Discussion Paper No. 765

ON THE COMPLEMENTARITY BETWEENLAW AND SOCIAL NORM:
A MODEL ANALYSIS WITH
SPECIAL REFERENCE
TO THE LIABILITY RULE FOR TORT
Atsushi Tsuneki
Yoshinobu Zasu

January 2010

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, JapanOn the Complementarity between Law and Social Norm: A Model Analysis with Special
Reference to the Liability Rule for Tort
Atsushi Tsuneki and Yoshinobu Zasu
1. Introduction
There have been extensive and complicated debates on how the state law and social
norm interact with each other. This argument dates back to Thomas Hobbes when heclaimed in his famous passage that “To this warre of every man against every
man…nothing can be unjust. The Notions of Right and Wrong, Justice and Injustice
have no place. Where there is no common power, there is no law; where no Law, noInjustice….”1 After the advent of Hobbes, John Locke made a counter-argument to theeffect that the state of nature has its own order that he calls the Natural Law. Then,David Hume went one step further and argued that the pre-legal rules of justice are
justifiable as establishing the common good among people.2 Contrary to the Hobbesianview, Locke and Hume found that the law does not establish a new legal rule fromscratch, but that it supersedes the pre-legal norm.3 In their view, the spontaneous ordertheory of the law that is prominent in the Chicago-school, which asserts that
decentralized social forces play a crucial role in shaping the social order, seems to havealready been set forth.4
Issues in the above theory that remain obscure are regarding how the law and thesocial norm interact with each other in the legalized modern society, whether the law
completely replaces the pre-existing social norm or they coexist, and whether theirinteraction achieves an efficient system of social rules or there is innate inefficiency.
A much more recent, yet no less important contribution by Ellickson (1991) has
revealed that in many critical aspects, law is irrelevant for the protection of social orderand is overridden by the social norm in the settlement of dispute over the protection oflegal right within a close-knit society. Another fundamental contribution by Macaulay
Hobbes (1651, part 1, chapter 13).
Locke (1690) asserted the existence of the Law of Nature and justified the property
right as its fundamental pillar. Hume (1740, book 3, part 2, section 6) emphasized thatthe system of the rules of justice is not intended by the persons who invented them toserve as means for public benefit, but is in its result very beneficial for people ingeneral.
3 As this article discusses, their arguments were succeeded by Hart (1994) in the area ofjurisprudence.
4 The spontaneous order theory of law was most eloquently extended by Hayek (1960,
1973). See also Demsetz (1967) and Posner (1981, ch.5-8) for the study of thedevelopment of law and justice in the pre-legal society.
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(1963) showed the same phenomenon particularly for the case of contract.
The purpose of this article is to provide an analytical model to clarify theinterrelationship between the law and the social norm to provide some suggestions forthe above problems. It aims to complement the research in Macaulay and Ellickson,
which adopted a more empirically oriented approach.
The next section presents an analysis of our basic model, and section 3 discusses its
legal and economic implications, where we show that in the basic model,
non-cooperative interaction between the law and social norm attains efficiency and thatthey are perfect substitutes to each other. Section 4 considers the cases where social
norm is determined on the basis of some misperceptions. In this model, we show thepossibility that an inefficient social system may persist. Furthermore, we illustrate thepossibility that law and social norm are complements to each other and that theexistence of the government could be second-best. Finally, section 5 briefly concludes thestudy.
2. Basic Model
Our model is based on the description of the society adopted by the classical article of
Coase (1960), where a nuisance dispute occurs and may be relieved by the court
adopting either the establishment of a legal right or the assignment of the liability. We
assume, for simplicity of the analysis, that the regulatory tool for recovering theefficient allocation of the activity is the strict liability rule to the injurers irrespective ofwhether it is a social norm or is promulgated as law.
This means that a substantive norm is assumed to be identical regardless of whether
it is a social norm or a law. The remedial norm is definitely different depending onwhether the rule is a law or a social norm.5 If the rule is legal, we assume, again forsimplicity, the public officer claims appropriate damages to injurers with the help ofstate force. When it is a social norm, this explicit exercise of state power is not allowed.
Therefore, the remedial norms should also be informal, for example, gossips for thedefective activities.6
Let us consider a society where the basic property right is established, and some
activity causes harm to the established property right, for example, noise, danger tohealth, and intrusion of land. We suppose that the society comprises two types ofvarious identical people: injurers and victims. Injurers engage in privately beneficial
For a relevant distinction between the substantive norm and the remedial norm (andother kind of norms), see Ellickson (1991, ch.11-14).
6 See Ellickson (1991, pp.211-221) for an informal enforcement of liability rule bynon-legal social relationship.
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2

activity, e.g., listening to music. We denote this activity as a, which provides benefitb(a) to the injurer who enjoyed. This activity simultaneously causes harm, e.g., noise,to the victim, which costs c(a). When engaging in their activity, the injurers are notconscious about this external cost, and they choose the level of activity neglecting thisexternal cost c(a). This means that the injurers choose an extremely high level ofactivity relative to the socially efficient level if there is no regulation either by law orsocial norm.
We conduct a standard partial-equilibrium analysis where the marginal utility ofmoney is constant and the aggregate social surplus (or“wealth”in Richard Posner’sterm) indicates the level of social welfare in monetary terms. All the people belonging to
the two parties are identical, and hence, the benefit of the representative injurer minus
the cost incurred by the representative victim, b a − c(a) shows social surplus.
We suppose that the enforcement of liability requires additional social cost, whether
it is implemented through the community or the government. When liability is levied by
the community or the government, we denote the level of liability damage per unit ofactivity as dc and dg respectively, and unit enforcement cost of levying damage as ec
and eg . Thus, the social surplus including the enforcement cost is b a − c a − ec dc a −eg dg a.7
We suppose that both the community and the government try to maximize thissurplus within the constraint they face with respect to the information available andthe incentive of the injurers in adopting their levels of activity. This assumption is basedon the wealth maximization hypothesis by Richard Posner.8 The welfare maximization
hypothesis for the working of social norm was presented by Ellickson (1991, ch.10), andits implications and limitations are extensively discussed. Some further implications
and the relevancy of this assumption will be discussed in the next section.
The basic incentive constraint they face as to the choice of activity is that the
injurers choose the level to equate the marginal benefit of the activity b′ a to themarginal damage cost dc + dg , i.e., b′ (a) = dc + dg .
3. Socially Optimal Interaction between the Law and Social Norm
3.1 Analysis
We assume that the damage levels levied by the community and the government arenonnegative, i.e., dc ≥ 0, dg ≥ 0. We also assume that −1 < ec − eg < 1, which meansthat the strategies of the community and the government, dc and dg are strategic
substitutes of each other.
8 See Posner (1981, ch.3) and Landes and Posner (1987, pp.1-24). As is well known, thishypothesis is criticized in many ways; however, we believe that it is useful as afirst-order approximation to government behavior, at least in the case of tort law.
7

3

Let us proceed to analyze the basic model presented in the last section and deduce its
consequences. In our model, two principals, namely, the community and the government,
maximize social surplus with respect to their own policy tools dc and dg , with the
incentive constraint of the injurers and the strategy of the other party as given.
Therefore, the government chooses dg to maximize(1)b a∗ − c a∗ − ec dc a∗ − eg dg a∗

for a given dc with the constraint(2)b′ (a∗) = dc + dg ,and the community chooses dc for a given dg to maximize (1) subject to (2).
For the following analysis, we parameterize the model to derive explicit solutions. We
suppose that b a = α𝑙𝑛a and c a = βa. From this parameterization, the constraint inα(2) boils down to the explicit solution of a∗ as a∗ = d c +d g . Substituting it into (1) andchoosing dg to maximize (1) given dc , we can find the optimal strategy dg∗ of thegovernment. The first-order condition with respect to dg can be solved as
(3)

dg∗ =

β + dc (ec − eg − 1)ifdg∗ > 0,0

ifdg∗ > 𝛽 + dc (ec − eg − 1).

This first-order condition can be illustrated as a Nash response function in Fig 1a.
[Figure 1a about here]
Similarly, we can solve the maximization problem of the community and derive thefirst-order condition with respect to dc given dg as
(4)

dc∗ =

β + dg (eg − ec − 1)0ifdc∗ > 0,ifdc∗ > 𝛽 + dg (eg − ec − 1).

This condition is illustrated as a Nash response function in Fig. 1b.
[Figure 1b about here]
Now, let us superimpose the two Nash response functions and find the Nashequilibrium strategies (dg∗ , dc∗) as an intersection of the two response functions. As
Figure 2 shows, the equilibrium depends on the level of eg and ec .
[Figure 2a, 2b about here]
When eg > ec , dg∗ = 0 and dc∗ = β is the Nash equilibrium, which means that theliability for the nuisance dispute is exclusively levied by the community, and thegovernment refrains from the resolution of the disputes, as shown in Figure 2a. In
contrast, when eg < ec is satisfied, dg∗ = β and dc∗ = 0, which means that liability to
the nuisance is levied exclusively through the law, and social norm does not deter thenuisance at all. In the middle case where eg = ec , any combination of the liability
4damages (dg∗ , dc∗) that satisfies dg + dc = β can be an equilibrium. Finally, it is obviousthat all of these equilibria are Pareto efficient. Therefore, the interaction of the law andsocial norm in this basic model is socially optimal.
3.2 Interpretation
The implications of the analysis in the previous subsection are evident. When there is adifference in the enforcement cost for the two branches of the society, the community
and the government, it is more efficient to use only one branch that can enforce thenorm with cheaper cost, for controlling the order of the society.9
However, in the Nash equilibrium we analyzed, we assumed that both branches
pursue independently to maximize social efficiency. With this assumption, the more
efficient branch of the society provides more liability for the deterrence of harm given
the strategy of the less efficient branch. Once the more efficient branch extends thelevel of liability, the less efficient branch decreases the level of liability to save its
enforcement cost. This process continues until only the more efficient branch
exclusively provides liability system. Therefore, social wealth maximization is attainedin the Nash equilibrium.
Which equilibrium is more relevant for our society? This surely depends on therelative amount of the enforcement costs eg and ec . One natural interpretation is that
ec is cheaper than eg , since the enforcement by the community does not require aformal legal system, including, a judge and police. In this case, the community plays therole of controlling the order and the government refrains from the enforcement of formal
law. It is this observation that Ellickson (1991) has found out within the close-knit
society. According to him, many disputes within such a small community are resolved
through the internal norm of the community itself without reference to the formal law
or the help of the judiciary of the government.
For the classical thinkers of the government, such as Locke and Hume, the argument
was the opposite. For them, it is the inefficiency and inadequacy of the informal social
norm and its enforcement power for protecting the social order that called for the
existence of the government and the law. Their argument was succeeded in the area oflegal theory by the classical contribution by Hart (1994).
According to Hart, the law is defined as the union of primary and secondary rules (seeHart (1994, pp.79-99)). Here, the primary rules of obligation are those rules that are

If there is no difference, any combination of the enforcement by the two branches canbe optimal. It is also obvious from the discussion below that social efficiency is attainedat the Nash equilibrium in this case.
95directly imposed on the citizens. A system of primary rules exists even in the pre-legal
society and it could form a meaningful social order, but there are several inconveniences
for the society that only adheres to primary rules. This is summarized by Hart in threepoints. The first aspect is uncertainty, which means that there is no procedure to resolve
disputes when there arises a question as to what the rules are or the precise scope ofsome given rule. The second aspect is the static character, which means the lack ofdeliberately adapting to the rules according to changing circumstances. The third
aspect is inefficiency, which means that there are no official agencies to enforce rules
authoritatively and that the enforcements are left to the individuals affected or to thegroup at large (op. cit. pp.91-94). He argues that such problems of the pre-legal society
are overcome by introducing three types of secondary rules that confer on individuals to
make authoritative decisions (op. cit., pp.94-98)).
In our present context, the most relevant issue is the inefficiency of the society
governed only by primary rules. In contrast to the previous argument, Hart argues thatthe world without any public organization for the enforcement of law is inefficientbecause in this world, many harmful activities are not deterred and disputes are left
unresolved; this leads to substantial social cost that can be avoided by introducing thesecondary rules of adjudication and establishing a public system of judiciary.10 A simple
way to reflect Hart’s observation in our analysis is to assume that enforcement cost of
the community is larger than that of the government, i.e., eg < ec . In this case, as ouranalysis shows, the pre-legal society is totally replaced with the legal world thatincorporates the rule of adjudication by the state.
Summarizing the argument in this section, in our model where both the community
and the government pursue efficient order independently, the resulting Nashequilibrium attains efficiency. In the equilibrium, either the government refrains fromany legal regulations and the social order is totally controlled by community
enforcement, or the informal regulations by the community is completely replaced withthe legal regulation by the government depending on which system has a lower
enforcement cost for adjudication. This means that there is no complementarity
between the law and social norm, and they are perfect substitutes to each other.
4. The Sources of Inefficiency and Complementarity
The arguments in the previous section show that the optimal system of social regulation

See Hart (1994, pp.93-94, 96-97). Locke (1690, chapter 9, paragraph 125) has alreadystated the following: “In the state of nature there wants a known and indifferent judge,
with authority to determine all differences according to the established law.”
106

uses only one mode of governance, depending on the relative cost-effectiveness of its
enforcement. Once it is assumed that both community and the government try to
maximize social wealth, the resulting non-cooperative Nash equilibrium is also optimal.
By relaxing the assumption of the rational wealth maximization by the community
in this section, we illustrate the possibility of the existence of Nash equilibria that are
not socially optimal when enforcement by the community is more cost-effective thanthat by the government. In this case, two interesting phenomena will occur. First, theintroduction of the law by the state could improve or worsen social welfare. Second,
there is a possibility of coexistence of both community norm and the law.
4.1 The Case where the Community Determines Social Norm without Considering its
Effect on the Enforcement Cost of Law
In the model we analyzed in the last section, it was assumed that social norm is chosen
to maximize social wealth. In particular, it was assumed that this optimization takes
into account the effect of social norm on the enforcement cost of the law. Given thatsocial norm is spontaneous and it is determined in a decentralized manner, thisassumption may not be quite relevant in some situations. We assume in this subsection
instead that social norm neglects its effect on the enforcement cost of the law. Therefore,social norm is now determined by the maximization of b a∗ − c a∗ − ec dc a∗ withrespect to dc , with the constraint in (2).
Adopting the same parametrization of the model in the previous section, thefirst-order condition is as follows:(5) dc∗ =β − dg ( ec + 1)
0

ifdc∗ > 0,ifdc∗ > 𝛽 − dg ( ec + 1).

Now superimposing the new Nash response function in (5) over the response function of
the government in (3), we find a situation depicted in Figure 3 for the case ec < eg , i.e.,
enforcement by the community is more cost-effective than that by the government.
[Figure 3 about here]
As this figure shows, there are three Nash equilibria of the non-cooperative game.
However, the equilibrium that uses both modes of governance dc and dg can be easily
checked as being unstable. Therefore, the two equilibria that use one mode ofgovernance to the level β are stable. It is obvious that the equilibrium that uses only
dc to that level is efficient, and therefore there is now a possibility that inefficient7equilibrium, which uses the law as the method of governance, survives.
The intuition is as follows. When the community chooses social norm without
considering its effect on the law enforcement cost, its deterrence level decreases because
the positive effect of the social norm to the law enforcement cost reduction owing to thedecrease in activity is neglected. The decrease in the level of social norm is stronger
when the level of dg is high because the neglected effect of social norm on the reductionof law enforcement cost is larger when the deterrence level of the law is high.
It cannot be precisely determined as to which of the two equilibria is likely to realize.
However, this result indicates that once the society is already legalized, it is unlikelythat the social norm prevails and replaces the law in a decentralized manner even if it isa more efficient method of regulation.
4.2 The Case where the Community Underevaluates the Cost of Activity
It is likely that the community determines the level of social norm with somemisperceptions of social parameters. Hart (1994, pp.92-93) defined this shortcoming of
the social norm as the static character, which means the lack of deliberately adapting to
the rules according to changing circumstances. For example, the parameter of themarginal social cost of activity β can change depending on the changing social
situations. When β means the marginal social cost of the noisy activity, this β canquickly increase as the society becomes larger and more densely populated. However, it
is quite reasonable to assume that the traditional social norm is determined on thebasis of older information on the damage occurred by the noise, or it is resistant to theadjustment owing to its character as a traditional convention.
We now capture this misperception effect of the community by evaluating the level oftrue β as θβ, 0 < 𝜃 < 1, where θ shows the parameter of the level on misperception by
the community. With this change, the new maximization problem that the community
faces is to choose dc to maximizeb a∗ − θc a∗ − ec dc a∗ − eg dg a∗(6)

for a given dg with the constraint in (2). Again, adopting the same parameterization
with the previous cases, the first-order condition for the community is now summarized
as
∗

dc =

θβ + dg (eg − ec − 1)ifdc∗ > 0,0

ifdc∗ > 𝜃𝛽 + dg (eg − ec − 1).

(7)
Superimposing the two Nash response functions (3) and (7) for the case ec < eg , we8see several possibilities for the Nash equilibrium. When θ is close to one, only thecommunity norm is adopted for the social regulation and the efficiency of theequilibrium is preserved. When θ is close to zero so that the misperception of thecommunity is very serious, dg∗ = β is chosen and only the legal regulation prevails. Fora medium level of β, the equilibrium depicted in Figure 4 arises, i.e., two modes of social
regulation, the law and social norm coexist.11[Figure 4 about here]
The intuition behind the result is evident. When the community considerably
under-evaluates the level of social cost of the nuisance, the level of liability imposed by
the community is less than sufficient, and it is not optimal to depend on the community
enforcement for controlling the activity, even if the enforcement cost by social norm ischeaper than the law. If the under-provision of the social norm is very conspicuous, thegovernment chooses high liability for the harm and replaces the enforcement by thesocial norm completely. However, if this under-provision of informal liability is not
sufficiently strong, the government chooses a mild level of legal liability, and uses boththe law and the social norm in a complementary manner for the control of social order.
Ellickson (1991, p.249) hypothesized that members of close-knit groups employ andmix informal and legal systems of social control in a manner that minimizes members’
total costs. This is what has happened in the present case. With regard to theadministrative cost, it is socially best to use only the social norm for the control of thesociety. However, when there is a misperception within the provision of social norm,
additional deadweight loss arises owing to the under-provision of liability damage fortort. If this under-provision is serious enough, the community adopts both the social
norm and the law complementarily to minimize the total costs for the members, whichin our case is the sum of the administrative cost and the deadweight loss owing to theincompleteness of the spontaneous liability system. Furthermore, it is even possiblethat only the legal liability system controls disexternalities without any inputs fromsocial norm if the misperception for the provision of social norm is extremely serious.
5. Conclusion
This article presented a model analysis of the interaction between the law and social

111

Formally three cases can occur. First, when θ ≥ 1+e g −e c , dc =θβ and dg =0, i.e., only1social norm is used. Second, when 1 + ec − eg < 𝜃 < 1+e g −e c , dc > 0 and dg >0, i.e.,
both the law and social norm are complementarily used for controlling the social order.
Third, when θ ≤ 1 + ec − eg , dc =0 and dg =β, i.e., only the law is used for the social
control.
9norm where the strict liability rule for tort can be levied either by the government or acommunity with different enforcement cost. When these two branches both act asrational welfare maximizers, the resulting non-cooperative Nash equilibrium is Pareto
efficient. In contrast, if the community chooses social norm with misperceptions,inefficient Nash equilibrium might arise by the legal intervention of the government. In
some other cases, there is a possibility that the introduction of the law could besecond-best even if the enforcement cost using social norm is cheaper than that of thelaw.
While our model builds on several simplifications, the real interaction between thelaw and social norm is far more complex. This means that it should be a very proliferatearea for future research in law and economics.12 However, it appears that most studies
in this area hitherto are chiefly either descriptive or empirical, and explicit model
analyses are rather limited. We hope that our analytical research will provide someinsight for encouraging further study in this area.

See McAdams and Rasmusen (2007) for the most recent extensive survey of thedevelopment of research in this area.
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REFRENCES
Coase, R.H. (1960), “The Problem of Social Cost,” Journal of Law and Economics 3, 1-44.
Demsetz, H. (1967), “Toward a Theory of Property Rights,” American Economic Review
57, 347-359.
Ellickson, R.C. (1991), Order without Law: How Neighbors Settle Disputes, Harvard
University Press.
Hart, H.L.A. (1994), The Concept of Law, Oxford University Press (1st ed. Published in1961).
Hayek, F.A. von (1960), The Constitution of Liberty, The University of Chicago Press.
Hayek, F.A. von (1973), Law, Legislation and Liberty, vol.1: Rules and Order, The
University of Chicago Press.
Hobbes, T. (1651), Leviathan.
Hume, D. (1740), A Treatise of Human Nature.
Kaplow, L. and S. Shavell (2002), Fairness versus Welfare, Harvard University Press.
Landes, W.M. and R.A. Posner(1987), The Economic Structure of Tort Law, Harvard
University Press.
Locke, J. (1690), Of Civil Government.
Macaulay, S. (1963), “Non-contractual Relations in Business: A Preliminary Study,”

American Sociological Review 27, 55-70.
McAdams, R.H. and E.B. Rasmusen (2007), “Norms and the Law,” 1573-1618 in A.M.
Polinsky and S. Shavell eds, Handbook of Law and Economics vol. 2, North-Holland.
Posner, E.A. (2000), Law and Social Norm, Harvard University Press.
Posner, R.A. (1981), The Economics of Justice, Harvard University Press.
Posner, R.A. (1999), “Social Norm and the Law: An Economic Approach,” American

Economic Review 87, 365-369.
Posner, R.A. and E.B. Rasmussen (1999), “Creating and Enforcing Norms, with Special
Reference to Sanctions,” International Review of Law and Economics 19, 369-382.
Shavell, S. (2002), “Law versus Morality as Regulators of Conduct,” American Law andEconomics Review 4, 227-257.
Zasu, Y. (2007), “Sanctions by Social Norm and the Law: Substitutes or Complements?,”

Journal of Legal Studies 36, 379-396.

11

dg

β

1 + 𝑒𝑔 − 𝑒𝑐dc0

Figure 1a

12

dg

1
1 + ec − eg

0

β

dc

Figure 1b

13

dg

0

β

dc

Figure 2a: 𝐞𝐠 > 𝐞𝐜

14

dg

β

dc

0

Figure 2b: 𝐞𝐠 < 𝐞𝐜

15

dg

β

β
1 + ec○0β
1 + eg − ecβdcFigure 3

16

dg

θβ
1 + ec − eg

β

●

0

θβ

β
1 + eg − ecdc

Figure 417