the figure. The p-values for the nonsignificant legislatures
are: SC .26, VT .12, 81st House .12, and 91st House, .12.
20
The exception is the Louisiana state house, where the majority party has nearly 80 percent of the
seats. The level of polarization in this legislature is also the lowest of all of the cases in our analysis.
We conjecture that in such cases, the logic of cross-party competition breaks down, and conditional
party government, if it exists at all, involves a faction within the majority, or a cross-party coalition.
21
To see how these numbers are calculated, consider the 106th House. Using the Groseclose-Snyder
data, the average distance between uncovered set outcomes and the majority party consensus point (C)
is .65, and the distance the consensus point and the closest uncovered set outcome is .33. The x-axis
values range from -1.26 to 1.21. Thus, expressed as a percentage of the x-axis range, the two
distances are 26.3% and 13.4%, which are the bars reported for this House session in figure seven.
22
Additional analysis – omitted here, but available on request – shows that the difference in the two
distances is higher given higher levels of polarization.
23
Recall that figure three shows these ideal points and uncovered set. As a look at the figure
confirms, this is a substantial distance.
24
Comparison of the two U. S. House data series shows that the Groseclose-Snyder estimates yield
higher estimates for the potential gains from agenda setting. Even so, the Poole-Rosenthal scores
suggest the potential gains from agenda-setting in the House are nontrivial.
25
A referee suggested that this finding might be driven by a few anomalous cases, a concern given the
small n. We replicated our analysis using a jackknife technique, yielding results that are identical to
those presented here. Results are available from the authors on request.