4^'
^,
I'
^4^
o/
tbC^
l*t^-
worKing paper
department
of economics
PATTERNS OF CONGRESSIONAL VOTING
Keith T. Poole
Kovard Rosenthal
No.
536
Revised
February 1990
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
PATTERNS OF CONGRESSIONAL VOTING
Keith T. Poole
Hovard Rosenthal
No.
536
Revised
February 1990
Patterns of Congressional Voting
ABSTRACT
Congressional
entire
call
roll
characterized by
call
voting has been highly
a
voting
record
from
1789
changes
This stability is such that,
in
Congressional
spatial analysis of
times,
Politically,
a
space
is
significant,
under certain conditions,
Since
voting patterns have
the
occurred
through the process of replacement of retiring or defeated
new members.
The
19S5.
at
of
In the modern era spatial positions are
run forecasting of roll call votes is possible.
II,
to
predominant major dimension with,
but less important second dimension.
very stable.
structured for most
The structure is revealed by a dynamic,
American history.
the
roll
short
end of World War
almost
entirely
legislators with
selection is far more important than adaptation.
Digitized by the Internet Archive
in
2011 with funding from
Boston Library Consortium IVIember Libraries
http://www.archive.org/details/patternsofcongre00pool2
I.
the United States
The Congress of
subject
to
myriad
a
requires
typically
Introduction
of
the
formal
assent
of
and
is
complex
a
informal
numerous
committees
institution
Legislative
rules.
Furthermore,
well as the support of party leaders.
legislative
subcommittees,
and
as
legislation is shaped not
only by the 535 members of Congress and attendant thousands of staff,
by influences arising in the executive,
action
organized lobbies,
but also
and from
the media,
One important outcome of these various processes are the
private individuals.
recorded roll call votes taken on the floors of the two houses of Congress.
Beneath the apparent complexity of Congress, we find that these roll call
decisions can largely be accounted for by
In
spatial
a
model
2
each
,
s-dimensional Euclidean space.
a
legislator
very simple dynamic voting model.
represented
is
by
point
a
in
Each roll call, whether it be a key vote on a
civil rights bill or a mundane motion to restore Amtrak service in Montana,
is
represented by two points that correspond to the policy consequences of the
and "nay"
"yea"
outcomes.
The spatial model holds that a legislator prefers
The extent of preference is expressed by
the closer of the two alternatives.
a
utility function.
point,
the
greater
The closer an alternative
the
preference
for
the
is
to
the
alternative,
legislator's
and
the
ideal
higher
the
utility.
Although our work shows that a low dimensional Euclidean model
largely
captures the structure of Congressional voting, we should stress that the work
says nothing about how specific issues get defined in terms of the structure.
We
cannot,
for example,
explain why Robert Bork was
rejected by the Senate
while a perhaps equally conservative Supreme Court nominee,
was confirmed by a 99-0 vote.
have been possible,
vote
on
the
basis
Later in the paper,
using our model,
of
announced
to
Antonin Scalia,
we do show that it would
have accurately predicted
positions
by
members
of
the
the
Bork
Judiciary
defined,
a
once the positions of the alternatives have been
In other words,
Committee.
can predict
spatial model
outcome.
the
But we have
to
leave
to
other research the all important task of predicting how substantive issues get
mapped into alternatives in the space.
What the spatial model does assert is that voting alignments must largely
process
— involving
positions.
spatial
with
consistent
remain
interest groups and the White House
lobbying
the
Thus,
— can
be seen as a set
of efforts to alter the location of the cutting line on an issue.
The development of supercomputing has enabled us to estimate the spatial
The spatial structure uncovered
model for the period from 1789 through 1985.
is
very stable,
with two exceptions that occurred when the two party system
The first was from 1815 to 1825,
had major break downs.
after the collapse of
the second was in the early 1850' s during the collapse
the Federalist party;
of the Whigs and the division over slavery.
the structure
Since the Civil War,
has been sufficiently stable that the major evolutions of the political system
can be traced out in terms of repositioning within the structure.
Depression,
The Great
witnessed a massive influx of "liberals",
for example,
but there
was no sharp break with pre-Depression voting patterns.
paper proceeds,
The
in
Part
II,
with a description of
the
behavioral
model that represents this simple structure of roll call voting and
explanation of the estimation method,
Three-Step
Estimation.
estimation technique,
tests of the method.)
the
space
stable
is
of
relative
low
statistical
In Part
issues
III,
dimensionality
positions.
dubbed D-NOMINATE for Dynamic Nominal
Appendix
(The
The
a brief
provides
in
details
the estimation,
concerning
and Monte Carlo
we present evidence that,
in
which
argument
legislators
in
Part
IV
the
on the whole,
occupy
is
temporally
directed
at
establishing that issues of slavery and civil rights for Afro-Americans are
the major source of exception to a unidimensional,
stable space.
In Part
V,
we briefly illustrate the predictive capacities of the model with an analysis
of the confirmation vote on the Bork nomination to the Supreme Court.
we point
conclusion,
to
On the one hand,
two key findings.
in
In the
contrast
to
political change must now be accomplished by the
earlier historical periods,
selection of new legislators through the electoral process rather than by the
adaptation of
legislators
changes
to
public
in
On
demands.
the
the possibility of major political change has been sharply reduced
other hand,
because
incumbent
average
the
between
distance
the
two
parties
major
has
fallen
dramatically in this century.
Estimation of a Probabilistic, Spatial Model of Voting
II.
An Overview of the Model
Expressions such as "liberal",
the
and "conservative" are part of
"moderate",
common language used to denote the political orientation of a member of
Such labels are useful because they quickly furnish a rough guide
Congress.
to the positions a politician is likely to take on a wide variety of
A
contemporary
liberal,
for
example,
oppose aid to the Contras,
minimtmi wage,
likely
is
a
politician
predict,
favors
with
a
Indeed,
support
increasing
the
oppose construction of MX missiles,
and support federal funding of
support mandatory affirmative action programs,
health care programs.
to
issues.
this consistency is such that just knowing that
increasing
the
minimum
fair degree of reliability,
wage
the
is
enough
information
to
politician's views on many
seemingly unrelated issues.
consistency
This
suggests
that
summarized
a
by
or
constraint
(Converse
politician's positions
a
simple
formal
on
a
structure,
1964)
wide
of
political
variety of
where,
as
opinions
issues
can be
mentioned
above,
legislators are points and roll calls pairs of points in an Euclidean space.
Insofar as
a
spatial model can capture Congressional roll call voting,
unnecessary to use
a
large number of dimensions.
it
is
We find that one dimension
captures
most
the
of
spatial
information while
a
second
dimension makes
a
Adding more dimensions does not
marginal but important addition to the model.
help us to understand Congressional voting.
Although
mathematical
dimensions are
the
abstractions,
reader
the
can
think of one dimension as differentiating strong political party identifiers
had a two party political system.
dimension
ranges
Democrat)
to
weak
differentiates
parties.
to
a
strong
loyalty
to
loyalty
party
one
to
Whig,
from
surprising,
is not
either party
(Federalist,
"liberals"
It
loyalty
"conservatives"
to
a
Another
Republican).
or
that one
(Democrat-Republican
strong
to
therefore,
within
the
party and
political
loyalty
consistent,
of
— especially
to
an
ideology have
voting
stable
during periods of stability
—a
second,
competing
two
Loyalty
similar behavioral
a
patterns.
or
dimension
The distinction between the two dimensions is a fine one.
implication
that
from
party
competing,
the United States has always
Except for very brief periods,
from weak ones.
This
the
is
reason
one dimensional model accounts
for most voting in Congress.
In Figure
1,
we show a two dimensional example of a legislator's
ideal
point along with the points representing the "yea" and "nay" alternatives on a
roll call vote.
The circles centered on the legislator represent contours of
the utility function employed
only
consideration,
consider
"nay"
the
the
in our
study.
legislator would
perpendicular bisector CC
outcomes.
Tnis
bisector,
termed
If
spatial
clearly vote
of
the
the
line
cutting
legislators who vote "yea" from those who vote "nay".
proximity were
"yea.
"
joining
line,
Furthermore,
the
should
1
about here
"yea"
and
pick
out
Those legislators whose
ideal points are on the "nay" side of the bisector should vote "nay".
Figure
the
We
because
"should"
say
the model
will
In this model,
it
successful
be
To allow for error,
accounting for every individual decision.
logit model.
obviously not
in
we employ the
only more likely that the legislator votes
is
for the closer alternative.
For
whose
legislator
a
point
ideal
cutting
the
Consequently,
will
line
most "errors"
probability
a
cutting
the
the
line,
close
zero
to
or
one.
legislators who voted "nay" when on the
(that is,
side of the line and vice-versa) in classifying actual data should fall
"yea"
top panels
The
error.
later use Figure 2 to return to the topic
We will
close to the cutting line.
of
have
on
Legislators with ideal points far
probability of voting "yea" will be 0.5.
from
falls
of
that
figure use
tokens
to
show the
estimated
ideal points of senators and the estimated cutting lines for two actual votes.
The dimensions of the space are related to policy areas considered by the
We will
legislature.
all
the behavior
allows
for
dimension
show that
dimensions can account for essentially
can be accounted for with a simple spatial model
that
probabilistic
adds
"1-"
We
voting.
significantly
in
some
say
"1-"
because,
Congresses,
clearly less important than the first.
That
is,
the
while
a
that
second
dimension
second
is
projecting all the diverse
issues treated by Congress onto one dimension accounts for about 80 percent of
the
individual
decisions and adding a second dimension adds only another 3
percent.
Of course,
time.
In
how specific issues map onto the dimensions may change over
the postwar period,
on overriding Truman'
s
1947 veto of
division along the first,
and
most
contrast,
other
an interpretation is fairly clear.
"economic"
the
left to right,
votes
tend
Taf t Hartley Act was
dimension.
to
line
up
Similarly,
on
this
The lineup
almost a pure
minimum wage
dimension.
final passage of the 1964 civil rights act in the Senate,
In
which was
close to a pure South-North vote, was almost a pure division along the second,
)
top
dimension.
bottom,
to
Quarterly as
Congressional
votes
"key"
Panama Canal treaty (See Figure 2),
1974 vote
15,
dividing
the
dimension.
on
parties
two
Figure
in
postwar
period,
such
internally at
an
angle
of
-45
the
votes,
left-right
the
to
as
by
and a May
I,
"Conservative Coalition"
be
to
the results of our scaling algorithm readily admit
interpretation.
line
the
in
designated
calls
roll
3
Indeed,
one
the
of
the Jackson amendment on SALT
tend
busing,
school
most
However,
2,
(The
than
Defining the first dimension to be roughly along a 45
we
can
differentiate
conservatives within each party.
dimension.
to more
scaling
liberals
(southwest
quadrant)
from
The orthogonal dimension is a party loyalty
algorithm does
not
This interpretation follows Poole and Daniels'
use
information
about
party.
(1985) two dimensional analysis
of interest group ratings.
A party dimension is present throughout nearly all
of
American history
while an orthogonal dimension captures internal party divisions.
Tnus,
division between southern and northern Democrats after World War
parallel
in
the
division
between
southerners
Democratic and Whig parties in the 1840'
and western Republicans from the 1870'
s
s
northerners
and
II
in
the
finds a
both
the
and in the division between eastern
through the 1930'
s.
The fact that there is more than one substantive summary of our results
is
not
troubling.
Indeed,
"liberal-conservative" vs.
the results.
Moreover,
the
"economiic"
"party"
vs.
"regional
or
social"
and the
interpretations both provide insight
the major finding of this study is
into
that an abstract
and parsimonious model can account for the vast bulk of roll call voting on a
very wide variety of substantive issues.
Our "I2"
departs from much of the
previous literature which has either exogenously imposed a larger nimber of
dimensions
(e.g.
Clausen 1973)
or used methodologies
for the recovery of spatial voting (Morrison 1972).
that were
inappropriate
Estimation Methodology
Our estimation includes every recorded roll call between
The Data.
1789 and
1985 except those with fewer than 2.5 percent of those voting supporting the
minority side.
For
given Congress
a
legislator having cast
least
at
year
(two
included
we
every
announced votes were
Pairs and
votes.
25
period),
Observations with other forms of non-voting (absent,
treated as actual votes.
excused) were not included in the analysis.
thus excluding near unanimous
After
The Spatial Parameters.
the estimation requires Euclidean
legislators with very few votes,
of Representatives,
for 9759 members of
the House
roll
two-dimensional
calls.
In
when
parameters
a
positions
spatial
calls and
roll
are
invariant
and 70,234
1714 senators,
requires
this
setup
in
locations
estimating
number
This
time.
303,882
is
nevertheless small relative to the 10,428,617 observed choices.
Additional parameters are required to allow for spatial mobility.
legislators
clearly
there
instance,
from a weak
(R-PA)
remarkable
the
is
occupy
not
do
liberal
to
a
stable
positions
conversion
strong
in
conservative
Schweiker
after being
tapped as
To allow for spatial
Ronald Reagan's vice presidential running mate in 1976.
movement,
of
Nonetheless,
time.
slight
legislator coordinates to be polynomial
we permitted all
improvement
functions
found great stability in legislator positions.
we
results frcn allowing
fit
in
For
space.
Richard
Senator
of
the
Some
linear
A
higher order
trend;
polynomials make virtually no additional contribution.
In
the estimated model,
identified only up to
dynamics
or
a
space
over
realignments,
the
In
intertemporally.
time.
As
legislators and roll
calls are
translation and rigid rotation. Vlien we speak later of
translations or rotations.
identified
the locations of
a
movement
contrast,
One
result,
is
the
always
relative
cannot
arbitrarily
we
discuss
can
relative
scale of
shrink
changes
in
any
to
the
or
global
space
stretch
the
degree
is
the
of
)
polarization
— when
system
political
the
of
legislators
spread
are
further
the system is more polarized.
apart in the space,
We use a specific functional model of
Functional Representation of the Model.
choice to represent our hypothesis that roll call voting is sincere Euclidean
voting subject to "error" induced by omitted factors.
quadratic functions of
extension
The
time.
where
model
we develop an s-dimensional
baggage,
To eliminate notational
legislator coordinates
are
higher order polynomials
to
is
direct.
Legislators
indexed
are
position is given by
=x
ikt
measured
is
x
i-xt
Ik
Ik
a
legislator's
Euclidean
k=l,2,...,s
Within a Congress,
four
in
t,
where
xt,
Ik
+
For each senator serving
constant.
)
Congresses.
terms of
in
time
At
i.
,...,x
(x
x
Time
by
or
more
time
Congresses,
held
is
three
all
coefficients are estimated; for each senator in three Congresses,
the constant
is estimated for
senators who
and linear coefficients are estimated;
only x
ik
served in only one or two Congresses.
indexed by
Each roll call,
j,
is represented by two points
one corresponding to an outcome identified with a "Yea"
to
the
"Nay"
(n)
The
vote.
(y)
in the space,
vote and the other
coordinates are written as z
and
Jyk
z
(We
.
Jnk
omit time subscripts on the roll calls.
If there was pure Euclidean voting,
only if his
"Nay"
or
location.
d
IJy
location were
her
In two dimensions,
=(x lit
r
(x
closer
12t
i2
lit
jnl
to
the
for example,
-z)+(x
-z)+(x
Jyl
each legislator would vote Yea if and
"Yea"
this would be:
-z)<
Jy2
-z)
,2
,
i2t
Jn2
location than
=d,2Ijn
to
the
voting
spatial
Pure
Ignores
To allow for error,
influence voting.
"errors"
the
omitted
or
we assume
variables
that
each legislator has a
that
utility function given by:
U(z)=u
ji
1
iji
+c.
= /3exp[-d^
u
1=
y.n
iJi
/8]
iji
iji
where P is an additional parameter estimated in the analysis,
model"
error which
and "8"
exponential,
parameter
The
independently distributed
the
as
log
inverse
the
of
"logit
a
is an arbitrary scale factor.
^
is
essentially
signal-to-noise
a
perfect spatial voting occurs
increased,
one.
is
is
c
— all
ratio.
As
is
P
probabilities approach zero or
The estimation was
history.
We have imposed a common p for all of U.S.
not substantially improved by allowing a distinct g for each Congress.
As a result of our choice of error distribution, we are able to write the
probability of voting "Yea"
as:
—
exp[u
Pr{"Yea")
=
ij
.
.
expiu
ijy
We chose the above specification for
First,
]
^-^^
.(1)
,
+ ex-Dlu
J
]
IJn
a nuinber
the spatial utility function (u)
of reasons:
This allows for
is bell-shaped.
the possibility that individuals do not attribute great differences to distant
alternatives.
proposal
For example,
Ted Kennedy might see little to choose from in a
that was at John Warner's
ideal point
rather than at Jesse Helms'.
But Helms might see a very large difference between two such proposals.
Second,
function
using
that
is
a
a
stochastic specification permits developing a likelihood
function of
function is dif f erentiable,
If
we
were
approach
in
concerned
one
the
it can be
solely
dimensional
with
coordinates
to
be
estimated.
As
this
raximized by standard numerical methods.
cdir.al
problems.
scaling,
Tnat
is,
we
we
could
could
eschew
start
this
with
a
configuration of legislators and then find a midpoint for each roll call that
minimized classification errors.
and
procedure
probability
iterated
be
then
classification
weights
scaling
Ordinal
choices.
reduced
further
be
heavily
likelihood,
a
can
fewer
makes
indeed
maximizing
process
This
legislators.
could
errors
classification
the midpoints could be held constant
Next,
errors
this
of
convergence.
to
errors
reordering
by
than
Such
which,
ours,
correspond
that
however,
form,
the
a
in
low
to
wholly
is
impractical in more than one dimension.
Finally,
by
using
probabilities
in
the
non-linear
logit
form
closed
would
model
form
logit
the
problt.
be
As
calculate
can
alternative
standard
The
(1).
we
error,
of
involves
this
the
our
to
numerical
more time is needed to estimate the model.
integration,
Further details about the estimation procedure appear in the Appendix.
III.
Spatial Structure of Congressional Voting
Let us begin by showing
typical,
Figure 2 shows all voting members of
model.
positions
and
vote
the
cutting
lines
for
a
National Science Foundation on April
2,
on
April
1978
18,
"snapshots"
the Senate
specific
two
and
treaty
recent
but
proposal
1981.
in
votes,
restore
to
of
voting
the
their estimated
Panama
the
funding
Canal
for
A "D" token represents
the
northern
o
Democrats,
"S"
Byrd (VA)).
R
token
southern Democrats,
Similar positions of senators produced overstriking.
is
always
overstruck by other
overstruck
S' s
those senators who were,
"errors."
and "R" Republicans (the one "I"
and
by
another
given their
cutting
errors
line
in
than
voting
for
are
those
S' s
location relative
and
are
D' s
to
the
an
always
shows
only
cutting line,
the probability of an error should be greatest
for senators closest to the cutting line.
pattern;
and
However,
The bottom part of each panel
D' s.
As explained above,
R
is Harry
far
who
more
are
The data conform to
likely
distant.
for
senators
V.'hen
expected
the
close
senators'
the
Euclidean
positions provide a clear indication of which side they should join,
10
to
forces
not
captured by our simple structure are rarely strong enough
produce a
to
vote that is inconsistent with the spatial model.
Figure 2 about here.
These two roll calls are quite representative of post World War
Typically,
in Congress.
calls divide at
roll
least
and have estimated cutting lines roughly parallel
9
tendency
The
2.
dimensional
cutting
for
provides
model
lines
to
of
two parties
the
the two shown in Figure
parallel
be
approximation
useful
a
to
one
voting
II
why
explains
that
accounts
a
one
most
for
voting decisions.
Returning to the question of "error", how general is the pattern shown by
the snapshots?
A straightforward method of fit
classifications
across
all
roll
The
calls.
the percentage of correct
is
classification results for
two-century history of both Houses of Congress are shown in Table
the
The
1.
table reports classification both for all roll calls in the estimation and for
"close"
calls where the minority got over 40 percent of the vote cast.
roll
classification is better than SO per cent for
With a two-dimensional model,
"close" votes as well as all votes.
Table
It can be
model
where
career.
percentage
trend
in
about here.
seen that a reasonable fit is obtained from a one-dimensional
each
On
1
legislator's
the
other
points
— from
hand,
position
there
adding
a
is
is
constant
considerable
second
dimension.
throughout
improvement
Allowing
legislator positions adds another percentage point.
his
— about
for
a
(That
or
her
three
linear
we
get
less of a boost in the percentages from the time trend than the dimensions is
expected.
When we add
per dimension.
a
time trend,
In contrast,
we add only one parameter per legislator
adding a dimension adds two parameters per roll
call as well as additional legislator parameters.
legislators
by
over
5-to-l,
it
is
not
il
Since roll calls outnumber
surprising that
classification shows
)
more improvement when we increase the dimensionality of the space than when we
increase the order of the time polynomial.
dimensions
parameters
more
Introducing
higher
or
understanding
of
dynamic
a
polynomials
order
political
the
in
— does
spatial
— through
appreciably
not
Adding
process.
model
extra
add
spatial
extra
our
to
parameters
results in only a very marginal increase in our ability to account for voting
consider adding to the two dimensional
For example,
decisions.
Allowing for a quadratic term in the time polynomial improves
in the Senate.
classification only by 0.3 percent at
of 1456 additional parameters
a cost
third
dimension improves
77,479
more
parameters
parameters per
more
2
(
the
Thus,
per
roll
and
call
percent
1.0
one
at
or
two
Allowing for both generates an
legislator).
percent.
1.1
classification by only
regularity
important
have
we
(2
Allowing for
dimensions x 728 senators serving in 4 or more Congresses).
only
linear model
a
cost
a
of
additional
improvement
found
is
of
that
somewhat over SO percent of all individual decisions can be accounted for by a
two-dimensional model where individual positions are temporally stable.
regularity
an
is
well-specified
pattern,
important
theoretical
decisions
space.
The
reflect
either
very
model
that
specific
sets
of
the
would
model
spatial
the
but
pattern does not
fix
cannot
logrolling and other forms of strategic voting
dimensionality
the
account
constituency
arise
for
from
of
a
the
likely
to
interests
or
are
other
and
This
that lie outside the paradigm
that forms the basis for our statistical estimation.
The Dimensionality of Congressional Voting
Since
empirical
evidence
low
dimensionality
result,
for
it.
we
will
First,
an
is
discuss
for
three
important
several
Houses,
and,
to
different
we
show
many,
sets
the
of
unexpected
supporting
increments
to
the
percent classified correctly when D-NOMINATE is estimated with as many as 21
dimensions.
Second,
we
evaluate
the
12
classification
ability
of
the
second
dimension from the two dimensions with linear trend estimation,
this to the first dimension.
dimensional
one
model
compare
we compare our ability to classify with a
Third,
with what
and
might
expected
be
calls were distributed within an s-dimensional
legislators
if
sphere.
we
Fourth,
and
roll
show that
the results of D-NOMINATE are reasonably stable when the algorithm is applied
to
subsets
content.
of
roll
Fifth,
calls
we show
been
have
that
defined
an alternative measure
that
terms
in
of
substantive
of
geometric
the
fit,
mean probability of the observed choices, gives similar results to those based
on classification percentages.
we compare the model's performance with measures of the diversity of
agenda,
the
agenda.
Seventh,
important role for
1.
since dimensionality may depend on the
Sixth,
a
we
which
ask
issues
American
in
history
led
to
an
second dimension.
Models of High Dimensionality.
our first
As
check on dimensionality of
our dynamic models, we selected three Houses and estimated the static model up
to 50 dimensions.
(1851-52) was chosen because it was one of
The 32nd House
the worst fitting Houses
two dimensions and thus was
in
exhibit high dimensionality.
The S5th House
was analyzed with other methods by Weisberg
House
is
part
of
a
when
period
the
two
is
included
because
it
appears
that
(1957-5S)
was chosen because it
[196S).
In
dimensional
dominates the one dimensional linear model.
good candidate to
a
Finally,
call
roll
addition,
linear
S5th
clearly
model
the 97th House
voting
the
(1981-82)
became
nearly
unidimensional at the end of the time series.
Figure 3 displays the classification gains for the 2nd through the 21st
dimensions for each of the three Houses.
The
classification percentage for
the first dimension was 70.2 for the 32nd House,
for
the
97th.
The bars
in
the
figure
indicate
78.0 for the 85th,
how much
dimension adds to the total of correctly classified.
labelled such that "3"
corresponding
(The horizontal axis is
corresponds to the fourth dimension,
13
the
and 84.1
etc.
)
Note that
bars
the
negative
drop
not
do
— because
smoothly--in
off
fact
occasion
one
on
the algorithm is maximizing likelihood,
bar
the
is
not classification.
Figure 3 about here.
The 97th House is at most two dimensional with the second dimension being
very
dimensions
two
After
weak.
classifications
added
the
are
There is a clear pattern of noise fitting beyond two dimensions.
to
the 97th,
the
85th House
is
strongly two dimensional
the decisions.
contrast
In
but again
there
is
While the 32nd does show evidence
little evidence for additional dimensions.
for up to four dimensions,
minuscule.
even four dimensions account for only 78 percent of
These results argue that either voting is accounted for by a
low dimensional spatial model or it is,
spatially chaotic.
in effect,
There
appears to be no middle ground.
2.
The Relative Importance of the Second Dimension.
presented
in
Table
second dimension,
and
1
and
second dimension by
(1989)
a
Figure
3
weak one
other
than
suggests
it
marginal
its
marginal
is
role
important
impact.
for
to
at
most
evaluate
Specifically,
a
the
Koford
argues that a one dimensional model will provide a good fit even when
spaces have higher dimensionality.
space,
that,
at
a
Although the evidence
For example,
in a
truly two dimensional
one dimension will have some success at classifying any vote
not strictly orthogonal to the dimension.
As a result,
in fit on the order of 3 percent may understate the
that
is
the marginal increases
importance of the second
dimension.
The natural question,
classifying by itself.
then,
is how well
To study this,
coordinates from our preferred model,
for each roll
call,
does the second dimension do in
we took the second dimension legislator
two dimensions with linear
trend,
and,
found a outpoint which minimized classification errors.
We used the minimum errors to compute overall classification percentages.
made the same computation for the first dimension.
We
Figure 4 about here.
The results of these computations for the House
The averages of
99
the
4.
biennial figures show the first dimension correctly
classifies 84. 3 percent of
votes but
the
The 70.8 percent
only 70.8 percent.
are shown in Figure
second dimension accounts
the
for
particularly unimpressive given that
is
predicting by the marginals would lead to 66.7 percent.
If
the two dimensions
were indeed of equal importance,
then in some Congresses dimension "two" might
do better than dimension "one".
But in all 99 Houses,
Senate results are
for
tad weaker
— 83. S
2,
and
17,
IS.
addition,
In
comparison between our two dimensions,
issue
the
of
The
"two"
does better
in
But clearly the second dimension is a second fiddle.
How Well Should One Dimension Classify?
3.
did better.
percent for one dimension versus 73.6
The marginals here were 66.1.
two.
Senates
a
"one"
unidiraensional
fit
In
addition to this empirical
following Koford
Specifically,
theoretically.
we
(1989),
we
consider
assume an
n-dimensional uniform spherical distribution of ideal points and consider the
projection of these ideal points, onto one dimension under the conditions of
errorless spatial voting in the n-dimensional space.
As for the distribution
of roll call cutting lines or separating hyperplanes, note that each roll call
hyperplane can be represented as tangent to a sphere of radius
common center with the ideal point sphere.
distribution
of
distribution
of
voting,
Cy
%
tangency
r,
we
points
make
use
is
of
For fixed
uniform
the
on
fact
that,
that has a
we assume that
r,
sphere.
the
r
with
As
errorless
for
the
the
spatial
there is a one-to-one relationship between r and the expected split y
in
the majority,
empirical
marginals,
distribution
100-y in the minority)
of
y,
that
is,
to define the distribution of
distribution of
r
the
r.
on the roll
historical
call.
We use
distribution
of
the
the
Given the empirically generated
and the assumed uniform distributions of tangency points and
15
one can calculate the percentage of correct classifications that
ideal points,
would be made by
we can calculate the exact percent correct for errorless spatial
For s=2,
For the empirical distribution of splits over all roll calls included
voting.
in
our
one-dimensional projection.
a
78.9 would be
analysis,
correctly
classified
in
both
House
the
Senate if legislators and roll calls were spherically uniform for s=2.
one-dimensional
the
spatial
voting.
percent
(Table
constant model might arise from perfect
with
However,
Thus,
1).
a
percent
incorrect
incorrectly
voting
correctly with probability 0.789.
would
classify
correctly
83.5
The S3. 5 percent voting correctly
have
only
error
their
projection with probability 0.211.
projection would
classify
better benchmark model would be two-dimensional
two dimensions would be projected
16.5
in
dimensional
two
correctly
we
dimensions,
two
voting with an error rate of 16.5 percent.
in
Thus,
the 80 percent correct classification we obtain
the case that
it might be
and
Therefore,
83.5(0.789)
+
"corrected"
a
The
by
an
one-dimensional
=
16.5(0.211)
69.4
percent of the individual votes.
For s
>
3,
we conducted simulations.
We had 5000 voters randomly drawn
within the unit sphere vote perfectly on 900 randomly drawn roll calls.
the empirical distribution of splits,
classified
declines
with
s.
As
Using
Table 2 shows how the percent correctly
dimensionality
the
increases,
the
percent
correct for a one dimensional projection approaches the average value of y or
the percent correct for the "Majority" model.
The table indicates that for a
one-dimensional
percent
distributions
model
to
of
ideal
classify at
points
the
and
80
cutting
level,
lines
must
the
be
underlying
"nearly"
one-dimensional rather than spread uniformly about some space of even modestly
higher dimensionality.
Table 2 about here.
16
Do Different Issues Give Different Scales?
4.
Management,
Social
Agriculture,
Welfare,
have
We
Defense Policy.
coded
terms of these five categories,
Miscellaneous.
sharp
If the
differences
in
by
represented
voting
Congressional
to our emphasis on
Clausen (1973) has argued that there are five "dimensions"
low dimensionality,
to
In contrast
Liberties,
Civil
every House roll
and,
areas
issue
the
for completeness,
and
from
call
a sixth
issues are really distinct dimensions,
legislator
coordinates
when
Government
of
Foreign
1789
1985
to
in
category termed
we ought to get
issues
the
and
are
scaled
separately.
To conduct this experiment of separate scalings,
because it had the largest number of roll call votes
we chose the 95th House
(1540).
There were 714
Government Management votes, 286 Social Welfare votes, 311 Foreign and Defense
votes,
and,
to
have
enough votes for
scaling,
229
in
a
combined Agriculture, Civil Liberties, and Miscellaneous.
two dimensional
residual
set
that
We then ran one and
(static) D-NOMIfv'ATE on each of these four clusters of votes.
Because it is difficult to directly compare coordinates from two dimensional
scalings,
we based our comparisons on correlations between all unique pairwise
'2
distances among legislators.
Correlations between the management, welfare, and residual categories for
one
dimensional
scalings
are,
as
shown
in
Table
3,
all
high,
around
Correlations between the foreign and defense policy category and
the
0.9.
other
'3
three were somewhat lower,
in the 0.7 to 0.8 range.
As a whole,
the results
hardly suggest that each of these clusterings of substantive issues generates
a
separate spatial dimension.
Table 3 about here.
When the same subsets of votes are scaled separately in two dimensions,
the correlations are somewhat lower than they are in one dimension
Table
3).
This
result
is
not
surprising.
17
The
95th
House
(again see
had
nearly
—
From the D-NOMINATE unldimensional scaling with linear
unidimensional voting.
trend
that
applied
was
the
to
whole
we
dataset,
find
that
dimension
one
correctly classifies S3 percent of the votes in each of the four categories.
With two dimensions
the
increase only
percentages
84
to
percent
Social
for
Welfare and Foreign and Defense and 85 percent for the other two categories.
14
Moving from one to two dimensions doubles the number of estimated parameters
with only slight
roll
calls
increases
four
into
in classification
categories
ability.
estimating
and
parameters,
by moving from one
fitting idiosyncratic "noise"
underlying
in
two
to
the data.
correlations between
strong
separately,
dimensions,
The
number
the
of
With a further doubling of
legislator parameters is effectively quadrupled.
all
breaking down the
In
one
likely
is
to
to the noise weakens
fit"
We
legislator positions.
also
be
the
note
that the spirit of Clausen's work suggests that each category should be scaled
in one dimension only.
In summary,
our breakdown of the 95th House in terms
of Clausen categories indicates that the categories represent highly related,
not distinct,
5.
"dimensions".
Evaluation
classification
by
Geometric
percentages,
Mean
the
Probability.
may
model
method that gives more weight to errors
than to errors close to the cutting line
—a
evaluated
be
that
addition
In
are
by
alternative
an
far from the
computing
to
cutting
line
vote by Edward Kennedy (D-MA)
to
confirm Judge Robert Bork to the Supreme Court would be a more serious error
than a similar decision by Sam Nunn (D-GA).
Such a measure is the geometric
mean probability of the actual choices, given by:
gmp = expClog-likelihood of observed choices/N),
where N is the total number of choices.
Summary gmps for the various estimations are presented in Table
pattern
matches
that
found
for
the
classification
percentages
gained by going beyond two dimensions or a linear trend.
18
1.
little
The
is
we plot the gmp for each House for the following models:
In Figure 5,
two-dimensional
A
(i)
positions
legislator
with
model
constrained
to
a
to
a
constant plus linear trend.
A
(ii)
one-dimensional
model,
positions
legislator
with
constrained
constant.
(iii)
A
one-dimensional model
that
estimated
is
Note that in this model
first 99 Congresses.
separately for each of
there
is
the
constraint on how
no
legislator positions vary from Congress to Congress.
Motivation for the third model came from
Rabinowitz
and
one-dimensional
that
(19S7)
within
the
American
time
span
a
recent argument by Kacdonald
political
of
any
one
conflict
is
Congress
but
basically
that
the
dimension of conflict evolves slowly over time.
Figure 5 about here.
Kacdonald-Rabinowitz
The
Congress,
is
within
sustained for the entire period following the Civil War.
shown in Figure
1853-54,
unidimensionality
hypothesis,
the gmp for model
5,
(iii)
has not fallen below 0.64
any
As
since
oscillating in the 0.64 to 0.74 range with the exception of the very
high gmps that occurred in the period of strong party leadership around the
turn of the century.
The hypothesis
of
slow evolution is
supported by our
result that voting patterns can be largely captured by a one dimensional model
where individual positions are constant in time.
model
(ii)
closely tracks the curve for model
slightly better tracking.
*
In Figure
(iii).
5,
Model
the curve for
(i)
provides a
Because political change is slow, roll call voting
reflects changes in the substance of American politics either as a trend for
an individual legislator in a two dimensional space or as replacement of some
legislators by others with different positions in the space.
6.
The Agenda
argument
and Dimensionality.
would be
that
short-term
One
basis for
coalition
19
the
Macdonald-Rabinowitz
arrangements
enforce
a
logroll
.
across issues that generates voting patterns consistent with a unidimensional
spatial
consideration
potential
Another
model.
in any two-year period,
unidimensional ity may reflect the fact that,
must
restriction
some
place
consideration.
can
that
given
be
run
Congress
time
for
Congresses that consider a diversity of issues
this is so.
If
issues
the
on
short
that
is
should be less unidimensional.
To
test
computed,
out
hypothesis,
diversity
this
finer-grained
set
of
We also coded all
developed
categories
13
crude
a
House roll
Peltzman
by
but very weakly
(R=.
362
19
index for Peltzman categories is explained by trend
geometric means
from,
the
counterhypothesis direction.
model fits better
two dimensional,
undoubtedly spurious.
at
trend model,
but
in
The result
a
the
is
The worst fitting years occur early in the time series
least as measured by these indices,
to the ability
as government
is more weakly
-.369 for Peltzman).
while the agenda has become more diverse over time.
agenda,
the
in
call set becom.es more diverse,
As the roll
(R=-.302 for Clausen,
linear
The indices
correlated with
Both indices are "significantly"
related to trend (R=-.405).
the
(R=-.709),
The index for the Clausen categories
has expanded over time.
The
(1984).
the variation
Just over half
).
18
calls using a
Herfindahl index was also computed for the Peltzman categories.
validate,
we
way,
the Herfindahl concentration index
for each of the 99 Congresses,
for the six Clausen categories.
least
at
in
Indeed,
is not
diversity of the
"significantly" related
(difference in geometric means) of the two dimensional model to
improve over the one dimensional linear model (R=-. C89 for Peltzman,
-.158 for
Clausen)
One
reason
for
hypothesis
is
Congresses
40-99,
deviation
of
that
0.062;
these
the
the
indices
index
for
basically
for
Peltzman,
have
negative
exhibited
Clausen
the
20
results
averaged
average
is
for
little
0.355
0.090
diversity
the
variation.
with
and
For
a
standard
the
standard
deviation
0.020.
the
In
100
last
votes are restricted to
consistently
have
sparked
this
(D-NOMINATE
errors)/(Number
by
the
voting
dimension
over
PRE
the
minority
on
spatial
in
We
terms.
marginals
[PRE
=
within
each
of
side)]
the
PRE
for
models
linear
the
1
-
the
and
one
in
two
We then filtered
We obtained PREs for 6 categories x 99 Houses.
dimensions.
and
We use PRE to control for differences in marginals across
computed
We
categories.
full
a
There have been relatively few issues
second
a
considering
demonstrate
Clausen categories.
had
narrow topical area.
a
Issues and the Second Dimension.
that
has
Low dimensional voting has not occurred simply because
wide-ranging agenda.
7.
Congress
years.
these into a subset that contains only those category-Congress pairs that were
(a)
based on at least 10 roll calls,
0.5,
and
(c)
dimensions.
spatial
had a two dimensional PRE of at least
(b)
had an increase in the PRE of at least 0.1 between one and two
20
In
and where
appear in Table
other words,
the
we found sets of roll calls that were highly
second dimension made an important difference.
These
4.
Table 4 about here.
It can be seen that the second dimension was "important"
first
24-31,
key.
Civil
23 Houses.
It
appeared
sporadically
the second dimension emerges
in 5 Houses,
Note for further reference, however,
Liberties
accommodated
by
(essentially
introducing
through the 75th Congress,
a
different
in
slavery)
second
in only 6 of the
areas.
In
and Civil Liberties
Houses
is
the
after the Compromise of 1S50,
that,
vanishes
dimension.
as
In
there are only 3 occasions,
an
issue
fact,
from
1853-54,
that
the
1S93-94.
is
32nd
and
1915-16 when the second dimension made a key difference,
each time only in one
issue
1930' s
area.
The
"realignments"
accommodated not by a shift
(Republicans in the
90' s
in
the
of
the
1890' s
space but
by
and Democrats in the 30'
21
s)
and
the
were
largely
infusion of new blood
in the existing space.
In
contrast
first
the
to
75
second
the
Houses,
systematically important in Houses 76 (1939-40) through 91
for the 80th Congress,
Liberties
there were only
category.
of
Moreover,
0.26).
80th
(The
eliminated
is
Civil
because
their PRE was 0.62
however,
Civil Liberties votes;
8
increase
an
dimensions,
frequent
only
in
case
one
was
Except
(1969-70).
every House in this period appears in the table.
most
the
is
dimension
in
(the
Congress) did the second dimension matter in fewer than two issue areas.
other
when
words,
consistently so
across
a
strongly
became
space
the
variety of
wide
dimensional,
two
topics.
As
stated
two
90th
In
became
it
earlier,
the
dimensions are not so much defined by topics as they are abstractions capable
of capturing voting across a wide set of topics.
from Congress 92 out,
Finally,
second dimension appears
the
only once
when the PRE is over 0.5, reaffirming our earlier conclusion that the House is
currently virtually unidimensional.
Table
shows
also
4
groups
of
roll
where
calls
increases PRE by 0.1 but the total PRE is below 0.5.
have
roll
calls
explain most of
where fit
is
"variance.
the
fraction of the entries here,
example,
our
in
two
improved
"
but
The first
where
50
the
second
dimension
In other words,
spatial
a
model
account
Houses
for
here we
does
higher
a
reflecting the poor fits in some years.
worst-fitting
Houses,
the
dimension helps the category with the most votes.
17th
and
32nd,
a
not
For
second
Government Management,
but
the PFIE remains low.
Agriculture,
particularly since
the
S9th House,
category that is not captured by a spatial model.
there were only three with at
seems
to
have
least
gradually fallen out
after World War
II,
10 votes
of
the
in
appears
(In
the
spatial
to
the first
category.
framework.
)
be
one
60 Houses,
Agriculture
Immediately
Agriculture had one-dimensional PREs over 0.6.
fifties and early sixties,
the
In
the
the one dimensional PREs fell but Agriculture still
22
agriculture
on
been
has
voting
In the seventies and eighties,
fit spatially via the second dimension.
largely non-spatial.
from
Indeed,
SSth
the
House
Agriculture has consistently the lowest PRE of the six categories.
forward,
We repeated the above analysis,
using the same filters,
results were
Results
The
coding.
quite
similar.
for the Peltzman
Peltzman'
for
21
Policy code were like those for the Clausen Civil Liberties code.
s
Domestic
As with the
voting in a variety of other areas also scaled on the second
Clausen codes,
dimension in Houses 76-91.
In
our analysis of PREs
summary,
findings of low dimensionality.
Particularly in recent times,
dimension has an impact on fit,
the
that is essentially non-spatial.
impact
is
reinforces our
when a second
agriculture,
on the one area,
22
Spatial Stability
We have seen that,
a
spatial model,
We address
stability of the model.
Does the model consistently fit the data in time? (2)
dimension stable in time?
I.
say "1-" dimensional,
a low dimensional model,
what of the tem.poral
(1)
to whatever extent roll call voting can be
Stability of Fit.
(3)
Feelings",
conflict
and
in
the
Inspection of Figure
early 1S50'
slavery was
over
periods of political
periods
when
a
political
twentieth century,
the data,
s
marked by
stability,
dimensional spatial model.
But
issues here:
three
Is the major,
5
shows that
first
there are only
Poor fit occurs between
Federalist party collapsed and gave way to
the
suffices.
Are individual positions stable in time.
occasions when spatial models fit poorly.
1825 when
captured by
roll
"Era
of
when the destabilization induced by
collapse
the
call
In contrast,
party
the
1S15
expires
the spatial model has
of
the
Whigs.
voting can be described
Thus,
by a
two
and
Good
the
in
low
voting is largely chaotic in unstable
and
a
new
one
is
formed.
In
the
consistently provided a good fit to
even if the agenda was buffeted by a fast pace of external events.
23
including four prolonged armed conflicts overseas and the Great Depression of
the domestic economy.
2.
Given the pace of events,
The Stability of the Major Dimension.
be possible for the major dimension to shift rapidly in time.
rapid shifts are
model,
foreclosed by our
extent
some
to
In our dynamic
imposition of
restriction that individual movement can be only linear in time.
gains
small
constitutes
in
evidence
that
legislators
models
polynomial
order
higher
from
fit
do
shift
not
back
it would
(see
and
the
While the
Table
forth
1)
the
in
we thought it important to evaluate stability in a manner that allows
space,
for the maximum possible adjustment.
perform
To
this
evaluation,
we
return
static D-NOMINATE was run 99 times,
dimensional,
to
model
(iii)
where
once for each Congress.
one
This
gets the best one dimensional fit for each Congress and allows for the maximum
adjustment
of
individual
Since
positions.
there
is
constraint
no
tying
together the estimates, we cannot compare individual coordinates directly, but
we
compute the correlations between the coordinates for members common to
Ccin.
two Houses or two Senates.
matrix,
Rather than deal with a sparse
99x99 correlation
we focus on the correlations of the first 95 Congresses with each of
This allows us to look at stability as far
the succeeding four Congresses.
out as one decade.
In the upper portion of Table
first
95
Congress,
Congresses
the
and
for
5,
four
we average these correlations across the
periods
of
history.
For
both Houses
of
table shows that the separate scalings are remarkably similar,
especially since the end of the Civil War.
on a stable alignment,
relative
to
his
After 1861,
colleagues,
term (t+1 and t+2).
Table 5 about here.
24
a senator could count
over an entire six year
)
lower portion of Table
In the
to save space,
5,
we display the individual
pairwise correlations only for situations where either the correlation of t+1
was less than 0.8 or a later correlation was less than 0.5;
periods
Consistent with
instability.
of
correlations
are
we show
is,
preceding discussion,
the
concentrated
overwhelmingly
that
in
pairs
where
at
the
low
least
one
Congress preceded the end of the Civil War.
further noteworthy
is
It
that
preponderance of
pair in the correlation in Congresses 14 to IS),
period around 1850.
for
and,
in the
where two solid
but simply cases of bad
fit where there is not a strong first dimension in some Congress.
geometric means below 0.5 for the House occur in Congresses
14,
24
(The only
15,
and
17,
Congress 17 has the lowest geometric mean for the 99 Senates.
32;
Subsequent to the Civil War,
(1909-1910),
the years
House 77 (1941-42),
the
end
and Senate 69,
correlation below 0.8
of Reconstruction,
Thus,
House 61
We note that none
(1925-26).
involve either the "realignments"
in question
the Great Depression.
there is only a t+1
which preceded
(1875-76),
for House 44
of
least one
(at
the House,
These cases are not spatial flip-flops,
major dimensions bear little relation to one another,
correlations
low
the
in the Era of Good Feelings
for both Houses of Congress,
fall,
a
of
the
1890' s
or
the realignments were not shifts in the space but
mainly changes in the center of gravity along an existing dimension. The first
dimension is remarkably stable;
the 40'
3.
s,
50' s,
Individual
and 60'
s
the
stability persists through the period in
when a second dimension was also important.
Stability and Reputations.
It
is
possible
correlations when individuals are moving in the space.
time
t
all had nearly equal trend coefficients,
highly correlated even
later than
if
they were
25
obtain
high
members serving at
their coordinates would remain
moving relative
t.
If
to
to
individuals elected
To assess
legislator
we
stability of
the
computed
individual
movement
annual
the
coefficients in our two dimensional,
movements
the
individual
whether an
implied
in
by
relative
in
space,
the
estimated
is
moving relative
trend
The
to
trend
Given that the space
linear estimation.
terms.
for each
the
identified only up to translations and rotations,
we estimate is
interpret
positions
one has
coefficient
legislators whose
tells
to
us
careers have
overlapped the individual's.
25
Average trends for each Congress are shown in Figure
The
6.
reports results only for legislators serving in at least 5 Congresses
a decade
— roughly
Similar curves for legislators with shorter careers would
or more.
systematically
appear
figure
above
those
plotted
in
figure.
the
annual
Thus,
movement decreases with the total length of service.
Figure 6 about here.
Two hypotheses are consistent with this observation.
legislators
legislators;
v/ith
abbreviated
of
service
tend
to
unsuccessful
be
their movement may reflect attempts to match up better with the
interests of constituents.
before Congress
— such
spatial
On the other,
short run changes in the key issues
as the Vietnam War or the current
trade gap
— may
position resembling an autoregressive random walk.
result
In
this
the estimate of the magnitude of true trend will be biased upward,
with
in the
case,
periods
On the one hand,
greater bias for shorter service periods.
Another
spatial
Figure
likely
period,
result,
movement
6.
in
is
one
we
see
limited for
as
more
important
legislators with
than
long
the
careers,
finding
that
shown
is
in
Prior to the Civil War there is a choppy pattern in the figure, most
part
a
consequence of
the
smaller
number
of
legislators
in
this
both in terms of the size of Congress and of the fraction of Congress
serving long terms.
The key result
occurs after the Civil War.
It
can be
seen that spatial movement, which was never very large relative to the span of
26
the
been
has
space,
in
secular
except
decline,
upturns
for
Since World War
realignment and the realignment following the Depression.
II,
individual movement has been virtually non-existent.
Wayne Morse
by
party defections
27
(The visibility of
proves
Thurmond
Strom
and
1890* s
the
in
rule.
the
An
)
immediate implication of this result is that changes in Congressional voting
of retiring
patterns occur almost entirely through the process of replacement
or defeated legislators with new blood.
28
Congress as a whole may adapt by,
Of course,
important than adaptation.
moving to protectionism when jobs are
example,
reputation
choose
changes
to
While
issues,
in
constituency,
their
to
mobility is likely to reflect
American politics.
adapt
to
relevant
in
spatial
lack of
foreign competition.
to
stable voting alignments.
be consistent with the preexisting,
current
lost
on
on
incomes,
demographics,
the
oiher
the
voters
Therefore
will
predictability
value
process
politician faces
a
[Bernhardt
of
of
might
that
etc.
are
adaptation may
In turn,
Ingberman
and
between maintaining
tradeoff
a
role
the
politicians
hand
one
the
result in voters believing the politician is less predictable.
averse
for
their cutting lines will typically
But as such new items move onto the agenda,
The
selection is far more
Politically,
risk
(19S5)].
established
an
reputation and taking a position that is closer to the current demands of the
Politicians also may find a reputation useful
constituency.
campaign
contributors.
demands,
increased
mixture
Some
incentives
to
reduced
of
maintain
a
change
reputation
in
and,
cultivating
in
constituency
perhaps,
other
factors are manifested by the reduced spatial mobility cf legislators.
IV.
Since
What is Not Stable
Civil
the
remarkably stable.
mapped
onto
political
a
War,
Issues
generalized
events
as
the
asid
Unidimensional: North amd South
American
have
politics,
in
spatial
largely been dealt with
liberal-conservative
"realignments"
27
of
the
dimension.
1890' s
and
has
terms,
in
of
being
such
major
terms
Zven
1930' s
been
have
been
s
accommodated in this manner (Figure
changed their positions to
During the realignments,
5).
somewhat greater extent
a
legislators
than usual
(Figure 6),
but the changes were largely ones of movement within the existing space.
over
time,
movement during the 30'
with,
for
realignment than during the 90"
s
into the
that has not fit
fits
restricted,
more
lesser
example,
s.
South" or perhaps "Race" may be used to label the major issue
"North vs.
model
become
has
movement
And
well
prior
to
liberal-conservative mapping.
Civil
the
War,
the
fit
While at times
less
is
pervasive.
the
The
conflict over the extension of slavery to the territories produced the chaos
in
voting
throughout,
the
in
lS50s.
the
In
20th
while
century,
voting
second dimension becomes important in the 1940'
a
is
50' s
s,
when the race issue reappeared as a conflict over civil rights,
with respect
to
rights
civil
racial
issue,
desegregation and voting rights
rather
than
fully
destabilizing
and 50'
s,
particularly
South.
The
system,
was
the
in
spatial
the
accommodated by making the system two dimensional.
To
this
point,
however,
analysis
our
has
We have only noted anomalies in the fits
directly.
categories
helped
somewhat,
but
Clausen's
in periods
However,
Liberties
Civil
Domestic Social Policy codes cover many non-race
speech and the Hatch Act.
the
race
issue
when race is
Results based on the Clausen and Peltzman
thought to have been a key issue.
all roll
examined
not
issues
and
such as
Peltzman'
freedom of
we have our own more detailed coding of
calls in terms of substantive issues.
There is a specific code for
Slavery and another for Civil Rights votes that mainly concern blacks rather
than other groups of individuals.
The
analysis for these
issues
is
contained
in
Table
6,
which provides
results for all Houses that had at least 5 roll calls coded for the topic.
The
like
first
appearance of slavery is
in
1809-10.
many that do not have a sustained appearance on
28
The
the
— we suspect
agenda — does not
issue
even
scale well,
the
fit,
in
16th Houses.
15th and
and disappears for over a decade,
two dimensions,
Although
these Houses
quite poor
are
until
overall
in
the slavery votes fit quite nicely along the first dimension.
Table 6 about here.
slavery votes in every House.
within
accommodated
From the late 1S30'
s
through 1846,
by
structure
spatial
the
substantial numbers of
there are
From the 23rd through the 3Sth House,
second
a
dimension.
The destabilization of
Classifications and PREs are high during this period.
the issue begins in 1847 and continues through 1852,
slavery is
period centered on the
a
There is a substantial reduction in the ability of the
Compromise of 1850.
spatial model to capture slavery votes.
number of slavery roll
A
temporary reduction in the actual
testifies to the difficulty of dealing
calls perhaps
with the issue.
The issue in fact could not be accommodated by the existing party system.
"Free Soilers" and "States Rights" adherents appear in Congress in increasing
numbers
in
early
the
1850' s
and
the
elections
of
mark
1856
virtual
the
completion of the process of the replacement of Whigs by Republicans.
As
the
party
system changed,
true
spatial
realignirient
From
occurred.
1853-54 onward, when the Kansas-Nebraska Act was passed,
slavery votes fit the
exceptionally well on the first dimension
in
model
when "slavery"
defined
this
.
Particularly,
represented a quarter of all roll calls,
dimension.
First
dimension
1853-54,
slavery most
classifications
and
likely
PREs
are
remarkably high.
The
North-South conflict persists
on
the
dimension via
"Civil
Rights"
votes from the Civil War through the 43rd House,
1873-74.
PREs remain high.
is suggested by the fact that
(The alternative label "race"
Classifications and
roll calls in the category "Nullification/Secession/Reconstruction"
up on the first dimension, but with somewhat lower
29
P?.Es
also line
than "Civil Rights".]
"Civil Rights" votes occur only sporadically.
From 1875 through 1940,
with
line
contention
our
realignment,
"race"
that
the
is
major
determinant
In
spatial
of
this period is stable and largely unidimensional.
reappears on the agenda in 1941-42.
"Civil Rights"
For the next
thirty
years it remains as an issue where the second dimension is always important.
Through 1971-72,
the
Indeed,
PRE.
the two dimensional scaling always adds at
dimension
first
several one dimensional PREs in Table
the
often
is
"orthogonal"
second dimension increased PRE by over 0.5.
detailed
coding
produced
issues
of
least five votes in a Congress,
other time in the 99 Houses
978
the
Rights;
In five instances,
Despite
occurrences
10 to
0.
Civil
to
are close to zero.
5
least
issue
of
fact
the
that
our
with at
codes
PRE improvement over 0.5 occurred only one
a
— Public
Works in 1841-42.
The pattern of PRE improvements is echoed by Figure
5;
the period from
roughly 1941-42 to 1969-70 is the only period where the two dimensional model
consistently and rather substantially out performs the other two models.
the second dimension curve
fact,
the Senate during this period,
(i)
is even further
s,
had
for
unlike slavery votes
In the House,
"Civil Rights" votes were never a substantial fraction of the
votes before Congress.
debate
(iii)
reflecting in part the many cloture votes the
Senate took on civil rights filibusters.
in the 1850'
above that of
In
shifted
The debate was contained.
from
one
of
changing
the
By the 1970'
status
s
and SO' s the
southern blacks
of
to
measures that would have a national impact on civil rights.
Correspondingly,
although
97th
civil
rights
votes
occur
in
the
93rd,
and
95th,
House,
the
second dimension no longer makes a major contribution.
The accommodation of
traced
out,
for
the
the
Senate,
Roosevelt's administration,
civil
in
rights
Figure
7.
issue
At
to
the
the political
inception
system is
of
race was not an important political issue,
primary concern of southern Democrats remained the South'
30
s
Franklin
and the
economic dependence
on Northern capital.
random sample of
southern Democrats appeared
result,
As a
Democrats or,
all
they were
extent
the
to
they represented the liberal wing of the party (Figure 7A).
of
issue
race
the
intensified in
the
rights was
when civil
dominant
the
differentiated,
As the importance
southern Democrats began
1940s,
differentiated from northern members of the party
1960s,
largely as a
(Figure 7B).
By
to
mid
the
item on the congressional
be
agenda,
southern Democrats had separated nearly completely (Figure 7C) and there was a
virtual three party system.
In
these years,
call votes on civil
roll
issues tended to have cutting lines parallel to the horizontal axis,
southerners,
at
Republicans,
to
increasingly
large
top
of
rest
of
the
the
numbers
Senate.
the
of
and
public
In
registered
gradually took on the national party's
minorities
employees.
and
picture,
the
29
later
black
role
of
few
a
highly
years,
opposing
conservative
confronted
southern
voters,
rights
with
Democrats
representing such groups
as
differentiation
of
Consequently,
the
southern from northern Democrats decreased (Figure 7D).
Figure 7 about here
the whole,
On
changes
in
the
the
process we
membership of
the
have
traced
out
occurred largely through
southern Democrat delegation
in
Congress.
Those who entered before the passage of key legislation in the 19d0s tended to
locate
in more
conservative positions
changes by southern Democrats have
than
those who
resulted in the
31
entered after.
19S0' s
being not
The
only a
period in which spatial mobility is low but also one which is nearly spatially
unidimensional.
V.
The
model
great
Predictions from the Spatial Model
stability
can be used
for
of
individual
positions
short-term forecasting.
vote on Judge Bork in 19S7.
To
The spatial positions,
from model (iii) estimation with only 19S5 data used.
31
ir.plies
that
illustrate,
sho-.^Ti
spatial
the
consider
in Figure
8
the
result
)
Figure
8
about here.
the five most liberal members
Quite early on in the confirmation process,
of the Judiciary Committee came out in opposition to Bork,
and the five most
The last four members of the committee to
conservative members supported him.
a finding parallel
take a public stance were between these two groups,
to our
earlier result that "errors" tend to occur close to cutting lines.
As
soon
as
Arlen
possible to predict,
since
against,
than Specter.
support
for
Specter
accurately,
remaining
the
At this time,
Bork,
one
made
(R-PA)
that
the
known
final
his
opposition,
it
was
committee vote would be 9-5
three undecided members were
all
more
liberal
using the fact that Grassley (R-IA) had announced
could predict
a
final
vote
Senate
of
59-41
against.
(The four senators between Specter and Grassley on the scale were predicted to
split 2-2,
In
Figure
senators elected since 1985 were predicted to vote on party lines.
8,
we
present
information
some
announcements as well as the final vote.
moderates-. tended
58-42.
to
on
Note that,
announce relatively late.
At the individual level,
of 93 of 100 senators.
the
temporal
ordering
of
echoing the committee,
The actual
final
vote was
the spatial model correctly forecast the vote
As was the case with Figure
2,
the errors tend to be
close to the cutting line.
VI.
Consensus
Conclusion:
sind
Impasse
Although the spatial model has an applied use in short-term prediction,
its greater relevance is in what
political system.
two
it
indicates about long-term changes in our
The average distance between legislators within each of our
major parties has remained remarkably constant
(Figure 9).
for more
than a
century
The maintenance of party coalitions apparently puts considerable
constraint on the extent of internal party dissent.
Figure
9
about here.
32
contrast,
In
the average distance between
legislators
the average distance between all
past
100
years.
33
The
the parties
— has
— and
by inference
shrunk considerably in the
between Edward Kennedy and Jesse
conflict
Helms
is
undoubtedly narrower than that which existed between William Jennings Bryan's
Symptomatic of the reduced range of conflict is
allies and the Robber Barons.
the willingness of most corporate political action committees to spread their
campaign contributions across the entire space,
the southwest quadrant excepted.
persists and although
liberals
within each party (Figure 7D),
sharply reduced.
34
and
Although,
a
the most liberal Democrats in
well-defined two party system
conservatives maintain stable alignments
the range of potential policy change has been
While our earlier contention (Poole and Rosenthal 1984) that
polarization increased in the 1970s is supported by Figure
more
relevant
consensus
special
the
pattern has been
can perhaps
best
be
toward
seen
in
a
national
of
the
nation
befall various groups of citizens.
recalling
the
Civil
War and
the
to
address
space,
period of
intense
fragility of democracy in some other nations.
of
concessions
to
and defense and
in
conflict
absorb
is
Revolution,"
indefinitely."^
33
surrounding
We do not pass
as manifest by
"Reagan
inequities
that
the
and by observing the
simply point to a regularity in a system that,
supposed
The
The benefits are perhaps made apparent by
labor movement in the late 19th and early 20ih centuries,
the
long-term,
cost
variety of
a
the
consensus.
alleged wasteful
the
interests in such programs as agriculture,
alleged failure
9,
likely
to
judgment but
its ability to
be
with
us
Appendix
The Estimation Algorithm
The algorithm employed to estimate the model simply extends the procedure
developed in detail in Poole and Rosenthal
restricted to unidimensional
,
(1985).
The
constant coordinates.
Here
earlier
briefly
we
was
model
sketch
the new procedure, D-NO.'ilNATE, with emphasis on modifications needed to handle
the more general model.
the procedure begins by using a starting value for ^ and a set
As before,
of starting values for the senator
coefficients are initially
set
parameters
polynomial
other
(The
.
These
zero.)
to
x^
obtained
are
by
metric
similarities scaling (Torgerson 1958; Poole 1990).
For the metric scaling, an agreement score is formed
legislators with
period
corr:on
a
cf
The
ser'v'ice.
percentage of tires they voted on the same side.
score
is
that
the
to
100
metric \infolding scaling in Poole and Daniels (1985).
The
subject
were
matrix
of
sii::ply
Scores var}' from
ratings
and thus are analogous to the interest group
pair
each
for
to
these
of
scores is converted into squared distances by subtracting each score from 100,
by
dividing
50,
and
squaring.
double-centered (the row and
is added,
col'^imn
The
matrix
are extracted from the cross product matrix
scaling procedure.
D-NO.'ilN.-.TE
common
distances
means are subtracted, and the matrix
product
to produce a cress
to each element)
squared
of
and
used
This procedure produces the starts fcr
mean
Eigenvectors
matrix.
start
to
the
metric
D-NO.'IIN.-.TE.
proceeds from the starts by using an alternating algorithim
procedure
in
psychocetrics)
coordinates are estimated on
the
coordinates and 5 constant.
Since
.
first
roll
In
a
first
dimension,
call
is
(a
stage,
the
roll
holding
the
legislator
coordinates
are
call
independent
across roll calls (for fixed S and legislator coordinates), each roll call can
be estimated separately.
In a second stage,
the
legislator
coordinates
are
2
estimated on the first dimension,
everything
holding
again
Because each legislator's choice depends only upon his
else
distances-
ovti
roll call outcomes, if ^ and the roll call alternatives are held
legislator's
choice
independent
is
of
those
of
higher
These two stages are then repeated for each
and
2
In
third
a
constant
values. Within each stage, we use the method of Berndt et al
.
all
Global
x
(1974)
parameters.
the
three stages define a global iteration of D-NOMINATE.
each
separately.
dimension.
obtain (conditional) maximum likelihood estimates of
the
legislators.
coordinate
stage, we estimate the utility function parameter p, holding
to
fixed,
other
all
legislator's
Independence allows us to estimate each
constant.
to
These
iterations
are
repeated until both the x's and the z's correlate above 0.99 with their values
at the end of the previous global iteration.
Constraints
In Poole and Rosenthal (1985) we explain in detail
underlying model presented in Part
X and z values can
magnitudes.
run
amok,
I
the
accurately represents behavior, estimated
taking
on
values
with
exceptionally
The problem is basically an identification problem.
large
Legislators
vote
who are highly liberal, for example, will tend to almost always
liberal side of an issue.
when
even
w-hy,
on
the
As there is thus not enough information to pin down
a precise location for these legislators,
their
The problem should net be exaggerated, however.
estimates
constrained.
are
Ve still knew, reliably, that
the individual is an extremist in the direction of the constrained estimate.
Similarly,
it is hard to pin down the location of a
where almost everyone votes on the same sice of the issue.
"Hurrah"
vote,
one
included
such
lopsided votes because, noisy as they are, they provide some information
that
helps us to differentiate legislators at the extremes of the space.
Ve
only
excluded roll calls that failed to have at least 2.5 percent of the vote
cast
for the minority side.
We
This cutoff rule reflects experimentation
A-
(Poole
and
3
Rosenthal 1985) with one dimensional esrimacion
resources to such
not
elected
alternative cutoff rules, but ve
1979-80
the
might
algorithm
dynamic
multidimensional,
better
of
result
A
exploring
from
allocate
to
Senate.
scarce
computer
a study.
accentuated
Identification problems are
by
error implicit in the assumption of a homoscedastic
some roll calls are highly
logit
will
D-NOMINATE
noisy.
obvious
the
specification
error.
try
to
In
fact,
arrange
their
cutting lines so that all legislators are predicted to vote vith the majority;
this vill cause the cutting line (and at least one z)
space spanned by the legislators and invoke a
drift
to
constraint.
outside
Conversely,
roll calls are noiseless, representing perfect spatial voting.
cutting line is precisely identified,
z.axiTrrjj^
Although
likelihood vill try to put
the
some
the
both
z's at a very large distance fron the legislators.
To deal vith these
identification
proble-s
constraints
,
unconstrained x estinates have been obtained on
are
imposed.
diinension,
the iLaMicjia
define
constraint
For each legislator, ve then define a constraining ellipse by
computing,
.After
and rcininuit coordinates for
Congress
each
are
used
a
to
coordinates:
-ay.
-or k-1
i-.k
y
anc zne origin aerine an ellipse.
X
ik
vhere T
2s 1/2
nin X
ilk
s
^
.ne X,
X
^
r.e
tnen conipute ror k-1,
I
- [tli is in the estiraticn in Congress t] and n
A-
-
T.
,
the
nuiaber
4
of Congresses served in by
Thus, averages
i.
over
taken
being
are
Congresses
all
for
which
the
in
the
Ik-
If the point defined
legislator was in the data set.
interior of
the
Otherwise, the parameters
and
x
estimated are set to zero and x
the ellipse.
In other words,
a
is
is
is
unconstrained.
being
currently
constrained to keep the legislator inside
legislator is not allowed
from the origin relative to others who overlap
Note that, unless T
x
is
dimension
the
on
x
the
legislator
the
ellipse,
legislator's
by
identical for all
i,
his
drift
to
her
or
too
service
the entire configuration
far
period.
not
is
constrained to the same ellipse.
A similar constraint is
Congress, we use the x
imposed
and the origin to
call cidpoint, defined by coordinates (z
j
the roll call is unconstrained.
roll
the
in
yk
Otherwise,
call
phase.
define an ellipse.
+2
j
nk
)/2,
If
roll
the
is inside the
coordinate
the
each
For
ellipse,
currently
being
estitiated is adjusted to keep the nidpoint within the ellipse.
Table A-1 about here
In the actual estimation, constraints were invoked for 4.2 percent of the
legislators in the two dimer-sional, linear House estication.
A check
of
the
estiiiates in the postwar period shows that
legislators
are
overwhelmingly known "extremists."
More
the
constrained
constraints
are
calls, where 14.1 percent are constrained.
However, breaking
calls by margin and by time period in Table
.A-1
lopsided roll calls.
scholars will be unconstrained.
roll
down
the
roll
First,
it is clear that,
constraints are most often invoked for
Constraints are invoked in under
calls that are closer than 55-45.
for
shows that the problem is less
serious than indicated by this aggregate percentage.
as argued above on theoretical grounds,
needed
Almost
all
roll
1
percent of
calls
of
interest
In contrast, constraints are needed
A-
the
on
roll
to
more
5
than half of the most lopsided votes.
Second,
controlling
fraction constrained is less beginning with the
margin,
for
Congress
76th
than
before.
period
modern
The larger overall proportion of constrained roll calls in the
the
simply reflects an increase in the relative number of lopsided "Hurrah" votes.
Standard Errors
The use of constraints im.plies that conventional procedures for computing
standard errors do not
apply.
problem
Another
with
standard
the
errors
produced by the D-NO.MINATE program is that they are based only upon a
of the covariance matrix.
the linear dynamic model comes, for exam.ple,
2
by
2
legislator
A standard error for a
outer product matrix computed vhen
portion
coefficient
solely from the inversion of
the
coordinates
are
the
legislator's
phase
estimated for a given dimension in the legislator
of
alternating
the
algorithm. The appropriate procedure would be to compute, at convergence,
estimated information ziatrix for all parameters and invert.
is impractical,
even on supercomputers.
in
Vith
the
computation
This
models
d}-r.aziic
the
covering
1789-1985, the matrices would be larger than 100,000 by 100,000.
Table k-2 about here
For the reasons outlined above,
the standard errors reported in the
must be viewed as heuristic descriptive statistics.
handle
To get a
on
text
the
reliability of the reported errors, we applied Ifron's (1979) bootstrap method
to estimate the standard errors cf the
(iii) estimation of the 94th Senate.
legislator
Tr.at is,
calls and drew 50 samples cf 1311 roll calls.
coordinates
we took the
fcr
a
actual
1311
model
roll
Each roll call was sampled with
replacement, so, in any particular sample, some actual
roll
appear while others will appear more than once.
D-NO.'^.IK.i.TE
Ve ran
calls
will
nor
for each of
the 50 samples and then computed the standard deviation cf
the
50
estimates
fcr each senator.
largest
bootstrap
The results appear in Table
A-
.-.-2.
Tr.e
6
.
standard error is 0.051, and 73 of 100 senators have bootstrap standard errors
under 0.03.
precisely
Since the space has a range of
apply
not
did
We
estimated.
multidimensional or dynamic estimation as
However,
time.
the senator locations are
units,
2
bootstrap
the
matter
a
economizing
of
at least in one dimension,
it is clear,
method
computer
that the dynamic model
estimates will be even more precise than those reported in Table A- 2.
because, typically,
three or more Senates,
to
This is
rather than one, have been used
to
estimate the location of a senator.
Consistency
In addition to
the
statistical
posed
problem
by
imposition
our
constraints, we have an additional problem that reflects the fact
Therefore,
we always have additional parameters to estim.ate as we add obser\*£tions
generates
what
is
known
econometrics literature.
is "incidental."
an
as
parameters"
"incidental
every
th^t
set of parameters.
legislator and every roil call has a specific
problem
.
in
In fact, every parameter we estimate, except for
As a result,
the
maximum likelihood does not apply.
"infinitely" many obser\'ations
,
proof
standard
Ve are
not
of
consistency
the
g'uaranteed
that,
even
maximum likelihood estimates will converge
the true values of the parameters.
of
At a practical level, this caveat is
This
the
^,
of
with
to
not
important. The key point is that data is being added at a far faster rate than
linear
dimensional
Assume
our
time
series were augmented by a new senate with 15 freshman senators and
500
roll
(ass'uming
they
parameters.
calls.
Consider the two
model.
we would eventually add 60 parameters for the senators
all acquired trend terms) and 2000 parameters for the roll calls.
these 2060 new parameters, we would have 50,000
The ratio of obser\'ations to
parameters
is
25
(100x500)
to
Representatives, a similar ratio would be over 100 to
A-
1.
1.
new
For
To estimate
obser^-ations
the
House
of
Ve suspect that many
7
errpirical papers published in professional social science
journals
have
had
far lower ratios.
problem
Haberman (1977) obtained analytical results on consistency for a
He treated the
closely related to ours.
subjects take
q
from
voting
In place of p legislators
testing literature.
model
Rasch
on
educational
the
q
roll
calls,
Each subject has an "ability" parameter and each
tests.
test
The role of "Yea" and "Nay" votes is played
has a "difficulty" parameter.
"correct" and "incorrect" answers.
A version of the Rasch model
Lord (1975) is in fact isomorphic with a one dimensional
by
analyzed
Euclidean
p
by
model
of
roll call voting developed by Ladha (1987).
Haberman considered increasing
which
a
•n
> p
~
n
.
In other words
->
integers
-
of
alwavs
the number of roll calls
,
}
for
exceeds
the
(c ),
"n
[v
n
In addition, make the (innocuous) technical ass-am.ption
number of legislators.
that log(a
)/v
° -n ' -n
secuences
as n
->
=.
L'ncer these
conditions,
Haberman
establishes
consistency for the R,asch model.
rev actual processes, including Congress, can be thought cf as satisfying
Haberman'
s
stringent requirement that p and
Haberman cites Monte Carlo studies by Vright
excellent recovery
for
between 20 and 80 and
q
conventional
of 500.
both
q
In D-NOMINATE,
m.odern Senate and i-35 in the modern House.
The
as
Douglas
and
maxim-um
grow
likelihood
n
grows.
But
that
show
(1576)
estimators
for
the effective p is 100 in
effective
c
is
about
p
the
900.
Similar .Monte Carlo evidence is contained in Lord (1975).
Another source cf comfort, in addition to the work en the P.asch model, is
provided by Poole and Spear (1990).
They proved, for a wide
distributions, that Poole's (1990) method of scaling
gives a consistent estimate cf the ordering of the
the modern period,
class
interest
legislators.
error
of
group
ratings
Since,
for
interest group scaling and D-NOMIKATE give similar results,
A-
it is likely chat D-NOMINATE also gives a consistent ordering.
Nonetheless,
model
D-NOMINATE
the
individual
uses
whereas the Poole (1990) method scales distances.
utility
unlike
is,
parameters.
in
the
Rasch
model,
D-NOMINATE
the
In
Thus, while the theoretical work of Haberman 1977 and
Spear 1990 and
previous
the
results
Carlo
Monte
model,
function
non- linear
a
directly
choices
of
the
Poole
and
suggestive,
are
it
is
appropriate to conduct direct Monte Carlo tests of our algorithm.
Monte Carlo Results
Previously, in Poole and
Summary of Previous Experiments.
dimensional
we reported on extensive .Monte Carlo studies of the one
algorithm.
estimated
(1987),
NOMINA.TE
senator
coordinates
We used a wide variety of
alternative
As "true" locations, we used
from a scaling of 297 1979 roll calls.
Rosenthal
the
sets of "true" roll call coordinates and used alternative "true" values
between 7.5 and 22.5.
recovered legislator
Over all runs, the
coordinates
and
the
correlations
squared
true
exceeded
ones
standard error of recovery of individual coordinates (the
of
between
the
0.98.
The
variability
Monte Carlo runs) was on the order of 0.05 relative to a space of
^
across
width
2.0.
Recovered ^'s are slightly higher than the true,
r.ecovery canie closer to
the
true value as the
increased.
one
number
of
obser\'aticns
was
dimensional estimates are highly accurate under the maintained
the model.
Moreover, as most cf the discussion in the
our
Thus,
paper
based on summaries of parameter estimates (for example. Figure
hypothesis
of
essentially
is
6
uses
^
to
average
distances), statistical significance would not be an issue.
Ve also did the
generating data with a
counterfactual
random
coin
experiment
toss.
The
of
setting
recovered
zero
by
distribution
cf
'
legislators was far more tightly unimocal than any recovered from actual data.
More importantly, the geometric mean probability was
A-8
only
0.507,
far
lower
9
than almost all values reported in Figure
5.
An Extensive Tesz of the Static Model in One and Two Dimensions
The vork
.
we
have just suimnarized was done under the assumption that the data was generated
by a true one dimensional world with a constant signal-to-noise ratio, p.
subsequently undertook
work
additional
that
D-NOMINATE with a true two dimensional world.
examines
In
performance
the
addition,
"Congress".
one
"Senate"
of
We did not pursue simulations of the d^mamic model
how
All the work
hypothetical
a
of
studied
we
robust D-NOMINATE was to violation of the constant ^ assumption.
was done using the static model on
Ue
single
because
such
simulations are too costly in com.puter time.
To simulate a "Senate", we had 101 "senators" vote
A20
on
roll
calls.
Finding good recovery with only 420 roll calls should bode well for our actual
estimations, since, in the past
votes in their careers.
to generate the
Thus,
simulation ve drew 84,640 -
2
centuries, legislators have
t»-o
averaged
choices,
"obser'/ed"
(choices) x 420 (roll calls)
x
101
909
each
in
(senators)
random numbers from the log of the inverse exponential distribution.
In each simulated Senate, we crew
fro2
Thus,
[-1,-i-l].
of length two;
senators'
the
coordinates
uniformly
in one dimension the senators were distributed en a
in two dimensions, on a square of width two.
line
Midpoints of roll
calls followed the same distribution.
In our simulation design, one comparison was a
vs.
/5,
a tr'je two dimensional world.
Vhen zhe variable
1/P uniformly from [.043,.125j.
23.26].
p
cr.e
A second was comparing
set equal to 15.75 to match t\-pical
variable ^.
tr-je
estimates
from
a
dimensional vcrld
world with a fixed
actual
model was used, for each roll
Tne p's were
The median of the distribution of the
third design factor was low vs. hi^h error
A-
thus
in
random
rates.
The
the
^'s
and
data,
call
was
error
drew
we
inte—.-al
[8.13,
15.75.
rate
a
is
The
the
.
percentage of choices that are for the
alternative,
further
percentage of choices for which the stochastic
error
that
dominates
After the legislator positions,
the midpoints have been assigned,
the error rate can be controlled by
rate
the
in
Low
the_ ^s
smaller
condition
close
to
about
14%,
the error rate was set to 30%,
above that
average
keep
the
level
the
classification error attained by D-NOMINATE with the Congressional
the High condition,
and
,
scaling
the
Scale factors were chosen to
distance, the greater the error rate.
average
The
spatial
the
portion of the utility function.
the distance between the "Yea" and "Nay" outcomes.
the
is,
of
data.
for
In
worst
the
Congresses in our actual scalings.
Our design yielded 8-2x2x2 conditions.
following sources of randomization:
(2)
condition,
We emphasize that each
simulations, for a total of 200.
roll calls;
each
In
(1)
utility of each choice;
25
had
the
legislators
and
simulation
spatial locations of
(3)
ran
we
variable
^ for each roll call (in
B condition only)
We computed two sets of statistics to assess the recovery by
D-NOMINATE.
First, we computed the 5C30 distances representing all distinct pairs
101 legislators.
For every one of the 200 simulations, ve did this
the "true" distances and the "recovered" distances.
Since
eliminates
all the information in the scaling.
arbitrary
recovered spaces
rotational
and
scale
time.
a
both
for
work
distances
Focusing on distances not
between
differences
but also reduces assessment to a
than looking at one dimension at
the
substantive
using the scaling will depend only on relative position in a space,
sujTJT.arize
of
single
Second,
we
only
true
criterion,
and
rather
cross -tabulated
the
"Yea-Nay" -predictions from the scaling with the "Y"ea-Nay" predictions from the
"true" spatial representation.
fit.
Comparing
simulated
The percent of matches is a
predicted
to
A- 10
"true"
predicted
good
is
measure
better
of
than
comparing simulated predicted to "true" actual because the scaling is designed
to recover the systematic,
spatial aspect of voting, not the
want to know how well D-NOMINATE scaling noisy data would
errors.
predict
So
we
voting
if
the noise were removed.
The
results
simulation
observation
is
Table
in
immediate
An
A- 3.
that the two dimensional world is not recovered as well as
one dimensional world.
is
presented
are
The number of
This is to be expected.
the
"observations"
identical in every design condition, but the parameter space is doubled
in
moving to two dimensions.
r
ITable A-3 aoout here.
Tne first column of the table shows
correlate with the "true".
]
well
how
recovered
the
distances
It can be seen that D-NOMIKATE is very robust with
Recovery
respect to variability in noise across roll calls.
senators
of
totally insensitive to whether the "true" world has a fixed ^ across all
calls or one with considerable variability.
decline with dimensionality.
P,.aising the
On
other
the
hand,
error level forces only
fit
is
roll
does
icoderate
a
deterioration in fit.
To some degree, the lack of higher t:£asures
reflects the constraints in
cf
fit
a
single
dinensicn, this has no impact, but in f-o dimensicns
the last
column
correlations
cf
ber'-een
"Congress".
the
the
.A-5
to
recovered
the
first.
solutions.
The
In
seen
last
In
one
comparing
in
col-^mn
reports
dimension,
one
into
coordinates
""tr-je"
The impact cf the constraints can be
Table
diniensions
The constraints force estit^ates
D-N'0.'<INA7E.
an ellipse when estimation is restricted to
come from a square.
two
in
these
correlations are slightly less than the correlations cf the recovered with the
true distances.
In two dimensions, the pattern reverses.
.As
constraints tend to get invoked for the same senators in all
.-•: 1
the
distorting
recoveries,
the
recovered points, particularly at low error levels, tend to be very similar.
second
the
The impact of the constraints is also seen in
distances between senators are more precisely estimated,
when the error level
is high.
in
column.
two
dimensions,
With a high error level, legislators
voting
periphery of the space have some "noise" in their
(The higher
constraints are invoked less frequently.
estimates in two dimensional "High" as
compared
percentage
space,
ratios
so
the
and
the
of
precise
dimensional
reflects the fact that the average distance is greater in the two
space than in the one dimensional
near
patterns,
one
to
of
true
The
"High"
dimensional
distances
to
standard errors tend to be greater.)
Actual vote predictions are less sensitive to whether the constraints are
results
The third column of the table shows
invoked.
clearly indicate the high quality of the recovery.
that
appear
At a low level
most
to
of
error,
the implications for predictions of actual choices from the spatial codel
recovered
nearly identical between the true space and the
only a slight deterioration (94 percent vs. 96) when two
estimated.
The fit is still good, but
levels of error.
In all cases,
than
less
standard
the
space.
errors
There
is
iiust
be
diaensions
perfect,
are
at
are
high
(very)
extrenely
sn:all,
demonstrating that our simulation results are insensitive to the set of random
numbers drawn in any one of the 200 simulations.
Tests Usir.g
F.eal
Data S-t Wizh
?-ancozi Sta.r~ir.g
Coordir.aces
.
v^'e
have seen that
the D-NOMINATE algorithm reliably recovers a "true" spatial configuration.
Ve
also are guaranteed, were there no constrained parameters, that D-NOMIN.ATE
is
an ascending algorithm- -the likelihood
alternating procedure.
convex.
is
improved
at
every
Nonetheless, the likelihood function is
step
not
of
globally
Either the lack of global convexity or the constraints problem
result in the recovery being potentially sensitive
A- 12
to
the
starting
the
could
values.
Perhaps even (slightly) better recoveries would result if
procedure were used.
from the agreement
either
D-NOMINATE can break down
matrix
provide
poor
starts
different starting
a
and
eigenvectors
the
if
procedure
Poole's
sensitive to starts or if D-NOMINATE is sensitive to minor differences in
output from Poole's procedure.
the results we report are a
Thus,
is
the
joint
test
of the sensitivity of the two procedures.
The test we carried out was to scale the 85th House and the 100th
Senate
(not included in our 99 Congress dataset) replacing the agreement matrix
random coordinates as input to Poole's procedure.
generated uniformly on [-1,+1].
The coordinates were
and
Both the 85th House
estimated in one, two, and three dimensions,
with
again
Senate
100th
simulations
10
with
for
were
each
dimension.
Again we assessed fit by averaging the (A5) pair'-ise correlations between
the distances generated by the 10 simulations.
Ve also co-puted
percentage of agreement in predicted choices ever the
simulations.
identical.
'^5
the
average
ccmpariscns of the 10
The recoveries
are
virtually
The fits do become less stable as the dimensionality is
increased
The results appear in Table A-4.
but this reflects only the general statistical principle that adding
parameters can reduce the precision
estimation.
cf
parameters are also estimated in the simulations.)
(N.b.
Thus,
The
colinear
roll
call
the fit deteriorates
more rapidly fcr the House, since there were cnly
against 225 for the Senate.
Table
Tnese results show that
A.-4
about here.
D-NO.'ilK.-.TE
combined with Poole's
procedure performs well in the joint test we carried out.
are essential to accurate recovery of the space.
more dimensions,
D-NO.'^IK.ATE
metric
Ve stress that both
Particularly
with
does a better job of recovery than the
A-i.5
scaling
two
or
output
cf
metric scaling.
On the other hand, D-NOMINATE itself does very poorly
begins with random starts.
Uhile
scaling
metric
the
results
are
enough to allow D-NOMINATE to
accurate as D-NOMINATE, they are good
if
it
not
as
converge
to a solution close to the true configuration.
The "Twist" Problem.
data,
The above experiment showed that with
our procedure is insensitive to
the
actual
In
starts.
"missing"
little
practice,
legislator votes on only a small slice of all roll calls in the history
"missing"
substantial
house of Congress, so there is very
in
modern
times,
membership
of
either
House
overlap in careers.
But when the
rapidly, the results become sensitive to the starts.
substantial
shifts
The problem is
With large amounts of missing
Poole's procedure provided poor starts to
D-NO.KIN.A.TE.
Our approach to this problem was to watch animated videos of the
when rapid movement induced a "twist" in the position
data,
scaling
senators,
of
ve investigated multiplying second diraension starts for certain years (in
nineteenth century only) by -1 --thereby flipping polarity.
very
greatest
for the House in the nineteenth century.
results,
a
"Kissing"
data.
data is not a problem as long as there is, as
of
a
the
Tne result was to
have a very slight improvement in the overall geometric mean
probability
and
to substantially reduce the magnitudes of estimated trend coefficients in
the
period in question.
In other words, when there is little overlap to
space together,
is
movement.
it
difficult
to
identify
the
parameters
tie
cf
spatial
The results reported in the paper reflect the highest gmps ve
been able to achieve; they also have lover trend coefficients
vith slightly lover gmps
.
(O'ur
use of changed
familiar vith our vork may see minor
those presented in conference papers.
starts
differences
than
explains
betveen
vhy
results
the
have
solutions
readers
here
and
Experiments vith different starts are a
standard procedure in the estimation of non- linear
14
maxim-j^m
likelihood models.)
NOTES
We thank John Londregan and Tom Romer for many helpful comments.
The estimation was performed
was supported in part by NSF grant SES-8310390.
on
Cyber 205s of
the
portions
Other
the
the
of
Our research
John Von
Neumann Center
analysis
were
at
carried
Princeton University.
out
at
Pittsburgh
the
Supercomputer Center.
The fact that roll call voting can be accounted for by a simple model
that
imply
not
does
complexities
strategic
all
Van Doren (1986) has stressed
mold.
calls
roll
conclusions.
have
In particular,
emphasized
that
Krehbiel
deal
great
a
fit
into
this
number of ways that focusing solely on
selection
"sample
induces
a
Congress
in
bias"
at
substantive
and Smith and Flathman
(19S5)
of
arriving
in
business
important
is
(1989)
handled
by
unanimous consent agreements or voice vote.
2
3
See Enelow and Hinich (1984) and Ordeshook (1986).
For a set of figures like those in Figure 2 covering all Congressional
Quarterly "key" Senate roll calls from 1945-85, see Poole and Rosenthal 1989b.
In addition,
the Jackson amendment
Poole and Rosenthal
post
The
Figure
The
7.
WII
split
and the Taft-Hartley,
is
treaty is analyzed in
1964 Civil Rights Act final
illustrated by
aptly
the
are
(19S9a).
panel
in
shown graphically
in
88th Senate
7.
Western Republicans, such as Borah (ID) and
and Frazier (ND) tend to be at the top of the figure along with the
two Progressives,
If
I
The postbellum Republican split continued into the
73rd Senate as shown in Figure
(ND)
1972 SALT
antebellum and postbellum divisions
Poole and Rosenthal 1989a.
Nye
the
and_ busing votes are analyzed in Poole and Rosenthal
passage,
4
(1988)
to
Lafollette (WI) and Norbeck (SD).
we were to allow every legislator to have trend parameters,
additional
parameters would be required for
smaller number
is
used
in
practice,
the
since no
trend
legislators serving in only one or two Congresses.
K-1
two
23,146
dimensional model.
A
estimated
for
term
is
tempted
One might be
generalize our model
to
to
coordinates cannot be identified simultaneously.
a
would
coordinate
small
equivalent
be
individuals
the weights and
However,
salience weights for each dimension.
allow
to
That
the Euclidean
weight
small
a
have
large weight and
a
is,
to
and
large
a
coordinate.
7
We
did
utility
make
not
distance
in
tenuous,
identified
(although senator
preserve
to
roll
the
locations and cutting
when data is generated,
in a Monte
Carlo experiment,
behavior that corresponds to our posited model,
outcome
coordinates.
In
the fact
empirically,
that,
call
lines
(/3).
roll
we are able
calls
are
recover
likely
This variation in error
make
for very noisy
estimation of
is
assuming
used
common
a
p,
we
still
estimates of legislator coordinates and cutting lines.
the
vary
to
level
and
outcome
the
form
used
the
in
quadratic
utility
utility
function.
specification
accurate
estimation
very robust
Ladha
and
obtain
Moreover,
legislator coordinates and of cutting lines may be
dimensional
to
When the Monte Carlo work generates the data with variable ^
D-NOMINATE
functional
by simulated
most distances are in the concave region of our
estimated utility function,
coordinates.
though,
practice,
substantially as to level of error
of
order
While identification that occurs via choice of functional form can be
are).
and
in
We did not use quadratic utility because
differentiability.
locations are not
linear
(19S7)
obtained
used
to
the
a
one
legislator
coordinates and cutting lines very similar to our one dimensional estimates
for recent Senates.
Ladha also shows
that
using a "probit"
rather than a
"logit" model for the errors makes little difference to the results.
up,
we believe we have a very robust procedure for recovery of legislature
coordinates and midpoints.
8
To sum
More details are available in the Appendix.
Southern Democrats are those from the eleven states
Kentucky,
and Oklahoma.
N-2
oi
the Confederacy,
We performed significance tests on our estimated roll
tested both
We
hypothesis that all
the null
roll
coordinates were zero
call
and the null hypothesis that the vote "split the parties."
To carry out
the
we began by estimating the legislator coordinates and p using sets of
tests,
that
calls
roll
coordinates.
call
eliminates
all
include
not
did
problems
statistical
the
vote
the
question.
in
discussed
the
in
procedure
This
Appendix.
The
Panama Canal Treaty vote was the 755th in our estimation for the 95th Senate.
we used the first 754 roll calls in that Senate to estimate the
For the test,
legislators and
last
896 votes
time
per
The NSF vote was the 70th in the 97th Senate.
fi.
in
significance
excluding
only
Senate.
that
the
we
test,
did
call
roll
avoid using
(To
rerun
not
The
configurations from these subsets of
calls
roll
those obtained from the dynamic estimation.)
supercomputer
of
dynamic
full
the
q-jesticn.
in
two hours
We used the
estimation
legislature
estirr.ated
virtually
are
identical
Treating P and the
to
estimated
x' s
we then used the roll call of interest
in this first step as fixed parameters,
to estimate the two-dimensional roll call coordinates.
The null hypothesis that all coordinates are zero implies that the "Yea"
and "Nay" outcomes occupy identical locations and thus that legislators flip
zero
are
eauivalent
is
the hypothesis that all coordinates
In other words,
fair coins on the vote.
to
more
the
hvpothesis
general
that
=
z
^~Z'-
z
Jnl
log-likelihood
the
is
simply
Jn2
Jy2
L(H )=N lnil/2)
where N
,
is
log-likelihood of
The
j.
h.>'oo thesis
null
Urkder__t±Le
.
and
z
Jyl
the
alternative,
the Panama Canal
For
D-NOMINATE.
the actual number voting or paired on roll
we
Treaty,
L(H
denoted,
L(H
find
)
),
=
call
computed by
is
L(K
-69.31,
)
=
a
2
-14.06.
d. f
(since
.
-22
10
Using the standard likelihood-ratio test, we obtain x =110.32 with 4
there
Similarly,
.
To test
created
a
Republicans
are
for the NSF vote,
the null hypothesis
pseudo-roll
call
Harry
3yrd
and
parameters
call
roll
4
in
we have
two
which
all
dimensions)
that
those
party-line
of
calculated
the
from
the
the
Democrats
We
"Nay".
coordinates
for
pseudo-roll
log-likelihoods
was
significant for 4 d.f..
N-3
p
<
then
the
Panama
call.
122.48
Tne
we first
the parties,
voted
estimated
Canal
the
(NSF)
chi-square
(170.74),
and
"Yea"
coordinates that maximized the log-likelihood for this roll call.
hypothesis was
and
x =110.24.
the vote split
that
vcted
in
2
again
all
outcome
The null
vote
were
statistic
extremely
1
that estimates of the legislator locations will not
however,
We can show,
be biased by strategic voting over binary amendment
286-284) in
1
a
12
(Ordeshook 1986,
complete information setting.
To save space,
we do not present a full
set of results for both houses
results are similar
Except where noted,
of Congress.
agendas
for
the
houses.
two
See the Appendix for discussion of why distances rather than coordinates
are analyzed when the analysis is not limited to unidimenslonal spaces.
13
It
is difficult
95th
the
foreign
Congress,
Intelligence,
or
Spying,
lower correlations on a specific item.
to pin these
and
on
11
Africa
South
Pensions or Veterans Benefits, 7 on the
on Arms Control,
14
policy
defense
Paiia.T.a
votes
or
included
Rhodesia,
Canal,
7
on
14
on
8
In
CIA,
Military
the B-1 Bcr.bsr,
cr.
5
and 5 on the United Nations.
Fits were not as good for the 49 votes in the Agriculture category, with
75 percent correct classifications in one dimension and 80 in two.
the small number of votes,
of
Because
Agriculture had to be placed in the Residual
category.
their hypothesis
Macdonald and Rabinowitz support
analysis
that
combines
our
model
results
(iii)
with
on
the
time
basis
series
of
of
an
state
returns in Congressional and Presidential elections.
Because
of
vast
the
amount
data
of
significance
involved,
statements made concerning Figure 5 would be of little value.
the
lowest
gmp for
biennial
our
scalings
Assume the null hypothesis were all
0.5.
Performing
approximation
that
a
v
Z-statistic of 63.78.
still be a hefty 9.65.
-v 2d.f.
-1
0.564
equal to
z' s
likelihood-ratio
2x
is
test
is
0,
for
normal
for
For example,
17th
scaling
that
for
large
d.f.
A^'ter
0.504 and 0.500 is of no substantive importance.
large number of observations,
we focus
significance.
N-4
on
yields
z' s
full dynamic model.
all,
the
a
To carry out the
appropriate likelihood-ratio test one would have to constrain the
would be a waste of computer resources.
using
the one dimensional
constant model is not very much better than 0.5 (gmp 0.504).
the
Congress.
the 2-statistic would
for the 17th Congress,
17th Congress only to be zero and reestimate
for
that is all probabilities
Even if the gmp was only 0.51,
Of course,
the
tests
the
for the
This
difference between
In general,
substance rather
given our very
than statistical
17
the close fit between the biennial scalings
Indeed,
In Figure 5 and
the
dynamic scaling shows that our results are not strongly influenced by the time
if we had scaled only the twentieth century,
For example,
period chosen.
the
results for that period would be almost identical to those obtained by scaling
all 99 Congresses together.
1
8
If
p
proportion of
the
is
given by H = Zp
2
H equals
.
1.0
category
in
the votes are
all
if
reach a minimum of
H would
Clausen categories,
the
calls
roll
index
the
a,
H
is
a
1/6
For
category.
in one
the
if
calls
roll
split evenly among the six categories.
19
note that every R reported
For descriptive purposes,
this paragraph
in
above 0.2 in magnitude is "significant" at 0.002 or better while those below
even at 0.1.
0.2 are not significant,
20
The
substantive
In particular,
filter.
analysis
the
is
not
are
results
sensitive
not
to
values
the
used
in
the
the 10 roll call requirement is sufficiently low that
affected by
lower
the
number
of
total
calls
roll
in
earlier years.
21
See Poole and Daniels
for similar conclusions based on interest
(19S5)
group scalings.
22
generally,
More
concentrated
geographically
are
redistribution
involve
that
issues
likely
not
to
captured
be
by
that
is
"spatial"
a
model.
23
There are no members common to the ist and 99th Congress and many other
pairs.
24
More
precisely,
correlation.
one
hypothesize
can
that
two
factors
will
affect
To capture fit,
One is that bad fits lower the correlatio.n.
the
we
created a variable that was the average of the two gmps for the Congresses in
the correlation.
The other is thai the correlation increases in time,
political system stabilizes,
the
5,
but
at
decreasing rate.
a
logarithm of the Congress number.
the
S
multiple
regressions
of
as the
This we measured as
Corresponding to the columns of Table
the
correlations
on
these
variables
all
showed coefficients with the expected signs.
T-statistics had p-levels below
0.005
fit
except
regressions.
0.25,
0.22,
for
the
coefficient
The R^ values were 0.33,
0.24,
on
the
0.29,
and 0.27 for the Senate.
K-5
0.20,
variable
in
the
two
t+4
and 0.24 for the House and
)
25
To obtain some
curves
in
the
D-NOMINATE
idea
of
used
we
figure,
standard
and
confidence
the
first
the
standard errors
Taylor
order
from
differ
produced
those
would
that
the
of
x
methods
series
bound
in
standard
a
MLE
setup
the
produced
by
estimate
to
As explained in the Appendix,
standard errors for the numbers plotted.
errors
intervals
these
because
the
standard errors for the x's are calculated without the full covariance matrix
For this reason,
and because D-NOMINATE uses heuristic constraints.
on non-parametric tests in the ensuing two footnotes.
Nonetheless,
we rely
our Monte
Carlo work suggests that the standard errors are reasonably accurate.
In the
the estimated standard errors are always below 0.0005 beginning in the
House,
5th House and below 0.0001 beginning in the 54th.
In the
15th Senate and 0.0001 with the S4th.
0.0005 begins with the
the average distance per year is always greater than 0.01.
reported in Figure
6
(smaller) Senate,
Thus,
In
contrast,
the numbers
would be precisely estimated even if the standard errors
on the x's were downwardly biased by a factor of
10!
We tested the proposition that mobility has decreased by carrying out a
non-parametric runs test (Mendenhall et
in
Figure
6
for
the
Congresses
50
al.
the
in
1985)
that compared the distances
nineteenth
alternative was less movement in the 20th century.
p=5xl0
—8
(In
).
this
(Z=4. S73,
later
and
with
the
43
The null hypothesis was no difference and the
Congresses in the 20th century.
rejected both for the Senate
century
p=5xl0
runs
)
tests,
The null hypothesis was
and for the House
we
use
the
(Z=5.293,
large
sample
approximation.
27
Runs tesis results comparing the first 22 Congresses in the twentieth
century with the 21 Congresses starting in 1945 reject the null h>'pothesis of
no difference under the alternative hypothesis of less movement since 1945.
For the Senate, we have 2=4.475, p=3xl0'^; for the House, 2=5.093,
28
Lott
(1987)
shows,
using
a
p=2xl0''''.
variety of interest group ratings,
that how
members of Congress vote is unrelated to whether or not they face reelection
or are planning to retire.
members of
the
House who
In addition,
Poole and Daniels
later are elected
change how they vote.
N-6
to
the
Senate
(1985)
also
show that
tend not
to
29
Cox and McCubblns
note
(1989)
far from the northern wing in the 1970'
their seniority violated.
reflect
the
Thus,
Southern Democrats who deviated
that
too
were punished in the House by having
s
the movement of Southern Democrats may also
internal dynamics of the majority party as well as constituency
changes.
30
provide
To
differentiation
of
statistical
backup
Northern
Southern Democrats,
To carry out
test.
the
and
(North-N
same
the
rank-ordered by distance,
and
concerning
carried
we
out
a
interpoint distance between
runs
the
opposite
or
statistic was
were
They
N-S.
calculated.
The
hypothesis was ihat there was no difference between same and opposite.
alternative was that opposite distances were greater than same.
p
<
p = 0.302,
Z = -0.52,
are:
8x10'^°,
88th;
p =
0.002,
The results
These results show that there
99th.
Although the runs for the 99th Senate are
less than expected by chance,
the null hypothesis D =
(Rqq" '^oq) ~
alternative hypothesis D
32
Tne
insignificant increase in differentiation from the 73rd to
decrease between the SSth and 99th.
31
null
a sharp increase from the 7Sth to the 88th and a substantial
the 78th Senate,
for Senate
then
73rd Senate; Z = -0.99, p = 0.161, 7Sth; Z= -17.65,
Z= -2.93,
was a very slight,
"significantly"
runs
Pairs were then tagged as to whether they
South-S)
or
statements
the
we calculated the
test,
each pair of Democratic senators.
were
for
with p
<
it
is
^^^-'''qo^'-^^co^
SxlO
<
^
also true that we reject
~
where R
,
using the one-tailed
'-'
is
the number of runs
t.
see Bullock (1981).
On this point,
Statistical
support
for
statement
this
furnished
is
by
a
McKelvey-Zavoina (1975) ordinal probit analysis where the dependent variable
l=Announced before Oct.
is coded
Oct.
on Oct.
2=Ajino'Linced
7,
7,
the regressors were a constant and the absolute value of the distance
7,
of the senator from the midpoint of Specter and Grassley,
the 72 non-committee members serving in 1985.
senator
chose
(60/72,
7/72,
an
two
distance
anno\incement
5/72)
the variance of
first
3=Aj:nounced after
The null hypothesis that each
according
to
was rejected with ?=5xl0'*.
set
to
0.
The
rejected with p=0.0019
null
and
second and third categories with p=0. 010.
of
the
As
to unity and
the probit was set
categories
was
date
the
is
a
zero
marginal
frequencies
standard procedure,
"cutpoint"
hypothesis
of
a
between the
zero
"cutpoint"
slope
between
on
the
The New York Times and Washing-ton
Pest were used as sources for the annoiincement dates.
N-7
and the sample was
33
As
with previous
precisely estimated.
figures,
numbers displayed
the
For example,
Figure
in
are
9
very
using the variance-covar iance matrices of
the estimated x coefficients for each legislator and Taylor series methods,
we
computed standard errors for the within party average distances shown in the
The
Z-statistic
estimate to the estimated standard error;
the minimum
(Previous
figure.
caveats
apply.
)
of
estimates,
the
differences
small
difference between the two within party distances.
more heterogeneous,
40,
48,
52,
53,
64,
75-99
(see
also
Because of the
graph will
When
be more heterogeneous than Democrats for some Congresses,
2.0 in these cases.
Z
often
be
the
Democrats
are
in Congresses 36,
Although the Republicans are estimated to
and 76-99.
66,
the
than 2.0 in magnitude
the Z is greater
the
we can directly compute a Z for the
For example,
"statistically significant".
in
of
(over 64 Congresses)
was 6.06 for House Democrats and 5.23 for House Republicans.
precision
ratio
the
is
the Z never exceeds
The greater heterogeneity of the Democrats in Congresses
Figure
reflects
7)
important
the
civil
rights
conflict.
Statistical significance is aided by the fact that our x's are more precise
for
these
years
as
a
result
of
longer
individual voting patterns
(Figure 6).
substantively
the
often
important,
periods
While
changes
in
of
service
and
heterogeneity are dwarfed
See Poole and Rosenthal 1989b.
For a similar substantive conclusion,
N-8
stable
statistically significant and
importance by the changes in the distance between the parties.
34
more
see Fiorina 1989,
141.
in
.
:
REFERENCES
"Candidate Reputation
Bernhardt, M. Daniel and Daniel E. Ingberman. 1985.
Public
27:A7-67.
Journal
of
Economics
and the Incumbency Effect."
Bronywn H. Hall, Robert E. Hall, and Jerry Hausman. 1974.
"Estimation and Inference in Nonlinear Structural Models." Annals of
Economic and Social Measurement 3/4:653-65.
Berndt, E.K.
,
"Congressional Voting and Mobilization of a
Bullock, Charles S. III. 1981.
Black Electorate in the South." Journal of Politics 43:553-82.
How Congressmen Decide
Clausen, Aage 1973.
St. Martin's.
.
A Policy Focus.
New York:
"The Nature of Belief Systems in Mass Publics."
Converse. Philip E. 1964.
Nev York: Free Press.
In Ideology and Discontent ed. David Apter ed.
,
Cox,
,
"Parties and Committees in the U.S.
Gary V. and Matthew D. McCubbins.
House of Representatives," manuscript. University of California, San
Diego.
Efron, Bradley. 1979.
"Bootstrap Methods: Another Look at the Jackknife."
Tne Annals of Statistics 7: 1-26.
Enelow, James and Melvin Hinich. 1984.
The Sratial Theory cf Voting
Cambridge: Cambridge University Press.
.
Congress Keystone of the Washington Establishmient
Fiorina, Morris. 1989.
New Haven: Y'ale University Press
:
Haberman, Shelby J. 1977.
"Maximum Likelihood Estimation
Response Models." The Annals of Statistics 5:815-41.
.
Exponential
in
Krehbiel, Keith. 1985.
"Unanimous Consent Agreements: Going Along in the
Senate." Journal of Politics 48:541-64.
Koford, Kenneth. 1989.
"Dimensions in Congressional Voting."
Political Science Review 83:949-962.
Ladha, Krishna K. 1987.
"Decision Making in the United
Congress." Ph.D. diss. Carnegie Mellon University.
Lord,
Ajnerican
States
F.M. 1975.
"Evaluation with A.rtificial Data cf a Procedure for
Estimating Ability
and
Item
Characteristic
Curve
Parameters.
Educational Testing Ser\'ice, Princeton, NJ P3-75-33.
Lott, John R.
"Political Cheating."
1987.
Public Choice 52:169-186.
Macdonald,
Stuart E.
and George Rabinowitz. 1987.
"Tne D}-namics of
Structural Realignment." A-merican Political Science Review 61:775-796.
k/pj^,T_
n
IOC'S
Econometrics
T
.
,-
.•
-
J
n-_,_^__- .^^
n.
1.-_,^,-
t-__.-.v,i.^
Cambridge: Cambridge University Press.
R-1
-•
_
"A Statistical Model for
McKelvey, Richard D. and William Zavoina. 1975.
Journal of
the Analysis of Ordinal Level Dependent Variables."
Mathematical Sociolor.v 4:103-20.
Mendenhall, William, Richard Scheaffer, and Dennis Wackersley. 1986.
Boston: Ducksbury.
Mathematical Statistics With Applications
.
"A Statistical Model for Legislative Roll Call
Morrison, Richard J. 1972.
Sociology 2:235-47.
Mathematical
of
Analysis." Journal
Ordeshook, Peter C. 1986. Game Theory and Political Theory
Cambridge University Press.
.
Cambridge:
"Constituent Interest and Congressional Voting."
Peltzman, Sam. 1984.
Journal of Law and Economics 27:181-200.
"Least Squares Metric, Unidimensional Scaling of
Poole, Keith T. 1990.
t^
T^cvc^o^^'^t'*"^'ka ^fcrthccmi'^P^
iva***
Mul t
i^
Li'^'^3.'^ ^ode'^s "
Poole, Keith T. and R. Steven Daniels. 1985.
"Ideology, Party, and Voting
1959-1980."
Ajr.erican
Political Science Review 79:
in the U.S. Congress
373-99.
Poole, Keith T. and Howard Rosenthal. 1984.
"The Polarization of American
Politics." Journal of Politics 46:1061-79.
"A Spatial Model
Keith T.
and Howard Rosenthal. 1985.
for
Legislative Roll Call Analysis." Ajnerican Journal of Political Science
29:357-84.
Poole,
Poole, Keith T. and Howard Rosenthal. 1987.
"Analysis of Congressional
Coalition Patterns: A Unidimensional Spatial Model." Legislative
Studies Quarterly 12:55-75.
Poole, Keith T. and Howard Rosenthal. 1988.
"Roll Call Voting in Congress
1789-1985: Spatial Models and the Historical Record."
In Science at the
John von Neumann National Supercomputer Center: Annual Research Report
Fiscal Year 1987
Princeton, N.J.: John von Neumann Center.
.
Poole, Keith T. and Howard Rosenthal. 1989a.
"Color A^nimation of Dynamic
Congressional Voting Models." Carnegie .Mellon University Working
Paper no. 64-88-89.
Poole, Keith T. and Howard Rosenthal.
VHS tape of Computer .Animations.
1989b.
"The D-NOMINATE Videos."
GSIA, Carnegie -Mellon University.
Poole, Keith T. and Stephen E. Spear. 1989.
"Statistical Properties of
Metric Unidimensional Scaling," Carnegie Mellon University working
Paper 88-89-94.
Smith, Steven
S. and Marcus Flathman. 1989.
Complex Unanimous Consent Agreements."
14:349-74.
Torgerson, W.
S.
1958.
"Managing the Senate Floor:
Legislative Studies Quarterly
rneorv and Methods of Scaling
R-2
.
New York:
Wiley.
Van Doren, Peter. 1986.
"The Limitations of Roll Call Vote Analysis: An
Analysis of Legislative Energy Proposals 19A5-1976." Presented at
the 1986 Annual Meeting of the American Political Science Association.
Weisberg, Herbert F. 1968.
"Dimensional Analysis of Legislative Roll
Calls."
Ph.D. diss. University of Michigan.
Wright, B.D. and G.A. Douglas. 1976. "Better Procedures for Sample-Free Item
Analysis." Research Memorandum No. 20, Statistical Laboratory, Department
of Education, University of Chicago.
R-3
Table
1.
Classification Percentages and Geometric Mean Probabilities
Senate
House
Number of
Dimensions
Number of
Dimensions
Degree of
Polynomial
(a)
1
Classification Percentage: All Scaled Votes
Constant
82.?''
84.4
Linear
83.0
85.2
Quadratic
83.1
Cubic
83.2
(b)
80.0
83.6
84.1
81.3
84.5
85.5
85.3
81.5
84.8
85.1
85.4
81.6
85.0
86.1
84.9
""
Classification Percentages: Votes With at Least 40% Minority
78.9
82.7
83.4
83.8
79.4
83.6
84.8
81.0
83.9
79.7
83.8
85.1
81.1
84.1
79.8
84.0
85.3
Constant
80.
Linear
80.9
Quadratic
-'''
Cubic
(c)
s''
82. 9
83.7
All Scaled Votes
Geometric Mean Probability:
.660
.692
.700
.709
.666
.704
.716
.684
.712
.668
.708
.721
.684
.714
.670
.70S
.725
Constant
.678
.696
Linear
.682
Quadratic
Cubic
.707
ihe percent of correct classifications on all roll calls that were included
in
the
scalings;
i.e.,
those
with at
least
2.5
percent
or
better
on
the
minority side.
The percent of correct classifications on all roll calls with at
least 40
percent or better on the minority side.
Higher polynomial models for 3 dimensions were not estimated because of
comouter time considerations.
Percent Correct Classifications,
Table 2.
One Dimensional Fit to S-Dimensional Space
"True"
House
Note.
Senate
"
Dimensionality
100.0
100.0
1°
78.9
78.9
Z''
74.8
74.7
3
73.2
-73.0
4
71.2
71.0
5
70.9
70.8
6
69.9
69.8
7
69.9
69.7
8
69.2
69.1
9
65.9
65.9
Majority Model
Legislators uniformly distributed on s-dimensonal sphere.
Roll call
lines distributed to reproduce marginals found in Congressional data.
Calculation based on closed form expression.
Table 3.
Interpoint Distance Correlations,
Clausen Category Scalings, 95th House
a
Category
UJ
[2)
[3]
U)_
(1)
Government Management
1.0
.914*
.796
.908
(2)
Social Welfare
.883''
1.0
.765
.881
(3)
Foreign and Defense Policy
.770
.654
1.0
.724
(4)
Miscellaneous Policy, Civil
iberties, & Agriculture
.832
.746
.613
1.0
Numbers above diagonal are correlations from one dimensional scalings.
Numbers below diagonal are correlations from two dimensional scalings.
Table
4.
Clausen Categories with 2nd Dimension PRE Increases at Least 0.1
PRE > 0.5
House CateR.
1
2
9
10
18
23
24
25
26
28
31
33
53
64
76
77
78
79
81
82
83
84
85
86
87
88
89
90
Mgt
Civil
Misc
F&D
Misc
F&D
Mgt
Mgt
Mgt
Civil
Civil
Civil
Civil
Civil
Mgt
Mgt
Welfr
Welfr
Civil
Civil
F&D
Civil
F&D
Welfr
Misc
Welfr
Civil
Misc
Welfr
Agr
F&D
Misc
Welfr
F&D
Welfr
Agr
«
PRExlOO
Votes 1-D
2-D
92
41
11
26
26
54
41
12
150
68
180
190
65
46
33
23
17
440
140
21
22
11
14
40
12
31
18
20
45
15
28
19
14
34
10
18
IS
10
12
Mgt
Agr
F&D
Agr
Civil
110
Welfr
32
20
36
36
14
Agr
F&D
Welfr
Agr
Civil
Civil
Misc
Civil
12
29
14
10
11
23
24
30
39
35
45
43
45
42
37
46
46
40
44
42
46
20
32
23
21
41
32
45
40
31
59
94
26
52
45
50
58
29
33
45
60
41
31
24
40
21
57
47
36
59
53
35
49
58
37
56
65
58
58
PRE > 0.5
House Cat eg.
91
94
Welfr
F&D
Misc
Misc
#
PRExlOO
Votes 1-D
2-D
65
63
26
48
53
44
40
44
64
55
52
55
52"
56
54
59
54
54
64
63
64
55
55
61
50
52
56
61
53
61
56
59
66
70
64
75
67
59
61
73
63
52
65
70
53
51
53
57
71
67
58
57
69
64
65
70
69
60
PRE < 0.5.
House Catec a Votes
Mgt
73
9
Civil
15
Civil
13
10
Civil
16
11
34
12
Misc
Mgt
49
15
25
F&D
15
17
Mgt
49
Civil
19
12
22
F&D
30
Welfr
24
11
Civil
30
30
Mgt
290
32
Civil
17
33
Agr
10
Welfr
17
40
Mgt
370
41
42
Mgt
2S0
Mgt
43
220
51
Agr
13
53
Agr
12
62
Welfr
16
Welfr
63
25
65
Agr
20
Welfr
66
27
67
Welfr
14
69
Agr
11
75
Welfr
16
77
Agr
16
SO
Welfr
19
84
F&D
16
86
F&D
24
17
89
Agr
90
Agr
29
91
Agr
12
92
Agr
24
93
Agr
49
94
Agr
40
95
Agr
49
97
Agr
23
PRExlOO
2-D
1-D
21
35
40
42
41
46
29
26
24
30
45
45
47
36
40
38
39
47
49
37
44
47
27
46
43
38
37
34
45
38
47
49
48
48
38
39
50
45
35
37
26
41
16
28
29
30
33
17
11
11
19
24
07
36
22
26
24
26
36
38
26
54
20
03
30
27
09
18
22
20
24
37
30
12
37
27
17
31
22
22
1
Table 5.
Correlations of Legislator Coordinates from Static, Biennial Scalings
Senate
House
Number of
Congresses
Averages
For Years
t+1
t+4
t+3
t+2
t+1
t+2
t+3
t+4
.85
.93
.90
.92
.81
.91
.88
.91
.75
.89
.87
.89
.68
.91
.63
.86
.81
.89
.84
.82
.77
.89
.86
.83
.80
.43
.46
.73
.76
.62
.05
.50
.95
18
.69
.86
.85
.806
.75
.62
.85
.44
.87
.68
.89
.79
.73
.84
.46
.77
.92
.88
.44
.76
.72
.67
.58
.78
.91
.75
.78
.43
.32
.55
.56
.71
.66
.89
.83
.64
.62
.49
.17
.89
.97
.77
1789-1860
1861-1900
1901-1944
1945-1978
.78
.90
.89
.95
.77
.87
.85
.93
.74
.86
.83
1789-1978
.86
.45
.47
.49
.79
36
20
22
.91
.86
.87
17
95
Individual
Congress
1
2
3
4
6
.
-.65
.
13
1.0
8
11
12
13
14
15
16
17
18
19
20
22
29
30
31
32
35
36
37
39
44
61
69
77
.79
.S3
55
.59
.75
.63
.19
-.22
.41
.31
.32
.50
.52
.75
.56
.63
.66
.89
.70
.33
.23
.86
.68
.85
.88
.24
.95
.96
.51
.87
.25
.94
.
.69
.77
75
.
.78
.72
.95
.89
.68
.98
.93
.76
.93
.89
.81
The notation t+k refers
to
-.24
.56
.42
.48
.68
.47
.50
.78
.22
.23
11
-.30
.39
.63
.74
.77
.82
.59
.77
.37
.72
.85
.66
.54
.44
.82
.90
.93
.65
.37
.47
.80
.79
.81
.76
-.
.67
.94
.91
.81
the
legislators serving in Congress
coordinates in Congress t+k.
.31
t,
correlation of legislator coordinates for
given in the left-hand column,
with their
Correlation computed only for those legislators
serving in both Congresses.
Results sho-^m
o.nly
for
those
cases where either
less than 0.8 for where any t+k correlation,
the
k = 2,3,4,
t+1
correlation was
was less than 0.5.
Table
20
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
37
38
39
40
42
43
48
49
56
67
77
78
79
81
85
86
87
88
89
90
91
92
93
95
96
97
Note.
PRE Analysis for SI avery and :ivil Rights Roll Calls
(
Total
Roll
Calls
Issue
and
Years
House
9
15
16
6.
SLAVERY
158
1805-1806
106
1817-1818
147
1819-1820
233
1827-1828
327
1833-1834
459
1835-1836
475
1837-1838
751
1839-1840
1841-1842
974
597
1843-1844
642
0-xD~ 1 OiD
1847-1848
478
1849-1850
572
1851-1852
455
1853-1854
607
1855-1856
729
1857-1858
548
1859-1860
433
1861-1862
638
1863-1864
600
CIVIL RIGHTS
1861-1862
638
1863-1864
600
1865-1866
613
717"1867-1868
1871-1872
517
1873-1S74
475
1883-1884
334
1885-1886
306
1899-1900
149
1921-1922
362
1941-1942
152
1943-1944
156
1945-1946
231
1949-1950
275
1957-1958
193
1959-1960
180
1961-1962
240
1963-1964
232
1965-1966
394
1967-1968
478
1969-1970
443
1971-1972
649
1973-1974
1078
1977-1978
1540
1979-1980
1276
1981-1982
812
J.
"One
Dim."
a nd
"Two
Issue
Roll
Calls
Percen t Correct
Classi f ication
One Dim Two Dim.
,.
13
13
16
9
5
65
92
88
82
76
70
39
27
84
44
81
79
86
84
80
84
80
73
71
75
70
92
95
92
88
92
95
88
90
88
SS
78
82
76
94
95
92
90
93
96
S
29
26
14
159
115
65
24
92
13
43
30
32
7
23
87
81
91
90
97
91
95
89
96
90
95
94
97
90
78
97
97
80
78
69
67
70
72
80
77
83
78
85
80
80
81
85
86
9
5
9
14
8
7
6
9
6
8
5
7
22
8
8
22
17
6
17
9
Dim.
73
92
87
"
refer
to
94
97
91
80
97
97
95
92
87
89
92
92
92
94
91
91
90
84
83
81
86
88
the
one
PRE
Over Marginals
One D im. Two Dim.
-.01
.84
.65
.52
.36
.39
.50
.49
.62
.43
35
.32
.36
.28
.79
.88
.79
.69
.79
.87
.22
.84
.63
.50
.44
.54
.73
.68
.76
.65
7Z
.48
.54
.42
.83
.89
.79
.73
.65
.90
.66
.83
.82
.91
.78
.25
.94
.90
-.01
.29
.00
.04
.67
.
.01
.08
.01
.33
.53
.35
.60
.45
.48
.56
.58
.50
diimensicinal
.
.81
.89
.91
.67
.82
.84
.91
.79
.33
.94
.91
.73
.76
.57
.69
.73
.74
.59
.82
.75
.73
.73
.55
.56
.58
•
.61
.59
and
dimensional dynamic scalings with linear trends in legislator positions.
two
Constrained Roll Calls by Margin
Table A-1.
Congresses 1-75
Percent
Margin
Total
Constrained
Percent
Roll Calls
Congresses 76-99
Total
Constrained
50-55
1.0
5933
0.5
1756
55-60
4.2
5012
2.6
1571
60-65
8.0
3510
4.4
1241
65-70
11.6
2788
8.0
1022
70-75
18.0
1949
13.3
791
75-80
24.5
1308
15.2
677
80-85
38.7
874
20.3
661
85-90
57.7
655
28.2
611
90-95
69.9
625
53.5
905
95-97.5
76.4
399
64.7
665
TOTAL
13.0
23053
16.3
9900
Table A-2.
•
Distribution of Bootstrap Standard Errors for Senators,
94th Senate
Range of
Bootstrap Standard Error
Number of
Senators
0.00-0.01
Note.
Roll Calls
0.01-0.02
11
0.02-0.03
62
0.03-0.04
21
0.04-0. 05
5
0.051
1
TOTAL
100
One dimensional scaling.
5
Monte Carlo Results for Simulated Data
Table A-3.
Proportion
Correct
Prediction
Percent
Precisely
Estimated
Pearson R
With True
Conf ig.
Error
Level
Stability
of
Solution
ONE DIMENSIONAL EXPERIMENTS
.995*
(.001)°
90. 8%"
Variable
.995
(.001)
Fixed
Variable
Fixed
Low
(14%)
High
(30%)
(.003:
.992"
(.004)
91.0
.963
(.003)
.977
(.006)
.970
(.001)
75. S
.910
(.011)
.947
(.013)
.976
(.003)
77.0
.918
(.004)
.958
(.009)
.962
rWO DIMENSIONAL EXPERIMENTS
894
.022)
71.7
.896
L.021)
69.6
.847
.026)
77. S
(,
,841
019)
SI.
(.
Fixed
.
(
Low
(14%)
Variable
Fixed
High
(30%)
A
Variable
Pearson
distances
(
(
.945
.003)
(,
.885
.017)
(.
.880
.005)
.841
(..017)
was
the
computed
estimated
and the true pairwise distances.
between
coordinates
the
for
.955
.024)
.962
.022)
(.
correlation
by
.942
.009)
(.
,
generated
(
5050
the
.851
.031)
unique
101
legislators
One correlation was computed for
the 25 simulations used in each design condition.
table is the average of these 25 correlations.
pairwise
each of
The number reported in the
Each true unique pairwise distance between legislators (n=5050) was treated
as
a
mean and a standard error was computed around
estimated distances.
twice
are
the
25
The entries show the percentage of true distances that
standard error.
this
this mean using
other words,
In
thepercentage
that
have a
"pseudo-t" statistic greater than 2.0.
Each predicted choice was compared to the true choice that would have been
made
had
there
been
no
stochastic
term
in
utility
the
percentage correct was computed for each of the 25 trials.
function.
A
This number is
the mean of these 25 percentages.
number
This
coordinates.
the
25
measures
estimated
configurations
measures
legislator configuration,
constant,
estimated
the
of
and
this
number
The n is 300.
Standard deviations are
number
stability
legislator
Pearson correlations were computed between each unique pair of
Pearson correlations.
This
the
noise
level
in
average
of
those
'."'
in parentheses.
sho'^Ti
the
C
the
is
'
>,
'
:?•
the
the roll call midpoint,
25
._
,
trials.
and the
(3
Holding
the
for the roll call
the percentage of times legislators who do not vote for the closest
alternative varies inversely with the distance between the alternatives.
error level is this percentage.
Distances between
to achieve the Low and High levels.
The
alternatives were scaled
Recovery From Random Starts
Table A-4.
Average Correlation of
Pairwise Distances From
Recovered Configurations
Dimensions
Proportion Agreement
of Predicted Choices
Recovered Configurations
85th HOUSE
.997
(.002)
.992
(.003)
.983
(.009)
.965
(.008)
.SS6
(.041)
.902
(.015)
100th SENATE
Note.
Numbers
replications.
in
table
(
.998
.002)
(,
(.
.984
.006)
(.
.937
(.,017)
(.
based
.991
.002)
.956
.009)
.918
.007)
on
45
comparisons
between
10
Standard deviations shown in parentheses.
441 representatives,
172 roll calls.
house because of deaths or resignations.
101 senators,
pairwise
335 roll calls.
Number of legislators exceeds size of
Figure
1
Increasing
Utility (u)
>
>
a
CO
2
O
O
o
<
2
IN'
2
u-0.49
STRONG LOYALTY,
VrTAK
FIRST PARTY
PARTY LOYALTY-
STRONG LOYALTY,
SECOND PARTY
o
o
a:
a:Qi
CM CO
CO
z
"^^
n-KX
s
Di^
M^
c
(0 U.
W
^ OJCO
cii
^r--,
-'^
Q.
^
< o
o 2
_I Q
_I 2:
o Z)
u.
< 2
-
w
LU
Q.
CS
C/5
o O
< Z >
U.
cr
—
_l
^^-^
CO 00
_
L>
d;
o =>
^
a:
o
0)
.'fe-.
< O
O 2
o
"O
Cri
u.
CM cn
CO •z.
CD
r—
o>
LU
CO
T—
CO
cc
O
UL
O
C3J
T- tC/)
lU
rCD
O
c
a
m
H
<
Z
UJ
<
Z
LU
CO
C
U.
Z
o
o
-~
_
TJ
O ^
o
LLI
c
CO
u.
u.
to
o
u
o
M
^
•^
ra
cs
^ > <
CM
UJ
cn
(3
IT)
T3
°
k.
< P
O <
5S
.
o ^
r>.
CD
<
<
o
o
=;
I—
k—
S
>_
LU
CL
UJ
O
CO
<D
^
o
I
-I
<
CD
LU
LU
<
<
Z
LU
LU
CO
"O
o
>.
O
k.
i. LL i-
O
C9
> <
—
£
"^
C3
<
-
a "3
o « w o o
t-
>
u.
o
FIGURE
3
CLASSIFICATION GAIN BY DIMENSIONALI
3
so
u
o
3
e
1
2
3
4
5
6
7
8
9
10
1 1
12 13 14 15
1
6 17 18 19 20 21
F4umb«r of Dim«na»on«
3
85th House (193
Roll Calls)
S
1
3
t
§
1
2
3
4
5
6
7
8
9
rWmDvT
10
or
1 1
12 13 14 15 16 17
1
S 13 20 21
LVTMRSOns
a.
s§o
u
e
3
3
1
2
3
4
5
6
7
a
9
10 11
12 13 14 15 16 17 18 19 20 21
o
o
S >
0--2
J;
c/;
o ^
O
C ^
i) •«M
vn
^^
,^
3
^^
c/:
"t:
o
' >
C
to
,^
1^
o o
in
t/j
cs
cs
c:
'O
<-«
w?
i/i
ir.
w^
o
rz
^
Uu
ii
133HH0D X\33H3d
UJ
in
o
LU
tr
=)
m
<
O
LL
<
LU
o
en
\—
o
bJ
O
XllliqOqOJd UD8[Aj 0IJ19UJ099
CD
LU
c:
JB9A Jed eouBisiQ eoBjeAv
"fO
^
a:
D$
d:
-
o
1-
as^
cs^ -
.
<*
CO
•
1
CO
2i
^
-^
'd-
en
T-
to
—
^v'
:^
ci
ci
Q
ci
1
ci
d:
cri
00
i^
Di
si
c:^
CO
CO
en
to
Ciia;-^
G
CC
-^
ci
**>
CO
Lo
1
,
CO
CO
^
^
,
Cii
"^
""
^n:.
''
t/so
uo
to
<
Z
LU
W
M
SENATE
Q
to""
,to
CO
-
-^
t^
- ^
Q
"A^
—
CO
r^
/-TV
*~
dOx
<^^^^ "g
too
^
coco
C
..
,
o
3
ra
o
;iII
o 6
o if}
ci
E
E
o
ci
u
a
c:
C2
II
Q
'3-
o
CO
CO
CO
CO
CD
to—
o
CO
00"
c:)
to
LU
to
CD
Q
to
<
Z
cr3o
^a^
LU
CO
G
Q G
^ G
.o
;=U:43
Q
CO
""a
to
en
LU
<
Z
LU
w
^
tn
o
CO
ai
CO
I
^>
.CO
J
r\
^
G CO,
to
tp
|5
to CO
^^r^
C/3
^.
®
c
c
o
II
CO
RGURE
8
THE BORK VOTE
JUDICIARY COMMITTEE
COMMITTED
UNDECIDED
OTHER SENATORS
ANNOUNCED
BEFORE OCT. 7
OTHER SENATORS
ANNOUNCED
ANNOUNCED
ON OCT. 7
AFTER OCT.
7
SARBANES
•0.8
SIMON
INOUYE
MblZENBAUM
MELCHER. HARKIN
KENNEDY
BURDICK, LEVIN. RIEGLE
KERRY, CRANSTON. PELL
LEAHY
ffi-o.e
BIDEN
BYFD
LMJTENBERG. MOYNIHAN
MITCHELL DODD
BAUCUS. ROCKE.-ELLER
GORE. PRYOR
BUMPERS. BRADLEY,
G'l£NN, ford
BINGAMAN, JOHNSON
PREDICTED
SASSER
ANTI-
BORK
CHILES
DIXON
EXCN
-0.4
DECONCINI
5=\TSEN
boren-
^^^^
PROXMIRE
-
HEFUN
Si^NNlS
NJrvN
hollings
-0.2
Hatfield*
CLTmNG
SP=S:'=R
LINE
DJP=\S=RG=R. COHEN
GFIASSLEY
.HELNZ
sTsffordcr.aflee',
packwood'
D'AMATO
KASTEN, DANFORTH
PRESSLER
SirVrNS. EVANS
kasse3aum
0.2
>
coch.ran,
<
>
e
UJ
w
o
=:
rudman
murkowski, nickles
tr:=le. mcconnell
BCSCHvVITZ, ROTH
L'JGAR. WILS-ON, DOLE
0.4
u
OUAYLE
SIMPSON
DOfvlENICI
HATCH
THURMOND
GARN. GOLDWATER
ARMS, HONG
KJM?ni=£Y
GRAMM, HECHT
MCCLURE
HELMS. VMLLC^. SYMVS
'Prediction
PREDICTED
3on<
i.
0.6
0.8
Warner*
errors
—
CT)
in
en
LU
T
Z)
O
CD
O)
CO
CO
00
5 5^^
a
^03
GOUD^SIQ
Date Due
otn^^s'
1?
MIT
3
TDflQ
LIBRARIES
0Q5fl3Dfll
2
I
«