The common law efficiency hypothesis and the evolution of the common law
The preceding two sections have painted a somewhat pessimistic view of lawyers, legal rules and the legal system. There is an alternative approach, however, which lends itself to a more optimistic view. The efficiency of the common law hypothesis begins with the working hypothesis that legal rules that are inefficient tend to be litigated more often compared to rules that are efficient. It then follows that if inefficient legal rules are contested with greater frequency, there is a greater chance that those rules will be overturned. As a result, common law rules will tend to evolve in the direction of efficiency, and lawyers are a source of efficiency rather than inefficiency. This section investigates this hypothesis using some basic principles of evolutionary game theory.
Evolutionarily stable strategies
In an evolutionary game, each player's payoff is a measure of its 'fitness', rather than their subjective wellbeing. Each player is programmed to follow a certain model of behaviour, which is inherited from its parents or is assigned to the player as a result of 'mutation'. If members of a population follow a strategy s whose fitness exceeds that of an alternative strategy s', then those members who follow s reproduce faster than those who follow s'. A profile of strategies is stable if each member's strategy is a best response to its environment.
The literature on evolutionary game theory has typically focused on situations in which players come from a single population and have symmetric payoffs. Consider, a situation in which pairs of members of a population of organisms are randomly matched with each other. The interaction between the two organisms is modelled as a twoplayer symmetric game. If a player has a strategy s and his opponent plays s', then the fitness of strategy s is given by u(s, s').
Now consider the notion of evolutionary stability. Suppose that s* is a candidate for stability. Then this strategy must be able to drive mutations out of the population. So, suppose that a fraction ? of the population mutates and plays the strategy s' instead. The expected fitness to a mutant is:
And the expected fitness of a nonmutant is:
For the mutation to be driven out of the population, we require
A strategy is said to be evolutionarily stable if there exists a ? > 0 such that (11.33) holds for all ? An alternative but logically equivalent definition is that in a twoplayer symmetric game, a strategy s' is said to be evolutionarily stable if and only if:
 1. (s*, s*) is a Nash equilibrium and
 2. u(s*, s) > u(s, s) for every strategy s which is a best response to s*.
This definition has limited applicability in the context of the evolution of legal rules, however, because the players rarely come from the same population and their payoffs are rarely symmetric. Instead, players usually have different but welldefined roles (such as a plaintiff and a defendant), and each player's payoff bears no resemblance to the payoff of the other  which rules out the possibility of symmetry. In these situations, a different definition of evolutionary stability is required.
Suppose that there are n different populations, with members with each population all identical (for example, in the plaintiffdefendant case, n = 2). Let (s_{1},...,s_{n}) be a strategy profile, where sj is the strategy chosen by a member of population i. The fitness of strategy sj to a player from population i is щ(s_{1},..., s_{t},..., s_{n}). If there is a mutation in population i so that a small fraction of the population has the strategy s' Ф s_{i}, then for s_{i} to be evolutionarily stable, it must be the case that щ(s_{1},..., s_{{},..., s_{n}) > u_{i}(s_{1},..., s',..., s_{n}). In an evolutionarily stable situation, this must hold for all populations, so that for a profile (s*,..., s*) to be an evolutionarily stable equilibrium, we must have:
for all s' Ф s*, and for all populations i = 1,...,n. But notice that the condition in (11.34) is just the definition of a Nash equilibrium in the strict sense. Hence finding at evolutionarily stable equilibrium in this situation is straightforward: it is equivalent to finding a strict Nash equilibrium.
In a legal context, evolutionary stability has been studied by Terrebonne (1981). In Terrebonne's model, there are two separate populations: injurers (defendants) and victims (plaintiffs). Pairs of individuals from each population are matched randomly. Injurers have two possible strategies: either to take care (C) or not (N). Taking care has a cost of c > 0. If injurers take care, there is no accident. If they do not take care, then there is an accident which has a cost of H > 0.
To maintain the evolutionary spirit of the model, it is assumed that victims acquire their strategies before an accident occurs. Hence victims have four possible strategies: they can either always sue (SS); never sue (DD); sue only when there is an accident (DS), or sue only when there is no accident (SD). Note that if an accident occurs, victims do not get to decide whether they will sue or not  their behaviour is dictated by the strategy that they have inherited before they know whether an accident has occurred.
The cost to the victim of filing a lawsuit is L > 0. The legal rule is characterised by the probability that the victim will be compensated if an accident occurs. Let e_{2} be the probability that an injurer who has not taken care is not forced to compensate the victim. In other words, this is the probability of a Type II error. The expected payoffs or 'fitness' of each strategy are shown in Table 11.8.1. The first entry in each cell is the expected payoff of the victim, and the second entry is the expected payoff of the injurer.
Let us find the evolutionarily stable strategies of this game. First, note that strategies in which victims sue when an accident has not occurred (the first two rows) will never be evolutionarily stable, since the payoffs to the victim from following the alternative strategies of (DS) and (DD) are strictly better when the injurer takes care, and are the same when the injurer does not take care. Hence they can never form part of an evolutionarily stable strategy for victims, and we can focus on the last to rows of the game. The transformed game is shown in Table 11.8.2.
Table 11.8.1 Payoffs in the evolutionary litigation/care game
Injurer 

C 
N 

Victim 
SS 
L,  c 
 H + (1  e_{2})H  L,  (1  e_{2})H 
SD 
L,  c 
H, 0 

DS 
0,  c 
 H + (1  e_{2})H  L,(1  e_{2})H 

DD 
0,  c 
H, 0 
Table 11.8.2 The transformed evolutionary game
Injurer 

C 
N 

Victim 
DS 
0,c 
H  (1  e_{2})H  L,(1  e_{2})H 
DD 
0,c 
H, 0 
To investigate the common law efficiency hypothesis, we need to compare the evolutionary stable strategies when the common law is efficient, with the evolutionarily stable strategies when the common law is inefficient. If victims only tend to sue when the common law is inefficient, and do not tend to sue when the law is efficient, then this would constitute support for the common law efficiency hypothesis.
Let us consider two broad classes of situations:
• Case 1: c > H
First, suppose that it is inefficient for the injurer to take care. Then an efficient legal rule will not allow the victim to recover any damages, and so a high value of e_{2} is efficient. For any e_{2}, we also have c > (1  e_{2})H, and so the injurer has a dominant strategy of never taking care. On the other hand, if the injurer does not take care, the victim will sue when (1  e_{2})H > L, which is only true when e_{2} is sufficiently low. But when c > H, a low e_{2} is inefficient. Hence, victims only tend to sue when the legal rule is inefficient. Hence the efficiency of the common law hypothesis will tend to hold.
• Case 2: c < H
Now suppose it is efficient for the injurer to take care. In this case, a low value of e_{2} is desirable from an efficiency point of view.
If e_{2} is sufficiently low, then c < (1  e_{2})H, and the injurer's evolutionarily stable strategy is to take care. On the other hand, if the injurer takes care, the victim's evolutionarily stable strategy as shown in the left hand column of Table 11.8.2 is to not sue. Hence, legal rules which are efficient will not tend to be litigated.
The only remaining possibility is when e_{2} is sufficiently large, so that the legal rule is inefficient. Then c > (1  e_{2})H, and the injurer will have a dominant strategy of not taking care.
In this situation, the victim will sue only if (1  e_{2})H > L. In other words, if the legal rule is inefficient and legal costs for the plaintiff are not too large, the evolutionarily stable strategies will lead to an outcome in which plaintiffs litigate. Hence the efficiency of the common law hypothesis will again tend to hold.
On the other hand, if c > (1 e_{2})H but (1 e_{2})H < L, the evolutionarily stable strategies will lead to an outcome in which plaintiffs do not litigate. In this situation, the efficiency of the common law hypothesis will not tend to hold. That is, inefficient legal rules will not be litigated, contradicting the efficiency hypothesis.
To summarise, this simple evolutionary model of the common law yields two conclusions:
1. Efficient legal rules will not be contested or litigated.
2. Inefficient legal rules will tend to be contested as long legal costs are
not too high.
Taken together, the results support the conclusion that the efficiency hypothesis should hold in a world of sufficiently low legal costs.