Digitized by the Internet Archive
in
2011 with funding from
Boston Library Consortium IVIember Libraries
http://www.archive.org/details/patternsofcongreOOpool
HB31
.M415
working paper
department
of economics
jTt«^.i^J?^«r7V. " J^T"^ ^'^WCt^Ti
PATTERKS OF CONGRESSIONAL VOTING
Keith T. Poole
Howard Rosenthal
No.
536
September 1989
massachusetts
institute of
technology
50 memorial drive
mbridge, mass. 02139
PATTERNS OF CONGRESSIONAL VOTING
Keith T. Poole
Howard Rosenthal
No.
536
September 1989
DEC 2 1^89
I
Revised September 1989
Patterns of Congressional Voting*
Keith
T.
Poole
Carnegie Mellon University
and
Howard Rosenthal
Carnegie Mellon University and MIT
thank Rom Romer for his many helpful comments.
Our research
was supported in part by NSF grant SES-8310390.
The estimation
was performed on the Cyber 205s of the John Von Neumann Center
at Princeton University.
Other portions of the analysis were
carried out at the Pittsburgh Supercomputer Center.
'We
ABSTRACT
Congressional
voting has been highly structured for most
The structure was disclosed by a dynamic,
American history.
of
call
roll
the entire roll
call voting record from 1789
to
1985.
of
spatial analysis
In
the modern era
legislators exhibit very stable voting patterns throughout their Congressional
careers.
This
stability is
such that,
under certain conditions,
forecasting of roll call votes is possible.
short
Since the end of World War
run
II,
changes in Congressional voting patterns have occurred almost entirely through
the
process
members.
of
replacement
Politically,
of
retiring
or
defeated
legislators
with
selection is far more important than adaptation.
new
I.
Introduction
The Congress of the United States
subject
to
myriad
a
requires
typically
of
formal
assent
the
is
informal
and
numerous
of
complex
a
committees
institution
Legislative
rules.
Furthermore,
well as the support of party leaders.
legislative
and
action
subcommittees,
as
legislation is shaped not
only by the 535 members of Congress and attendant thousands of staff, but also
by influences arising in the executive, organized lobbies,
the media,
and from
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 a very simple dynamic voting model.
In
spatial
a
model
2
each
,
s-dimensional Euclidean space.
legislator
is
represented
by
a
point
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" outcomes.
"yea"
The spatial model holds that a legislator prefers
the closer of the two alternatives.
a utility function.
point,
greater
the
The extent of preference is expressed by
The closer an alternative is to the
the
preference
for
the
alternative,
legislator's
and
the
ideal
higher
the
utility.
The development of supercomputing has permitted us to estimate this model
for the period from 17S9 through 1985.
model
is
very stable and it breaks down precisely when the political system
breaks down;
party,
and,
division
The spatial structure uncovered by the
first,
second,
over
from 1815 to
1825,
after the collapse of the Federalist
in the early 1850' s upon the collapse of the Whigs and the
slavery.
Since
the
Civil
War,
the
structure
has
been
sufficiently stable that the major evolutions of the political system can be
traced
out
Depression,
was
terms
in
of
within
repositioning
the
structure.
witnessed a massive Influx of "liberals",
for example,
sharp break with pre-Depression voting patterns.
no
stability of
structure permits
the
The
Great
there
but
addition,
In
the
short-term forecasting of key roll
call
votes.
paper proceeds,
The
in
Part
description of
with a
II,
the
behavioral
model that represents this simple structure of roll call voting and
dubbed D-NOMINATE for Dynamic Nomina l
explanation of the estimation method,
Three-Step
Estimation.
statistical
estimation technique,
tests of the method.
the
space
is
relative
stable
In Part
)
low
of
Appendix
(The
issues
dimensionality
positions.
The
the estimation,
in
concerning
details
provides
and Monte
we present evidence that,
III,
a brief
in
legislators
which
argument
Part
in
Carlo
on the whole,
temporally
occupy
IV
the
directed
is
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 present an illustration of the predictive capacities of the model
with
an
analysis
Supreme Court.
hand,
of
the
confirmation
In the Conclusion,
vote
on
the
Bork
nomination
we point to two key findings.
in contrast to earlier historical periods,
to
the
On the one
political change must now be
accomplished by the selection of new legislators through the electoral process
rather than by the adaptation of
demands.
been
On the other hand,
sharply
reduced
because
incumbent
legislators to changes
the possibility of major
the
average
distance
political
between
in public
change has
the
two
major
parties has fallen dramatically in this century.
II.
Estimation of a Probabilistic, Spatial Model of Voting
An Overview of the Model
Expressions such as "liberal",
"moderate",
and "conservative" are part of
the common
language used to denote the political orientation of a member of
Congress.
Such labels are useful because they quickly furnish a rough guide
to
A
likely to take on a wide variety of issues.
the positions a politician is
contemporary
example,
for
liberal,
is
a
favors
politician
predict,
Indeed,
support
increasing
the
and support federal funding of
support mandatory affirmative action programs,
health care programs.
to
oppose construction of MX missiles,
oppose aid to the Contras,
minimum wage,
likely
this consistency is such that just knowing that
increasing
minimum
the
wage
with a fair degree of reliability,
information
enough
is
politician's views
the
to
on many
seemingly unrelated issues.
consistency or
This
suggests
that
by
legislators
are
simple
a
points
Euclidean space.
call voting,
{Converse,
formal
and
pairs
is unnecessary to use
that one dimension captures most
of
opinions
political
variety of
as
points
of
Insofar as a spatial model
it
of
where,
structure,
calls
roll
1964)
on a wide
politician's positions
a
summarized
constraint
issues
can be
mentioned
above,
in
a
s-dimensional
can capture Congressional
We find
large number of dimensions.
a
the
spatial
information while a
dimension makes a marginal but important addition to the model.
roll
second
Adding more
dimensions does not help us to understand Congressional voting.
Although
dimensions
the
are
mathematical
abstractions,
the
reader
can
think of one dimension as differentiating strong political party identifiers
from weak ones.
had a two party political system.
dimension
ranges
Democrat)
to
competing,
weak
party
differentiates
the United States has always
Except for very brief periods,
from
strong
loyalty
to
loyalty
either
(Federalist,
"liberals"
It
from
Whig,
surprising,
is not
to
one
party
or
party
to
(Democrat-Republican
strong
loyalty
Republican).
"conservatives"
that one
therefore,
within
to
a
or
second,
Another
dimension
two
competing
the
parties.
to
a
Loyalty
The distinction between the two dimensions is a fine one.
loyalty
political party and
implication
stable
consistent,
of
that— especially during periods
an
to
ideology have
voting
—a
behavioral
similar
This
patterns.
of stability
a
reason
the
is
one dimensional model accounts
for most voting in Congress.
In Figure
we show a two dimensional example of a
1,
legislator's
ideal
point along with the points representing the "yea" and "nay" alternatives on a
The circles centered on the legislator represent contours of
roll call vote.
the utility function employed
only
consideration,
consider
"nay"
the
in
our study.
perpendicular bisector CC
This
outcomes.
clearly vote
legislator would
the
bisector,
line
the
of
termed
spatial proximity were
If
the
cutting
legislators who vote "yea" from those who vote "nay".
"yea.
Furthermore,
"
joining
the
should
line,
the
"yea"
and
pick
out
Those legislators whose
ideal points are on the "nay" side of the bisector should vote "nay".
Figure
1
about here
We say "should" because the simple model of voting we have outlined will
obviously not be successful in accounting for every individual decision.
allow for error,
we employ the logit model.
In this model,
is
it
To
only more
likely that the legislator votes for the closer alternative.
For
whose
legislator
a
ideal
point
probability of voting "yea" will be 0.5.
from
the
cutting
Consequently,
"errors"
(that
line
when we
is,
will
look at
have
the
a
on
falls
cutting
line,
the
Legislators with ideal points far
probability
actual
the
data,
we
close
to
zero
or
should find most
legislators who voted "nay" when on the "yea"
one.
of
the
side of the
line and vice-versa) close to the cutting line.
We will later use Figure 2 to
return to the topic of error.
of
show the estimated
ideal
The
top panels
that figure use
tokens
to
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
all
the behavior
allows
We
voting.
significantly
adds
dimensions can account for essentially
can be accounted for with a simple spatial model
that
probabilistic
for
dimension
show that "1-"
We will
legislature.
some
in
"1-"
say
Congresses,
clearly less important than the first.
while
because,
projecting all
That is,
second
dimension
second
the
a
that
is
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,
how specific issues map onto the dimensions may change over
In the postwar period,
time.
an interpretation is fairly clear.
on overriding Truman's 1947 veto of
division along the first,
and
other
most
"economic"
Taft Hartley Act was almost a pure
the
tend
line
to
minimum wage
Similarly,
dimension.
left to right,
votes
The lineup
on
up
this
dimension.
final passage of the 1964 civil rights act in the Senate,
contrast,
In
which was
close to a pure South-North vote, was almost a pure division along the second,
top
to
bottom,
Congressional
dimension.
Quarterly as
However,
votes
"key"
Panama Canal treaty (See Figure 2),
15,
vote on school busing,
1974
dividing
the
two
parties
most
of
in
the
the
roll
postwar
designated
calls
period,
the Jackson amendment on SALT
tend
to
internally at
be
an
such
I,
of
-45
to
the
the
and a Kay
"Conservative Coalition"
angle
as
by
votes,
left-right
dimension.
Indeed,
the results of our scaling algorithm readily admit
one interpretation.
line
in
Figure
2,
to more
than
Defining the first dimension to be roughly along a 45
we
can
differentiate
conservatives within each party.
liberals
(southwest
quadrant)
from
The orthogonal dimension is a party loyalty
)
dimension.
algorithm does
scaling
(The
information
use
not
This interpretation follows Poole and Daniels'
(1985)
about
party.
two dimensional analysis
of interest group ratings.
A party dimension
present throughout nearly all of American history
is
while an orthogonal dimension captures
internal party divisions.
Thus,
division between southern and northern Democrats after World War
parallel
between
division
the
in
southerners
Democratic and Whig parties in the 1840'
and western Republicans from the 1870'
s
and
northerners
the
finds a
II
both
in
the
and in the division between eastern
s
through the 1930
4
s.
The fact that there is more than one substantive summary of our results
is
not
troubling.
"liberal-conservative" vs.
the
Moreover,
results.
"economic"
the
Indeed,
"party"
we
vs.
"regional
or
social"
and
interpretations both provide insight
believe
our
major
scientific
result
to
the
into
be
the
finding that an abstract and parsimonious model can account for the vast bulk
of roll call voting on a very wide variety of substantive issues.
departs
from much of
imposed
number
larger
a
previous
the
literature
dimensions
of
which has
either
Clausen,
(e.g.
Our "I2"
exogenously
1973}
used
or
methodologies that were inappropriate for the recovery of spatial voting (see
Morrison,
1972).
Estimation Methodology
The Data
Our estimation includes every recorded roll
except
those
minority side.
with
fewer
For
legislator having
a
cast
treated as actual votes.
than
2.5
percent
given Congress
at
least
25
(two
votes.
of
year
call
those
between 1789 and 1985
voting
period),
Pairs
and
we
supporting
included
announced
votes
the
every
were
Observations with other forms of non-voting (absent,
excused) were not included in the analysis.
The Spatial Parameters
After thus excluding near unanimous roll calls and legislators with very
the estimation requires Euclidean locations for 9759 members of the
few votes,
House
Representatives,
of
and
senators,
1714
70,234
calls.
roll
In
a
two-dimensional setup this requires estimating 303,882 parameters when spatial
This number is nevertheless small relative
positions are Invariant in time.
to the 10,428,617 observed choices.
Additional parameters are required to allow for spatial mobility.
There
are examples of legislators who clearly do not occupy stable positions in the
Schweiker
there
instance,
For
space.
is
from a weak
(R-PA)
the
remarkable conversion of Senator Richard
liberal
to
a
conservative
strong
after
tapped as Ronald Reagan's vice presidential running mate in 1976.
being
To allow
for spatial movement, we permitted all legislator coordinates to be polynomial
functions of time.
However,
we found great stability in legislator positions.
A slight improvement in fit results from allowing linear trend;
higher order
polynomials make virtually no additional contribution.
In the estimated model,
the locations of legislators and roll calls are
identified only up to a translation and rigid rotation. When we speak later of
dynamics
realignments,
or
translations
identified
space
or
the
rotations.
In
intertemporally.
over
time.
polarization
of
As
the
apart in the space,
a
movement
contrast,
One
result,
political
is
the
always
arbitrarily
we
discuss
system
— when
shrink
changes
legislators
in
are
any
to
relative scale of
cannot
can
relative
space
the
or
global
stretch
the
degree
spread
is
the
of
further
the system is more polarized.
Functional Representation of the Model
We use a specific functional model of choice to represent our hypothesis
that roll
call voting is sincere Euclidean voting subject
to
"error"
induced
)
by
omitted
factors.
eliminate
To
baggage,
we
down
write
coordinates are quadratic
legislator
s-dimensional model where
a
functions of
The extension to higher order polynomials is direct.
time.
Legislators
)
Euclidean
where
k=l,2,...,s
Within a Congress,
Congresses.
of
legislator's
a
t,
Ik
Ik
each senator serving
For
constant.
Ik
terms
in
x
=x +xt+xt,
Ikt
measured
time
At
i.
,...,x
(x
X
is
by
indexed
are
position is given by
Time
notational
four
in
more
or
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.
Each roll call,
indexed by
is represented by two points
j,
one corresponding to an outcome identified with a "Yea"
to
the
"Nay"
vote and the other
The coordinates are written as z
vote.
(n)
(y)
in the space,
and z
(We
.
Jnk
Jyk
omit time subscripts on the roll calls.
If there was pure Euclidean voting,
only if his
"Nay"
d
location were closer
or her
location.
In two dimensions,
=(x ilt
Ijy
(x
spatial
influence voting.
to
for example,
i2t
Jyl
voting
Jnl
ignores
To allow for error,
location than to
the
this would be:
<
Jy2
12t
the
"Yea"
the
-z)+(x -z)
-z)+(x -z)
lit
Pure
each legislator would vote Yea if and
= d
IJn
Jn2
"errors"
or
omitted
variables
that
we assume that each legislator has a
utility function given by:
U(z)=u
1
u
ji
iji
+c iji
= |3exp[-d^
,
l=y,n
/S]
where ^ is an additional parameter estimated in the analysis,
c
is
a
"logit
.
model"
which
error
and "S"
exponential,
The
parameter
essentially
is
3
We have imposed
a
the
as
log
of
inverse
the
arbitrary scale factor.
is an
common
signal-to-noise
a
perfect spatial voting occurs
increased,
one.
independently distributed
is
— all
As
is
^
probabilities approach zero or
The estimation was
history.
for all of U.S.
(i
ratio.
not substantially improved by allowing a distinct
for each Congress.
/3
As a result of our choice of error distribution, we are able to write the
probability of voting "Yea"
as:
=exp[u
Pr("Yea")
]/(exp[u
ijy
'^
ij
]
+exp[u
ijy
(1)
])
iJn
We chose the above specification for a number of reasons:
the spatial utility function (u) is bell-shaped.
First,
This allows for
the possibility that individuals do not attribute great differences to distant
alternatives.
For example,
Ted Kennedy might see little to choose from in a
proposal that was at John Warner'
s
rather than at Jesse Helms'
ideal point
But Helms might see a very large difference between two such proposals.
using a stochastic specification permits developing a likelihood
Second,
function that
is
a
function of
function is dif f erentiable,
If
we
were
approach
concerned
one
in
coordinates
the
with
dimensional
A.s
this
maximized by standard numerical methods.
it can be
solely
estimated.
be
to
ordinal
That
problems.
we
scaling,
could
we
is,
eschew
could
start
this
with
a
configuration of legislators and then find a midpoint for each roll call that
minimized classification errors.
and
classification
legislators.
procedure
maximizing
probability
This
indeed
a
errors
process
makes
likelihood,
choices.
could
can
fewer
further
be
then
be
weights
scaling
of
could be held constant
reduced
iterated
classification
heavily
Ordinal
the midpoints
Next,
errors
this
reordering
convergence.
to
errors
by
than
that
form,
ours,
Such
which,
correspond
however,
the
is
to
a
in
low
wholly
s
'
impractical in more than one dimension.
Finally,
by
using
probabilities
in
the
non-linear
logit
closed
form
would
model
form
logit
the
'
of
probit.
be
alternative
standard
The
(1).
As
calculate
can
we
error,
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
recent
but
typical,
Figure 2 shows all voting members of
model.
"snapshots"
the Senate
positions and the cutting lines for two specific votes:
vote
and
a
National Science Foundation on April
2,
treaty
Democrats,
Byrd
on
"S"
(VA)).
D' s
1978
18,
southern Democrats,
7
proposal
1981.
for the Panama Canal
restore
line,
S' s
"errors."
As
explained
and
D' s.
close
expected pattern;
to
the
cutting
errors
line
than
is Harry
there
that
is
S'
The bottom part of each
given their location relative to the
above,
in voting
for
the
northern
A "D" token represents
the
probability
should be greatest for senators closest to the cutting line.
the
for
an R token is always overstruck by another R and
However,
panel shows only those senators who were,
to
funding
and "R" Republicans (the one "I"
are always overstruck by other
cutting
to
voting
the
their estimated
Some senators have sufficiently similar positions
overstriking.
and
April
in
of
are far more
those who
are
an
of
The data conform
likely for
distant.
error
senators
When senators'
Euclidean positions provide a clear indication of which side they should join,
forces
not
captured
by
our
simple
structure
are
rarely
strong
enough
to
produce a vote that is inconsistent with the spatial model.
Figure 2 about here.
These two roll
calls are quite
typical
10
of
post World War
II
voting in
)
o
That
Most roll calls divide at least one of the two parties.
Congress.
is,
the estimated cutting lines are typically roughly parallel to the two shown in
Figure
The tendency for cutting lines to be parallel explains why a one
2.
dimensional
provides
model
approximation
useful
a
that
accounts
for
most
voting decisions.
Returning to the question of "error", how general is the pattern shown by
A straightforward method to measure the fit of the model
the snapshots?
simply
across
count,
to
The
both
Congress
of
calls,
percentage
the
classification results for the
classifications.
Houses
roll
all
shown
are
in
Table
is
correct
of
two-century history of
table
The
1.
reports
classification both for all roll calls in the estimation and for "close" roll
calls
where
minority
the
two-dimensional model,
over
got
percent
40
of
the
vote
With
cast.
a
classification is better than 80 per cent for "close"
votes as well as all votes.
Table
It
model
about here.
can be seen that a reasonable fit is obtained from a one-dimensional
where
career.
each
On
percentage
trend
1
in
legislator's
the
other
points
— from
there
hand,
adding
legislator positions
less of a boost
expected.
a
by
adds
constant
considerable
second
time trend,
In contrast,
call as well as additional
legislators
a
is
is
dimension.
throughout
improvement
Allowing
another percentage point.
his
— about
for
a
(That
or
over
linear
we
get
is
we add only one parameter per legislator
adding a dimension adds two parameters per roll
legislator parameters.
5-to-l,
her
three
in the percentages from the time trend than the dimensions
When we add
per dimension.
position
it
is
not
surprising
Since roll calls outnumber
that
classification shows
more improvement when we increase the dimensionality of the space than when we
increase the order of the time polynomial.
11
Introducing more parameters
dimensions
higher
or
understanding
of
in
— does
polynomials
order
political
the
dynamic
a
spatial
— through
appreciably
not
extra
Adding
process.
model
add
spatial
extra
our
to
parame,ters
results in only a very marginal increase in our ability to account for voting
consider adding to the two dimensional
For example,
decisions.
linear model
Allowing for a quadratic term in the time polynomial improves
in the Senate.
classification only by 0.3 percent at a cost of 1456 additional parameters
dimensions x 728 senators serving in
Allowing for a
or more Congresses).
4
third
dimension improves classification by only 1.0 percent
77,479
more
parameters
parameters per
only
Thus,
per
and
call
roll
one
or
at
the
regularity
important
have
we
cost
a
of
additional
two
Allowing for both generates an
legislator).
percent.
1. 1
more
2
(
(2
improvement of
found
that
is
somewhat over SO percent of all individual decisions can be accounted for by a
two-dimensional model where individual positions are temporally stable.
regularity
important pattern,
an
is
well-specified
theoretical
space.
The decisions
reflect
either
very
model
the
that
spatial
specific
but
sets
the
would
model
of
pattern does not
fix
cannot
account
constituency
arise
dimensionality
the
and
for
This
of
the
likely
to
interests
or
are
other
from a
logrolling and other forms of strategic voting that lie outside the paradigm
that forms the basis for our statistical estimation.
The Dimensionality of Congressional Voting
Since
empirical
result,
evidence for
increments
dimensionality
low
to
it.
the
we will
First,
the
seco.nd
an
important
and,
to
unexpected
many,
discuss a variety of different sets of supporting
restricting ourselves to three Houses,
percent classified correctly wnen D-NOMINATE
with as many as 21 dimensions.
of
is
Second,
is
show the
estimated
we evaluate the classification ability
dimension from the dynamic,
12
we
two
dimensions with
linear
trend
estimation,
and compare
this
ability to classify with
if
a
the first dimension.
to
Third,
we compare our
one dimensional model with what might be expected
legislators and roll calls were distributed within a s-dimensional sphere.
Fourth,
we show that the results of D-NOMINATE are reasonably stable when the
algorithm is applied to subsets of roll calls that have been defined in terms
of
substantive content.
we show that an alternative measure of fit,
Fifth,
gives similar results
the geometric mean probability of the observed choices,
to those based on classification percentages.
Sixth,
since dimensionality may
depend on the agenda, we compare the model's performance with measures of the
diversity of the agenda.
Seventh,
we ask which issues in American history led
to an important role for a second dimension.
1.
As
our
first
check
Models of High Dimensionality
on
the
dimensionality
of
dynamic
our
models,
selected three Houses and estimated the static model up to 50 dimensions.
we
The
32nd House (1851-52) was chosen because it was one of the worst fitting Houses
in
two
dimensions
dimensionality.
and
was
thus
a
candidate
good
to
exhibit
high
(1957-58) was chosen because it was analyzed
The 85th House
with other methods by Herbert Weisberg (1968).
In addition,
the S5th House is
part of a period when the two dimensional linear model clearly dominates the
one dimensional linear model.
Finally,
the 97th House
(1981-82)
is
included
because it appears that roll call voting 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
the first dimension was 70.2 for the 32nd House,
for
the
97th.
The
bars
in
the
figure
classification percentage for
78.0 for the S5th,
indicate how much
dimension adds to the total of correctly classified.
13
the
and S4.
1
corresponding
(The horizontal axis is
labelled such that "3"
not
drop
— because
the
bars
the'
negative
do
corresponds to the fourth dimension,
off
smoothly
algorithm
— in
fact
on
)
occasion
one
maximizing
is
etc.
log
Note that
the
bar
likelihood,
is
not
classification.
Figure 3 about here.
^]
The 97th House is at most two dimensional with the second dimension being
After
very weak.
two
dimensions
added
the
classifications
are
There is a clear pattern of noise fitting beyond two dimensions.
to
In contrast
the 85th House is strongly two dimensional with little evidence
the 97th,
for additional dimensions.
dimensions,
minuscule.
While the 32nd does show evidence for up to four
even four dimensions account for only 78 percent of the decisions.
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.
Although
The Relative Importance of the Second Dimension
the
evidence
presented
in
Table
marginal role for at most a second dimension,
1
and
Figure
3
suggests
and a weak one at that,
it
a
is
important to evaluate the second dimension by other than its marginal impact.
Specifically, Koford (1987) argues that a one dimensional model will provide a
good fit even when spaces have higher dimensionality.
two dimensional space,
vote
that
marginal
is
not
increases
in a truly
one dimension will have some success at classifying any
strictly orthogonal
in
For example,
fit
on
the
to
order
the
dimension.
of
3
percent
As
may
result,
the
understate
the
a
importance of the second dimension.
The natural question,
classifying by itself.
then,
is
how well does the second dimension do in
To study this,
we took the second dimension legislator
14
coordinates from our preferred model,
each
for
errors.
roll
call,
found
two dimensions with
which
cutpoint(s)
the
linear trend,
and,
classification
minimized
We used the minimum errors to compute classification percentages.
We
made the same computation for the first dimension.
Figure 4 about here.
The results of these computations for the House
classifies 84. 3 percent of
votes but
the
The 70.8 percent
only 70.8 percent.
are shown in Figure
is
the
second dimension accounts
than
dimension
But
"one".
in
all
99
Houses,
(although the difference was slim in the 17th House).
a
weaker
tad
— 83.8
percent
marginals here were 66.1.
for
one
dimension
In addition,
"two"
"one"
best
did
The Senate results are
versus
73.6
for
The
two.
does better in Senates
2,
17,
But clearly the second dimension is a second fiddle.
and 18.
How Well Should One Dimension Classify?
3.
In
dimensions
If the two
then in some Congresses dimension "two" might
were indeed of equal importance,
better
for
particularly unimpressive given that
predicting by the marginals would lead to 66.7 percent.
do
4.
figures show the first dimension correctly
the 99 biennial
The averages of
9
addition
following
Koford
theoretically.
to
comparison
empirical
this
consider
we
(1987),
Specifically,
we
assume
the
an
between
issue
our
of
two
dimensions,
unidimensional
uniform
n-dimensional
fit
spherical
distribution of ideal points and consider the projection of these ideal points
onto
one dimension under
n-dimensional space.
of y to 100 - y
sphere.
In
the
conditions of errorless
the case of errorless spatial voting,
(such as 65 to 35)
For a split of
r(y) through the origin.
spatial
y,
the
a
in
the
given split
can be represented as a slice through the
slice must be tangent
For fixed
voting
y,
to
a
sphere of
radius
we assume the splits are generated by a
uniform distribution of tangency points over the sphere with radius r(y).
15
For
this distribution one can calculate the percentage of correct classifications
that would be made by a one-dimensional projection.
For s=2, we can calculate the exact percent correct for errorless spatial
For the empirical distribution of splits over all roll calls included
voting.
in
our
79.8 would be
analysis,
classified correctly
in
both
House
the
Senate if legislators and roll calls were spherically uniform for s=2.
one-dimensional
spatial
voting.
percent
(Table
constant model might arise from perfect
with
However,
Thus,
1).
a
projection would
classify
correctly
83.5
The 83.5 percent voting correctly
have
only
error
their
projection with probability 0.212.
incorrect
classify
correctly
correctly with probability 0.798.
incorrectly would
voting
dimensional
two
better benchmark model would be two-dimensional
in two dimensions would be projected
percent
we
dimensions,
two
voting with an error rate of 16.5 percent.
16.5
Thus,
the case that the 80 percent correct classification we obtain in
it might be
the
and
Therefore,
83.5(0.798)
+
"corrected"
a
The
by
an
one-dimensional
=
16.5(0.212)
70.1
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.
one-dimensional
the
distributions
model
to
of
ideal
classify
points
at
and
SO
The table indicates that for a
percent
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
4.
contrast
In
Do Different
to
our
Issues Give Different Scales?
emphasis on
low
Clausen
dimensionality,
(1973)
has
argued that there are five "dimensions" to Congressional voting represented by
the
Social Welfare,
issue areas of Government Management,
17S9
from
call
completeness,
distinct
We have coded every House
and Foreign and Defense Policy.
Liberties,
a
to
1985
in
terms
of
these
five
sixth category termed Miscellaneous.
dimensions,
we
ought
to
get
Agriculture,
categories,
roll
for
If the issues are really
differences
sharp
and,
Civil
legislator
in
coordinates when the issues 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-NOMINATE 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
distances among legislators.
Correlations between the management, welfare, and residual categories for
one
dimensional
Correlations
scalings
are,
as
shown
in
Table
3,
all
high,
around
between the foreign and defense policy category and
three were somewhat lower,
in the 0.7 to 0.8 range.
As a whole,
the
0.9.
other
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
17
(again see
Table
result
This
3).
surprising.
not
is
The
95th
House
had
nearly
From the D-NOMINATE unidimensional scaling with linear
unidimensional voting.
trend that was applied to the whole dataset,
classifications for 83 percent of
the
votes
we find one dimensional correct
in
each of
the
four
clusters.
With two dimensions the percentages increase only to 84 percent
categories.
for Social Welfare and Foreign and Defense and 85 percent for the other two
categories.
12
Moving
from
one
to
two
dimensions
doubles
the
number
estimated parameters with only slight increases in classification ability.
of
In
breaking down the roll calls into four categories and estimating separately,
the number of legislator parameters is effectively quadrupled.
doubling of
parameters,
all
by
moving from one
likely to be fitting idiosyncratic "noise"
to
dimensions,
two
in the data.
With a further
one
is
The fit to the noise
weakens the underlying strong correlations between legislator positions.
We
also 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,
Evaluation bv Geometric Mean Probability.
5.
In
addition
"dimensions".
to
computing
classification percentages,
the
model
may be
evaluated by an alternative method that gives more weight to errors that are
far from the cutting line than to errors close to the cutting line
—a
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 = exp( log-likelihood of observed choices/N),
where N is the total number of choices.
Summary gmps for the various estimations are presented in Table
18
1.
The
—
matches
pattern
that
found
for
classification
the
percentages
little
is
gained by going beyond two dimensions or a linear trend.
In Figure
we plot the gmp for each House for the following models:
two-dimensional
A
(13
5,
with
model
positions
legislator
constrained
to
a
constant.
again with legislator positions constrained to a
A one-dimensional model,
(ii)
constant.
(iii)
A one-dimensional
model
that
is
estimated separately for each of
the
Note that in this model there is no constraint on how
first 99 Congresses.
legislator positions vary from Congress to Congress.
Motivation for the third model came from
and
Rabinowitz
that
(1987)
within
one-dimensional
American
span
time
the
a
political
of
any
Macdonald-Rabinowitz
The
Congress,
is
is
Congress
but
that
5,
the
about here.
hypothesis,
within
unidimensionality
sustained for the entire period following the Civil War.
shown in Figure
1853-54,
5
one
basically
conflict
13
dimension of conflict evolves slowly over time.
Figure
recent argument by Macdonald
the gmp for model
(iii)
any
As
has not fallen below 0.64 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.
14
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
19
space or as replacement of some
.
legislators by others with different positions in the space.
15
The Agenda and Dimensionality
6.
One basis for the Macdonald-Rabinowitz argument would be that short-term
coalition arrangements enforce a logroll across issues that generates voting
'
patterns consistent with a unidimensional
Another potential
spatial model.
consideration is that short run unidimensionality may reflect the fact that,
in
any
that
Congress must place some restriction on the
two-year period,
can be given
for
time
consideration.
this
If
is
issues
Congresses
so,
that
consider a diversity of issues should be less unidimensional.
test
To
this
out
diversity hypothesis,
set
of
13
least
a
crude
developed
categories
by
Peltzman
but very weakly
Peltzman
index
over time.
trend
is
The
Both
from
indices
the
counterhypothesis direction.
model fits better
17
Just over half
).
(R=-. 302
undoubtedly spurious.
(R=-.709),
as
the Clausen categories
index for
means
362
explained by trend
(R=-.405).
geometric
[R=.
two
are
As the roll
for Clausen,
at
correlated
trend
model,
-.369 for Peltzman).
with
but
the
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
expanded
call set becomes more diverse,
while the agenda has become more diverse over time.
agenda,
variation in the
more weakly related to
is
linear
The indices
government has
"significantly"
dimensional,
the
The
(1984).
Herfindahl index was also computed for the Peltzman categories.
validate,
we
way,
We also coded all House roll calls using a
for the six Clausen categories.
finer-grained
at
the Herfindahl concentration index
for each of the 99 Congresses,
computed,
in
is not
Indeed,
diversity of the
"significantly"
related
(difference in geometric means) of the two dimensional model to
improve over the one dimensional linear model
Clausen)
20
(R=-. 089 for Peltzman,
-.158 for
reason
One
hypothesis
is
Congresses
40-99,
that
deviation
of
deviation
0.020.
the
index
In
last
the
average
the
100
0.090
is
diversity
the
variation.
with
0.355
Congress
years,
for
little
averaged
Clausen
for
Peltzman,
for
0.062;
exhibited
have
indices
the
results
negative
basically
these
for
and
has
For
a
standard
the
standard
had
and
full
a
Low dimensional voting has not occurred simply because
wide-ranging agenda.
votes are restricted to a narrow topical area.
Issues and the Second Dimension
7.
There have been relatively few issues that have consistently sparked a
We demonstrate this by considering the PRE
second dimension in spatial terms.
over the marginals
[PRE =
1
-
(D-NOMINATE errors)/{Number voting on minority
within each of the Clausen categories.
side)]
differences
in
marginals
across
We
Houses.
then filtered
these
category-Congress pairs that were
a
(a)
0. 1
PRE
use
computed
control
to
PRE
the
for
for
the
We obtained FREs for 6 categories x
into
subset
a
contains
that
only those
based on at least 10 roll calls,
two dimensional PRE of at least 0.5,
at least
We
categories.
linear models in one and two dimensions.
99
We
and
between one and two dimensions.
had
(b)
had an increase in the PRE of
(c)
18
In other words,
we found sets
of roll calls that were highly spatial and where the second dimension made an
important difference.
These appear in Table
4.
Table 4 about here.
can be seen that the second dimension was "important"
It
first
24-31,
23 Houses.
1S50,
appeared
sporadically
second dimension comes forth in
the
the key.
It
Note for further reference,
Civil
accommodated
Liberties
by
(essentially
introducing
a
in
5
however,
slavery)
second
21
different
In
Houses
Liberties
is
after the Compromise of
vanishes
dimension.
areas.
and Civil
Houses,
that,
in only 6 of the
I.n
as
an
fact,
issue
from
that
the
is
32nd
there are only 3 occasions,
through the 75th Congress,
1853-54,
"realignments"
The
area.
accommodated not by a shift
(Republicans in the 90'
In
contrast
the
in
the
and
1890' s
space but by the
first
the
75
second
the
Houses,
most
the
frequent
category.
there were only 8 Civil Liberties votes;
dimensions,
increase
an
dimension
(1969-70).
of
is
Civil
eliminated because
their PRE was 0.62 in two
however,
Moreover,
0.26).
80th
(The
was
Except
every House in this period appears in the table.
for the 80th Congress,
is
largely
infusion of new blood
systematically important in Houses 76 (1939-40) through 91
Liberties
were
1930' s
and Democrats in the 30' s) in the existing space.
s
to
of
only
in
one
case
(the
Congress) did the second dimension matter in fewer than two issue areas.
other
words,
when
consistently so
space
the
across
and
each time only in one
1915-16 when the second dimension made a key difference,
issue
1893-94,
'
became
strongly
wide variety of
a
two
dimensional,
As
topics.
stated
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.
Finally,
from Congress 92 out,
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
4
also
shows
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
the
fit
is
"variance.
fraction of the entries here,
example.
in
our
two
improved
"
but
first
The
where
50
Houses,
a
spatial
dimension helps the category with the most votes.
the PRE remains low.
22
model
Houses account
the
dimension
In other words,
reflecting the poor fits
worst-fitting
second
the
17th
in
and
for
here we
does
a
higher
some years.
32nd,
a
not
For
second
Government Management,
but
Agriculture,
particularly since
S9th House,
the
category that is not captured by a spatial model.
there were only three with at
seems
to
have
votes in the category.
gradually fallen out
of
the
II,
spatial
60 Houses,
Agriculture
)
Immediately
framework.
Agriculture had one-dimensional PREs over 0.6.
agriculture has been
the
In
the one dimensional PREs fell but Agriculture still
In the seventies and eighties,
fit spatially via the second dimension.
largely non-spatial.
Indeed,
from
the
voting
SSth House
Agriculture has consistently the lowest PRE of the six categories.
We repeated the above analysis,
coding.
the first
10
fifties and early sixties,
forward.
(In
one
the
be
to
least
after World War
on
appears
The
results were quite
for the Peltzman
using the same filters,
Results
similar.
for
Peltzman' s
policy code were like those for the Clausen Civil Liberties Code.
Clausen codes,
19
Domestic
As with the
voting in a variety of other areas also scaled on the second
dimension in Houses 76-91.
our analysis of PREs reinforces our
summary,
In
findings of low dimensionality.
Particularly in recent times,
dimension has an impact on fit,
the
that is essentially non-spatial.
impact
is
when a second
on the one area,
agriculture,
20
Spatial Stability
We have seen that,
spatial model,
a
to whatever extent
low dimensional model,
what of the temporal stability of
(1)
roll call voting can be captured by a
say "1-"
the model.
dimensional,
We address
Does the model consistently fit the data in time? (2)
dimension stable in tine?
of
."igure
spatial models fit poorly.
5
three
Is
But
issues here:
the" major,
first
Are individual positions stable in time.
(3)
1^
Inspection
suffices.
Stability of Fit
shows
that
there
are
Poor fit occurs between
23
only
1S15
two
and
occasions
1S25 when
when
the
Federalist party collapsed and gave way to the "Era of Good Feeling",
and in
the early 1850* s when the destabilization induced by the conflict over slavery
was
by
marked
stability,
model.
roll
In
collapse
the
call
contrast,
Whigs.
the
of
Thus,
voting can be described by a
voting
largely chaotic
is
spatial
unstable periods when a
the
In
the spatial model has consistently provided a good fit
the
political
of
dimensional
low
in
political party expires and a new one is formed.
periods
in
agenda was buffeted by a fast pace of external
to
twentieth century,
the data,
events,
even if
including
four
prolonged armed conflicts overseas and the Great Depression of the domestic
economy.
The Stability of the Ma ior Dimension
2.
Given the pace of events, it would be possible for the major dimension to
shift rapidly in time.
In our dynamic model,
rapid shifts are to some extent
foreclosed by our imposition of the restriction that individual movement can
be
only
linear
in
polynomial models
shift
back
time.
(see Table
forth
and
While
in
1)
the
small
the
gains
in
fit
from higher
order
constitutes evidence that legislators do not
we
space,
thought
important
it
to
evaluate
stability in a manner that allows for the maximum possible adjustment.
To
perform
dimensional,
this
evaluation,
we
return
to
model
(iii)
where
static D-NOMINATE was run 99 times, 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
no
constraint
tying
together the estimates, we cannot compare individual coordinates directly, but
we can compute the correlations between the coordinates for members common to
two Houses or two Senates.
matrix,
Rather than deal with a sparse
21
99x99 correlation
we focus on the correlations of the first 95 Congresses with each of
the succeeding four Congresses.
This allows us to look at stability as far
24
)
out as one decade.
In the upper portion of Table 5,
first
we average these correlations across the
Congresses and for four periods
95
of
of
the table shows that the separate scalings are remarkably similar,
Congress,
After 1861,
especially since the end of the Civil War.
a senator could count
over an entire
relative to his colleagues,
stable alignment,
on a
both Houses
For
history.
six year
term (t+1 and t+2).
Table 5 about here.
we display the individual
to save space,
In the lower portion of Table 5,
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 of
are
we show
is,
Consistent with the preceding discussion,
instability.
correlations
that
overwhelmingly
concentrated
pairs
in
where
at
the
low
least
one
Congress preceded the end of the Civil War.
It
further noteworthy that
is
for both Houses,
fall,
in the Era of Good Feelings
correlation in Congresses 14 to IS),
These
1850.
cases
preponderance of the
a
are
and,
spatial
not
for the House,
there
is
not
a
strong
first
dimension
but
in
least one pair
two
some
House
44
(1909-1910),
of
22
Congress.
14,
(The
15,
only
17,
and
Congress 17 has the lowest geometric mean for the 99 Senates.
Subsequent to the Civil War,
for
major
solid
simply cases of bad fit
geometric means below 0.6 for the House occur in Congresses
32;
in the
in the period around
where
flip-flops,
dimensions bear little relation to one another,
where
(at
correlations
low
the years
(1875-76),
the Great Depression.
is
only a
t+1
correlation below 0.8
which preceded the end of Reconstruction,
House 77 (1941-42),
in question
there
and Senate 69,
(1925-26).
involve either the "realignments"
Thus,
House
61
We note that none
of
the
1890' s
or
the realignments were not shifts in the space but
25
mainly changes in the center of gravity along an existing dimension. The first
the stability persists through the period in
dimension is remarkably stable;
the 40'
s,
and 60'
50' s,
the
second dimension was also important.'
a
Individual Stability and Reputations
3.
It
when
s
is possible to obtain high correlations
space.
If
serving
members
time
at
when individuals are moving in
all
t
had
equal
their coordinates would remain highly correlated even
coefficients,
were moving relative to individuals elected later than
To assess the stability of
legislator
nearly
computed
we
coefficients in our two dimensional,
movement
implied
whether an
in relative
movements
the
by
linear estimation.
space,
the
estimated
individual
is
moving relative
to
trend
Given that the space
one has to
trend coefficient
The
terms.
they
for each
the
in
we estimate is identified only up to translations and rotations,
interpret
if
t.
individual positions
annual
the
trend
legislators whose
tells us
careers have
overlapped the individual's.
I
'
Average trends for each Congress are shown in Figure
23
The figure
6.
reports results only for legislators serving in at least 5 Congresses
a
decade or more.
appear
— roughly
Similar curves for legislators with shorter careers would
systematically
above
those
plotted
in
the
figure.
Thus,
annual
movement decreases with the total length of service.
Figure 6 about here.
Two hypotheses are consistent with this observation.
legislators
legislators;
with
abbreviated
before Congress
the
of
service
tend
to
be
unsuccessful
their movement may reflect attempts to match up better with the
interests of constituents.
in
periods
On the one hand,
spatial
— such
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.
26
result
In
this
s
with
the estimate of the magnitude of true trend will be biased upward,
case,
greater bias for shorter service periods.
Another
movement
spatial
Figure
result,
period,
see
important
more
as
legislators with
limited for
finding
the
than
long careers,
that
shown
is
in
Prior to the Civil War there is a choppy pattern in the figure, most
5.
likely
is
we
one
part
in
consequence
a
of
smaller number
the
legislators
of
this
in
both in terms of the size of Congress and of the fraction of Congress
The key result
serving long terms.
occurs after the Civil War.
can be
It
seen that spatial movement, which was never very large relative to the span of
the
been
has
space,
secular
in
except
decline,
upturns
for
realignment and the realignment following the Depression.
II,
individual movement has been virtually non-existent.
party defections
Morse
by Wayne
and
Thurmond
Strom
24
25
in
the
1S90'
Since World War
(The visibility of
proves
the
rule.
An
)
immediate implication of this result is that changes in Congressional voting
patterns occur almost entirely through the process of replacement
or defeated legislators with new blood.
important than adaptation.
Congress as a whole may adapt by,
Of course.
But as such new items move onto the agenda,
be consistent with the preexisting,
The current
reputation
choose
to
relevant
in
spatial
to
their
changes
constituency,
to
foreign competition.
their cutting lines will typically
mobility is likely to reflect
While
issues,
in
lost
on
on
the
one
demographics,
the
other
the
hand
voters
Therefore
a
will
value
politician
predictability
faces
a
tradeoff
27
the
role
politicians
incomes,
etc.
of
might
that
are
process of adaptation may
result in voters believing the politician is less predictable.
averse
for
stable voting alignments.
American politics.
adapt
to
lack of
selection is far more
Politically,
moving to protectionism when jobs are
example,
of retiring
[BerrJiardt
and
In turn,
Ingberman
between maintaining
an
risk
(1985)].
established
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
reduced
of
reputation
maintain a
to
change
cultivating
in
constituency
in
perhaps,
and',
other
factors are manifested by the reduced spatial mobility of legislators.
What is Not Stable and Unidimensional: North and South
IV.
Since
Civil
the
political
a
American
generalized
events as
politics,
accommodated in this manner (Figure
of
the
terms
in
changed their positions to a somewhat greater extent
being
of
have
1930' s
During the realignments,
5).
been
Even such major
and
1890' s
have
terms,
liberal-conservative dimension.
"realignments"
the
spatial
in
largely been dealt with
Issues have
remarkably stable.
mapped onto
War,
legislators
than usual
(Figure 6),
but the changes were largely ones of movement within the existing space.
over
time,
movement
become
has
movement during the 30'
s
more
restricted,
with,
realignment than during the 90'
example,
for
been
And
lesser
s.
"North vs. South" of perhaps "Race" may be used to label the major issue
that has not fit
into
the
fits
prior
to
model
well
While at times the
liberal-conservative mapping.
Civil
the
War,
the
fit
is
pervasive.
less
The
conflict over the extension of slavery to the territories produced the chaos
in
voting
throughout,
in
the
1850s.
In
the
20th
century,
while
voting
a second dimension becomes important in the 1940' s,
is
50' s
spatial
and 50'
s,
when the race issue reappeared as a conflict over civil rights,
particularly
with respect
South.
The
system,
was
rights
civil
to
racial
issue,
desegregation and voting rights
rather
than
fully
destabilizing
the
in
the
accommodated by making the system two dimensional.
To
directly.
this
point,
however,
our
analysis
has
not
We have only noted anomalies in the fits
examined
the
in periods
race
issue
when race is
Results based on the Clausen and Peltzman
thought to have been a key issue.
categories
helped
somewhat,
Clausen's
but
issues
Domestic Social Policy codes cover many non-race
speech and the Hatch Act.
However,
and
Peltzman's
such as
freedom of
Liberties
Civil
we have our own more detailed coding of
all roll 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.
issues
these
analysis for
The
contained
is
results for all Houses that had at least
like
The first
appearance of
many
do
that
scale well,
the
fit,
15th and
not
slavery is
have
a
sustained
Table
6,
which provides
roll calls coded for the topic.
in
The
1809-10.
appearance
on
— we suspect
agenda — does not
issue
the
and disappears for over a decade,
even in two dimensions,
15th Houses.
5
in
Although these Houses are quite poor
in
until
overall
the slavery votes fit quite nicely along the first dimension.
Table 6 about here.
From the 23rd through the 3Sth House,
slavery votes in every House.
accommodated
within
the
there are substantial numbers of
From the late 1830'
structure
spatial
s
through 1846,
by
a
Compromise of 1850.
There
is
a
a
period centered on the
substantial reduction in the ability of the
spatial model to capture slavery votes.
number of slavery roll
dimension.
The destabilization of
Classifications and PREs are high during this period.
the issue begins in 1847 and continues through 1852,
second
slavery is
calls perhaps
A temporary reduction in
the actual
testifies to the difficulty of dealing
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
the
early
1850'
s
and
the
29
elections
of
1856
mark
the
virtual
completion of the process of the replacement of Whigs by Republicans.
As
the
party system changed,
true
1853-54 onward, when the Kansas-Nebraska Act was passed,
model exceptionally well on the first dimension
defined
First
dimension.
this
.
dimension
From
slavery votes fit the
Particularly,
1853-54,
in
slavery most
represented a quarter of all roll calls,
when "slavery"
occurred.
realignment
spatial
classifications
likely
PREs
and
are
remarkably high.
The
North-South conflict persists
on
dimension via
the
1873-74.
votes from the Civil War through the 43rd House,
(The alternative label "race"
PREs remain high.
"Civil
Rights"
Classifications and
is suggested by the fact that
roll calls in the category "Nullification/Secession/Reconstruction"
also line
up on the first dimension, but with somewhat lower PREs than "Civil Rights".)
From 1875 through 1940, "Civil Rights" votes occur only sporadically.
line
with our
realignment,
contention
that
"race"
is
the
major
determinant
of
In
spatial
this period is stable and largely unidimensional.
"Civil Rights" reappears on the agenda in 1941-42.
For the next thirty
years it remains as an issue where the second dimension is always important.
Through 1971-72,
PRE.
Indeed,
the two dimensional scaling always adds at least
the
first
dimension
often
is
"orthogonal"
several one dimensional PREs in Table 6 are close to zero.
the
second dimension increased PRE by over 0.5.
detailed
coding of
issues
produced
least five votes in a Congress,
other time in the 99 Houses
978
a PRE
— Public
of
10 to
Civil
the
Rights;
In five instances,
Despite
occurrences
to
0.
the
issue
fact
codes
that
our
with at
improvement over 0.5 occurred only one
Works in 1841-42.
The pattern of PRE improvements is echoed by Figure
5;
t.he
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.
30
In
the second dimension curve
fact,
is even further above
(i)
Senate took on civil rights filibusters.
"Civil Rights"
1850' s,
debate
had
shifted
from
one
unlike slavery votes
the House,
In
votes were never a substantial fraction of the
By the 1970'
The debate was contained.
votes before Congress.
changing
of
status
the
civil
votes
rights
occur
the
in
93rd,
and SO' s the
to
Correspondingly,
and
95th,
s
southern blacks
of
measures that would have a national impact on civil rights.
although
for
(iii)
reflecting in part the many cloture votes the
the Senate during this period,
in the
that of
97th
House,
the
second dimension no longer makes a major contribution.
The accommodation of
traced
out,
the
for
civil
the
Senate,
Figure
in
system is
issue to the political
rights
the
At
7.
inception
Franklin
of
Roosevelt's administration, race was not an important political issue, and the
primary concern of southern Democrats remained the South'
on Northern capital.
economic dependence
s
southern Democrats appeared largely as a
As a result,
random sample of all Democrats or,
they were differentiated,
extent
the
to
As the importance
they represented the liberal wing of the party (Figure 7A).
of
the
race
intensified in the
issue
1940s,
southern Democrats began to be
differentiated from northern members of the party
1960s,
when civil
the dominant
rights was
(Figure 7B).
By
item on the congressional
the
mid
agenda,
southern Democrats had separated nearly completely (Figure 7C) and there was a
virtual three party system.
In
these years,
roll call votes on civil rights
issues tended to have cutting lines parallel to the horizontal axis,
southerners,
at
Republicans,
to
increasingly
large
the
the
top
of
rest
of
numbers
the
the
of
picture,
Senate.
registered
and
In
a
later
black
few
highly
years,
voters,
opposing
conservative
confronted
southern
with
Democrats
gradually took on the national party's role of representing such groups as
minorities
and
public
employees.
Consequently,
31
the
dif f ere.ntiation
of
southern from northern Democrats decreased (Figure 7D).
27
Figure 7 about here
On
the
changes
in
whole,
the
process we have
membership of
the
the
traced out
occurred largely
through
southern Democrat delegation in Congress.
Those who entered before the passage of key legislation in the 1960s tended to
conservative positions than those who entered after.
in more
locate
changes by southern Democrats have resulted
in
the
1980' s
28
being not
The
only a
period in which spatial mobility is low but also one which is nearly spatially
unidimensional.
V.
Predictions from the Spatial Model
The great stability of individual positions does not suffice to make the
spatial model predictive.
Predicting
roll call requires knowledge of the
a
cutting line in addition to knowledge of legislator positions.
model
is
therefore not useful
prediction at
for
issue has been "mapped" onto the space.
an early
For example,
spatial
The
before
stage,
an
the spatial model is not
relevant to explaining why, of two perhaps equally conservative recent Supreme
Court
nominees,
one,
Antonin Scalia,
was
confirmed by a 99-0 vote
whereas
another, Robert Bork, was rejected.
What the spatial model does assert is that voting alignments must largely
remain
process
of
consistent
— involving
efforts
to
with
spatial
positions.
Thus,
interest groups and the U'hite House
alter
the
location
lobbying and other aspects of
of
the
cutting
— can
line
on
be seen as a set
an
Once
issue.
mapping have been completed,
the
lobbying
the
the
spatial
model can be used for short-term forecasting.
To
(Figure
illustrate,
8).
The
consider
spatial
the
vote
positions
in
estimation with only 1985 data used.
32
on
the
Judge
Bork
figure
in
result
the
fall
from
of
model
19S7
(iii)
)
Figure 8 about here.
the five most liberal members
Quite early on in the confirmation process,
and the five most
of the Judiciary Committee came out
in opposition to Bork,
conservative members supported him.
The last four members of the committee to
take a public stance were between these two groups,
finding parallel to our
a
earlier result that "errors" tend to occur close to cutting lines.
As
soon
possible to predict,
since
against,
for
the
accurately,
remaining
Bork,
one
made
(R-PA)
known
the final
that
opposition,
his
was
committee vote would be 9-5
undecided members were
three
it
all
more
liberal
using the fact that Grassley (R-IA) had announced
At this time,
than Specter.
support
Specter
Arlen
as
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 19S5 were predicted to vote on party lines.
we
8,
present
information
some
announcements as well as the final vote.
At
the
individual
vote of 7 of 100 senators.
level,
the
the
29
temporal
The actual
spatial model
ordering
of
echoing the committee,
Note that,
moderates tended to announce relatively late.
58-42.
on
vote was
final
incorrectly forecast
As was the case with Figure
2,
the
the errors tend to
be close to the cutting line.
VI.
Consensus and Impasse
Conclusion:
Although the spatial model has an applied use in short-term prediction,
its greater relevance
political system.
two
is
in what
it
indicates about long-term changes
The average distance between legislators within each of our
major parties has remained remarkably constant
{Figure 9).
in our
for
mere
than
a
century
The maintenance of party coalitions apparently puts considerable
constraint on the extent of internal party dissent.
Figure
9
about here.
33
In
contrast,
the average distance between
years.
100
30
The
inference
legislators--has shrunk considerably in the
the average distance between all
past
the parties--and by
between Edward Kennedy and Jesse Helms
conflict
is
undoubtedly narrower than that which existed between William' Jennings Bryan's
allies and the Robber Barons.
Symptomatic of the reduced range of conflict is
the willingness of most corporate political action committees to spread their
the most liberal Democrats in
campaign contributions across the entire space,
31
the southwest quadrant excepted.
a well-defined two party system
Although,
persists and although liberals and conservatives maintain stable alignments
the range of potential policy change has been
within each party (Figure 7D),
sharply reduced.
that
polarization
long-term,
While our earlier
contention
increased
1970s
the
in
is
(Poole
and Rosenthal,
supported
Figure
by
1984)
9,
more relevant pattern has been toward a national consensus.
the
The
cost of consensus can perhaps best be seen in the alleged wasteful concessions
to
special interests in such programs as agriculture,
and defense and
space,
in the alleged failure of the nation to address a variety of inequities that
befall various groups of citizens.
The benefits are perhaps made apparent by
recalling the Civil War and the period of
intense
conflict
labor movement in the late 19th and early 20th centuries,
fragility of democracy in some other nations.
surrounding the
and by observing the
We do not pass
judgment but
simply point to a regularity in a system that,
as manifest by its ability to
absorb
is
the
supposed
"Reagan
Revolution,"
indefinitely.
34
likely
to
be
with
us
Appendix
The Estimation Algorithm
The algorithm employed to estimate the model simply extends the. procedure
developed
detail
in
and Rosenthal
Poole
in
constant coordinates.
restricted to unidimensional,
for
k>2
and
=
x
=
x
is
for
all
we
Here
i)
=0
z
Jlk
the
new
handle
the
sketch
briefly
was
11
with emphasis
D-NOMINATE,
procedure,
(That
ik
=0
x
11
earlier model
The
(1985).
needed
modifications
on
to
more general model.
the procedure begins by using a starting value for
As before,
of
starting
values
are
coefficients
for
the
initially
senator
parameters
set
zero.
to
similarities scaling (Torgerson,
For
the metric
scaling,
with
common
legislators
a
an agreement
period
score
analogous
score
The
ratings
metric unfolding scaling in Poole and Daniels
(1985).
are
interest
the
to
metric
simply
is
Scores vary from
group
thus
by
formed for each pair of
is
percentage of times they voted on the same side.
and
obtained
are
polynomial
1990).
service.
of
other
(The
.
These
)
Poole,
1958;
x
and a set
/3
were
that
the
100
to
subject
The matrix of
to
these
scores is converted into squared distances by subtracting each score from 100,
dividing
by
and
50,
squaring.
matrix
The
of
double-centered (the row and column means are subtracted,
is
are
added,
to produce
each element)
to
extracted
from
scaling procedure.
the
cross product
a
distances
squared
and the matrix mean
Eigenvectors
cross product matrix.
matrix
used
and
is
start
to
the
metric
This procedure produces the starts for D-NOMINATE.
D-NOMINATE proceeds from the starts by using an alternating algorithm
common
procedure
in
psychometrics)
coordinates
are
estimated
coordinates
and
/3
on
separately.
In
first
Since
constant.
across roll calls (for fixed
be estimated
the
(i
In
.
roll
first
a
dimension,
call
stage,
the
roll
holding
the
legislator
coordinates
and legislator coordinates),
a
second stage,
A-1
(a
are
call
independent
each roll call can
legislator coordinates are
the
.
estimated
on
the
dimension,
first
again
everything
holding
else
constant.
Because each legislator's choice depends only upon his own distances to
roll call outcomes,
if
choice
legislator's
(i
is
and the roll call alternatives are held fixed,
independent
of
Independence allows us to estimate each
those
legislator's
coordinate
separately.
These two stages are then repeated for the each higher dimension.
stage,
we estimate the utility function parameter
and z values.
obtain
P,
In a third
holding constant all x
Within each stage, we use the method of Berndt et al.
maximum likelihood estimates of
(conditional)
three stages define a global
iteration of D-NOMINATE.
repeated until both the x's and the
each
legislators.
other
all
of
the
the
(1974)
parameters.
Global
to
These
iterations are
correlate above 0.99 with their values
z' s
at the end of the previous global iteration.
In Poole
and Rosenthal
(1985)
we explain
in detail
underlying model accurately represents behavior,
run amok,
why,
even when the
estimated x and z values can
taking on values with exceptionally large magnitudes.
this problem,
After unconstrained x estimates have
constraints are imposed.
been obtained on a dimension,
the
To deal with
maximum and minimum coordinates for each
Congress are used to define constraint coordinates:
T
max X
2
Itk
mm
2>
X
1/2
Itk
tk
For each legislator, we then define a constraining ellipse by computing,
for k=l
s
L
n
Ik
1
The X
tv
t.€T
and the origin define an ellipse.
y
L
H
X
n
ik
1
where T
= {tli
is
t€T
We then compute for k=l
s
X
Itk
in the estimation in Congress t} and n
A-2
=
IT
I,
the number
of Congresses served in by
averages
Thus,
legislator was
interior
in
the
data
1
from
the
relative
unless T
is
x
to
for
legislator
the
2
x
the
the
in
is
unconstrained.
is
currently
dimension
the
on
the
which
being
Ik
ik
is constrained to keep the legislator inside
Ik
other words,
In
origin
Note that,
and
x
Congresses
all
point defined by
the
If
ellipse,
estimated are set to zero and x
the ellipse.
over
taken
set.
parameters
^
the
Otherwise,
being
are
legislator's
the
of
i.
legislator
a
not allowed
is
overlap his
others who
identical for all
her
or
drift
too far
service
period.
to
the entire configuration
i,
not
is
constrained to the same ellipse.
A
similar
Congress,
constraint
we use the x
roll
call
is
unconstrained.
roll
the
in
and the origin to
defined by coordinates
call midpoint,
the
imposed
is
define an ellipse.
z
+
(z
Jyk
Otherwise,
Jnk
)/2,
each
the roll
If
inside the ellipse,
is
coordinate
the
For
phase.
call
currently being
estimated is adjusted to keep the midpoint within the ellipse.
Constraints
The
identification
problems
lead
that
to
necessarily a consequence of specification error.
constraints
the
are
The problems would
not
arise
even if the actual process generating congressional roll call decisions were
precisely the one outlined in Part
by
the
obvious
homoscedastic
specification
logit
D-NOMINATZ will
error.
error
In
try to arrange
predicted to vote with the majority;
least one z)
a
to drift outside the
constraint.
spatial voting.
Conversely,
implicit
some
fact,
the
the problems are accentuated
However,
I.
roll
in
the
calls
assumption
are
cutting line so that all
highly
of
a
noisy.
legislators are
this will cause the cutting line
(and at
space spanned by the legislators and invoke
some roll calls are noiseless,
Although the cutting
line
A-3
is
representing perfect
precisely identified,
maximum
will
likelihood
try
at
z' s
very
a
distance
large
from
the
at
the
Again a constraint is needed.
legislators.
Likewise,
a
constraint
constraint
ellipsoid
is
needed
noiseless
for
legislators
The problem should not be exaggerated,
extremes of the space.
the
both
put
to
we
invoked,
is
know,
still
When
however.
reliably,
that
the
individual is an extremist in the direction of his/her estimate.
Standard Errors
'
•
The constraints forced many of our estimates to the boundary rather than
the
interior of
the parameter
linear model for
the House
percent
legislator
the
of
space.
14.1
(For
example,
percent of
the
roll
were
on
the
estimates
in
two dimensional
the
call
estimates and 4.2
boundary.
As
)
such,
Another
conventional procedures for computing standard errors do not apply.
problem with the standard errors produced by the D-NOMINATE program is that
they are based only upon a portion of the covariance matrix.
A standard error
for a legislator coefficient in the linear dynamic model comes,
for example,
solely from the inversion of the 2 by 2 outer product matrix computed when the
legislator's coordinates are estimated for a given dimension in the legislator
phase
of
compute,
the
at
and invert.
alternating
convergence,
The
algorithm.
the estimated
This computation is
appropriate
would
be
to
information matrix for all parameters
impractical,
the dynamic models covering all of U.
procedure
S.
even on supercomputers.
history,
With
the matrices would be larger
than 100,000 by 100,000.
For the reasons outlined above,
the standard errors reported in the text
must be viewed as heuristic descriptive statistics.
Consistencv
In
addition
parameters problem.
to
the
problem
of
constraints,
we
have
an
incidental
Because every legislator and every roll call has its own
A-4
we add parameters as we add observations;
set of parameters,
thus the standard
At
consistency property of maximum likelihood does not apply.
at
far faster
a
rate
practical
The key point is that data is being added
this caveat is not important.
level,
a
than parameters.
Consider
the
dimensional
two
linear
Assume our time series were augmented by a new senate with 15 freshman
model.
We would eventually add 60 parameters for
senators and 500 roll calls.
the
senators (assuming they all acquired trend terms) and 2000 parameters for the
roll
estimate
To
calls.
to
For the House of Representatives,
1.
would
we
parameters,
have
50,000
The ratio of observations to parameters ratio is
(100x500) new observations.
25 to
new
2060
these
a
similar ratio would be over 100
We suspect that many empirical papers published in professional social
1.
science journals have had far lower ratios.
Haberman (1977) obtained analytical results on consistency for a problem
closely related to ours.
literature.
testing
place
In
in fact
is
voting
on q
educational
roll
calls,
p
A version of the Rasch model analyzed by
and "incorrect" answers.
(1975)
legislators
p
the
The role of "Yea" and "Nay" votes is played by
has a "difficulty" parameter.
Lord
of
from
Each subject has an "ability" parameter and each test
subjects take q tests.
"correct"
treated the Rasch model
He
isomorphic with a one dimensional Euclidean model of
roll call voting developed by Ladha (19S7).
Haberman
which a
> p
n - -^n
considered
.
In
other words,
number of legislators.
that
log(q )/p
n
n
increasing
->
->
CO.
of
the number of roll
In addition,
as n
sequences
integers
{q
},
{p
}
for
calls always
exceeds the
^
make the (innocuous) technical assumption
Under these conditions,
Haberman establishes
consistency for the Rasch model.
Few actual processes,
Haberman'
s
stringent
including Congress,
requirement
that
p
A-5
and
can be thought of as satisfying
q
both
grow
as
n
grows.
But
Haberman cites Monte
recovery
excellent
studies
Carlo
maximum
conventional
for
between 20 and 80 and q of 500.
modern Senate and 435
by Wright
in
the
In D-NOMINATE,
Douglas
and
likelihood
estimators
show
for
p
the effective.? is 100 in the
The effective 'q
modern House.
that
[1976)
about
is
900.
Similar Monte Carlo evidence is contained in Lord (1975).
The D-NOMINATE model differs from the Rasch model
function
non-linear
the
of
Although
parameters.
in
utility is
that
theoretical
Haberman' s
results and the previous Monte Carlo results are suggestive,
a
appropriate
it is
to conduct direct Monte Carlo tests of our algorithm.
Monte Carlo Results
Summary of Previous Experiments
Previously,
in Poole and Rosenthal
(1987),
we reported on extensive Monte
Carlo studies of the one dimensional NOMINATE algorithm.
we used the estimated senator coordinates from a
coordinates
Over
used
We
calls.
and
runs,
all
wide
a
alternative
used
the
variety
squared
scaling
alternative
of
"true"
correlations
coordinates and the true ones exceeded
sets
values of
0. 98.
of
of
297
"true"
1979
roll
roll
call
between 7.5
/3
between
locations,
As "true"
the
recovered
and
22.5.
legislator
The standard error of recovery
of individual coordinates (the variability across Monte Carlo runs) was on the
order of 0.05 relative to a space of width 2.0.
higher than the true.
Recovered
our one dimensional
Thus,
accurate under the maintained hypothesis of the model.
discussion in the paper
estimates
(for
are
slightly
Recovery came closer to the true value as the number of
observations was increased.
the
^' s
example.
is
estimates are highly
Moreover,
as most
of
essentially based on summaries of parameter
Figure
uses
6
average
distances),
statistical
significance would not be an issue.
We
also
did
the
counterf actual
experiment
A-6
of
setting
/3
to
zero
by
data
generating
with
coin
random
a
recovered
The
toss.
distribution
of
legislators was far more tightly unimodal than any recovered from actual data.
More
importantly,
geometric mean probability was only 0.507,
the
than almost all values reported in Figure
5.
far
lower
.
An Extensive Test of the Static Model in One and Two Dimensions
The work we have just summarized all was done under the assumption that
the
generated
was
data
signal-to-noise
ratio,
by
true
a
dimensional
subsequently
We
/3.
one
world
undertook
with
constant
a
work
additional
that
examines the performance of D-NOMINATE with a true two dimensional world.
addition,
In
we studied how robust D-NOMINATE was to violation of the constant
(B
All the work was done using the static model on one "Senate" of a
assumption.
We did not pursue simulations of the dynamic
hypothetical single "Congress".
model because such simulations are too costly in computer time.
To
simulate a
we had
"Senate",
101
"senators"
vote on 420
roll
calls.
Finding good recovery with only 420 roll calls should bode well for our actual
estimations,
votes
in
since,
the past
in
their careers.
Thus,
simulation we drew 84,840 = 2
centuries,
two
to
generate
(choices)
the
x 420
legislators have averaged 909
"observed"
calls)
(roll
choices,
x
101
in
each
(senators)
random numbers from the log of the inverse exponential distribution.
In
simulated
each
Senate,
from [-1,+1].
Thus,
of length two;
in two dimensions,
we
drew
the
senators'
coordinates
uniformly
in one dimension the senators were distributed on a line
on a square of width two.
Midpoints of roll
calls followed the same distribution.
We had a 2x2x2 design for the simulations.
dimensional world vs.
world with
actual data,
a
fixed
a
/3,
One comparison was a true one
A second was comparing a
true two dimensional world.
set
and a variable
equal
|3.
to
15.75
to
match
When the variable
A-7
(3
typical
estimates
model was used,
from
for each
call we drew
roll
interval
15.75.
[8.13,
uniformly from
1//3
23.26].
The
[.043,. 123].
IB'
s
were thus
The median of the distribution of the random
the
s
was
/3'
We define the
high error rates.
The third design factor' was low vs.
in
error rate as the percentage of choices that are for the further
alternative,
that is the percentage of choices for which the stochastic error dominates the
spatial portion of the utility function.
lis,
After the legislator positions,
the error rate can be controlled by
and the midpoints have been assigned,
scaling the distance between the "Yea"
average distance,
the greater
outcomes.
and "Nay"
smaller the
The
Scale factors were chosen to
the error rate.
keep the average rate in the Low condition close to 14%,
about
level of
the
classification error attained by D-NOMINATE with the Congressional data.
the error rate was set
the High condition,
the
In
above that for the worst
to 30%,
Congresses in our actual scalings.
Our design yielded 8=2x2x2
simulations,
conditions.
/3
(2)
each
we
condition,
ran 25
We emphasize that each simulation had the
for a total of 200.
following sources of randomization:
roll calls;
In
(1)
utility of each choice;
spatial
(3)
locations of legislators and
3 for each roll call
(in variable
condition only).
We computed two sets of statistics to assess the recovery by D-NOMINATE.
First,
we computed the 5050 distances representing all distinct pairs of the
101
legislators.
the
"true"
For every one of the 200 simulations,
distances and the "recovered"
distances.
we did this both for
Since substantive work
using the scaling will depend only on relative position in a space,
summarize all the information in the scaling.
eliminates
arbitrary
recovered spaces
than
looking
at
but
one
scale
and
rotational
also reduces assessment
dimension
at
a
time.
A-S
distances
Focusing on distances not only
differences
to
a
Second,
between
true
single criterion,
we
and
rather
cross-tabulated
the
"Yea-Nay" predictions from the scaling with the "Yea-Nay" predictions from the
"true"
spatial representation.
fit.
Comparing
The percent of matches
predicted
simulated
to
is
good measure of
a
predicted
"true"
better
is
than
comparing simulated predicted to "true" actual because the scaling is designed
to
spatial aspect of voting,
recover the systematic,
not
So we
the errors.
want to know how well D-NOMINATE scaling noisy data would predict voting if
the noise were removed.
simulation
The
presented
are
results
in
Table
An
A-1.
immediate
observation is that the two dimensional world is not recovered as well as the
This is to be expected.
one dimensional world.
is
The number of "observations"
but the parameter space is doubled in
identical in every design condition,
moving to two dimensions.
,
.
Table A-1 about here.
first
The
column of
the
correlate with the "true".
table
It can be
shows
how
well
seen that D-NOMINATE is very robust with
Recovery of senators
respect to variability in noise across roll calls.
totally insensitive to whether the "true" world has
calls
one
or
with
considerable variability.
decline with dimensionality.
recovered distances
the
On
a
fixed
the
/3
other
is
across all roll
does
fit
hand,
Raising the error level forces only a moderate
deterioration in fit.
To
some
degree,
the
lack
higher measures
of
reflects the constraints in D-NOMINATE.
an
ellipse when estimation is
dimension,
this has no
come from a square.
the
last
column
correlations
of
between
but
in
fit
in
two
to
a
single
two dimensions
"Congress".
t.he
"true"
The im.pact of the constraints can be seen
Table
the
A-1
to
recovered
dimensions
The constraints force estimates into
restricted
impact,
of
the
first.
solutions.
A-9
The
I.n
last
one
In
one
coordinates
in comparing
column
dimension,
reports
these
)
correlations are slightly less than the correlations of the recovered with the
true distances.
two dimensions,
In
the pattern reverses.
the distorting
As
constraints tend to get invoked for the same senators in all recoveries,
recovered points, particularly at low error levels,
impact of
The
constraints
the
tend to be very similar.
seen in the second column.
also
is
distances between senators are more precisely estimated,
With
when the error level is high.
high error level,
a
periphery of the space have some "noise"
estimates
dimensional
two
in
"High"
as
two
in
The
dimensions,
legislators near the
their voting patterns,
in
constraints are invoked less frequently.
the
and
the
higher percentage of precise
(The
compared
to
dimensional
one
"High"
reflects the fact that the average distance is greater in the two dimensional
space
than
in
dimensional
one
the
space,
ratios
so
of
true
distances
to
standard errors tend to be greater.
Actual vote predictions are less sensitive to whether the constraints are
The
invoked.
third col\imn of
table
the
results
shows
clearly indicate the high quality of the recovery.
that
appear
to
most
At a low level of error,
the implications for predictions of actual choices from the spatial model are
nearly identical between the true space and the recovered space.
only a slight deterioration
estimated.
levels
of
The
fit
error.
is
In
(94 percent
still
all
but
good,
cases,
vs.
the
95)
less
is
when two dimensions must be
than perfect,
standard
There
errors
are
at
high
(very)
extremely
small,
demonstrating that our simulation results are insensitive to the set of random
numbers drawn in any one of the 200 simulations.
Tests Using Real Data But With Random Starting Coordinates
We
spatial
have
seen
that
configuration.
the
D-NOMINATE algorithm reliably recovers a
Nonetheless,
since
A-10
the
likelihood
function
"true"
is
not
the recovery is potentially sensitive to the starting values.
globally convex,
Perhaps even [slightly) better recoveries would result if a different starting
D-NOMINATE can break down either
procedure were used.
from
the
agreement
matrix
provide
poor
and
starts
the
if
Poole'' s
eigenvectors
procedure
is
sensitive to starts or if D-NOMINATE is sensitive to minor differences in the
output from Poole's procedure.
Thus,
the results we report are a joint
test
of the sensitivity of the two procedures.
The test we carried out was to scale the S5th House and the 100th Senate
(not included in our 99 Congress dataset)
replacing the agreement matrix with
The coordinates were again
random coordinates as input to Poole's procedure.
generated uniformly on
estimated
in
one,
two,
[-1,+1].
and
three
Both the S5th House and
dimensions,
with
100th Senate were
simulations
10
for
each
dimension.
Again we assessed fit by averaging the (45) pairwise correlations between
the distances generated by the 10 simulations.
We also computed the average
percentage of agreement in predicted choices over the 45 comparisons of the 10
The results appear in Table A-2.
simulations.
identical.
The recoveries are virtually
The fits do become less stable as the dimensionality is increased
but this reflects only the general statistical principle that adding colinear
parameters
can
reduce
the
precision of
estimation.
parameters are also estimated in the simulations.
more rapidly for the House,
)
(N.b.
Thus,
The
roil
call
the fit deteriorates
since there were only 172 roll call votes there as
against 335 for the Senate.
Table A-2 about here.
These results show that D-NOMINATE combined with Poole's metric scaling
procedure performs well in the joint test we carried out.
are
essential
to
accurate recovery of the space.
A-11
We stress that both
Particularly with two or
more dimensions,
D-NOMINATE does a better job of recovery than the output of
metric scaling.
On the other hand,
with
begins
random
D-NOMINATE itself does very poorly if it
While
starts.
results
are
not
as
enough to allow D-NOMINATE to converge
they are good
accurate as D-NOMINATE,
scaling
metric
the
to a solution close to the true configuration.
The "Twist" Problem
experiment
above
The
procedure
is
insensitive
to
showed
the
little
with
that
starts.
In
actual
"missing"
practice,
data,
our
legislator
a
votes on only a small slice of all roll calls in the history of a house of
Congress,
a
so there is very substantial "missing"
problem as
long as
there
is,
as
in modern
results become sensitive to the starts.
nineteenth
the
times,
"Missing" data is not
substantial
overlap
But when the membership of either House shifts very rapidly,
careers.
in
data.
With
century.
in
the
The problem is greatest for the House
large
amounts
of
missing
Poole's
data,
procedure provided poor starts to D-NOMINATE.
Our approach to this problem was to watch animated videos of the scaling
results.
When rapid movement induced a "twist"
in the position of senators,
we investigated multiplying second dimension starts for certain years
nineteenth century only) by -1
— thereby
flipping polarity.
(in the
The result was to
have a very slight improvement in the overall geometric mean probability and
to substantially reduce the magnitudes of estimated trend coefficients
period in question.
In other words,
space
is
together,
movement.
it
difficult
in the
when there is little overlap to tie the
to
identify
the
parameters
of
spatial
The results reported in the paper reflect the highest gmps we have
been able to achieve;
they also have lower trend coefficients than solutions
with slightly lower gmps.
(Our
use of
familiar with
see
minor differences
our
work
may
A-12
changed
starts explains why
between
results
readers
here
and
Experiments with different starts are
those presented in conference papers.
a
standard procedure in the estimation of non-linear maximum likelihood models.
)
Why a Supercomputer is Needed
supercomputer
A
obviously
is
score matrices nearly 10,000 by
agreement
to
extract
10,000.
A
needed
eigenvectors
supercomputer
is
from
also
essential to D-NOMINATE.
The large memory of a supercomputer is critical.
step each legislator's estimate
independent of all
is
entire roll call record as a batch.
call-by-roll
entire
data
set
However,
call.
must
Similarly,
having
accessed,
be
the
in
others,
the
this step
processing each legislator's
can be done as an iteration over the legislators,
roll
Since in the legislator
the roll call step can be done
utility function
memory
step,
enough
large
where
the
hold
all
To
make
to
observations is essential to rapid processing.
The
original
processing efficient
"transpose"
data
ICPSR
in
the
the data set.
Cyber 205 FORTRAN made
transposed data
in
it
set
organized
is
legislator phase,
The
by
roll
we first used a Cyber 205
to
large memory of the 205 and the BIT mode of
possible
memory during
for
the
us
to
store
both
the
data
and
the
Even
entire execution of D-NOMINATE.
with this use of memory and with a highly vectorized code,
dimensional
call.
estimating the two
linear model for the House requires approximately three hours of
processing time.
These
computations might be
attempted
could be read from disk repeatedly.
on
smaller
The
data
The repeated disk reads plus the slower
processing time would make for a very long com.putation.
problems,
computers.
Of
course,
smaller
say a few hundred legislators and several hundred roll calls would
be feasible on a large workstation.
A- 13
NOTES
does
not
imply
that
strategic
all
complexities
fit
Congress
in
into
this
Van Doren (1986) has stressed a number of ways that focusing solely on
mold.
"sample
induces
calls
roll
emphasized
that
selection
Khrebiel
In particular,
conclusions.
have
call voting can be accounted for by a simple model
that roll
The fact
great
a
bias"
in
of
substantive
at
and Smith and Flathman
(1986)
deal
arriving
business
important
(1989)
handled
is
by
unanimous consent agreements or voice vote.
2
3
See Enelow and Hinich (1984) and Ordeshook (1986).
For a set of figures
Quarterly
"key"
(1989b).
In
Senate
addition,
those in Figure 2 covering all Congressional
like
roll
calls
from
1945-85,
Jackson amendment
the
to
Poole
see
the
1972
analyzed in Poole and Rosenthal (1988) and the Taft-Hartley,
Act
final
passage,
and
busing
votes
are
analyzed
in
and
SALT
Rosenthal,
I
treaty
is
1964 Civil Rights
Poole
and
Rosenthal
(1989a).
4
The post WWII
Figure
6.
is
aptly illustrated by the 88th Senate panel
in
The antebellum and postbellum divisions are shown graphically in
Poole and Rosenthal
the 73rd Senate
(ID)
split
as
(1989a).
The postbellum Republican split continued into
shown in Figure
Western Republicans,
6.
such as Borah
and Nye (ND) and Frazier (ND) tend to be at the top of the figure along
with the two Progressives, Lafollette (WI) and Norbeck (SD).
5
If we were
to
allow every legislator to have trend parameters,
additional parameters would be required for
smaller number
is
used
in
practice,
since
the
no
trend
legislators serving in only one or two Congresses.
N-1
two
23, 146
dimensional model.
term
is
A
estimated for
did
We
not
make
identified
linear
distance
in
tenuous,
(although senator
locations and cutting
when data is generated,
in a Monte
call
lines
outcome
coordinates.
practice,
In
substantially as to level of error
the fact
empirically,
that,
(/3).
roll
we are able to
calls
This variation in error
make
for
very noisy estimation of
is
used
assuming
a
common
/3,
we
still
estimates of legislator coordinates and cutting lines.
vary
to
level and
outcome
the
form used
the
in
quadratic
utility
utility
function.
specification
(19S7)
obtained
|3
accurate
estimation
very robust
Ladha
and
obtain
Moreover,
legislator coordinates and of cutting lines may be
dimensional
likely
are
When the Monte Carlo work generates the data with variable
D-NOMINATE
functional
recover the
most distances are in the concave region of our
estimated utility function,
coordinates.
though,
by simulated
Carlo experiment,
behavior that corresponds to our posited model,
of
preserve
to
While identification that occurs via choice of functional form can be
are).
and
order
in
use quadratic utility because the roll
We did not
differentiability.
locations are not
utility
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
coordinates and midpoints.
7
To sum
legislature
More details are available in the Appendix.
Southern Democrats are those from the eleven states of the Confederacy,
Kentucky,
and Oklahoma.
N-2
g
We performed significance tests on our estimated roll call coordinates.
We tested both the null hypothesis that all roll call coordinates were zero
To carry out the
and the null hypothesis that the vote "split the parties."
we began by estimating the legislator coordinates and
tests,
eliminates
all
the
include
not
did
that
calls
roll
statistical
vote
the
question.
in
problems discussed
using sets of
procedure
This
'
Appendix.
the
in
/3
The
Panama Canal Treaty vote was the 755th in our estimation for the 95th Senate.
For the test, we used the first 754 roll calls in that Senate to estimate the
legislators and
896
last
the
The NSF vote was the 70th in the 97th Senate.
/3.
votes
that
in
Senate.
supercomputer time per significance test,
estimation
only
excluding
roll
from
these
configurations
the
legislature
avoid
(To
using
hours
two
of
we did not rerun the full dynamic
call
question.
in
subsets
of
estimated in this first step as fixed parameters,
estimated
The
calls
roll
identical to those obtained from the dynamic estimation.
x' s
We used
virtually
are
Treating
)
and the
/3
we then used the roll
call of interest 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
fair coins on the vote.
are
zero
equivalent
is
the hypothesis that all coordinates
In other words,
to
the
more general
hypothesis
that
=
z
=
z
z
Under
.
the
L(H )=N Jn(l/2), where N
J
j.
null
Jn2
Jy2
is
hypothesis
^^
the
log-likelihood
^
and
z
Jnl
Jyl
is
simply
^ ^
the actual number voting or paired on roll
call
J
log-likelihood of the alternative,
The
D-NOMINATE.
For
Panama Canal Treaty,
the
denoted,
L(H
find L(H
we
)
),
=
is
computed by
L(H
-69.31.
)
=
a
-14.06.
Using the standard likelihood-ratio test, we obtain x =110.32 with 4
d.f.
(since there are 4 roll call parameters in two
-22
2
10
Similarly, for the NSF vote, we have x =110.24.
dimensions)
and
p
<
.
To
created
test
a
Republicans
hypothesis that the vote split the parties,
the null
pseudo-roll
and
Harry
call
Byrd
in
which
voted
all
"Nay".
Democrats
We
then
voted
that
those
party-line
of
calculated
the
from
significant for
the
the
coordinates
for
pseudo-roll
log-likelihoods
was
4 d.f..
N-3
the
Panama
estimated
call.
122.48
The
Canal
the
(KSF)
chi-square
(170.74),
and
"Yea"
coordinates that maximized the log-likelihood for this roll call.
hypothesis was
we first
again
all
outcome
The null
vote
were
statistic
extremely
9
To save space,
results are similar
Except where noted,
of Congress.
set of results for both houses
we do not present a full
for
two
the
houses.
See the Appendix for discussion of why distances rather than coordinates
are analyzed when the analysis is not limited to unidimensional spaces.
It
the
95th
Congress,
foreign
Intelligence,
or
Spying,
on
11
on Arms Control,
votes
policy
defense
and
Pensions or Veterans Benefits,
12
lower correlations on a specific item.
is difficult to pin these
South
Africa
or
included
Rhodesia,
7 on the Panama Canal,
8
14
on
7 on the B-1
on
In
CIA,
Military
Bomber,
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.
of the small number of votes,
Because
Agriculture had to be placed in the Residual
category.
13
Macdonald and Rabinowitz support
analysis
combines
that
our
model
hypothesis on the basis
their
results with
(iii)
series
time
of
of
an
state
returns in Congressional and Presidential elections.
14
Because
of
vast
the
amount
of
data
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
y
2-statistic of 53.78.
still be a hefty 9.65.
-v 2d. f
.
-1
0.564
equal to
z' s
likelihood-ratio
Ix
is
test
is
0,
for
normal
for
For example,
17th
the
large
for
d.f.
and
for the 17th Congress,
reestimate
would be a waste of computer resources.
the
0.504 and 0.500 is of no substantive importance.
large number
of
observations,
full
After all,
N-4
yields
a
the one dimensional
To carry out the
z' s
dynamic model.
the
for the
This
difference between
In general,
we focus on substance rather
significance.
the
the Z-statistic would
appropriate likelihood-ratio test one would have to constrain the
zero
Congress.
using
scaling
that
constant model is not very much better than 0.5 (gmp 0.504).
17th Congress only to be
for
that is all probabilities
Even if the gmp was only 0.51,
Of course,
tests
given our very
than statistical
8
Indeed,
dynamic scaling shows
period
time
scalings
biennial
the
results are not
our
For
example,
for
results
of
that
chosen.
the
century,
fit
close
the
period
that
we
if
had
would
be
Figure
to
the
influenced by
the
in
strongly
5
twentieth
scaled
only
almost
identical
the
those
to
obtained by scaling all 99 Congresses together.
If
p
the
is
given by H = Zp
the
proportion of roll
calls
in
category
a,
the
index
H
is
a
2
.
H equals
Clausen categories,
1.0
if
H would
the votes are in one category.
all
reach a minimum of
1/6
if
the
For
calls
roll
split evenly among the six categories.
17
note that every R reported in this paragraph
For descriptive purposes,
above 0.2 in magnitude is "significant" at 0.002 or better while those below
0.2 are not significant,
1
The
filter.
the
substantive
results
In particular,
analysis
is
not
even at 0.1.
are
not
sensitive
to
the
values
used
in
the
the 10 roll call requirement is sufficiently low that
affected by
lower
the
number
of
total
roll
calls
in
earlier years.
19
See Poole and Daniels
(1985)
for similar conclusions based on interest
group scalings.
20
More
generally,
geographically
issues
concentrated
are
that
involve
likely not
to
redistribution
be
captured
by
that
a
is
"spatial"
model.
21
There are no members common to the 1st and 99th Congress and many other
pairs.
N-5
s
22
)
More
can hypothesize
one
precisely,
that
two
factors will
the
To capture fit,
One is that bad fits lower the correlation.
correlation.
affect
we
created a variable that was the average of the two gmps for the Congresses in
The other is that the correlation increases in time,
the correlation.
Corresponding to the columns of Table
the logarithm of the Congress number.
5,
the
8
regressions
multiple
the
of
correlations
except
23
0.22,
To
curves
0.24,
D-NOMINATE
the
idea of
standard
the
used
we
figure,
and
on
differ
variable
fit
the
variables
all
in
two
the
t+4
and 0.24 for the House and
0.20,
0.29,
first
from
those
standard errors for the
the
standard errors
order
produced
x' s
intervals
confidence
Taylor
standard errors for the numbers plotted.
errors
these
and 0.27 for the Senate.
obtain some
in
coefficient
the
The R^ values were 0.33,
regressions.
0.25,
for
on
T-statistics had p-levels below
showed coefficients with the expected sign.
0.005
This we measured as
but at a decreasing rate.
political system stabilizes,
as the
that
of
the
would bound
x
methods
series
produced by
estimate
to
As explained in the Appendix,
in
MLE
standard
a
setup
the
these
because
the
are calculated without the full covariance matrix
and because D-NOMINATE uses heuristic constraints.
For this reason,
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 64th.
In the
(smaller) Senate,
0.0005 begins with the 15th Senate and 0.0001 with the 84th.
the average distance per year is always greater than 0.01.
Thus,
In contrast,
the numbers
reported in Figure 6 would be precisely estimated even if the standard errors
on the
24
x' s
were downwardly biased by a factor of
We tested the proposition that mobility has decreased by carrying out
non-parametric runs test (Mendenhall et
in
10!
Figure
6
for
the
50
Congresses
Congresses in the 20th century.
al.
,
the
in
1986) that compared the distances
nineteenth
p=6xl0
(2=4.873,
p=5xl0"'^)
—
).
(In
this
and
century
with
the
43
The null hypothesis was no difference and the
alternative was less movement in the 20th century.
rejected both for the Senate
a
later
runs
approximation.
N-6
tests,
The null hypothesis
and for
we
use
the House
the
wa"s
(Z=5.293,
large
sample
25
Runs
tests results comparing the first 22 Congresses
in
twentieth
the
century with the 21 Congresses starting in 1945 reject the null hypothesis 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, Z=5. 093, p=2xl0"'^.
Lott
shows,
(1987)
using a variety of
that how
interest group ratings,
members of Congress vote is unrelated to whether or not they face reelection
or are planning to retire.
Poole and Daniels
addition,
In
(1985)
show that
members of the House who later are elected to the Senate also do not change
how they vote.
27
provide
To
differentiation
test.
To
of
backup
for
Northern
Southern
Democrats,
and
carry out the test,
we
each pair of Democratic senators.
were
the
same
statements
statistical
(North-N
rank-ordered by distance,
and
the
we
carried
concerning
out
a
Pairs were then tagged as to whether they
runs
or
opposite
N-S.
statistic was
They
calculated.
were
alternative was that opposite distances were greater than same.
2 = -0.52, p = 0.302, 73rd Senate; 2 = -0.99, p = 0.161,
p < 8xl0"^°,
88th,
was a very slight,
the 78th Senate,
2= -2.93,
p = 0.002,
a sharp
Although the runs for the 99th Senate are
it
<
is
also true that we reject
^ ° using the one-tailed
'^^^qq^'^^^rS^
with p < 8xlO"
where R is the number of runs
^
,
t.
On this point,
2= -17.65,
increase from the 78th to the S8th and a substantial
less than expected by chance,
alternative hypothesis D
28
The results
These results show that there
99th.
the null hypothesis D = ^^99" ^qq^ ~
for Senate
The
insignificant increase in differentiation from the 73rd to
decrease between the 88th and 99th.
"significantly"
78th,
then
The null
hypothesis was that there was no difference between same and opposite.
are:
runs
calculated the interpoint distance between
South-S)
or
the
see Bullock (1981).
N-7
29
support
Statistical
for
statement
this
furnished
is
by
a
McKelvey-Zavoina (1975) ordinal probit analysis where the dependent variable
is coded l=Announced before Oct.
Oct..
2=Announced on Oct.
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
an
announcement
was
5/72)
7/72,
(60/72,
rejected with p=5xlO
categories
two
set
to
rejected with p=0. 0019
distance was
and
of
between the
the "outpoint"
zero
a
frequencies
standard procedure,
is
hypothesis
null
The
0.
As
.
marginal
the
to
-4
to unity and
set
and the sample was
The null hypothesis that each
according
date
the variance of the probit was
first
3=Announced after
7,
of
zero
a
slope
between
"cutpoint"
on
the
The New York Times and Washington
second and third categories with p=0.010.
Post were used as sources for the announcement dates.
30
As
with previous figures,
precisely estimated.
numbers
the
displayed
Figure
in
are
9
very
using the variance-covariance matrices of
For example,
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-statlstic
estimate to the estimated standard error;
the minimum
(Previous
figure.
caveats
apply.
)
of
the
estimates,
small
two within party distances.
difference between the
40,
48,
52,
53,
54,
in
the Z is greater than 2.0
the
in these cases.
76-99
(see
also
these
individual
often
years
reflects
7)
a
result
voting patterns
substantively
often
in Congresses 35,
the Z never exceeds
important
the
civil
of
longer
(Figure 6).
important,
the
periods
While
changes
in
of
rights
x' s
service
conflict.
are more precise
and
more
32
See Poole and Rosenthal
heterogeneity are dwarfed
(19S9b).
For a similar substantive conclusion,
N-8
stable
statistically significant and
importance by the changes in the distance between the parties.
31
be
The greater heterogeneity of the Democrats in Congresses
Figure
as
graph will
in magnitude
Statistical significance is aided by the fact that our
for
Because of the
When the Democrats are
be more heterogeneous than Democrats for some Congresses,
2.
Z
Although the Republicans are estimated to
and 75-99.
55,
the
For example, we can directly compute a Z for the
"statistically significant".
more heterogeneous,
differences
of
(over 54 Congresses)
was 6.06 for House Democrats and 5.23 for House Republicans.
precision
ratio
the
is
see Fiorina (19S9,
pp.
141)
in
REFERENCES
Bernhardt, M. Daniel and Daniel E. Ingberman (1985). "Candidate Reputation
and the Incumbency Effect." Journal of Public EconoTnics 27:47-67.
Bronywn H. Hall, Robert E. Hall, and Jerry Hausman (1974).
E.K.
"Estimation and Inference in Nonlinear Structural Models. " Annals of
Economic and Social Measurement 3/4:653-66.
Berndt,
,
"Congressional Voting and Mobilization of a
Charles S. Ill (1981).
Journal of Politics 43:663-82.
Black Electorate in the South."
Bullock,
Aage (1973).
St. Martin's.
Clausen,
Converse,
Philip
E.
How Congressmen Decide:
A Pol lev Focus
.
New York:
"The Nature of Belief Systems in Mass Publics,"
Ideology and Discontent
New York: Free Press.
(1964).
in David Apter,
ed.
,
.
The Soatial Theory of Voting
Enelow, James and Melvin Hinich (1984).
Cambridge: Cambridge University Press.
.
The
Congress: Kevstone of the Washington Establishment
Fiorina, Morris (1989).
New Haven: Yale University Press.
.
Shelby J. (1977).
"Maximum Likelihood Estimation in Exponential
Response Models." The Annals of Statistics 5:815-41.
Haberman,
"Unanimous Consent Agreements:
Khrebiel, Keith (1986).
Journal of Politics 48:541-64.
Senate."
Going Along in the
Koford, Kenneth (1987).
"Testing Theories of Legislative Voting: Dimensions,
Ideology, and Structure. "
California Institute of Technology, Social
Science Working Paper 653.
Krishna K. (1987).
"Decision Making in the United States
Congress." Ph.D. dissertation, Pittsburgh: Carnegie Mellon University.
Ladha,
Lord,
Lott,
F.M.
(1975)
"Evaluation with Artificial Data of a Procedure for
Estimating
Ability
Characteristic
Curve
and
Item
Parameters."
(Educational Testing Service, Princeton, NJ R3-75-33).
John
R.
(1987).
"Political Cheating.
"
Public Choice 52: 169-186.
Macdonald, Stuart E. and George Rabinowitz (1987).
"The Dynamics of
Structural Realignment."
American Political Science Review 81:775-796.
Maddala,
G.
(1983).
Econometrics
.
Limited-Dependent and Qual i tatjve Variables in
Cambridge University Press.
Cambridge:
McKelvey. Richard D. and William Zavoina (1975).
"A Statistical Model for
the Analysis of Ordinal Level Dependent Variables. "
Journal of
Mathematical Sociologv 4: 103-20.
Mendenhall, William, Richard Scheaffer. and Dennis Wackersley (1986).
Mathematical Statistics With AdoI icat ions
Boston: Ducksbury.
.
"A Statistical Model for Legislative Roll Call
Morrison, Richard J. (1972).
Analysis."
Journal of Mathematical Sociology 2:235-47.
Game Theory and Political Theory
Ordeshook, Peter C. (1986).
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
Keith T. (1990).
Multivariate Linear Models." Psvchometrika (forthcoming).
Poole,
"Ideology, Party, and Voting
Poole, Keith T. and R. Steven Daniels (1985).
American Political Science Review 79:
in the U.S. Congress 1959-1980."
373-99.
"The Polarization of American
Poole, Keith T. and Howard Rosenthal (1984).
Journal of Politics 46: 1061-79.
Politics. "
"A Spatial Model for
Keith T. and Howard Rosenthal (1985).
Legislative Roll Call Analysis. " American Journal of Political Science
Poole,
29: 357-84.
"Analysis of Congressional
T. and Howard Rosenthal (1987).
Coalition Patterns: A Unidimensional Spatial Model. "
legislative
Studies Quarterly 12:55-75.
Poole, Keith
"Roll Call Voting in Congress
Poole, Keith T. and Howard Rosenthal (1988).
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 Animation of Dynamic
Congressional Voting Models. " GSIA Working Paper no. 64-88-89.
Poole. Keith T. and Howard Rosenthal (1989b).
"The D-NOMINATE Videos."
VHS tape of Computer Animations.
GSIA, Carnegie-Mellon University.
Steven S. and Marcus Flathman (1989).
"Managing the Senate Floor:
Complex Unanimous Consent Agreements. " Legislative Studies Quarterly
Smith,
14:349-74.
Torgerson,
W.
S.
(1958).
Theory and Methods of Scaling
.
New York:
Wiley.
Van Doren, Peter (1986).
"The Limitations of Roll Call Vote Analysis: An
Analysis of Legislative Energy Proposals 1945-1976. " Paper presented at
the 1986 Annual Meeting of the. American Political Science Association.
Weisberg, Herbert F. (1968).
"Dimensional Analysis of Legislative Roll
Calls."
Ph.D. Dissertation, 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.
TABLE
1
Classification Percentages and Geometric Mean Probabilities
SENATE
HOUSE
Dimension
Dimension
Degree of
Polynomial
(a)
12
3
Classification Percentage: All Scaled Votes
Constant
82.7^84.4
Linear
83.0
85.2
Quadratic
83.1
Cubic
83.2
(b)
12
3
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
Constant
80.5^82.9
Linear
80.9
Quadratic
Cubic
(c)
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
83.7
Geometric Mean Probability:
Constant
.678
.696
Linear
.682
Quadratic
Cubic
All Scaled Votes
.660
.692
.700
.709
.666
.704
.716
.684
.712
.668
.708
.721
.684
.714
.670
.708
.725
.707
The pe.'-cent of correct classifications on all roll calls that were
included in the scalings; i.e., those with at least 2.5 perce.nt or better on
the minority side.
a)
The percent of correct classifications on all roll calls with at least 40
percent or better on the minority side.
b)
Higher polynomial models for 3 dimensions were not estimated because of
computer time considerations.
c)
TABLE 2
Percent Correct Classifications, One Dimensional Fit to S-Dimensional Space
"True"
House
100.
a
Senate
Dimensionality
1^
100.
7S. 9
78. 9
2^
74. 8
74. 7
3
73. 2
73.
4
71. 2
71.
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
Roll
Legislators uniformly distributed on s-dimensonal sphere.
lines distributed to reproduce marginals found in Congressional data.
Calculation based on closed form expression.
call
TABLE 3
Interpoint Distance Correlations, the Clausen Category Scalings, 95th House
(1)
(2)
'(3)
(4)
(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
Liberties, & Agriculture
.832
.746
.613
1.0
a)
Numbers above diagonal are correlations from one dimensional scalings.
b)
Numbers below diagonal are correlations from two dimensional scalings.
1
TABLE 4
Clausen Categories with 2nd Dimension PRE Increases at Least
PRE > 0.5
PRExlOO
House Categ. * Votes 1-D
2-D
PRExlOO
PRE > 0.5
2-D
House Categ. « Votes 1-D
2
Mgt
Civil
Misc
9
F8.D
1
10
18
23
24
25
26
28
31
33
53
64
76
77
78
Misc
F&D
Mgt
Mgt
Mgt
Civil
Civil
Civil
Civil
Civil
Mgt
Mgt
Welfr
Welfr
Civil
Civil
F&D
Civil
F8.D
79
81
82
83
Welfr
Misc
Welfr
Civil
Misc
Welfr
Agr
85
86
87
88
89
90
41
11
26
26
54
12
150
68
180
190
65
46
33
23
17
41
440
140
21
22
11
14
40
12
31
18
20
45
15
28
19
14
FS,D
34
Misc
Welfr
10
18
18
10
12
FS.D
84
92
Welfr
Agr
Mgt
Agr
F&D
Agr
Civil
Welfr
Agr
F&D
Welfr
Agr
Civil
Civil
Misc
Civil
110
12
29
14
10
32
20
36
36
14
11
23
24
30
39
35
45
43
45
42
37
46
46
40
44
42
46
20
32
23
21
56
65
58
58
56
54
59
54
54
64
63
64
55
55
61
50
52
56
61
53
32
45
40
61
56
59
66
59
94
26
52
45
50
58
29
33
45
60
41
31
70
64
75
67
59
61
73
63
52
65
70
53
51
24
40
53
57
21
71
67
57
47
36
59
53
35
49
58
37
'
91
Welfr
F8.D
94
Misc
Misc
65
63
26
48
53
44
40
44
64
55
52
55
52"
41
31
0.
58
57
69
64
65
70
69
60
PRE
Cone.
9
10
11
12
15
15
17
19
22
24
30
32
33
40
41
42
43
51
53
62
63
65
66
67
69
75
77
80
84
86
89
90
91
92
93
94
95
97
< 0.5.
Categ.
Mgt
Civil
Civil
Civil
Misc
Mgt
F&D
Mgt
Civil
F&D
Welfr
Civil
Mgt
Civil
Agr
Welfr
Mgt
Mgt
Mgt
Agr
Agr
Welfr'
Welfr
Agr
Welfr
Welfr
Agr
Welfr
Agr
Welfr
FS.D
F&D
Agr
Agr
Agr
Agr
Agr
Agr
Agr
Agr
# Votes
PRExlOO
2-D
1-D
73
16
15
13
16
28
29
30
33
34
49
25
49
12
30
11
30
290
17
10
17
370
280
220
13
12
16
25
20
27
21
26
41
11
11
19
24
07
36
22
26
24
26
36
38
26
34
20
03
30
27
09
18
11
22
20
24
37
30
24
17
29
12
24
49
40
49
23
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
17
14
16
16
19
16
35
40
42
12
37
27
17
31
22
22
TABLE 5
Correlations of Legislator Coordinates from Static, Biennial Scalings
Averages
For Years
House of Representait ives
t + 1^
,
Number of
Congresses
Sena te
.951
t+2
.770
.874
.850
.930
t+3
.736
.864
.828
.913
t+4
.633
.859
.809
.889
.852
.933
.901
.923
t+2
.807
.913
.875
.907
t+3
.748
.891
.871
.890
t+4
.681
.907
.858
.869
.860
.839
.816
.767
.893
.863
.832
.803
.446
.468
.489
.790
.433
.459
.734
.757
.621
.049
.501
.951
.179
-.645
.691
.862
.853
.796
.754
.620
.854
.435
.870
.676
.891
.787
.734
.840
.456
.768
.918
.884
.435
.762
.721
.670
.580
.783
.909
.745
.781
.432
.322
.552
.562
.707
.659
.893
.830
.637
.616
.314
-. 114
.393
.629
.736
.770
.816
.588
.770
.492
174
-.302
.369
.717
.850
.659
.542
.439
.819
.886
.968
.895
.928
.651
.370
.467
.802
.771
.791
.807
.761
1789-1860
1861-1900
1901-1944
1945-1978
.780
.897
.890
1789-1978
t+1
36
20
22
17
95
Individual
Congress
1
2
3
4
6
8
11
12
13
14
15
16
17
18
.790
.752
.829
.549
.589
.411
.517
.626
.308
.320
.502
.747
.886
.698
.325
.225
.858
.677
.851
.878
.242
.950
.925
128
1.00
.
.983
188
-.244
-.219
.557
.634
.659
.558
.417
.479
.678
.962
.471
.502
.
19
20
22
29
30
31
32
35
36
37
39
44
.694
.770
61
.751
.719
.953
.890
69
77
.775
.681
.511
.872
.251
.941
.
.783
.218
.232
.755
.930
.889
.674
.944
.912
.811
.806
The notation t+k refers to the correlation of legislator coordinates for
legislators serving in Congress t, given in the left-hand column, with their
coordinates in Congress t+k.
Correlation computed only for those legislators
serving in both Congresses.
b
Results shown only for those cases where either the t+1 correlation was
less than 0.8 for where any t+k correlation, k = 2,3,4, was less than 0.5.
a
TABLE 6
PRE Analysis for Slavery and Civil Rights Roll Calls
:ouse
9
15
16
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
Years
SLAVERY
1805-1806
1817-1818
1819-1820
1827-1828
1833-1834
1835-1836
1837-1838
1839-1840
1841-1842
1843-1844
1845-1846
1847-1848
1849-1850
1851-1852
1853-1854
1855-1856
1857-1858
1859-1860
1861-1862
1863-1864
Total
Roll
Calls
Issue
Roll
Calls
158
106
147
13
13
16
233
327
459
475
9
751
974
597
642
478
572
455
607
729
548
433
638
600
CIVIL RIGHTS
1861-1862
638
1863-1864
600
1865-1866
613
1867-1868
717
1871-1872
517
1873-1874
475
1883-1884
334
1885-1886
306
1899-1900
149
1921-1922
362
1941-1942
152
156'
1943-1944
1945-1946
231
1949-1950
275
1957-1958
193
1959-1960
ISO
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
5
70
39
27
84
44
8
29
26
14
159
115
65
24
92
13
43
30
32
7
23
87
9
5
9
14
8
7
6
9
6
8
5
7
22
8
8
22
17
6
17
9
Correct
Classif ication
One Dim. Two Dim.
•/.
65
92
88
82
76
81
84
SO
84
80
73
71
75
70
92
95
92
88
92
95
89
96
90
95
94
97
90
78
97
97
80
78
69
67
70
72
80
77
S3
78
85
SO
SO
81
85
86
73
92
87
81
79
86
91
88
90
88
89
78
82
76
94
95
92
90
93
96
90
97
91
95
94
97
91
80
97
97
95
92
87
89
92
92
92
94
91
91
90
84
83
81
86
88
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
.72
.48
.54
.42
.83
.89
.79
.73
.65
.90
.66
.83
.82
.91
.78
.25
.94
.90
-.01
.29
.00
.04
.01
.08
.01
.33
.53
.35
.60
.45
.48
.56
.58
50
.67
.91
.67
.82
.84
.91
.79
.33
.94
.91
.73
.76
.57
.69
.73
.74
.59
.82
.75
.73
.73
.55
.56
.58
.
.81
89
.
.61
.59
TABLE A-1
Monte Carlo Results for Simulated Data
Pearson R
With True
Error
Level
Conf ig.
Percent
Precisely
Estimated
Correct
Classification
With True Config.
Proport.
Stability
of
Solution
ONE DIMENSION EXPERIMENTS
Fixed
Low^
.995^
(.001)^
90. S%^
995
(.001)
91.
.970
(.001)
75.8
.976
(.003)
77.0
.962
(.003)
.992"
.004)
(,
(147.)
Variable
Fixed
High (30%)
Variable
.
.963
977
.
.006)
(.003)
(
.910
(.011)
(
.013)
.918
(.004)
(
.958
.009)
.
947
TWO DIMENSION EXPERIMENTS
Fixed
.
894
71.7
(.022)
Low
(.
,945
,003)
(,
(
.885
,017)
(
,851
,031)
(
.880
.005)
(
.841
.017)
(147.)
Variable
Fixed
High
.955
.024)
.942
,009)
(,
.896
(.021)
69.6
.847
(.026)
77.8
.841
(.019)
81.5
(,
,962
.022)
(307.)
Variable
A Pearson correlation was computed between the 5050 unique pairwise
distances generated by the estimated coordinates for the 101
legislators
and the true pairwise distances.
One correlation was computed for each
of the 25 simulations used in each design condition.
The number reported
in the table is the average of these 25 correlations.
Each true unique pairwise distance between legislators (n=5050) was
treated as a mean and a standard error was computed around this mean
using the 25 estimated distances.
The entries show the percentage of true
distances that are twice this standard error.
In other words, the
percentage 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 the utility function.
A
This number
percentage correct was computed for each of the 25 trials.
is the mean of these 25 percentages.
This number measures the stability of the estimated legislator coordinates.
Pearson correlations were computed between each unique pair of the 25
estimated configurations and this number is the average of those Pearson
correlations.
The n is 300.
Standard deviations are shown in parentheses.
This number measures the noise level in the 25 trials.
Holding the
legislator configuration, the roll call midpoint, and the /3 for the
roll call constant, the percentage of times legislators who do not vote for
the closest alternative varies inversely with the distance between
The error level is this percentage.
the alternatives.
Distances between
alternatives were scaled to achieve the Low and High levels.
TABLE A-2
Recovery From Random Starts
Dimensions
Average Correlation
Pairwise Distances
Recovered Configurations
Proportion Agreement
Predicted Choices
Recovered Configurations
85th HOUSE
.997
(.002)
992
(.003)
.983
(.009)
.965
(.008)
.886
(.041)
.902
(.015)
.998
(.002)
.991
(.002)
.984
(.006)
.956
(.009)
.937
(.017)
.918
(.007)
.
100th SENATE
Numbers in table based on 45 pairwise comparisons between 10 replications.
Standard deviations shown in parentheses.
b
b
441
representatives, 172 roll calls.
Number of
of house because of deaths or resignations.
101
senators,
335 roll calls.
legislators exceeds size
Figure
1
Increasing
Utility (u)
Ed
>
z
o
2
O
O
a
Z
u-0.49
Ed
sa
STRONG LOYALTY,
V,TAK
FIRST P.\RTY
PARTY LOYALTY-
STRONG LOY.\LTY.
SECOND P.\RTY
o
3^
r«-
"D
0)
u
—
o —c
Z axj)
a. < z
-J
< o
O z
_i Q
J Z
o Z)
u.
0)
cc
LL.
cc
U.
CM CO
CO
o>
z
^
UJ
T- cc
CO
O)
o
H
r»-
cn
UJ
cc
a
cn
H
<
Z
ai
en
o
o
UJ
HI
£535
a u. z
H
<
Z
(A
o
HI
ID
Q
«
e»
o
Kb
o. u.
13
u.
CO
a>
o
C
(0
t3
z><
II
•a
in
0)
_
.
CO
o
< HO <
H oc
o
m
w
n.
UJ
cc
r>.
<
T-
T- <.
Z
o>
UJ
<
Z
UJ
CO
o
o>
o
>«
"*
T)
U
^ O w O
T3
Q. U. f-
«
c
CO
O)
> <
> O —O
< H >
"O
>.
*-
O
u-
FIGURE
3
CU\SSIrlCATION GAIN BY DIMENSIONALI
3
S§o
o
1e
3
m
m
o
S
1
2
3
4
5
6
7
8
9
Humbmr
10
1 1
12 13 14 15 16 17 18
1
9 20 21
of DirT>«naions
&
5
3
5
32nd Hou8« (455
Roll Colla)
a.
s
o
u
t
3
3
-1
H
1
2
3
i
4
r
5
H
6
7
8
9
10
1 1
1
i-
i
12 13
1
4 15
1
6 17
I
1
I
8
1
9 20 21
e
o
o =
c s
§••3
•1-2
«3
t-
«J
o o
5
.5
rs
«
UU
133HH00 lM33H3d
\
—
GO
Q_
Li-
Q)
n
w
CD
LJJ
d
D
O
1-L_
o
1z
LU
^
UJ
>
O
1
<
C/D
0)
_j
,
03
C
CO
_Q
1
c
Z)
JB9X Jad eouBisiQ eSEjaAv
LU
CO
Z)
o
in
LU
n:
o
m
<
m
o
Q_
<
o
en
h1x1
o
O
LU
X:^iIiqDqojd ud9;a| ou:^9luo9Q
o
Si CO
,
ry^:^
2i
CO
2^
—
I
CO
—
ci ai
i
'^
Di
^
CO
C/D
-=i
CO
CO
r^
Q
Si
CO
ai
CO
CO
to
Hi
CO
CO
CO
n3
3
E
CO
Q
CO
Q
<
Z
^
CBD
C/V3
UJ
<
Z
m
ai
CO
CO
^^
.C"
LU
(0
c
en
Q
CO_
^
Bii
CO LO
3
CO
E
o
c^
ai
Di
CO
i
in
CO
CO
CO
o
co"
^
®
to—
Q
00
^ K
LU
5^
< 2
Z ^
HI
W
.^ii-
CO
00
-sr^ai
O)
CO tA„
^co
a^
,'^
-
UJ
Qo
^
c)5o
<
Z
CO
:^
:r
trrcoco
^,
LJ
^
1
CJ
CO
Q
C/)
-o
C
C
a>
FIGURE 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
-
SIMON
0.8
5-0.6
m
INOUYE
METZENBAUM
MELCHER. HARKIN
KENNEDY
BURDICK, LEVIN, RIEGLE
KERRY, CRANSTON, PELL
LAUTENBERG. MOYNIHAN
MITCHELL DODD
BAUCUS, ROCKEFELLER
LEAHY
BIDEN
BYRD
GORE, PRYOR
BUMPERS, BRADLEY.
GLENN, FORD
BINGAMAN, JOHNSON
PREDICTED
SASSER
ANTI-
BORK
CHILES
DIXON
EXCN
-0.4
DECONCINI
BENTSEN
PROXMIRE
^EICKER
boren"
SIcNNIS
HEFUN
NUIsN
boilings
0.2
hatfleld"
CUTTING
SPECTER
DURENBERGER COHEN
GRASSLEY
HEINZ
UNE
staftord"
packwood*
KASTEN, DANFORTH
PRE.=iSI FR
Chaffee',
D'AMATO
STEVENS, EVANS
KASSEBAUM
0.2
UJ
>
<
>
COCHRAN, RUDMAN
MURKOWSKI, NICKLES
TRIBLE,
UJ
en
z
o
u
MCCONNELL
BoscHwrrz. roth
LUGAR, WILSON. DOLE
0.4
OUAYLE
SIMPSON
DOMENICI
HATCH
THURMOND
0.6
GARN. GOLDWATER
ARMSTRONG
0.8
HUMPHFEY
GRAMM, HECHT
MCCLURE
HELMS. WALLOP. SYMMS
'Prediction
errors
warner"
PREDICTED
PRO-
BORK
c
c 2 o
00
LU
O
<
CO
en
I ? 0)
>
_
CD
m Q
CD
cc
Q 3
<
CL
en
LU
cz
Q
LL
CD
CL
LJ
LJ
cn
CD
LJ
m
O
CO
CD
—
O
I-
ui
C3^
00
-o
CD
LJ
O
<
00
LJ
G)
o
LO
«
o
90UD:^sia
00
23
8 5
U09
h'f'lc^
Date Due
ji^m^
MIT LIBRARIES DUPL
3
1
Toao oosva^as
a