a complete characterization of efficient liability rules: comment
TRANSCRIPT
A Complete Characterization of Efficient LiabilityRules: Comment
Jeonghyun Kim
Received September 17, 2002; revised version received April 2, 2003Published online: November 10, 2003
� Springer-Verlag 2003
In a recent article, Jain and Singh (2002) prove that a condition they call neg-ligence liability is necessary and sufficient for any liability rule to be efficient. Inthis note I criticize their result on two accounts: First, their result cruciallydepends on implicit restrictions they impose on the liability assignment function.If we drop the assumption that the liability apportionment between two non-negligent parties is constant for all combinations of non-negligent care levels, theequivalence between the condition of negligence liability and the efficiency ofliability rules breaks down. Second, their attempt to drop the assumption ofuniqueness for the social optimum improves the generality of the model at asubstantial cost, since it must be accompanied by a new assumption that ispossibly even more unrealistic. The importance of the uniqueness assumption isshown in a simple discrete care model, in which comparative negligence maylead to an inefficient outcome when the existence of two social optima leads us tointerpret due care as a varying standard based on the other party’s actual choice.
Keywords: efficient liability rules, negligence-based rules, liability assignmentfunction, condition of negligence liability, uniqueness of social optimum.
JEL classification: K13, D61.
1 Introduction
It is a well-established fact that in the standard tort model1 with bilateral
precaution and full information, the rules of simple negligence, negligence
1 The basic model assumes risk-neutral parties, fixed level of activity, noadministrative costs and perfect compensation. Since Brown’s (1973) pathbreak-ing analysis, the conventional literature usually assumes that cost-of-care andexpected loss functions are continuous and there exists a unique social optimum.
Vol. 81 (2004), No. 1, pp. 61–75DOI 10.1007/s00712-003-0013-2
with a defense of contributory negligence, comparative negligence, strict
liability with a defense of contributory negligence, and strict liability with a
defense of dual contributory negligence, all give both the injurer and the
victim correct incentives for efficient precaution, if the legal standard of care
for each party is set equal to the socially efficient level.2 We can summarize
the common features these rules share by the following two properties:
Property 1 (P1): The non-negligent party escapes from liability com-
pletely if the other party is negligent.
Property 2 (P2): When both parties are non-negligent, the whole accident
burden falls on one predetermined party for all combinations of care
levels.3
In this note, the term ‘‘negligence-based rules’’ will be used to refer to the
group of liability rules that satisfy (P1) and (P2). It is remarkable to see
that the issue of liability apportionment between two negligent parties is
beside the point in terms of the efficiency of liability rules. Any variation
of the sharing rule, which is applied when both parties are negligent, turns
out to achieve an efficient outcome as long as the rule also satisfies the
above two properties.4 In fact, (P1) and (P2) together comprise a suffi-
cient condition for efficient liability rules.
In their interesting paper recently published in this journal, Jain and
Singh (2002) try to extend the main result of the tort literature. Their main
theorems show that (P1), which corresponds to what they call the con-
dition of negligence liability, is both a necessary and a sufficient condition
for any liability rule to be efficient. They also argue that such a result
holds in a very general framework in which neither continuity in the cost-
of-care function nor uniqueness of the social optimum is assumed. This is
2 For example, see Shavell (1987).3 Under the rules of simple negligence, negligence with a defense of con-
tributory negligence, and comparative negligence, non-negligent victims mustbear the whole accident burden as long as injurers are found to be non-negligentas well. Under the rules of strict liability with a defense of contributory negli-gence (the reverse Hand rule) and strict liability with a defense of dualcontributory negligence, non-negligent injurers bear the whole accident burdenfor non-negligent victims.4 This was established in the process of verifying the efficiency of comparative
negligence. See Landes and Posner (1980), Haddock and Curran (1985), and Rea(1987).
62 J. Kim
a remarkable achievement in the sense that they completely characterize
efficient liability rules in the general context by providing a simple,
intuitively clear condition as the if-and-only-if condition for efficiency.
In this note, however, I will criticize Jain and Singh (2002) on two
grounds. First, their main theorems crucially depend on implicit restric-
tions they impose on the liability assignment function. It will be shown in
Sect. 2 that their method of defining liability rules based on proportions
of non-negligence instead of costs of care restricts a priori the scope of
possible liability rules. A liability rule is excluded from their consider-
ation if it does not satisfy the following two properties: (i) the liability
assignment function is constant for all non-negligent care levels of one
party, when the other party’s negligent care level is given, and (ii) it is
constant for all combinations of non-negligent care levels, when both
parties are non-negligent. Two examples will be presented below to show
that if we drop this hidden assumption and deal with more general lia-
bility rules, the condition of negligence liability (i.e., (P1)) is only a
necessary, but not a sufficient condition for efficiency; and the condition
of negligence liability plus the hidden assumption is only a sufficient, but
not a necessary condition for efficiency.
Second, I argue that Jain and Singh’s dropping of the assumption of
uniqueness for the social optimum may improve the generality of the
model, but does so at a substantial cost. This issue will be discussed in
detail in Sect. 3. Jain and Singh (2002) successfully reinforce the gener-
ality of their theorems by constructing a model that can include both dis-
crete and continuous precaution cases. However, their attempt to allow for
the possibility of multiple social optima must be accompanied by the
following stringent assumption: The judicial choice of one among several
efficient optima must be known to everybody before the accident, and
everybody must believe that the court will stick to that choice. To illustrate
the importance of assuming uniqueness for the social optimum, I construct
a simple example in which a binary and alternative care technology enables
two social optima to exist. Wewill see that, under the special circumstances
of this model, the principle that the legal standard of care is set at the
socially efficient level should be interpreted as implying a varying standard
based on the other party’s actual choice, rather than implying a fixed
standard set at one arbitrarily chosen optimum. The analysis of the game’s
equilibrium under comparative negligence illustrates that an efficient
outcome is not guaranteed, even though the rule satisfies the condition of
negligence liability (i.e., (P1)) and Jain and Singh’s hidden assumption.
A Complete Characterization of Efficient Liability Rules: Comment 63
2 Conditions for Efficient Liability Rules
2.1 The Model
Suppose that there are two parties, a potential injurer (defendant) and a
potential victim (plaintiff) who engage in certain activities that inflict
damages on the victim if an accident occurs. We use the same notation as
used in Jain and Singh (2002):
C � set of all feasible c, where c denotes the cost of care taken by
the victim.
D � set of all feasible d, where d denotes the cost of care taken by
the injurer.
L(c,d) � expected loss due to an accident (= monetary value of the harm
from an accident multiplied by the probability of accidents
occurring).
It is naturally assumed that a higher level of care by either party, given
the other party’s care level, does not result in a greater expected accident
loss; i.e., Lðc; dÞ � Lðc0; dÞ for c > c0, and Lðc; dÞ � Lðc; d 0Þ for d > d 0 .The social goal is, as usual, to minimize the total social cost (TSC)
defined by the sum of care-taking costs of each party and the expected
accident cost; i.e., TSC ¼ cþ d þ Lðc; dÞ. Let M denote the set of all
TSC-minimizing configurations of costs of care.
Jain and Singh’s attempt to fully generalize the framework of the
standard tort model is reflected in the following two points. First, they do
not put any restriction on the sets C and D, except that they are non-
empty. By doing so, the analysis can successfully include both discrete
and continuous variable models with regards to cost-of-care and expected
loss functions. Second, they do not impose any restriction on M either,
except that it is non-empty. In other words, they do not assume a unique
solution to the TSC minimization problem.
2.2 The Liability Assignment Function
Our main interest is to verify the primary characteristics of efficient lia-
bility rules, that is, liability rules that induce both the injurer and the
victim to take socially optimal care levels. Let us define the general
liability assignment function as f ðc; dÞ ¼ x, where x represents the pro-
portion of the accident loss borne by the victim, for given care levels of
both parties. (1� x is of course the proportion of the accident loss borne
64 J. Kim
by the injurer.) Every liability rule specifies f ðc; dÞ in its own way, for all
feasible c and d; for example, the negligence rule with contributory
negligence as a defense is defined by:
f ðc;dÞ¼ 0 if c�due care for the victim and d<due care for the injurer;1 otherwise:
n
Jain and Singh, however, do not use this general definition. Not-
withstanding that the liability assignment function can be well defined
directly from c and d, they first introduce two new functions p and q(p. 109):
For ðc�;d�Þ 2M ; pðcÞ ¼ 1 if c � c�; pðcÞ ¼ cc�
if c < c� and c� > 0;
qðdÞ ¼ 1 if d � d�; qðdÞ ¼ dd�
if d < d� and d� > 0 :
It follows from the above definitions that pðcÞ and qðdÞ can be inter-
preted as implying the proportion of non-negligence of the victim and the
injurer, respectively.5 Then, Jain and Singh define the liability rule indi-
rectly as a function of p and q (p. 111):
f ðp; qÞ ¼ ðx; yÞ ¼ ½xðp; qÞ; yðp; qÞ�;
where xþ y ¼ 1, and x represents the proportion of the accident loss
borne by the victim.
This way of defining liability rules, based on proportions of non-
negligence, has the merit that the liability assignments are not affected
by a change of monetary units. Note, however, that by using
this approach, they actually add a hidden restriction to the scope of
liability rules they consider. Because the Jain and Singh f is defined
as a function of proportions of non-negligence, it follows from the
5 This interpretation follows from the ‘‘technical’’ notion of negligence/non-negligence that characterizes the parties’ behavior in terms relevant from theefficiency point of view (Jain and Singh, 2002, p. 107). The ‘‘legal’’ notion ofnegligence/non-negligence, on the other hand, is relevant for determining theactual behavior of the parties. If c�½d�� is set as the legally binding due care levelfor the victim [injurer] under a liability rule, pðcÞ½qðdÞ� will represent the victim[injurer]’s proportion of non-negligence from the legal notion as well as from thetechnical notion.
A Complete Characterization of Efficient Liability Rules: Comment 65
definition of pðcÞ and qðdÞ that, translating back to the generally de-
fined f :
ðA1Þ If d < d�; then for all c � c�; f is constant at f ðc�; dÞ;ðA2Þ If c < c�; then for all d � d�; f is constant at f ðc; d�Þ;ðA3Þ For all c � c� and d � d�; f is constant at f ðc�; d�Þ :
I call these three conditions taken together the Jain and Singh hidden
assumption.6 It implies that increasing one’s care level does not at all
affect the proportion of the accident loss one should bear, as long as one is
already in the non-negligence zone. In other words, Jain and Singh take it
for granted that (i) one party’s non-negligent behavior is always treated
equally for the given negligent care level of the other party, no matter how
high one’s care level is ((A1) and (A2)), and (ii) if both parties are non-
negligent, each party’s share of the accident loss is constant for every
possible combination of care levels ((A3)).
Their Remark 2 (p. 111) shows that the rules of strict liability, no
liability and every form of negligence-based rule can be well defined by pand q. This is because those rules have no conflict with the above
restrictions on f . However, some liability rules may in fact be inconsis-
tent with the Jain and Singh hidden assumption, for example, the relative
negligence rule analyzed by Brown (1973), Assaf (1984), and Feldman
and Frost (1998). Therefore, we can conclude that, while Jain and Singh’s
setup of C; D; and L is fully general, the liability rules they deal with are
not. In fact, this restrictive feature turns out to be crucially related to their
main findings on efficient liability rules.
2.3 Is the Condition of Negligence Liability Sufficient for Efficiency?
Jain and Singh’s nongeneral definition of liability rules generates a ten-
sion between their mathematical and verbal definition of the condition of
negligence liability, the most important concept in their paper. According
to their mathematical definition (p. 114), a liability rule f satisfies the
condition of negligence liability if and only if ½8p 2 ½0; 1Þ�½f ðp; 1Þ ¼ð1; 0Þ� and ½8q 2 ½0; 1Þ�½f ð1; qÞ ¼ ð0; 1Þ�. According to their verbal
definition (p. 107 and p. 114), a liability rule satisfies the condition of
6 In fact, as I will point out below, (A3) matters most in their main theorem;(A3) is the crucial part of the Jain and Singh hidden assumption.
66 J. Kim
negligence liability if and only if its structure satisfies the following two
conditions:
Condition 1 (C1): Whenever the injurer is non-negligent and the victim is
negligent, then the entire loss in case of an accident must be borne by
the victim.
Condition 2 (C2): Whenever the victim is non-negligent and the injurer is
negligent then the entire loss in case of an accident must be borne by
the injurer.
Note that (C1) and (C2) together are equivalent to what we called (P1)
earlier. These two conditions specify the rule for the case where one party
is negligent and the other party is not. However, we can now note that
(C1) and (C2) combined are not completely equivalent to the Jain and
Singh mathematical definition of negligence liability: the mathematical
expression actually carries over more information than (C1) and (C2),
because it contains the implicit qualification imposed on the function fitself. That is, Jain and Singh’s mathematical expression of the negligence
liability condition is equivalent to (C1) and (C2) plus the Jain and Singh
hidden assumption discussed above. The Jain and Singh hidden
assumption is composed of three conditions, (A1) – (A3), but since (C1)
and (C2) superimpose a stronger requirement over (A1) and (A2),
respectively, only (A3) is relevant in explaining the discrepancy between
their mathematical and verbal definition of the negligence liability con-
dition. I paraphrase (A3) in the following way:
Condition 3 (C3): Whenever both parties are non-negligent, the propor-
tion of the accident loss borne by each party is constant.
Through their Propositions 1 and 2, Jain and Singh try to show that the
condition of negligence liability is a sufficient condition for efficient
liability rules, for any choice of C, D, L, and ðc�; d�Þ 2 M .7 The
importance of (C3) in the process of proof is straightforward, since
7 Since they allow for the possibility of multiple optima, the process to provethat the condition of negligence liability is sufficient for efficiency takes twosteps: Proposition 1 shows that ðc�; d�Þ is a Nash equilibrium. Then, Proposition2 shows that all possible Nash equilibria are total-social-cost minimizing.
A Complete Characterization of Efficient Liability Rules: Comment 67
without it, we cannot eliminate the possibility of one or both parties
choosing to deviate upward from an efficient pair ðc�; d�Þ. The followingexample makes it clear that (C1) and (C2), which correspond to Jain and
Singh’s descriptive definition of the negligence liability condition, are not
sufficient to guarantee an efficient outcome when we deal with general
liability rules.
Example 1: Consider a standard continuous cost-of-care variable model
with a unique social optimum ðc�; d�Þ. As I indicated earlier, let the
generally defined liability assignment function f ðc; dÞ represent the
proportion of the accident loss borne by the victim. Consider the fol-
lowing specific liability rule:
f ðc; dÞ ¼
0 if d < d�,
1 if c < c� and d � d�,
1 if c � c�; d � d�; and c� c� � d � d�,
0 if c � c�; d � d�; and c� c� > d � d�.
8>>><>>>:
This rule satisfies (C1) and (C2), but violates (C3). It is clear that the
victim has an incentive to deviate upward from ðc�; d�Þ, unless the ex-
pected accident cost at the social optimum is zero.8 It follows that the
unique optimal pair ðc�; d�Þ is not a Nash equilibrium, and therefore, this
liability rule is not efficient.
It is worthwhile at this point to compare Jain and Singh’s mathematical
definition of the negligence liability condition (i.e., (C1) and (C2) plus a
hidden assumption (C3)) with the common properties of all negligence-
based rules, which were summarized by (P1) and (P2) earlier. We find that
(P1) is exactly identical to the combination of (C1) and (C2): The non-
negligent party is completely off the liability hook if the other party is
negligent. But (P2) is a stronger condition than (C3), because it not only
specifies the constant liability apportionment between two non-negligent
parties, but also requires the constant apportionment to be all or nothing.9
So all negligence-based rules satisfy the mathematical version of the
negligence liability condition, but the reverse does not hold.
8 The condition for the victim’s upward deviation is given by c� þ e < c�þLðc�; d�Þ for an arbitrarily small positive number e .9 For the generally defined f , (P2) can be expressed by the condition
f ðc; dÞ ¼ constant at 0 or 1, for all c � c� and d � d�.
68 J. Kim
We can learn from Jain and Singh’s Propositions 1 and 2 that a suf-
ficient condition to guarantee efficiency can be obtained by weaker
requirements than the properties of negligence-based rules (i.e., (P1) and
(P2)). That is, (P1) (=(C1) and (C2)) and (C3) together imply the effi-
ciency of any liability rule. But Example 1 makes it clear that (C3) cannot
be done away with.
2.4 Is the Condition of Negligence Liability Necessary for Efficiency?
Jain and Singh’s Proposition 3 states that the condition of negligence
liability is a necessary condition for efficient liability rules. But again, this
is a limited result, because they impose a restriction on the domain of
liability rules by excluding a priori the possibility that (C3) is not met. So
the legitimate question should be whether each condition (C1), (C2) and
(C3) is a necessary condition for efficiency, when we consider general
liability rules. The same logic used in the proof of the Jain and Singh
Proposition 3 is valid in proving that (C1) and (C2) are both necessary for
a liability rule to be efficient for any choice of C;D; L and ðc�; d�Þ 2 M .
However, we can show that (C3) is not a necessary condition for effi-
ciency with the following example.
Example 2: As in Example 1, assume a standard continuous cost-
of-care model with a unique optimum ðc�; d�Þ . Consider the following
specific liability rule:
f ðc; dÞ ¼
0 if d < d�,1 if c < c� and d � d�,1 if c� � c � c� þ Lðc�; d�Þ and d � d�,0 if c > c� þ Lðc�; d�Þ and d � d�.
8><>:
This rule satisfies (C1) and (C2), but violates (C3). Although (C3) is
not met, nobody has an incentive to deviate from ðc�; d�Þ. It turns out tobe the unique Nash equilibrium, implying that this liability rule is effi-
cient. This result indicates that the hidden restriction (C3) is not a nec-
essary condition for efficient liability rules.10
In conclusion, Jain and Singh’s main theorem that the condition of
negligence liability is a necessary and sufficient condition for efficient
10 This example can easily be generalized to the Jain and Singh frameworkwith variable C and D sets and multiple optima.
A Complete Characterization of Efficient Liability Rules: Comment 69
liability rules in a general framework does not hold when we drop their
hidden restriction on f and deal with all conceivable liability rules. Their
verbal description of the condition of negligence liability, which corre-
sponds to (C1) and (C2) combined, is a necessary, but not a sufficient
condition for efficient liability rules. Their mathematical description of
the condition of negligence liability, which corresponds to (C1), (C2), and
(C3) combined, is a sufficient, but not a necessary condition for efficient
liability rules. (See Fig. 1 in Sect. 4 for the graphical illustration of the
result.)
3 The Uniqueness of the Social Optimum
3.1 Multiple Social Optima with a Fixed Standard of Care
In contrast to the conventional literature that typically assumes the
uniqueness of the social optimum, Jain and Singh do not rule out
the possibility of multiple optima. They argue, ‘‘it is remarkable that the
standard assumptions on costs of care and expected loss functions turn
out to be completely irrelevant for the question of the efficiency of lia-
bility rules. In particular, the question whether or not there is a unique
configuration of care levels at which total social costs attain their mini-
mum turns out to be irrelevant. . .’’ (p. 108).As long as we deal with a unique social optimum, there is no
ambiguity in the principle that the court sets the legal standard of care at
the socially efficient level. However, with multiple optima, this principle
does not pinpoint the due care level; it only provides a group of can-
didates. Note that what Jain and Singh (2002) actually prove is that the
existence of multiple social optima does not affect the main result, if the
legal standard of care is set and enforced at any one predetermined
point belonging to the multiple optima. However, what is the criterion
for selecting one among a number of efficient candidates? Let’s suppose
that the court will pick one for whatever reason it may have. Is it
reasonable to assume that the injurer and the victim know in advance
which one, among many, will be enforced by the court, after an accident
occurs?
This implies that Jain and Singh’s model with multiple social optima
puts a greater information burden on the players of the game. Not only
must they believe that the standard of care is set at an efficient level, but
they must also know the court’s criterion for choosing one among
70 J. Kim
multiple optima, which are not distinguishable based on efficiency. In
short, allowing multiple social optima in the basic model requires a new,
strong assumption regarding the court behavior. The court should
always announce to the public, before accidents occur, which point
among many optima will be chosen to represent the standard of care,
and everyone must believe that the court will stick to this necessarily
arbitrary choice.
3.2 Multiple Optima with a Varying Standard of Care
The discussion above suggests that the court’s selection of a legal stan-
dard of care, among multiple candidates, would be difficult to predict
before an accident. But, under special circumstances, we may have a
reasonable way to fully characterize the court’s behavior in deciding one
party’s negligence/non-negligence, without the court’s prior announce-
ment of which one among many optima it will use. This sub-section
explores this possibility through an example from a binary choice model.
I will show that it appears unreasonable and arbitrary for the court to
adopt one of two optima as a fixed standard of care, and thus everyone
should expect the court to apply a varying standard of care, which is
contingent on the other party’s actual choice. Finally, the importance of
the uniqueness assumption for the social optimum will be established by
showing that a rule satisfying (C1) – (C3) may lead to an inefficient result
in this multiple optima case.
Suppose that the precaution variable is binary. In other words, there
are only two available strategies for the injurer and the victim: to take
precaution or not.11 If neither party takes precaution, accidents occur
with a given probability. Let L denote the expected accident loss to the
victim in that case. We assume that the precaution technology is
alternative (redundant) and the prevention effect is perfect; i.e., if either
party takes precaution, the probability of accidents falls to zero. The
cost of precautionary behavior to each party is assumed to be the same
and given by c. Assume c < L is satisfied; i.e., one party’s care-taking
11 Seemingly, it looks like a highly limited setup compared to the standardcontinuous variable model. But, as Grady (1989), and Feldman and Frost (1998)convincingly argue, the discrete dichotomous model can be a better description ofreality than the continuous model in many cases.
A Complete Characterization of Efficient Liability Rules: Comment 71
behavior is cost-justified, given that the other party does not take pre-
caution.
The alternative care technology implies that precaution is equally
effective whether provided by one party or by both parties simulta-
neously. Since the precaution cost for both parties is the same, it is clear
that efficiency requires either one party or the other, but not both, to take
precaution. So there exist two symmetric, efficient precaution pairs, ðc; 0Þand ð0; cÞ.
In this case, what would be a reasonable interpretation of the principle
that due care is set equal to the socially efficient level? If we follow Jain
and Singh’s method, the court must arbitrarily choose one pair, either
ðc; 0Þ or ð0; cÞ; as the legal standard of care. This implies that although
both parties have exactly the same cost structure and prevention tech-
nology, one arbitrarily selected party is required to take precaution so as
not to be found negligent, while the other party is immune from being
found negligent. This does not sound plausible.
I think a more plausible form of court behavior would be the following.
Rather than arbitrarily choosing between two optima as a fixed due care
standard, the court could in fact apply a varying standard of care to each
party, which is cost-justified given the other party’s actual behavior. That
is, the standard of care for each party could be set at ‘‘precaution’’ if and
only if the other party takes no precaution. If neither party takes pre-
caution, both parties will be deemed negligent.12
Since the parties could reasonably expect such court behavior, we can
now complete the game structure under a liability rule which uses the
legal notion of negligence.
Example 3: Consider either the pure comparative negligence rule or the
equal division rule in the binary and alternative care model we assumed
above. With varying standards of care, we can construct the game’s
payoff matrix as the following:
The first [second] entry in each cell represents the expected cost to the
victim [injurer] in each scenario. In particular, both parties will be found
INJURERPrecaution (P) No Precaution (NP)
VICTIMPrecaution (P) c , c c , 0
No Precaution (NP) 0 , c 12L , 1
2L
12 The same interpretation can be found in Chung (1993).
72 J. Kim
negligent in the (NP, NP) case, so the expected damage will be split
equally.13 It is obvious from the payoff structure that the pure compara-
tive negligence rule or the equal division rule does not necessarily pro-
duce an efficient result. For example, if c > 12L, ‘‘No Precaution’’
becomes a dominant strategy for both parties, irrespective of the other’s
choice. We then have a unique Nash equilibrium of the game at (NP, NP),
which is an inefficient outcome.
Note that both the pure comparative negligence rule and the equal
division rule satisfy conditions (C1) – (C3), which comprised a suffi-
cient condition for efficiency in the preceding section.14 So this
example illustrates the importance of assuming uniqueness for the
social optimum. Without uniqueness, it may be reasonable to adopt a
varying standard of care, and with such a standard, the equilibrium of
the game may be inefficient even though the usual efficiency condi-
tions hold.
4 Summary and Conclusion
Jain and Singh (2002) is a remarkable achievement in the tort literature,
completely characterizing efficient liability rules in a general framework.
However, I have shown in this note that if we drop the hidden assumption
they impose on the liability assignment rules, the equivalence between the
13 When both parties are at fault, the pure comparative negligence ruleapportions the accident cost in proportion to their relative degree of fault. In thepresent model, where both parties are identical in terms of the ability to preventthe accident, the only possible apportionment is the equal split. This makes purecomparative negligence the same as the equal division rule, which was thegoverning rule in early admiralty cases.14 This should not be understood as a counter-example to Jain and Singh’s
theorem, because their method requires the court to pick one efficient point andenforce it as a fixed due care. If, for example, the court sets the standard of carefor each party at (P, NP), the injurer is always exempted from being foundnegligent. Therefore, the injurer has no incentive to prevent the accident, andknowing this, the victim will take precaution. In other words, Jain and Singh’sapproach eliminates the possibility that both parties are found negligent. Thepayoff structure in (NP, NP) cell in Example 3 changes into (L; 0) or (0; L),making the game’s result always efficient. Of course, as indicated in the previoussub-section, this approach must assume first that the court explicitly announcesbefore the accident which pair, between two efficient pairs (P, NP) and (NP, P),will be adopted as the legal standard of care, and everybody believes thatannouncement.
A Complete Characterization of Efficient Liability Rules: Comment 73
condition they call negligence liability and the efficiency of liability rules
breaks down. Fig. 1 illustrates this point graphically, by comparing
each set of liability rules that satisfy various conditions introduced in this
note.
In Fig.1, the set of liability rules satisfying the Jain and Singh hidden
assumption (i.e., (A1), (A2), and ðA3Þð¼ðC3ÞÞ combined) is represented
by the area circumferenced by a thick dashed-line. As long as we restrict
our attention to this area only, the condition of negligence liability (i.e.,
ðP1Þð¼ðC1Þ&ðC2ÞÞÞ is necessary and sufficient for efficiency as Jain and
Singh’s main theorems prove. (See the shaded area in Fig. 1.) However,
when we deal with the set of all liability rules, the condition of negligence
liability is only a necessary condition for efficient liability rules, and the
condition of negligence liability plus the Jain and Singh hidden
assumption ð¼ðP1Þ þ ððA1Þ þ ðA2Þ þ ðA3ÞÞ ¼ ðP1Þ þ ðA3ÞÞ is only a
sufficient condition for efficient liability rules.
I have also criticized Jain and Singh’s attempt to allow for the
possibility of multiple social optima on two grounds. First, dropping
the usual uniqueness assumption requires the introduction of a new
and possibly less realistic assumption that everybody knows which one
among many optima has been adopted as the standard of care by the
court, and everybody believes that the court will stick to that choice.
Second, in a model without uniqueness, where the existence of mul-
tiple optima leads to the use of a varying standard of care, the equi-
librium may be inefficient even though conditions normally sufficient
for efficiency hold.
Fig. 1. Efficient liability rules and various conditions
74 J. Kim
Acknowledgements
I am deeply grateful to Prof. Allan Feldman for his valuable comments andguidance in preparing this note. I also thank two anonymous referees for theirhelpful comments.
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Address of author: – Jeonghyun Kim, Department of Economics, BrownUniversity, Providence, RI 02912, USA (Present affiliation: Fair CompetitionPolicy Division, Korea Information Strategy Development Institute, Kyunggi-Do, 427-710, Korea; e-mail: [email protected])
A Complete Characterization of Efficient Liability Rules: Comment 75