The last few years have seen a small but increasing number of legal practices and corporations developing a combined decision and risk analysis approach to litigation decision-making for use in determining optimal settlement, arbitration, pre-trial, trial and appeal strategies.

For all businesses, litigation is a risk. Not only does it have significant upside as well as downside consequences, but it also involves complex rational and sometimes irrational behaviour. It is time consuming, stressful and expensive. It is to the advantage of both businesses and lawyers to develop a comprehensive approach to the “out-of-court” settlement strategies versus costly drawn-out trials or arbitration proceedings.

There is an implicit assumption that businesses are concerned with the bottom line and need a concise quantitative analysis that demonstrates that the legal strategy selected will yield the highest likelihood of a victory with the biggest expected value (EV). However, the best business decision is not based on quantitative analysis alone. Litigation may impact on creditors, lenders, customers, investors, stock market analysts and employees of both claimant and respondent. To bring together these diverse issues involves the use of Decision Theory-based analysis.

Decisions are made to achieve goals; they are based on beliefs about what actions will achieve these goals. Decisions become more complicated when they involve uncertain options, where each alternative has one of several possible consequences, the probability of occurrence of which is unknown. Each alternative is associated with a probability distribution, and moreover a choice among these probability distributions.

When the probability distributions are unknown, as in legal actions, a decision under uncertainty occurs. Decision making is difficult at every stage of litigation. Decision makers and lawyers have to answer such questions as:

The methodology that is used to help decision makers and lawyers answer such questions and, at the same time, increase their confidence is based on decision analysis.

Decision analysis has its roots in Decision Theory, which is a body of knowledge and related analytical techniques of different degrees of formality designed to help a decision maker choose among a set of alternatives in light of their possible consequences.

Careful application of decision analysis techniques can lead to better decisions, since it can help people understand more thoroughly the problems they face. Such an understanding includes the structure of the problem as well as the uncertainty and tradeoffs inherent in the alternatives and outcomes. As a result, the lawyers and the problem owners can:

In an effort to simplify many complex decision tasks, a natural strategy has been to try to “divide and conquer,” given that the decomposition will provide judgements that are simpler and easier than holistic or global judgements.

A good decision is one that is made on the basis of a thorough understanding of the problem and careful thought regarding important issues. The overall strategy is to decompose a complicated problem into smaller pieces that can be more easily analysed and understood. These smaller parts can then be brought together to create an overall representation of the decision situation, so that a course of action can be agreed.

The approach that is followed in decision analysis is depicted in Figure 1. The first step in any decision analysis is to identify the decision situation and to understand the decision maker’s objectives in that situation. When the objectives are identified, the next step is to explore the alternatives. Apart from finding the alternatives, knowledge of one’s objectives also indicates how the outcomes must be measured and what kind of uncertainties should be considered in the analysis.

The next two steps consist of decomposing the problem in order to understand its structure and measuring the uncertainties and the values associated with it. The decomposition is related to structuring the problem in smaller and more manageable pieces. Once the model has been built, sensitivity analysis is conducted. During this stage, the aim is to make changes in one or more aspects of the model and examine whether the optimal decision changes. In this interactive process, the decision maker’s perception of the problem changes, beliefs about the likelihood of various uncertain eventualities may develop and change, and preferences for outcomes not previously considered may mature as more time is spent on reflection.

The first step in solving a legal problem is to identify the individual elements, classified into values and objectives, decisions to make, uncertain events, and consequences.

Values and objectives: Generally, the term value is used to refer to things that matter to the decision maker. Similarly, an objective is a specific element that he/she wants to achieve. An individual’s objectives taken together make up his or her values. Litigation in business usually involves only one primary objective -- money -- but can involve others such as establishing a precedent or even revenge!

Decisions to make: With the decision context understood and the values acknowledged, the lawyer and the decision maker can begin to identify specific elements of the decision to be made. Clemen² argues that it is important to recognise that many situations have as a central issue a decision that must be made right away and that in many cases one decision leads eventually to another in a sequence. Identifying the immediate decision to make is a critical step in understanding a difficult decision situation. Moreover, it is impossible to build a model of the decision situation without knowing exactly what the problem at hand is. Finally, it is important to realise that future decisions may depend on exactly what has happened before.

Uncertain events: Many important decisions have to be made without knowing what will happen in the future or what precisely the ultimate outcome will be from a decision made at the present. Uncertain future events must be dovetailed with the sequence of decisions, showing exactly what is known before each decision is made and what uncertainties still remain.

Consequences: A consequence can be defined as what happens in respect of each of the objectives. The decision makers usually think about the consequences at the end of the time line after all the decisions have been made and all the uncertain events have been resolved. This is the point at which people consider whether they have made a profit or a loss. Since the primary objective in the court cases we are dealing with is usually money, all that is important at the end is profit, cost, or total wealth. Therefore, all the consequences of the problem may be measured in monetary terms.

After identifying the generic structure of a legal dispute process, a model of the formal legal process is developed. It is important to discover the probability of a specific award when a dispute is taken to court or arbitration. For this purpose, a generic model is used which is altered according to each case.

In this generic model, the judge may appoint an award to the claimant after hearing the evidence presented by both sides. In the model the claimant’s counsel presents each of his/her items of evidence, which the defendant’s barrister cross-examines each time for each item. Then the defendant’s barrister presents counter-evidence. The claimant’s barrister subsequently may cross-examine the counter-evidence.

The decision analysis approach to such a problem is to help the decision maker and the lawyer understand how the judge is going to make a decision by dividing the whole task into smaller parts (decomposition) and by asking them to estimate individual probability distributions for each part. The next step is to determine the combined effect of these individual distributions using Bayes’s theorem in order to obtain a probability distribution that will reflect the judge’s decision.

Bayes’s theorem is a mathematical formalisation of the process of learning from experience.⁶ It allows people to construct judgements of the probability of an hypothesis on the basis of judgements about the probability of observed data given the hypothesis and about the prior probability of the hypothesis. Its outputs are a set of revised opinions, modified to include the impact of the data as well as the prior information.

Since the parameters in many of the data in a court model are not known precisely, we express them using probability distributions. Subsequently, we use Monte Carlo analysis to find the probabilities connected to the awards made by the judge.

Monte Carlo simulation is an essential tool for developing a model of uncertainty. Winston⁷ argues that “Monte Carlo simulation is the simulation where the random numbers used for each trial are analogous to a spin of the roulette wheel at a casino. Like the spins of the roulette wheel, the random numbers used to generate demands for each trial are independent.” Monte Carlo simulation involves the use of a computer to generate a large number of possible combinations of circumstances that might occur if a particular course of action is chosen.

The output of a Monte Carlo simulation in the case depicted in Graph 1 shows the expected value (EV=average) of damages awarded to be 317,571. The range of awards in the simulation is between 0 and 1.2m with a 95% confidence limit of 1m.

After having calculated the probabilities of the awards appointed by the judge to the claimant for each specific case, the next step is to evaluate the strategies that resolve the dispute. In order to accomplish this, we build a decision tree.

Click here to see figure enlarged.

Decision trees can help decision makers develop a clear view of the structure of a problem⁴ and, as a result, make it easier to determine the possible scenarios which can result if a particular course of action is chosen. Usually, decision problems are multi-stage in character, since a choice of a given option may result in circumstances that require another decision to be made.

Decision trees show all possible decision options and chance events with a branching structure. Decision trees proceed chronologically, left to right, showing events and decisions as they occur in time. In a tree diagram, the number on each branch of the tree is the probability of following that branch, given that one has got as far as the root of the branch in question (the roots are on the left). To calculate a probability of getting to the end of a branch, on the right, all probabilities along the way must be multiplied. By working backwards from the final nodes, we assign an expected monetary value to each node and show at each choice node which decision is best. In this way the tree is solved. An example of a decision tree is shown in Figure 2.

This kind of diagram helps people think of all the possibilities.¹ It is especially useful when the probabilities of the various branches are influenced by different sorts of factors, so that some of these probabilities might be constant over a variety of circumstances that affect the others.

There are drawbacks to the use of decision trees in so far as the number of alternatives can grow almost exponentially, making them difficult to follow or to validate. Continuous pruning is required to keep them under control. An alternative approach is to use belief nets. Belief nets are isomorphic with decision trees but are easier to understand and communicate the relationship of all the elements of the problem, and they can cope with substantial sophistication and complexity. Figure 3 is an example of a litigation model.

Again Monte Carlo simulation of the negotiation process is used to determine the value of the outcome. This can be compared with the output of the trial simulation in order to decide at what point to end negotiations and push for trial.

The best decision is the one that most meets the needs of the decision maker in all possible ways; i.e., it is an optimal fit solution and not necessarily the optimised solution found in the quantified risk analysis (QRA). In order to determine the optimal fit solution, some further analysis has to be undertaken with the objective of maximising the decision maker’s utility or minimising his regret.

The concept of risk preference is widely appreciated in investment portfolio management. It is just as important to understand that the concept of the risk profile of the decision maker will also impact directly on the choices made. Graph 3 shows three generic profiles: the risk seeker, the risk avoider, and the risk neutral decision maker.

The risk profile determines the decision makers’ tolerance of uncertainty to achieve a desired objective.

The first approach is called Multi-attribute Utility Theory. In this technique all the attributes of the possible outcome are ranked and weighted in a cost-benefit analysis to determine the best fit decision. The process will usually involve a facilitated decision workshop for which a wide variety of software packages are available to aid the decision process.

For a person who is risk neutral, maximising expected monetary value (EMV) is the same as maximising utility. For large corporations that make decisions involving amounts which are small relative to their assets, it is reasonable to assume a risk neutral profile. The utility gained from winning or lost from not winning is a function of the litigants’ wealth; therefore, for a business, it is a complex function that includes the firm’s assets, profitability, future cash flows, time horizon, business context combined with the personal criteria of the decision maker, and any other non-monetary issues. When modelling this, the EMV is first determined and then its sensitivity to various risk profiles. It should be appreciated that the translation of EMV to utility can be a difficult task.

Utility theory remains almost unchanged from its original conception by von Neuman and Morganstern back in 1947, however, it is not without faults. There exists substantial empirical research showing that decision makers, under certain circumstances, make logically inconsistent choices. Other theories have been developed to a explain the illogical decisions e.g. prospect theory, but given the limits of utility theory it remains the most practical and useful tool for determining the “best” decision at present.

An alternative approach that has found favour with both decision analysts and behavioural economists is based on Regret Theory.⁵ Regret is defined as the psychological reaction to making the wrong decision where wrong is determined by actual outcomes rather than in relation to the information available at the time the decision was made.³ As with utility maximisation, this methodology incorporates the risk profile of the decision maker. To date practical applications of regret theory appear limited, although some success has been reported in the financial sector with portfolio selection; it should be expected that this will change in the near future as developments in regret modelling advance significantly.

The best decision, whether based on either the utility or regret theories will, in all likelihood, be significantly different from the decision based on EV alone, because with the use of risk and decision analysis it is possible to incorporate and evaluate far more issues than traditional quantitative risk management approaches permit.

Identifying and structuring the uncertainties of a decision situation that is related with a legal case according to the above analysis can provide lawyers and decision makers with a better understanding of the issues they face and show to them the best decision according to their objectives -- money or otherwise. The benefits of this approach can be summarised as:

The Benefits of Litigation Strategies & Risk Management

This analysis is neither intended to replace the decision maker’s or the lawyer’s intuition, nor to relieve them of the obligations in facing a litigation; or to be, worst of all, a competitor to their personal style of analysis, but to complement, augment and generally work alongside them in exemplifying the nature of the problem, providing a coherent structured process of analysis as a check and, most importantly, validating the justification for any decision.

1. Baron, J. (1994). Thinking and Deciding (2nd edition). Cambridge University Press.

2. Clemen, R. (1996). Making Hard Decisions: An Introduction to Decision Analysis (2nd edition). Duxbury Press.

3. Dembo, R. S. and Freeman, A. (1998) Seeing Tomorrow. John Wiley

4. Goodwin, P. and Wright, G. (1997). Decision Analysis for Management Judgment (2nd edition). John Wiley.

5. Loomes, G. and Sugden, R. (December 1982) Regret theory: an alternative theory of rational choice under uncertainty. The Economic Journal, 92 pp805-824.

6. von Winterfeldt, D. and Edwards, W., Decision Analysis and Behavioural Research, Cambridge University Press, 1986.

7. Winston, W. L. (1996). Simulation Modeling Using @Risk. Duxbury Press.

Posted March 11, 2002.