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Using Network Analysis To Gauge The Justices’ Relative Importance In Oral Arguments – Above the Law

Anecdotes
and
research
support
the
notion
that
oral
arguments
do
not
often
influence
case
outcomes.
Chief
Justice
John
Roberts
said
as
much
in
an
interview
with
Bryan
Garner
for
the Scribes
Journal
in
2010
:
“The
oral
argument
is
the
tip
of
the
iceberg

the
most
visible
part
of
the
process

but
the
briefs
are
more
important.” 
In
fact,
a
series
of studies including my
own
work
 points
to
the
justices
generally
asking
more
questions
to
the
parties
they
eventually
vote
against
on
the
merits
which
corroborates
the
point
that
the
justices
often
know
the
way
they
will
vote
based
on
concerns
they
have
with
the
opposing
side’s
position
by
the
point
of
oral
argument.

Once
again,
Chief
Justice
Roberts
elaborated
on
this
point.
This
time
in
response
to
Garner’s
question:

“When
you
approach
an
oral
argument
as
a
judge,
to
what
extent
do
you
have
a
tentative
vote
in
mind?
Is
there
a
kind
of
rebuttable
presumption”?

Roberts
replied:

“It
really
varies
on
the
case.
Some
cases
seem
clear.
You
look
at
the
briefs,
and
you’re
just
not
persuaded
by
one
side,
and
you
are
by
another,
so
you
do
go
in
with
kind
of
.
.
.
I’m
kind
of
leaning
this
way.
Usually,
you’ve
got
concerns.
I’m
leaning
this
way,
but
I
need
a
better
answer
to
this
problem…So
even
when
you’re
tentatively
leaning,
you
have
issues
that
you
want
to
raise
that
give
the
other
side
a
chance
to
sway
you.”

In
the
same
set
of
interviews,
Justice
Scalia
pointed
to
why
attorneys
should
still
value
oral
arguments:

“…one
of
the
benefits
of
oral
argument

you
can
put
things
in
perspective
the
way
a
brief
can’t.
Say,
‘Your
Honor,
we
have
five
points
in
the
brief,
but
you
know,
what
we
think
is
the
most
important,
what
this
case
really
comes
down
to
.
.
.’
and
then
boom!
Hit
your
big
point.
And
I’ll
think,
‘Oh,
yeah,
I
read
your
brief
last
week,
and
all
I
remember
from
it
is
that
lengthy
point
three,
but
that’s
not
the
one
that
you
want
to
talk
about.’”

While
oral
arguments
may
not
often
sway
justices’
final
votes,
they
hold
significant
value
in
other
respects.
These
sessions
allow
justices
to
clarify
the
legal
issues,
test
the
strengths
and
weaknesses
of
both
sides,
and
signal
which
arguments
they
find
compelling
or
problematic.
This
process
frames
the
conversation
in
ways
that
can
affect
how
parties
refine
their
positions
and
how
cases
are
understood
by
the
public.
Litigating
attorneys,
through
these
exchanges,
often
gain
a
clearer
sense
of
where
each
justice’s
concerns
lie,
shaping
their
strategies
both
in
the
current
case
and
in
future
litigation.

Even
if
votes
are
often
predetermined,
a
justice’s
influence
during
argument
can
steer
the
conversation,
frame
legal
questions,
and
potentially
impact
the
policy
outcomes
or
legal
frameworks
that
emerge
from
a
case.

Maybe
it
is
time
to
rethink
the
value
of
oral
arguments
as
something
more
than
impacting
the
justices’
votes.
In
past,
I
and
others
have
focused
 on
the
idea
that
one
of
the
main
goals
of
oral
arguments
is
dominating
the
speaking
time
available
as
a
means
to
share
ideas
and
prevent
other
justices
from
talking.
Ultimately
though,
the
justices
that
speak
the
most
on
the
current
Court
tend
to
be
in
the
Court’s
majority
least
frequently.
Given
the
disconnect
between
majority
votes
and
speaking
time,
what
other
ways
can
we
measure
the
justices’
influences
in
oral
arguments?
The
answers
are
supplied
by
looking
at
oral
arguments
since
Justice
Jackson
joined
the
Court
at
the
beginning
of
the
2022
Supreme
Court
Term
and
moving
through
the
first
week
of
oral
arguments
during
this
2024
Term.


The
Tools

Imagine
a
group
of
people
at
a
dinner
party.
Some
people
speak
frequently,
while
others
contribute
less
but
often
respond
to
certain
individuals.
As
the
night
progresses,
you
might
notice
patterns—certain
voices
dominate,
others
are
echoed
or
referenced,
and
some
people
are
frequently
the
focus
of
the
group’s
attention.
Even
if
you
weren’t
listening
to
the
content
of
what
was
being
said,
you
could
still
gather
insights
about
the
dynamics
at
play:
who
leads
the
conversation,
who
influences
others,
and
who
helps
connect
different
parts
of
the
group.
These
interactions
can
tell
us
a
lot
about
the
relationships
within
the
group,
even
if
the
content
of
the
discussion
is
unknown.

This
is
much
like
what
network
analysis
does
in
a
more
formal
context.
In
the
case
of
Supreme
Court
oral
arguments,
network
analysis
helps
us
map
out
and
understand
the
complex
interactions
between
justices
and
attorneys.
By
tracking
who
speaks
when,
who
references
whom,
and
how
much
space
in
the
conversation
each
participant
occupies,
we
can
construct
a
network
of
these
interactions.
To
build
this
network,
data
is
collected
from
transcripts
(thanks
to
R
code
supplied
by
Jake
Truscott’s SCOTUSText)—each
utterance
is
logged,
along
with
who
spoke
it
and
who
they
were
responding
to
or
referencing.
This
data
was
then
analyzed
to
uncover
patterns
of
influence,
centrality,
and
participation,
much
like
observing
the
dinner
party
conversation
from
a
broader,
structural
perspective.

The
value
of
network
analysis
lies
in
its
ability
to
highlight
the
underlying
structure
of
interactions
that
may
not
be
immediately
apparent
from
simply
reading
the
text
of
a
transcript.
By
focusing
on
who
is
influencing
or
directing
the
conversation,
and
how
often
participants
engage
with
one
another,
network
analysis
provides
a
lens
for
understanding
the
dynamics
of
oral
arguments
beyond
individual
statements.
It
also
offers
insights
into
the
court’s
decision-making
process,
even
if
that
influence
isn’t
reflected
in
the
final
vote.

The
network
graphs
are
constructed
by
treating
each
justice
as
a
“node”
(a
point
in
the
graph)
and
each
interaction
between
them
as
an
“edge”
(a
line
connecting
nodes).
For
example,
if
one
justice
speaks
after
another
or
references
them,
a
line
is
drawn
between
their
nodes.
The
strength
of
these
connections
is
weighted
in
these
analyses
by
factors
like
how
many
times
they
speak
in
sequence
or
how
many
words
they
contribute.
The
resulting
graph
shows
not
just
individual
behavior
but
the
relational
structure
of
the
court,
revealing
who
is
central
to
the
conversation
and
how
ideas
flow
between
the
justices.
The
graph
below
shows
an
utterance
(turn
taking)
network
chart
of
the
justices
from
arguments
with
justices
and
attorneys
mapped
based
on
their
interactions.


Measures

The
analysis
below
looks
at
three
different
measures
based
on
utterances,
word
counts,
and
references
to
other
justices
during
oral
arguments. 
To
assess
a
justice’s
importance
during
oral
arguments
lies
in
the
ability
to
capture
multiple
dimensions
of
influence
that
raw
word
counts
alone
cannot.
Utterance
centrality,
which
considers
the
relationship
between
the
current
and
previous
speaker
based
on
who
speaks
when,
reveals
how
integrated
a
justice’s
speech
is
within
the
conversational
flow,
highlighting
their
role
in
maintaining
or
shifting
the
dialogue.
This
metric
emphasizes
the
justice’s
connection
to
the
broader
exchange
of
ideas
rather
than
just
the
volume
of
their
speech.

Word
count
centrality,
while
also
looking
at
speaker
pairs,
adds
a
quantitative
dimension
by
weighting
each
speaker’s
contribution
based
on
the
number
of
words
spoken.
This
highlights
the
depth
or
elaboration
of
a
justice’s
participation.
It
shows
not
only
who
speaks
but
how
much
they
contribute
substantively
in
terms
of
word
volume,
providing
insight
into
how
much
space
they
take
up
in
the
conversation.
A
justice
might
dominate
discussions
even
if
they
don’t
speak
frequently,
simply
through
more
extensive
interventions
when
they
do.


References

Reference
centrality
shifts
the
focus
from
speech
quantity
to
the
relational
influence
a
justice
has
by
being
referenced
by
others.
It
reflects
the
extent
to
which
their
ideas
or
arguments
are
considered
important
or
persuasive
by
their
peers.
A
high
reference
centrality
suggests
that
other
justices
find
their
points
critical
enough
to
revisit,
indicating
their
indirect
influence
through
the
prominence
of
their
contributions
in
others’
reasoning.
Here
is
the
network
map
of
the
justices’
references
to
each
other
where
node
and
edge
sizes
relate
to
a
justices’
importance
in
this
network
and
the
importance
of
their
interaction
with
the
other
justices.

The
centrality
measure
used
in
this
article
is
eigenvector
centrality
which
is
a
measure
of
how
important
each
justice
is
in
a
network
based
on
who
they
are
connected
to
in
a
manner
similar
to
the
dinner
party
example
above.
To
calculate
the
eigenvector
centrality
for
the
justices
based
on
their
interactions,
I
organized
the
data
to
focus
on
the
exchanges
between
justices
looking
at
which
justices
referenced
other
justices
in
their
oral
argument
speech.

The
eigenvector
centrality
scores
for
the
justices
revealed
a
distinct
hierarchy
of
influence.
Justice
Alito
emerged
as
the
most
central
figure
with
a
score
of
1,
indicating
his
prominent
position
within
the
referencing
network.
Following
him,
Justice
Gorsuch
(0.857)
and
Justice
Sotomayor
(0.873)
demonstrated
significant
influence,
reflecting
their
active
engagement
in
referencing
discussions.
Justice
Kagan
(0.809),
along
with
Justices
Barrett
and
Jackson,
both
at
0.826,
also
exhibited
noteworthy
levels
of
connectivity
and
reference
interactions.

In
contrast,
Chief
Justice
Roberts,
with
a
centrality
score
of
0.256,
stood
out
as
the
least
influential
in
terms
of
referencing,
suggesting
that
he
is
less
frequently
cited
by
his
peers.
This
discrepancy
illustrates
the
value
of
eigenvector
centrality,
as
it
reveals
insights
that
individual
reference
counts
alone
may
obscure.
For
instance,
while
Justice
Barrett
had
the
highest
individual
reference
count
with
42
references
to
Justice
Alito,
this
does
not
fully
capture
the
interconnectedness
that
eigenvector
centrality
provides.
Her
centrality
score
of
0.826 reflects
a
more
intricate
role
in
the
referencing
dynamics
compared
to
the
sheer
volume
of
references.

Overall,
the
use
of
eigenvector
centrality
in
this
analysis
offers
a
more
comprehensive
understanding
of
the
influence
and
interactions
among
justices.
It
highlights
not
only
who
is
referenced
the
most
but
also
identifies
the
justices
whose
references
are
most
consequential
within
the
judicial
discourse.

The
limitation
of
relying
solely
on
individual
reference
counts,
however,
becomes
evident
when
considering
the
nuances
of
judicial
influence.
For
instance,
a
justice
may
have
a
high
reference
count
but
may
not
be
cited
by
justices
who
hold
significant
sway
in
the
judicial
discourse.
Conversely,
a
justice
with
fewer
references
may
be
more
frequently
cited
by
the
most
influential
members
of
the
court,
thereby
elevating
their
centrality
and
importance
in
the
network.


Utterances

For
the
other
two
network
measures
I
tracked
how
many
times
each
justice
spoke
and
with
whom
they
interacted,
specifically
looking
at
the
speaker
in
each
row
and
the
speaker
in
the
row
directly
above
it. 
I
eliminated
the
attorneys’
remarks
from
these
graphs
so
that
the
sequence
of
speaking
only
focused
on
the
justices’
speech. 
I
also
removed
any
utterances
of
Chief
Justice
Roberts
of
fewer
than
five
words
thereby
eliminating
instances
where
he
calls
on
other
justices
to
give
them
an
additional
turn
during
arguments.
After
counting
the
interactions,
I
created
a
table
that
represented
how
many
times
each
justice
interacted
with
another
justice.
The
next
measure
looks
at
utterance
or
turn-taking
patterns.

The
results
reveal
the
eigenvector
centrality
scores
for
each
justice,
highlighting
their
relative
importance
based
on
the
interaction
patterns.
Justice
Gorsuch
has
the
highest
score
of 1,
indicating
that
he
is
at
the
center
of
the
interaction
network
among
the
justices.
Justice
Jackson
follows
with
a
centrality
score
of
0.462,
suggesting
that
while
she
is
not
as
central
as
Justice
Gorsuch,
she
still
plays
an
important
role
in
the
network.
Chief
Justice
Roberts
and
Justice
Sotomayor
have
scores
of
0.291
and
0.294,
respectively,
placing
them
in
a
moderately
central
position
within
the
network.
Justice
Thomas
has
the
lowest
score
at
0.041,
implicating
his
minimal
influence
in
this
network.


Word
Counts

Lastly,
word
count
centrality
results
are
generated
based
on
the
number
of
words
spoken
by
each
justice
during
their
interactions.
This
measure
reflects
not
only
the
individual
contributions
of
the
justices
but
also
how
these
contributions
relate
to
one
another
in
the
context
of
the
discussion.

In
the
analysis,
each
justice’s
utterances
are
once
again
paired
with
those
of
the
previous
speaker.
The
word
count
of
the
current
speaker’s
utterance
is
summed
for
all
interactions
with
their
preceding
speaker,
which
allows
the
establishment
of
directed
connections
between
speakers
based
on
their
contributions.

The
word
count
centrality
results
for
the
justices
reflect
their
levels
of
influence
during
discussions,
based
on
the
number
of
words
they
contributed
in
comparison
to
one
another.
Utilizing
the
eigenvector
centrality
algorithm
on
this
graph,
the
analysis
identified
Justice
Jackson
as
having
the
highest
word
count
centrality
value
of
1,
indicating
a
dominant
role
in
the
discourse.
Other
justices,
such
as
Chief
Justice
Roberts
and
Justice
Kagan,
also
displayed
significant
centrality
values
of
0.961
and
0.950,
respectively.


Conclusion

While
according
to
Chief
Justice
Roberts,
oral
arguments
may
not
be
as
important
as
briefs,
the
interaction
of
the
three
centrality
measures
used
in
this
analysis—word
count
centrality,
utterance
centrality,
and
reference
centrality—provides
a
nuanced
understanding
of
the
justices’
relative
influence
during
oral
arguments.
Justice
Jackson
exhibits
the
highest
word
count
centrality,
indicating
a
prominent
presence
in
the
discussions.
Justice
Alito
shows
high
reference
centrality,
signifying
that,
despite
a
lower
volume
of
spoken
contributions,
he
is
frequently
cited
by
others,
suggesting
a
role
in
shaping
the
discourse
without
necessarily
leading
it.
In
contrast,
Justice
Thomas
has
lower
scores
across
all
measures,
indicating
a
relatively
reduced
presence
in
the
interactions.
These
findings
illustrate
a
complex
landscape
of
influence
among
the
justices,
where
verbal
contributions,
their
relevance
to
ongoing
discussions,
and
the
frequency
with
which
justices
are
referenced
interact
to
define
their
relative
standing
in
oral
arguments.
This
analysis
underscores
that
influence
within
judicial
discourse
is
more
multifaceted
than
meets
the
eye.




Adam
Feldman
runs
the
litigation
consulting
company
Optimized
Legal
Solutions
LLC.
For
more
information
write
Adam
at [email protected]
Find
him
on
Twitter: @AdamSFeldman.