A
Reduction-Graph
Model L.
Karl
Department
of Ratio
Branting
of Computer
University Laramie,
Science
of Wyoming
Wyoming
82071-3682
[email protected]
Abstract
.edu precedent quacy
This
paper
proposes
as a justification of reasoning
steps,
predicates of which This
model
satisfies
decidendi theory
under
from
effect.
based
of
model
pendency
and
criteria
By
contrast,
fails
of precedential
effect
terial
liter-
tant which
its
effect.
for
on the
casethe
de-
theory
of
Every
tive
model
to individual
ies, at least dendi,
past
implicitly,
the content
thoritative
paper
termed
the
the ratio structure
stract argues
level
to subsequent
tion
of this
relate
predicates
graph
model,
abstract some
to specific
the jurisprudential
of a precedent the au-
tails
of which
facts.
literature
@
relate
Decidendi
of Ratio
of a satisfactory distinct
is for
how
this
of new
cases.
must
mechanisms ability
possible.
on legal
would
to account
be detailed
alternative
of precedents, reliable
$1.50
examining -1 ()
for
the
sources reliable
empirical few
[Gar85].
such
However,
its processes
Sec-
and
mechacom-
in terms
describing
legal
the
reasoning
are
source
of information
studies
of judges’
problem
empirical
introspection
en-
phenomenon.
for
in
is introspection but
described.
be evaluated
use of precedents
Unfortunately, One
most
model
phenomenon
the proposed
of precedent-based The
the
Mod-
computational Finally, must
knowledge
phenomenon
section
First,
be precisely
be defined.
S.veral
ab-
must
for
computer
tasks.
a set of appropriate
of their
to other
all or part of this material is granted provided distributed for direct commercial advantage, the title of the publication and its date appear, and by permission of the Association for Computing or to republish, requires a fee and/or specific
1993 ACM 0-89791 -606-9/93/0006/0040
paper
required
showing
els
attorneys’ Permission to copy without fee that the copies are not made or ACM copyright notice and the notice is given that copying is Machinery, To copy otherwise, permission.
of this
Criteria
putational
steps,
The next
indepen-
implementa-
emphasis and
of what
to do”
the knowledge
reasoning
as a
of precedent-
be able
Evaluation
nisms
is a justification
predicates
under
is intended
is used in the resolution
three
ond,
which
of reasoning
The
a
precedential
“symbol-level”
process.
to be modeled
decz’dendi,
under
its
description
on identifying
Development
and applying
of ratio
of a series and
2
advocat-
cases.
a model
of a precedent
consisting
predicates
of any particular
theory
is, a “specification
should
dent
the
with
an impor-
deci-
is authorita-
identifying
of the precedent
proposes
decidendi
that
effect
that
system
knowledge
embod-
Predicting,
[New82]
precedent-based
that
of ratio
that
the binding
reduction
some of which abstract
model
cases all require
elements
This
cases.
elements
precedent
cases necessarily
of a precedent
ing, and justifying on subsequent
of legal
some
as to subsequent
those
model
therefore
computational
refers
reduction-graph
a reasoning
Introduction
how
sec-
of legal
of the ma-
to satisfy
representing
reasoning,
fourth
case together
fails
controls
knowledge
argues
model
of representations
metric
adethree
and
The
case-based
a case is decided
The based
criteria.
the
Section
model
of each precedent
relevance criterion:
controls
a purely
these a purely
consisting
for
decidendi.
reduction-graph
that
facts
the
of ratio
satisfies
global
decision,
1
it
shows
how
to account
the
precedent
facts.
for ratio
shows
a case is decided
ratio
some
to specific
model
that tion
a set of criteria
provides
of models
describes
abstract
the jurisprudential
the
which
precedential
predicates
adequacy
particular,
decidendi of a series
relate
predicates
four
identified In
ratio
of which
abstract
abstract
of
consisting
some
to other relate
ature.
a model
structure
Decidendi
studies on one’s
exist. own
is notoriously
the law’s
use un-
“tradition
assumptions”
and
solving.
of
[Ris90]
as embodied another ings
in jurisprudential
alternative.
are often
While
rather
risprudential
ideas
widely
decidendi
The
writ-
avoid
reasonably
survive
to contain
ratio
fort
h in
the
of
of
agenda,
prolonged
ju-
an element
of truth.
the
The
fications
almost
The second tification
The
to resolve
is that
not
contain
that
language
the issues
sary language
first
As
part
judijusti-
of a written
early
of the
this
ratio
judicial
like
that
the
legal
propositions
the issues in one case should evantly
similar
test
determining
for
ratio
future
believed
apply
cases.
the
A
whether
sition
of
be grounded
negation
of the ratio
which
unique
the
case
must
erwise”
[Cro79]
Instead,
a gradation
in
abstraction
case
to
tion.
Rupert
[Cro79] ufacturer Lord
this
of a bottle snail
Atkin’s
of law justifying
opinion the
●
facts
satisfy
contained decision.
oth-
beer two The
●
are useful
specific
lecases
in deciding
examples
of spe-
Accordingly, case facts
for the precedential
expressions
specific “[I]t
facts
effect
can-
of past
of the
centrality
of prece-
include:
is the facts,
and not
the general
in precedents
. . . which
of the decisional
“Judgments facts
must
be
rules
of
serve as the
process.”
read
of the case in which
[Cro79] ●
Law”
[CR81]
in
they
light
of
the
are delivered.”
at 44.
“It
is clear
that
representation
of
of the
the man-
containing
47.
a
propositions was very
facts
‘operative
livered.”
important
one from
context
outcome. with
part
doctrinal facts’ should
of a
[Gar87]
be studied
“not as for
“ and Gilmore’s quote
divorced the language
at
Corbin’s
statements
“never
an opinion, in which
”
approval
cases should
. . . their
factual 41
that
that
the
quotes
for their
language Vaughn 360. 1Bole v. Horton, 2A.C. 562 (1932).
and
so much ment
general:
the most
for cases is the representation
Gardner
admonition
consumer.
first
of new
condi-
the example
to the ultimate
reason-
abstract
facts
provide
omits
case.
in legal
between
such. concepts.
that
must
of the
at 56.
of the
this
in English
with
satisfy
foundation
ranging
a case holding
of ginger
liable
Typical dents’
determined.
specific
can point
v. Stevenson,2
decomposed
decided
be
Cross in “Precedent
illustrated
Donoghue
the
rules
that account
“without
of propositions
from
abstract
been
seldom
facts
specific
they
propo-
of a precedent
of uncertainty the
sat-
of either
decision.
specific
Precedents
law found
of law
have
can
BP91].
not fully
[Wam94].
proposition
and
of ratio
without
rather
A
concepts
of these propositions
in generality
a model
Eu-
is dictum
. . . reasonable
cases.
have
of the case, the proposition
of in-
. . . owes a duty
a different
source
“gap”
facts
the outcome
left
possibility
decidendi
cific
by
con-
they
the negation
in the
resolve
changing
than
ratio
primary
ing is the
both
test:
cases because
could
he
which
to take
require
The
[Gar87,
to rel-
proposition
that
new
proposition
court
would
The
of
accepted
was proposed
if the deciding
examination
all sug-
equally widely
a given
of a precedent
gene Wambaugh:
required
termediate
it
the prin-
alike
he
that
the ultimate
in
no reasonably
Cross observes
unneces-
and
be treated
form
consumer
which
as to show
with
3.
decidendi
economy,
cases should
specific:
to reach
the
isfy Wambaugh’s
frequently
for the resolution that
af-
care.
jus-
as 1673,1
decisions and
can
to in-
directly
of products, a form
them in
to the
them.
part
him
is supis that
judges
written
is not
necessary
of law that
every
the court
Predictability,
2.
more
sells in such
gal
ciple that
is the
was much
sumer
the case.
gest
second
and
to
he
be likely
. . . closely ....
intends
have written
unnecessary
before
persons
care
which
would
by his act
of
the issues before
is authoritative.
was recognized
are
propositions
to apply
omissions
foresee
fected
implicitly
characterization
invariably
containing
purport
or
that
by two observations.
cial decisions
or
reasonable
of ratio
consists
explicitly
This
take
A manufacturer
opinion,
decision.
acts
jure
critical
characteristics
a precedent
law,
must
serve
frequently
can be distinguished:
1.
ported
A party
and
a descriptive
recognized
propositions
to
that
are likely
Four
set
than
provides
jurisprudential
contradictory
a prescriptive scrutiny
literature
state-
general from
the
was de-
4.
The
not
ratio
only
decision, the
decidendi
the but
also
material
though that
specific
tio decidendi,
hart’s
ratio.
over
publication facts
purported
sought
clusion
facts
The view
but
on them.
facts
that
most
important
the
It
no duty outside
danger,
or (2)
judge
has based
and
creates
law” of
breach
in
“the
his
con-
it
are
HI.
[Go030].
and
The
branch ratio the
impossible
decidendi facts,
merely
regarded
court,
and
facts.
It is often
certain
the
facts
for
sary
to know
were
in the mind
selection (loss
reference
regarded it
what
portions
the example
when at 73.
of Bourhill
facts
the
v. Young,3
were found
Young,
a motorcyclist,
was
cause of his own negligence
when and
at excessive
with
a car
tram.
At
about
the
accident,
the
and Mrs.
Bourhill
was
lision
saw blood
accident
side what plated that
would
92 (1943).
as a result Bourhill
ought
area
arise
heard on the
Mrs.
Young
as the
ing. 3A.C.
and
shock.
he passed
of the
Bourhill
the
road
of ner-
of the
the
alone should
facts
of a tree
ma-
how
either
of
be decided: except
that
collides
with
of a car,
of fireworks
damaged
same
the
by Young
instead
explosion
ratio-
from
as Bourhill
driven truck
controlling
determine
and
the
causes
the
by an early
and hit
Mrs.
in physical
winter
Bourhill
on
injuries.
The
Under
in
passes
the
alighting
the
cover
facts
and
Mrs. causing
first
tram
second
Mrs. 2 but
same
as
her
by
emotional Bourhill
not the
that
side
missing
a severe
rationale,
except
on the
Bourhill,
rationale,
hypothetical
the
as Bourhill
shock. could
re-
hypothetical results
1.
would
be
reversed. An
adequate
model
of precedent
minimum,
account
for these
acteristics
of ratio
decidendi.
characteristics for models
can function
four
should,
recognized
char-
Accordingly, as evaluation
of precedent-based
at a these
criteria
reasoning.4
The
Reduction
of Ratio Legal
after
was out-
to have contemhis careless
3
Graph
Model
Decidendi
col-
suffered
of potential
from
from
collided the
Mrs.
nervous
be-
beyond
time
was stopped and
speed 50 feet
alighting. the
same
H2.
inches
to be ma-
killed
a tram
flowing
decision
resulting
Under
terial:
tram
the
the head,
the
of the law
[Cro79]
of to
to come loose
Young
why
be neces-
of the court
the following
●
as material
may
foreseeable
the
on those
to know
purpose
storm
to
by
based
essential
was made.
gives
the
as material
were
this
by
decision
and
in which
to formulate
to
owes a duty
a consequence
hypothetical
resultant
is quite
driving
to be recoverable.
a fireworks
Goodhart’s
driver
remote
the motorcycle
is that: it
too
is impossible
facts
(1) a driver
of his
damages
knowledge
the following ●
the
alone
of the following
area of reasonably
although
of duty
terial
of the
the
in respect
persons,
Without nale,
the
of care
persons
argued
instead
criticism
decision:
shock
is by his choice
the judge
which
owes
against
and the decision
to determine
vous
the judge
be sought
facts
underlies
rationales
focused
not be
action
two
that
of the
Bourhill’s
it is impossible
to such
exclusion
Mrs.
was dismissed.
the material
care
Goodhart
on which
must
From
Good-
of a case . . . must
as seen by
based
material
to the
conclusion
was that
estate
Arthur
of ratio
justifications.
in the reasons
material
following
decidendi
his decision”
of ra-
are not per se sufficient
of precedents
ratio
Al-
emphasized
on this
Young’s
which
to any model
of a model
on the
“the
facts
and
decision.
have
A consensus
the decades
judge’s that
the
are essential
specific
to represent
to
facts
under
scholars
The decision
includes
erial
theory
lead
legal
facts
mat
the
facts
numerous
emerged
of a precedent
precedent’s
danger driv-
a
warrants,
i.e.,
propositions
conditions
under
which
fied,
widely
in
vary
a legal
abstraction
expressing predicate [BP91].
the
is satisAt
one
4The four characteristics described here constitute only A discussion of a partial description of ratio dec:dendi. additional attributes of ratio together with an analysis of the adequacy of the reduction-graph model in terms of these additional attributes is set forth in [Bra93].
extreme
are general
quirements
for
abstract
rules,
a legal
predicates
the defendant failure
fails
collections
of facts, language,
by
Brown. who
expressed
(e.g.,
gence because icaJ care
Dr.
he failed
operation
relationship
of different
warrants
care).
reduction
tween under
which
particular, in
description count dard
express
was a failure
of reasonable
(e.g.,
be-
is satisfied. justify in
Jones’
to conform
In con-
the
case-
failure
matching
conditions
the facts
of some
conclusion.
to the
quires
inference.
contain
abstract
Warrants features
tures
to the specific
facts
the sponges
reduction
tween
the
(e.g.,
of a new
operators features
the reduction
operator
the sponges
of failure
to exercise
matching
the facts
than
failures
that
used during reasonable of an exemplar
as a goal-
to Brown
that
resulted
un-
from
abdominal
a
cavity
to conform
applies
such
to match
path
from
facts
of a case.
negligence
fail-
proximately
re-
mits
the
be-
establishing
identifies surgery care).
ators
and
of
Brown,
can in turn
that
‘In an unfortunate proliferation of terminology, this author has previously referred to exemplars as “exemplarbased explanations” and “precedent constituents” [BP91].
tis from
imply
failed left
is termed
rule
that
duty,
and
negligence
to
the care,
caused
be reduced
and that
that to the
The
of that
of reasonable
professional Jones
subgoals
to be established,
per-
subgoals
of
breach
of
harm.
These
by reduction
of the case: that
the sponge
representation
harm
of
1 repre-
an inference
top.
breach
proximately
to the facts
the operation,
predicate
be reduced
a duty
tor rendering
Similarly,
to
Figure
to be established
care,
caused goal
duty,
subgoals
failure as a kind
to the facts
that
this
of a war-
of the warrant
of the
is at the
of reasonable
surgery)
facts
The
a pred-
representations
of constructing
predicate
liability,
case (e.g.,
specific
process the
are
all reductions
the antecedents
in terms
duty
the
with
are possible.
re-
that
consists
together
a justification the
both
of reasonable
conclusion
of the case. Various
a justification
in
the
to a case therefore
in
care)
gap
for
sents
to count
because
standard
the
to moni-
to failing
surgery
to the
failing
community).
for the predicate
to the facts
to establish
(e.g.,
is similar
during
A justification icate
inference facts
level
used
care of the medical
fea-
to bridge
require
oxygen
the sponges
abstract
during
and
liability
in Brown’s
of different
arise
exemplars
reasonable these
used
abstract
to count
case may
of
that
case typically
other (e.g.,
Matching
for
the
the antecedents
of a new
antecedents.
quires
warrant
matching
facts
a new case re-
of the new case with
their
ure to count
by Jones
equivalence
rant
community)
about
authoritative
However,
a warrant
left
an operation.
to
to the stan-
care of a medical
a conclusion
represented
Jones’
for the injuries
sponge
necessary
Establishing
for
during
tor blood
are exemplars. quires
der negligence
a new
themselves
connection
that
Dr.
justification,
graph,
to use reason-
expressed
(e.g.,
a
a set of conditions
operators
1: The
reduction
antecedents
are
feature
of facts
Figure
reduction
care of a med-
the
and
abstract
language
sponges
the
of failure
feature
terms
f-of
Bmwl v. hmm
differ-
expresses
operators
reduction
clusions
by
of reasonable
they
the
at
for the same conclusion
an abstract
H
on
a second
warrants
operator
is a kind
since
/
in Brown,
required
pdhmilis k a f0teree8bla .M15qucnm d—led qwnga
ml Cs.mting Spmgel vrnfuea ,iuW of MnmUbk && Cue
med-
surgery
was left
between
Reduction
warrants,
duty of reasonable mrdimi mm if~ ,eadaing s.icu
a
for negli-
reasonable
is expressed
of the standard
community
case-
to satisfy
during
and
of generality
taxonomic
able
by
was liable
bet ween
Each
ical
the
suffered
the sponge).5
operators.
breach
Jones
peritonitis
relationship
ent levels
care and
in a concrete
a sponge
to remove
The
if
are known
sponges
As a result,
of other
are exemplars,
to exercise
counting
developed
extreme
re-
is negligent
cause of harm
that
the
in terms
an action
At the other
predicate
express
to use reasonable
description legal
predicate
(e.g.,
is the proximate
the plaintiff).
which
services to count
oper-
Jones was a docin operating sponges
during
Brown
developed
during
the operation.
a goabeduction
on
peritoniThis graph.
dwy .( r.asambk cam & brexhof hat 4.(Y & _ Px~*.=-
1
gether
[email protected]
d.y of raso.abk mcdicd care IS a k,nd of d.y of Ieamnabk to
P2
b would and
III’s
cause
H2’s
strongest
respecof wrongfea-
distance, strongest match
then match
to
be to
130urhilJ. However,
suppose
thetical,
H3,
the
of the
side
alighting,
in
missing
which tram
that the from
there
is a third
motorcyclist which
her by inches.
the At
to
HI
‘The
infeasibility in [AR88].
of devising
on
Plaintiff
such a weighting
adequately
model
of Bourhill
and
coherence
P2
not
all
and
and
is also the
the
from
at
on on
P2 were
effects
Bourhill the
the
being under
.8 Thus,
standing
of different
to H2
facts theory
decided
inadequate,
apBour-
or less coher-
from only
approach
as the other
H2 are more
depends
In sential
summary,
this
alone,
possible
for
exemplar-based
any adequate
a model
of ratio
based reasoning
to
ratios
view
and is therefore
5
Conclusion
This
paper
reasoning
model
that
of ratio
consists
implicitly
dendi
is
moment,
has
under
only
subscribes
subject
a precedent timate
is es-
decidendi,
of exemplarto Goodhart’s
to Cross’s
precedent’s
tion
operator reduction warrants
scheme is
a model
the
include
result
the
the
proposed
which
(1)
each in
the
justification connecting graph. in the
8A
of
authoritative
appearin~
critique.
warrant
This
(2)
collection
deciof
the
ul-
graph
of
each
reduc-
warrants
in
comprises
justification
recent to apply
for
reduction
and
precedent’s
ratio elements
successive
of the prototypes-and-deformations may now be intended
discussed
global
of the precedents.
this
hypo-
passes
that
> the
If
of fore-
and adjacent
by a unit
m
contradicts
the transformations
P2 to
Bourhill
model
can
justifications
the
–Dzl,
( 1–3)
doing setting
feature.
of consequences
respectively,
could
–Fz[+b[lll
values
for case n, a and b are the weights values
This
scheme
and
transformed
but
on the fore-
on the directness
tively ture
by Bour-
by P2. weight
were ~ a[Fl
function
l?!
that
the first
be controlled
a higher
than
of in-
than
no plausible
the transformations
approach a
a > b. Thus,
the
case that
However,
the same inadequacy
HI
P2
which
suppose
under
be controlled
ap-
provide
justification
example,
should
by placing
would
to
and
if such a weight-
it
hill
and
be the
b > a, which
Whether
ent than
a given
feature
and
hill
in a particular
connection
is greater
the transformation
from
proaches.
be no no-
explicit
Bourhill
be modeled
would
direct
result
hypothetical,
Finally, suffers
First,
or negate
be devised,
which
respects.
~.
of the
on these
from
130urhiH,
weighting
same
wrongdoing @,
that
H3’s 1(=
the
it must
P2,
that
effect
ap-
differ
the featural
dividual ory, under
possi-
Second,
have
At first ing
in two
by the claimant.
proach
would
there
tend
three
the dimensioned
approach
changing
direction
with
approach
approach
the featural that
each
from
by a
H3’s difference
have
is no
Thus,
implies
feature seeability
at all in its Bourhill and
motorcyclist’s
distance
/=
and hypothetical.
not
from
Thus,
should there
injury.
distance
dimensional
a distance
is fl a2–ll+b]O–
Bourhill
since
H3,
P2 by
but
It differs
H3 clearly
as Bourhill,
~
feature
feature.
Plaintiff.
from
P2 is /~-a[2–2+b0–21=@,
~. None
injuring
of 1 in each feature.
difference
miss)
off,
5, differs
directness
foreseeability
miss)
Figure
goes
Figure
of 2 in its
P2
H2
in
that
description model
suggests
to the explanations,
w the facts, of precedents [McC9 1]. This refinement represent a departure from Goodhart’s view.
that
it
as well would
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if any such warrant
were false, then the decision
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