Negligence, Causation and Information
Stephen Marks*
This note suggests a model to unify, in a sim-
ple information-based framework, the notion
of negligence and the various notions of caus-
ation. In effect, the model demonstrates that
negligence, probabilistic cause and cause-in-
fact represent an identical concept applied to
different information sets. This note uses the
unified framework to develop a simple al-
gorithm for the practical application of the
principles of causation in the law of negligence.
Ce commentaire prgsente un module qui uni-
fie ]a notion de negligence et les diverses no-
tions de causalit, dans un cadre simple fond6
sur rinformation. En fait, ce module d6-
montre que la n gligence, la probabilistic cause
et la cause-in-fact repr6sentent un concept
identique appliqu6 A de difttrents ensembles
d’information. Ce commentaire emploie un
cadre unifi6 en vue de davelopper un algo-
rithme simple devant servir ‘application pra-
tique des principes de causalit6 dans l’tude
du tort de negligence.
*Of the School of Management, Boston University.
McGill Law Journal 1985
Revue de droit de McGill
1985]
I. Background
NOTE
To establish liability in negligence, it is not sufficient merely to show
that the defendant is negligent. It is also necessary to show that the negligent
action was somehow closely connected to the damage suffered by the plain-
tiff. The courts apply a number of doctrines to determine whether there is
a sufficient connection. The court may decide that although the action of
the defendant was negligent, it did not “cause” the accident or it was not
“proximate to” the accident.
Example 1. A driver using due care runs over the plaintiff’s dog which ran
unexpectedly into the street.
Example 2. A bus driver who is carelessly travelling at excessive speed arrives
at a location just in time for the bus to be hit by an unseen falling rock from
an adjacent cliff. The plaintiff, a passenger, sues.
Example 3. A fire negligently set by the defendant, who was carelessly playing
with gasoline, merges with a fire of natural origin and destroys the plaintiff’s
house.
In the first case, the defendant escapes liability because he exercised
due care, that is, he was not negligent. In the second case, the defendant
escapes liability owing to lack of probabilistic cause. In the third case, the
defendant escapes liability owing to lack of cause-in-fact, also called direct
causation or but-for causation.’
Thus, there are three theories that explain the outcomes of these three
cases. It would be desirable if all three could be unified within a single
framework. A major obstacle to unifying the doctrines of negligence and
causation has been the following fact: a model of causation must explain
cases in which a defendant who has exercised a socially non-optimal level
of care can still escape liability owing to lack of causation.
It would appear that negligence must be something quite different from
causation because negligence depends on optimal care and causation does
not. If we look at these concepts in terms of information, we see that neg-
ligence, probabilistic cause, and cause-in-fact represent an identical concept
‘The notions of probabilistic cause and cause-in-fact used here are those defined by S. Shavell,
“An Analysis of Causation and the Scope of Liability in the Law of Torts” (1980) 9 J. Legal
Stud. 463 at 468:
One action is a probabilistic cause of a consequence relative to another action if
the probability of occurrence of the consequence is higher given the first action than
given the second.
Ibid. at 467:
One action is a cause-in-fact of a consequence relative to another action if, given
the state of world, the consequence would have been different had the second action
been taken.
McGILL LAW JOURNAL
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applied to different information sets. Thus, a simple unified theory is pos-
sible. This theory yields a simple practical algorithm for the solution of
problems of causation.
II. The Algorithm and Its Application
An example of a problematic case is that of Weeks v. McNulty.2 The
defendant, Frank McNulty, was the owner of the Hotel Knox which was
destroyed by fire in 1897. Arthur E. Weeks, who was a guest in the hotel at
the time, was killed in the fire. His wife sued to recover damages for the
death of her husband, alleging that the defendant was negligent in failing
to provide fire escapes as required by local ordinance. The evidence, how-
ever, indicated that Arthur Weeks never went to the window to look for a
fire escape: “It is not shown that deceased was at a window, or in any position
where a fire escape would have afforded him any benefit whatever.”‘ 3 Thus,
the court held that the question of negligence was irrelevant since “no causal
connection between the violation of the ordinance and the injuries sustained
by the plaintiff” 4 had been shown.
The analysis of the issues involved in this case, and in the hypothetical
cases cited earlier, begins with an algorithm for negligence and causation.
This algorithm is presented below, followed by its application to Weeks.
The algorithm and the underlying model are explained in Part IV.
Algorithm for Negligence and Causation
1. The court should determine:
a. ex ante information. This is information known at the time defendant
chose c, the action. This information is represented by S.
b. accident type. This information includes knowledge that the accident, if
it occurs, will be of a certain type. This information is represented by T.
c. ex post information. This is all the information known at the time of
trial. This information is represented by V.
2. The court should determine:
a. the socially optimal action to be taken by the potential injurer given what
was known to him at the time the action was chosen (S). The socially optimal
action is represented by c*. Note that c* depends only on S.
2101 Tenn. 495, 48 S.W. 809 (S.C. 1898) [hereinafter Weeks cited to S.W.].
3Weeks, ibid. at 812. If he had looked out the window, he would have seen it was possible
to leap to an adjoining building. Since he did not do this, the court concluded that he never
looked for an escape out the window.
41bid.
1985]
NOTE
b. the actual action chosen. This action is represented by c.
3. The court should determine:
a. given S (ex ante information), whether the expected loss of c is greater
than that of c*. If it is, then there is negligence, i.e., ELV’c(c,S) > ELVC(c*,S)
b. given T (accident type), whether the expected loss of c is greater than
that of c*. If it is, then there is probabilistic cause, i.e., ELVic(c,T) >
ELVi(c*,T)
c. given V (ex post information), whether the expected loss of c is greater
than that of c*. If it is, then there is cause-in-fact, i.e., ELvic(c,V) >
ELc’c(c*,V)
4. Liability results if, given S, T, V, and c* = f(S) and action c,
ELVc(c,S) > ELvIc(c*,S)
ELVic(c,T) > ELI(c*,T)
and EL vc(cV) > ELVIC(c*,V)
Application of the Algorithm to Weeks v. McNulty
1. Determine the information sets:
a. S
building capable of burning
b. T–fire
c. V
decedent never looked for a fire escape
2. Given S, determine:
a. c* = install fire escapes
b. c = do not install fire escapes
3. Compare expected loss of c with that of c*:
a. given S, expected loss greater with c –
thus negligence
b. given T, expected loss greater with c –
thus probabilistic cause
c. given V, expected loss not greater with c –
thus no cause-in-fact.
4. No liability for defendant.
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III. The Model Explained
A. Definitions and Assumptions
In general, there are many accidents that can occur and many persons
who can affect the probability and the severity of injury. For expositional
ease I use the case of one potential injurer and a potential victim who is
passive, that is, a potential victim who can affect neither the probability of
occurrence nor the severity of the accident. All of the basic ideas can be
presented using this simple framework. (The extension to multiple potential
injurers and to nonpassive victims is straightforward and does not affect
the basic results.)
The injurer chooses an action, c, from a set of possible actions. If we
were omniscient, we could observe the state of the world in complete detail
at the time the action was chosen. Given this perfect information, we could
determine whether the ensuing chain of events would lead to an accident
and, if so, we could determine the extent of injury.
In the real world, there is uncertainty. The amount of uncertainty de-
pends on the amount and the type of information that we have at a given
time. The algorithm categorizes information as ex ante (S), ex post (V), and
as information as to accident type (T).
Even if we do not have perfect information we can estimate expected
loss by assigning probabilities to outcomes based on the information that
we have.5 Given the available information (I) and the action chosen by the
potential injurer (c), the expected loss to the potential victim is represented
by
EL’c”c.I)
where I is replaced by S, T, or V depending on the information assumed.
For example, ELviC(c,S) represents the expected loss to victims of action c
given what is known when action c is taken. In Weeks, it is the expected
injury to potential victims from all types of possible accidents given that
no fire escapes were installed.6 ELVi(cT) is the expected loss from a given
type of accident. In Weeks, it is the expected loss owing to fire. We pretend
that we are at the point of choosing the action (in this case, the choice of
whether to install fire escapes) and ask how this choice affects the likelihood
51 will call a loss an “expected loss” even if it is certain. More rigorous set-theoretic definitions
of information and expected loss are given in the Appendix for the interested reader. The above
definitions, however, capture the essence.
6An action also imposes a cost on the potential injurer, sometimes called the “cost of care”.
This can be represented by EL”I(c,S).
19851
NOTE
and severity of injury if a fire should occur. ELviC (c,V) is the loss we would
expect when choosing an action given that we know everything that is known
at the time of trial, such as whether the decedent looked for a fire escape.
The socially optimal action in the circumstances depends only on S,
the information known at the time the action was taken. It is called c* and
can be represented as a function of S (c* = f(S)).7
B. Negligence
A system of negligence liability is one that incorporates the doctrine of
negligence as defined below. Recall that at the time of trial S, T and V are
known, but at the time the defendant chose the action only S was known.
Doctrine of Negligence. The defendant is liable for damages by reason of action
c, given S, T, and V, and c* = f(S) only if
ELVIC(c,S) > ELv’c(c*,S).
First we find the optimal action, c*, given what the defendant knew at
the time of choosing the action. Then we compare c and c* assuming that
we know only what was known at the time the action was chosen. If, given
this information, the choice of c inflicts on the rest of society a greater
expected loss than c*, then the defendant is deemed negligent.
Of course, in tort law, liability will not be assigned on the basis of
negligence alone. There must be negligence, harm and a causal connection
between the two. Without this causal connection, the defendant will escape
liability. The reasons for limiting the scope of liability are twofold: one, to
make the system conform to our notions of fairness, and two, to lower the
amount of damages paid and the resultant transaction cost losses. 8 Both
these goals are accomplished without the loss of behavioural efficiency through
the application of the doctrines of causation: cause-in-fact and probabilistic
cause.
7The expected cost to society given the information known at the time of the action, S, and
given the action, c, is ELVIC(c,S) + EL”i(cS).
We want people to choose the action that minimizes social costs. We call this action c*. A tort
system is said to be behaviourally efficient if it induces potential injurers to adopt c*.
8As Shavell has stated, supra, note I at 465, “restricting the scope of liability results in a
decline in the administrative costs connected with the use or threatened use of the legal system”.
More important, however, is the notion that it is unfair to make a negligent defendant pay for
injuries that are unrelated to the defendant’s action. Without some requirement of a connection,
the negligence of a defendant would leave him or her potentially liable for any and all accidents,
related or not.
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C. Cause-in-Fact
Recall again that at the time of trial S, T, and V are all known, but at
the time the defendant chose the action only S was known. The doctrine
of cause-in-fact incorporates all information known at the time of trial.
Cause-in-Fact. The defendant is liable for damages by reason of action c, given
S, T, and V, and e = f(S), only if
ELVc(c,V) > ELVIC(c*,V).
First we find the optimal action, c*, given what the defendant knew at
the time of choosing the action. Then we compare c and c* assuming that
we know everything that we know at the time of trial. If, given this infor-
mation, the choice of c inflicts on the rest of society a greater expected loss
than c*, then there is direct causation. An example of a negligent defendant
escaping liability for lack of cause-in-fact is the case where a fire negligently
set by the defendant merges with a fire of natural origin and destroys the
plaintiff’s house. Assume that the defendant was playing with gasoline. The
optimal action, given what was known at the time of the action, was not
playing with gasoline. Given what is known at the time of action, playing
with gasoline inflicts higher expected losses on others than not playing with
gasoline and thus, it is negligent. Given what is known at the time of trial,
however, playing with gasoline results in the same loss as not playing with
gasoline so the defendant escapes liability even though he adopted a sub-
optimal level of care.
The same can be said about Weeks. Given what is known at the time
the defendant became the owner of the hotel, it is clear that fire escapes
should have been installed. Not installing fire escapes is negligent. Given
what is known at the time of trial, however, it is clear that even with fire
escapes the loss to the plaintiff would have been the same. Thus, the de-
fendant escapes liability.
D. Probabilistic Cause
The doctrine of probabilistic cause depends on an intermediate amount
of information, more than that available ex ante, but less than that available
ex post. Recall again that S, T, and V are known at the time of trial, but
only S was known at the time the action was chosen.
1985]
NOTE
Probabilistic Cause. A defendant is liable for damages by reason of action c,
given S, T, and V and c = f(S) only if
ELviC(c,T) > ELVic(c*,T).
First we find the optimal action, c*, given what the defendant knew at
the time of choosing the action. Then we compare c and c* assuming that
we know that the accident will be of type T. If, given this information, the
choice of c inflicts a greater expected loss than c*, there is probabilistic
cause.
An example in which a negligent defendant escapes liability owing to
lack of probabilistic cause, is the case of a bus driver who, negligently trav-
elling at high speed, arrives at a location just in time for the bus to be hit
by a falling rock, injuring the plaintiff. Given what is known at the time of
choosing the action, the optimal action is not to speed as speeding inflicts
higher expected losses on others than not speeding. Thus, it is negligent.
Given what is known at the time of trial, not speeding would have avoided
the loss. Thus, there is cause-in-fact. However, given this type of accident
(rocks falling) and the information known at the time of the choice of action,
it is clear that speeding and not speeding produce the same expected loss.
(In fact, the probability of being hit by a rock may even be lower if one is
speeding.) Therefore, we conclude that there is no probabilistic cause.
E. An Equivalence Theorem
In order to contrast these doctrines, I will state them again.
Equivalence Theorem. A defendant is liable for damages by reason of action
c, given S, T, and V, and c = f(S), only if
EL vc(c,S) > ELVic(c*,T)
ELvi-(c,T) > EL i(c*,T)
and ELVc(c,V) > ELv’C(c*,V)
(negligence)
(probabilistic cause)
(cause-in-fact).
This is the central result of this paper. It can be restated as follows:
Equivalence Theorem: Negligence, probabilistic cause and cause-in-fact are the
same expected loss concept applied to different information sets.
Finally, a few technical comments are in order. First, the known theo-
rems on efficiency remain intact. In a negligence system, negligent defend-
ants can be excused from liability for lack of probabilistic cause or for lack
of cause-in-fact without impairing behavioural efficiency. The proof of this
becomes trivial using this information framework. 9 Another less known
result is that the doctrine of unusual, unrelated, or unforeseeable accidents
9The proof is in the Appendix which is provided to demonstrate how easily theoretical
problems are resolved within an information-based framework.
REVUE DE DROIT DE McGILL
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(also known as the foreseeability doctrine) is not a causation concept at all
but is nevertheless behaviourally efficient if correctly applied in a negligence
system.10 Lastly, the introduction of multiple potential injurers can lead to
game behaviour with inefficient equilibria. This problem, which is the result
of embedding causation in a negligence system, is resolved by the doctrine
of joint liability.”
III. Examples
The algorithm involves three steps. First, determine the information
sets. Second, determine the optimal action given what the defendant knew
(or should have known) at the time the action was taken while also noting
the action the defendant did in fact take. Third, compare the optimal action
with the actual action given the three information sets to determine the
effect on the expected loss of the plaintiff.
Example 1: Berry v. Sugar Notch Borough 12
The plaintiff, Bryan C. Berry, was a motorman who operated a trolley
car on a line running through the borough of Sugar Notch. The plaintiff was
operating the trolley at excessive speed during a windstorm. While passing
under a large chestnut tree, the tree was blown down crushing the trolley
car and injuring the plaintiff. The condition of the tree before the accident
was questionable and the borough was found negligent in not having re-
moved it. The borough, however, sought to bar recovery based on contrib-
utory negligence, arguing that if the plaintiff had not been speeding, then
the trolley car would not have been at the precise place where the tree fell
at the precise time that it fell. The court must rule on the issue of contrib-
utory negligence.
1. Determine the information sets:
a. S = speeding can be dangerous
b. T = random unseen object strikes trolley
c. V = tree fell at point x, time t
2. Given S, determine
a. c*
70 km/h or less
b. c = llO km/h
1’This is also shown in the Appendix.
“A discussion of this is beyond the scope of this note. However, its solution is straightforward.
12191 Pa 345, 43 A. 240 (S.C. 1899).
1985]
NOTE
137
3. Compare expected losses of c and c*:
a. given S, expected loss greater with c; thus negligence
b. given T, expected loss not greater with c; thus no probabilistic cause
c. given V, expected loss greater than c; thus cause-in-fact.
Verdict: Plaintiff Not Barred (Lack of Probabilistic Cause)
Note-. The court finds direct causation since if the plaintiff were not speeding
he would not have been at point x, at time t.
Example 2: New York Central Railroad Co. v. Grimstad13
Angell Grimstad fell off a barge into the water. He could not swim. His
wife, Elfrieda Grimstad, ran immediately to the cabin to fetch a small line.
The barge was not equipped with life buoys. When she returned, Mr Grim-
stad had disappeared. The jury found that the New York Central Railroad
Company had been negligent in not equipping the barge with life-preservers.
Yet the court reversed the decision on appeal, speculating that the time
necessary to fetch and use a life-preserver is probably the same as with a
small line, and that Mr Grimstad would have drowned anyway.
1. Determine the information sets:
a. S = people fall overboard and drown
b. T = drowning
c. V = decedent disappeared quickly
2. Given S, determine:
a. c* = have life-preservers
b. c = no life-preservers
3. Compare expected losses:
a. given S, expected loss greater with c; thus negligence
b. given T, expected loss greater with c; thus probabilistic cause
c. given V, expected loss not greater with c; thus no cause-in-fact.
13264 E 334 (2d Cir. C.A. 1920).
McGILL LAW JOURNAL
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Verdict: Not Liable (Lack of Cause-in-Fact)
Example 3: Kirincich v. Standard Dredging Co. 14
Stefan Kirincich was a deck-hand on a derrick barge owned by the
Standard Dredging Company. Kirincich fell into the water and cried for
help. The other dock-hands repeatedly tossed small lines but failed to toss
anything more buoyant. Stefan Kirincich finally drowned. His brother sued.
1. Determine the information sets:
a. S = people fall overboard and drown
b. T = drowning
c. V = decedent could not find the lines thrown to him
2. Given S, determine:
a. c* = throw large buoyant object
b. c = throw thin non-buoyant rope
3. Compare expected loss of c and c*:
a. given S, expected loss greater with c; thus negligence
b. given T, expected loss greater with c; thus probabilistic cause
c. given V, expected loss greater with c; thus cause-in-fact.
Verdict: Liable 15
V. Conclusion
This note makes two points. First, it demonstrates that the notions of
negligence, probabilistic cause, and cause-in-fact can be integrated into a
simple, unified framework based on information. Indeed, the model dem-
onstrates that negligence, pr6babilistic cause, and cause-in-fact represent an
identical concept applied to different information sets. The second point is
that this framework can be used to develop a simple and practical algorithm
for applying these doctrines to actual case experience.
141 12 E2d 163 (3d Cir. C.A. 1940).
15Other cases to which the algorithm can be applied include City ofPiqua v. Morris, 98 Ohio
St. 42, 120 N.E. 300 (S.C. 1918) and Ferroggiaro v. Bowline, 153 Cal. App. 2d 759, 315 P.2d
446 (Dist. C.A. 1957).
NOTE
19851
Appendix
Formal Notation
The following discussion formalizes some of the concepts in the body
of the note. All optimization is assumed to be in terms of expected value.
The injurer chooses an action, or level of care, from a set of actions. There
is also a set of random states of nature. A state of nature and an action
define the world in complete detail. Let
C = set of actions (or levels of care) for the potential injurer
e a member of set A (an action or level of care)
.=
s – a random state
set of random states of nature
The essence of the analysis is the creation of various partitions of the
set r3 ranging from coarse to fine (see diagram). The coarsest partition is the
partition of 25 into subsets that represent the amount of information known
at the time of the defendant’s action. These are called “ex ante information
sets” and are represented by Si. For example, if the ex ante information
set is S, , then the defendant knew at the time of his or her action that the
true state of nature was one of thosed in S, . The Si are further partitioned
into accident types. At the time of trial we know what type of accident
occurred. There are many possible classification schemes. An accident type
is represented by Ti. Each type is again partitioned into sets that represent
the amount of information known at trial. After the accident, it is possible
to know not only the accident type, but also many of the circumstances that
surround the accident. Thus, we partition each accident type into sets called
“ex post information sets”. These are represented by Vi. This is the finest
partition observable ex post.
The state of nature along with the action of the potential injurer de-
scribes the world in complete detail, so that given these it is possible to
determine whether an accident occurs, the amount of the loss and upon
whom it falls. In particular, we can divide the loss between that which falls
on the potential injurer and that which falls on the rest of society (victims).
These are represented respectively below:
L’i~(c,s)
LVIC(c,s)
(falls on potential injurer)
(falls on potential victim)
Note that Lini includes the cost of care.
To each state of the world is attached a probability: p(s).
REVUE DE DROIT DE McGILL
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(/2
(/2
C’n
C/2
(22
(/2
‘0
;(/
“4(/
N/
.0 ~
0
20
0, C.)
1985]
NOTE
If we knew that the true state of nature were in some subset I of 6 then
we could define PI(s) as the probability of occurrence of s given I. It can be
written:
Ps(s) = p (s)
s p (s).
SEl
Thus, if we knew that the true state of nature were in some subset I,
we could write the expected losses given action c as:
EL”jn(cI) = _ p,(si)LnJ(c,sj)
ELVIC(c,I) = I p,(s 1)Lvc(csi).
SjEI
We multiply each possible loss with its probability to get expected loss.
These are the formal definitions of the concepts used in the paper.
Efficiency
To show that we can remove a subset of accidents from the scope of
liability, if the expected harm of that subset is not affected by the defendant’s
action, is straightforward. For example, divide the set S into two subsets,
T, and T 2 , and note ELVIC(cS) = ELvIc(c,T,) + ELVc(c,T 2) and assume
ELvc(c,T,) > ELvIc(c*,Tt)
ELVIC(c,T 2) — ELc(c*,T 2).
We excuse liability for type T2 accidents even if the defendant did not use
the optimal level of care, c*. Now note from the definition of c* that
ELVc(c,S) + EL”‘i(c,S) > EL(c*,S) + ELVIc(c*,S).
Subtracting ELvic (c,T 2 ) from the left-hand side and subtracting EL-
vic (c*,T 2 ) from the right-hand side yields
EL c(c,T,) + EL”i(c,S) > ELVic(c*,T,) + ELi”J(c*,S)
and this implies
ELvIC(c,T,) + EL’j(cS) > ELiU(c*,S).
The left side represents expected cost to the injurer if c is adopted and the
right side represents the expected cost to the injurer if c* is adopted. The
potential injurer will adopt c*. (The same argument holds for V.) Thus,
excusing liability for lack of probabilistic cause or for lack of cause-in-fact
does not impair efficiency.
McGILL LAW JOURNAL
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Foreseeability
Another application of the information approach is to the doctrine of
unusual, unrelated, or “unforeseeable” accidents. (Note that the use of the
word “unforeseeable” is a misnomer since one can assign a probability to
any event no matter how bizarre or unlikely it seems.) In applying this
doctrine, the court must do three things. First, it must set the standard of
care while taking into consideration all possible events. Second, it must
divide accidents into types, identifying those that are unusual, unrelated,
or “unforeseeable”. Third, the court must excuse liability for the class of
unusual, unrelated, or “unforeseeable” accidents only if the expected loss
of this class of accidents is small. If this is done properly, there will be no
effect on behavioural incentives. Consider Palsgrafv. Long Island Railroad
Co.’ 6 The defendant’s conductor was careless in helping a passenger board
a train. The passenger dropped a package containing fireworks which ex-
ploded, causing a set of weigh-scales to fall, thus injuring the plaintiff. The
defendant, through its employee, was clearly negligent. In fact, there existed
negligence, direct causation and proximity. Yet the defendant escaped lia-
bility. This is an efficient result. To see why, consider the case where the
plaintiff’s care is irrelevant. We can write the social loss function (assuming
again only one potential injurer) as
EL(c,S) = ELViC(c,S) + EL”j(c,S).
Suppose that this function is minimized at c*. Note that included in
ELViC(c,S) are all possible accidents. Divide the accidents into two types. This
division is made ex ante.
ELs(c,S) = ELVI(cT,) + ELv’c(c,T 2 ) + EL “J(cS).
I will assume that ELvic (c,T 2 ) is small in a sense to be made more
precise below. Note that
ELv”c(c,T,) + ELVic(cT 2) + EL “‘(cS) :- ELViC(c*,S) + ELiJ(c*,S).
I will assume that ELvic (cT 2 ) is small enough that
ELVic(c,T,) < ELiC(c*,S). We can call this second class of accidents the case of unusual, or "unrelated" or "unforeseeable" accidents. From the above two inequalities we get ELvc(c,Ti) + ELni"(c,S) > ELinJ(c*,S).
The left-hand side of the inequality is the expected loss incurred by the
injurer by adopting c. Note that the injurer is liable for Type 1 accidents.
16248 N.Y. 339, 162 N.E. 99 (C.A. 1928) [hereinafter Palsgraf].
1985]
NOTE
143
The right-hand side is the expected loss of adopting the optimal c*. It is
clear that the potential injurer will adopt c*.
This means that even if we excuse liability in Type 2 accidents, the
potential injurer will adopt optimal care. Again, there are three conditions:
(1) the optimal level of care must be determined using all accidents; (2) the
division into liable and nonliable accidents must be made ex ante, (3) the
ex ante expected loss from nonliable accidents must be small in the sense
described above.
Palsgrafis a case involving an unusual accident. Although the dividing
line between usual and unusual is not clear, it is sufficient to know that if
we divide accidents into two classes, those certainly usual and those possibly
unusual, the expected loss in the second class is small. This is clearly the
result in Palsgraf
