ALTERNATIVE DISPUTE RESOLUTION
COMING TO AN AGREEMENT: A MATHEMATICAL APPROACH TO SETTLING DISPUTES BERNARD O‘BRIEN
INTRODUCTION
S
ince the early 1960s there has emerged amongst both academic lawyers and economists an ever-growing interest in the study of law and economics. This has now become such an amorphous and diverse field of academic interest that there are encyclopedias on law and economics. It has also become an intellectual discipline in its own right. So much so that it has readily spread across that great divide between the common law and the civil law traditions. Whilst much of the scholarship in this area is essentially of theoretical interest only with no immediately foreseeable practical applications there are some areas where that is not quite true. One of those areas is what I would call “Settlement Theory”. This is a formal theory about the way litigants and their legal advisers settle disputes. What is sought to be developed in this endeavour is what is called a formal system. A formal system is a system of logic built on axioms or assumptions from which theorems or conclusions are derived by the application of a rigorous process of reasoning. Whilst this can be very mathematical, it doesn’t always need to be and in fact there are some outstanding examples which are devoid altogether of both numbers and mathematical symbols. A famous example of which is Ronald Coase’s article on “The Problem of Social Cost”. For this work and others he was awarded the Nobel Prize in 1991. That article contains no equations at all but makes copious reference to some 19th century English cases in actions in nuisance. From that article is derived the now famous Coase Theorem, one formulation of which states: “…that if trade in an externality is possible
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and there are sufficiently low transaction costs, bargaining will lead to a Pareto efficient outcome regardless of the initial allocation of property” Essentially the same methodology is adopted when analysing how the parties to a dispute would arrive at a settlement. In the first instance the analysis shows that there is what is called the basic model. Whilst this model represents a very good place to start, however, its effectiveness in terms of modelling the real world is limited by the assumptions upon which it relies. Initially the model proceeds as an application of Decision Theory but it quickly becomes an analysis in Games Theory. Settlements in both criminal and civil matters are so pervasive that if a matter goes to trial that is seen as a failure. Why did the settlement process fail to resolve the dispute? That is a question which would be posed by those responsible for the administration of the court caseload, it is not the first question a practitioner would ask. A practitioner would ask what can this analysis tell me about how I can get the best result for my client? This paper will look at this area of study principally from that point of view. In doing so I will put to one side settlements in crime and personal injuries and focus exclusively on commercial litigation.
THE BASIC MODEL As we all know the overwhelming majority of cases settle before a trial is concluded. The question is how is the decision to settle arrived at? There is a branch of mathematics which is formally known as decision theory which analyses decisions which involve risk. The mathematics involved in decision theory
is quite simple and straight-forward. It can best be explained by taking, as an example, a simple piece of litigation. P sues D for breach of contract and is seeking $100,000 in damages. We will assume that from the commencement of the action to judgment solicitor/client costs will be $40,000 and taxed costs will be $30,000. We will also assume, again for the sake of simplicity, that solicitor/client costs and taxed costs will be the same for both P and D. It is far from certain that P will win, however we can derive an estimate of P’s chances of success. Let us assume that P’s chances of success are 60%, we can now analyse the nature of the decision which P faces by the use of the following diagram.
FIGURE 1:
If P wins, he will get $100,000 in damages, he will have paid $40,000 in solicitor/client costs and will be paid in taxed costs $30,000. That information is set out at the top diagram. Therefore, if he wins, he will be paid a total of $90,000 and he has a 60% chance of that happening which is therefore 0.6 x 90,000 = 54,000. If he loses, he will have paid $40,000 and will have to pay a further $30,000 in taxed costs, which gives a total of $70,000, which has a 40% probability of occurring, thus 0.4 x -70,000 = -28,000.
