a complete characterization of efficient liability rules: comment

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.


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.


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.


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.


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.


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.

References

Assaf, G. B. (1984): ‘‘The Shape of Reaction Functions and the Efficiency ofLiability Rules: a Correction.’’Journal of Legal Studies 13: 101–111.

Brown, J. P. (1973): ‘‘Toward an Economic Theory of Liability.’’ Journal ofLegal Studies 2: 323–350.

Chung, T.-Y. (1993): ‘‘Efficiency of Comparative Negligence: a Game TheoreticAnalysis.’’ Journal of Legal Studies 22: 395–404.

Feldman, A. M., and Frost, J. M. (1998): ‘‘A Simple Model of Efficient TortLiability Rules.’’ International Review of Law and Economics 18: 201–215.

Grady, M. F. (1989): ‘‘Untaken Precautions.’’ Journal of Legal Studies 18: 139–156.

Haddock, D., and Curran, C. (1985): ‘‘An Economic Theory of ComparativeNegligence.’’Journal of Legal Studies 14: 49–72.

Jain, S., and Singh, R. (2002): ‘‘Efficient Liability Rules: Complete Character-ization.’’ Journal of Economics/Zeitschrift fur Nationalokonomie 75: 105–124.

Landes, W. M., and Posner, R. A. (1980): ‘‘Joint and Multiple Torts: an Eco-nomic Analysis.’’ Journal of Legal Studies 9: 517–556.

Rea, S. A., Jr. (1987): ‘‘The Economics of Comparative Negligence.’’ Interna-tional Review of Law and Economics 7: 149–162.

Shavell, S. (1987): Economic Analysis of Accident Law. Cambridge, Mass.:Harvard University Press.

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

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