United Kingdom Journals

Computer Simulation of Judicial Behaviour

Tom Allen

<Tom.Allen@durham.ac.uk>

Michael Aikenhead

<Michael.Aikenhead@durham.ac.uk>

Robin Widdison

<Robin.Widdison@durham.ac.uk>

All of the Centre for Law and Computing,
University of Durham.

Copyright © 1998 Tom Allen, Michael Aikenhead and Robin Widdison.
First Published in Web Journal of Current Legal Issues in association with Blackstone Press Ltd.

* We would like to acknowledge the support of the Nuffield Foundation who funded this research and the advice of Professor Nigel Gilbert of the University of Surrey who acted as project consultant.

Summary

This article reports on a preliminary investigation we have undertaken to find out whether computer-based simulation would be a suitable method for studying consistency in judicial decision-making.

Contents

Introduction
Existing work on modelling judicial systems

1. Economic Theory
2. Game Theory

Existing models of similar social phenomena

1. Influence Models
2. Cultural Inheritance Models

Criticisms of modelling the judicial system
Conclusion

Bibliography

Introduction

This article reports on a preliminary investigation we have undertaken into the possibility of using computer-based models to study consistency in judicial decision-making. Plainly, it is desirable that the set of statements on a single point of law should be consistent. Within the judicial system, there are many factors that make it difficult to achieve consistency, as statements of law on a legal issue are often made by more than one judge and a single judge may make several statements of law on an issue. Virtually all legal system have formal hierarchies of decision-making, where superior courts have the power to resolve inconsistent statements of lower court judges. In practice, however, only a very small number of disputes reach the superior court. At any given time there is therefore likely to be a degree of inconsistency in the decisions rendered by different judges on certain points of law. In any case, the rules of precedent do not explain why judges obey the rules of precedent. Neither do they indicate the degree of consistency that is likely to be present at any given time. Plainly, this is an area that is worthy of legal study. However, empirical study is not possible; one cannot devise an experiment to vary the rules of precedent or the structure of the courts in order to find the rules or structure that are most likely to achieve a high degree of consistency. This article therefore investigates whether computer-based simulations would be a suitable means of investigating the area.

One example may illustrate the practical value of this investigation. In 1992, the Audit Commission published a report on the proportion of pupils who were given statements of special educational needs by their local education authorities. The report revealed that the proportion of pupils statemented by some local authorities was about 100 times that of other authorities. (see Audit Commission 1992, pp 14-15) The Audit Commission concluded that the variation could not be explained as the result of differences such as the relative wealth of districts. Rather, the differences could only be explained by vagueness of the statutory definition of 'special educational needs'. Authorities applied different definitions simply because the statutory definition was ambiguous. Plainly, inconsistency amongst the local authorities' 'judges' on the legal meaning of 'special educational needs' was very high. At the time, there were very few means for resolving this inconsistency. Parents could appeal to the Secretary of State, but his or her decisions were not normally published. In effect, there was a decision-making system without a clear appellate structure. There would have been different means of raising the consistency of the authorities' decisions, such as publishing decisions of the Secretary of State, or centralising the decisions in a single body, or penalising authorities that exceeded a certain level of statementing. Modelling might have been helpful in selecting the most effective means of achieving consistency.

We begin by examining the existing work on modelling judicial systems before considering related work in other social sciences. Influence and cultural inheritance models provide interesting ideas for the modelling of judicial behaviour. Nevertheless, there are fundamental differences between judicial hierarchies and other social hierarchies. We examine how these differences would affect the approach to modelling judicial systems. We then discuss the weaknesses that any model is likely to have. The utility of a model depends upon how accurately it describes the system's social agents, their attributes, their relationships with other social agents and the events to which they react. In legal theory, the reduction of any one of these aspects of the legal system to an essentially economic model is highly controversial. The article examines one aspect of the controversy. In particular, a programmable model must use a relatively small set of social actors who operate a decision function that is the product of a relatively small set of variables, but it is debatable whether this is an accurate reflection of any modern legal system. Arguably, any model that is reasonably accurate is likely to be trivial. The article closes by sketching the outline of the possible responses to this point.

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Existing work on modelling judicial systems

1. Economic Theory

Economic models have been widely used in all aspects of legal analysis. Most economic models examine the effect of legal rules on the decisions made by non-legal actors. For example, the effects of different rules of liability on safety has been the subject of extensive economic analysis. In a sense, these economic models do not apply directly to the rules of precedent, since they presuppose a sharp difference between legal actors and non-legal actors. This is not a significant matter, however. The economic studies differentiate between legal and non-legal actors only to emphasise that the legal rules are fixed, insofar as the non-legal actors are concerned. In other words, they are encoded explicitly as externally-derived criteria in the decision-making process. In the legal context, the rules of binding precedent are often described by lawyers as though they are external to the process of judicial decision making. In this sense, the judges are themselves non-legal actors in that they act in response to rules. Hence, for the limited purpose of analysing the effect of rules of precedent on curial systems, we could treat it as a further example of the effect of legal rules on non-legal actors.

The first extensive economic analysis of curial systems was made by Landes and Posner (see Landes and Posner 1975). They focus on the creation and 'depreciation' of precedent. They treat precedent as a type of capital stock yielding a flow of valuable information and they study the creation and depreciation of the capital stock of precedent. Precedent depreciates over time as it is consulted with decreasing frequency and its influence on the decision-making declines. Like other types of capital stock, precedent requires an initial investment. In the case of precedent, the initial investment is shared by a large number of participants, including the litigants, the state, the judges and the case reporters.

Although Posner and Landes do not discuss the point at length, it is clear that the question of investment raises the general problem of 'public goods'. One example of a public good is a lighthouse. The construction of a lighthouse is clearly valuable to all ship-owners but it is often not economically worthwhile for a single ship-owner. Not only is the benefit often less than the cost, but it is impossible to recoup the cost by charging others for the information provided by the lighthouse. In some respects, this is the case with precedent. Those who invest in the creation of precedent are generally not in a position to recoup the cost from subsequent users.⁽¹⁾ Consequently, there is a real risk that those who bear the cost of creating the capital stock of precedent will decide not to make the investment. To some extent, this already occurs. For example, parties sometimes decide that it would be too costly to take a matter to court because it raises a disputed point of law and is therefore likely to necessitate a longer trial. If the cost of producing the precedent is less than the subsequent saving to other potential litigants, the economically valuable act of producing precedent will not occur. From the economic perspective, the incentives must be present for the continued production of precedent.

What makes the legal system so interesting is the apparent absence of any such incentives for litigants and judges. Posner and Landes studied the motivations of litigants, whereas our immediate interest is with judges. Judges are bound by rules of precedent, but these rules do not specify the reward or penalty for obedience and disobedience to these rules. That is, a judgment that violates the rules of precedent can be overturned by a higher court but there is no immediate penalty for the judge that wrote the decision. Moreover, there is no apparent incentive for creating precedent. A precedent cannot be created unless it is reported in some detail, but in general a judge need not offer extensive reasons for a decision. The rules of precedent do not seem to offer an explanation of why judges follow them. They exist as meta-rules on judicial decision-making, but there seem to be meta-meta-rules that explain why the meta-rules are followed.

This is the level of activity that Posner and Landes investigate, although they study the behaviour of litigants rather than judges. That is, they assume that judges produce precedent and conform to the rules regarding precedent, but do not attempt to explain why judges do so. From our perspective, they have demonstrated that a model can be constructed that can explain some aspects of consistency, although it is not directly applicable to our area of interest.

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2. Game Theory

An alternative approach to that of Posner and Landes is that of game theory. So, for example, Rasmusen looks at how a judge's desire to influence other judges can contribute to judicial restraint (see Rasmusen 1994). His work is interesting because he uses a model to demonstrate how the selfish decisions of individual judges produces consistency in the system as a whole. His model involves a series of judges, each of whom decides a series of cases. Any given judge decides one case as a matter of first impression. In the remaining cases, the judge decides to either follow or overrule an earlier precedent. Since Rasmusen intends to examine how the desire for influence affects the tendency to follow precedent, he begins with two basic assumptions regarding influence. First, judges lose influence by following the precedents set by predecessor judges; second, judges gain influence when their precedents are followed by their successor judges. He also takes an economic view of decision-making, in that each judge decides whether to follow precedent by seeking to maximise their 'profits', in terms of the influence they receive. A judges therefore gets a 'positive payoff' whenever his precedent is followed, and a 'negative payoff' whenever he succumbs to the influence of earlier judges by following precedent. The judge then determines his total payoff for each possible number of precedents that he follows and selects that number that gives maximum payoff.

Clearly, the judge cannot calculate the positive payoff, and hence his total payoff, unless he knows how subsequent judges will treat his precedent. If he can predict the actions of subsequent judges, he can formulate his own strategy. Strategies may have several alternatives. For example, if a judge knows that subsequent judges will follow his precedent, irrespective of his own actions, the best course of action would be to refuse to follow any existing precedents. This minimises his negative payoff from following precedent, without affecting his positive payoff from being followed. Suppose, however, that the judge knows that subsequent judges follow a strategy whereby they follow his precedent only if he has followed every existing precedent. If he gets more payoff from being followed, then he should follow all precedent. If, however, the negative payoff of following exceeds the positive payoff of being followed, he should not follow any precedents.

Rasmusen uses this model to study different equilibria in the model. The model is in equilibrium if no judge has any incentive to depart from the strategy, given that other judges will not depart from it. The identification of equilibria is important, because Rasmusen seeks to identify when the desire to follow influence can form a stable, lasting constraint on judicial action. Rasmusen argues that there are many possible equilibria, but not all of them are desirable. Some of them are systems where precedent is uniformly ignored; others are systems where precedent is followed uniformly by all judges, but if one judge changes strategy and refuses to follow precedent, the entire system of precedent breaks down. Clearly, neither system is desirable in the practical world. The most desirable would be a system where judges are encouraged to follow a strategy whereby he/she follows the precedents of judges who follow the precedents of other judges, but do not follow the precedents of judges who do not follow other judges. This should result in a stable equilibrium where precedent is followed without external penalty or reward.

As a general comment, Rasmusen's sought to use the model to derive some practical ideas for making the desire to influence work effectively as a constraint. His method was acceptable, in the sense that he examined how changing the variables in the mathematical model resulted in different equilibria. The interpretation of changing these variables also seemed fair. However, from our point of view, the interpretations did not seem especially useful. For example, he observed that the mathematical model shows that the likelihood that a given judge will follow precedent is increased if the value of the negative payoff is as low as possible. The practical interpretation of this is simply that the actual adherence to precedent in the real world would be increased if only judges with a strong preference for following precedent were appointed.

Put this way, the mathematical model does not seem to tell us anything we do not already know. However, with greater knowledge of the preferences of decision-makers, it may be possible to make the model more useful. For example, it can be argued that the English method of selecting judges reinforces the system of precedent. English judges are generally drawn from a fairly narrow social class and follow a similar career path prior to appointment to the bench. This tends to make judges, as a class, more likely to comply with rules of behaviour without being subject to formal penalties or rewards. By contrast, other types of officials who have the power to make legal decisions may be drawn from much broader backgrounds and collectively they are likely to form a less cohesive community. For example, the individuals who make legal decisions at the local authority level (such as the decision to provide a statement of special educational needs) may not form a community that is as cohesive as the judicial community. Accordingly, more overt penalties or rewards may be needed to ensure a high level of consistency. More generally, the decision-making system for local authorities should also be designed with the personal characteristics of the typical local authority 'judge' in mind. We believe that modelling could provide a powerful means of tailoring the curial system to the particular system in question. Empirical studies of compliance behaviour might indicate the characteristics of the decision-makers and modelling should indicate which incentives and appellate structures would work best with those characteristics to ensure that rules are followed.

Rasmusen observes that judges make decisions according to their expectations of the strategy to be followed by other judges. This points to the key weakness in his work: judges have no power to change their expectations, and in fact the simulation as a whole does not attempt to determine how expectations are created. Rasmusen acknowledges this point, as he states that "Game theory takes expectations as part of the primitive assumptions of the model; it is, indeed, one of game theory's weaknesses that it must do so." (Rasmusen 1994, p 78.) But these are some of the most interesting questions. The meta-rules of precedent are in turn governed by the meta-meta-rules of judicial behaviour regarding the need for a system of precedent. An interesting model would explore the evolution of these meta-meta-rules. Indeed, some of the social science models discussed below examine how the interaction between individuals and group can change the rules and strategies of behaviour.

There is the argument that a single model must confine itself to a given level or levels of rules. In legal study, there may be an interesting cross-relation between the various rules. For example, the rules of precedent sometimes evolve in response to the development of the rules themselves. Judges are inclined to interpret previous cases in order to suit the rule they intend to set in the case before them. In some cases, they may attempt to change the rules of precedent quite explicitly in order to set a rule in a particular case. Accurate models might therefore require a level of self-reference, or recursion, in order to capture the essence of the decision-making process. This is a point that sophisticated models of curial structure should incorporate.

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Existing models of similar social phenomena

Computer simulations of behaviour have been used in other social sciences. We have found that some of these simulations model behaviour that is sufficiently similar to judicial behaviour to warrant further investigation. There is one material difference, however, that might be thought to limit the utility of non-legal models. In particular, the formality and rigidity of curial hierarchy does not seem to be duplicated in other social hierarchies (at least, not in social hierarchies that have been modelled). Cases on appeal follow fairly clear routes from one court to another and the powers of superior courts over inferior courts are defined with relative clarity. Individual judges occupy fixed positions within the hierarchy and the communication between judges on matters relating to precedent occurs through formal channels. This is not to say that this is a simple area of law, but the point is that the structure of decision-making is probably clearer than it is in other social hierarchies. By contrast, models of non-curial social systems deal with hierarchies that are fluid and often obscure. The objects of exchange are well-defined, more apparent and fixed; in a curial system, the objects of exchange are not well-defined. As the economists note, it is not apparent what a judge receives when he or she takes the time to write a judgment.

To date, it appears that the relevant work on social science models falls into several broad categories. The first category may be loosely described as 'influence models', because they seek to explain how some social actors gain influence over other social actors. The second comprises 'cultural inheritance' models. They examine how a cultural inheritance, being a body of knowledge, is developed and passed on inter-generationally. Both of these provide interesting ideas for the modelling of judicial behaviour.

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1. Influence Models

A number of social science models explore the links between influence, exchange and individual motivation. Gaining influence over other social actors usually involves some sort of exchange. Many exchanges are superficially altruistic in the sense that they appear to be unequal and yet voluntary. These models seek to discover why the apparently disadvantaged actor participates in the exchanges and what these exchanges contribute to the system as a whole.

This question of motivation also arises in the curial system. Indeed, Rasmusen's model explores it in some depth. An example further from curial systems is Axelrod's study of the emergence of political actors from an aggregation of smaller political actors (see Axelrod 1995). In his model, actors begin with given amounts of 'wealth'. One actor demands 'tribute' (i.e. a payment of wealth) from another; if tribute is not paid, 'war' breaks out. Actors lose wealth in war, with the poorer actor losing more. When war breaks out, other actors join the fight on the side of the actor with which it has the strongest 'commitment'. Commitments are formed by payment and receipt of tribute. Axelrod ran through this model through a number of histories, where he varied the starting conditions of relative wealth. From these histories, he observed several characteristics of the model. Overall, it appears that alliances and new actors emerge from self-interested actions, but there is no guarantee that lasting peace will develop as a result.

The differences between the politics of military alliances and the judicial system are quite pronounced. On closer examination, however, there are some interesting parallels. Curial consistency could be described as a by-product of 'alliances' between judges based on a system of 'tribute'. A judge who follows the decision of another judge could be said to have paid tribute in the form of prestige and influence. The analogue of an alliance is not so clear, however. In the political model, alliances protect political powers when attacked by other powers. However, there is no sense that modern courts are under 'attack' from other courts. One might argue that the protection in the legal system is not against other courts, but perhaps against the legislature or executive; alternatively, one might argue there is a general benefit to all courts from the maintenance of a general climate of 'peace'. Both arguments operate on the basis that the continued survival of the judiciary as a specialised institution relies on an outward appearance of unity and consistency. If courts were unable to offer a unified, consistent view on important points of law, the reaction from other branches of government and the public might be that there is no need for the courts. We might therefore adapt Axelrod's model so that wealth is not lost through wars, but when certain levels of inconsistency are reached; at the same time, there would also be a certain benefit to individual judges from challenging another decision, if it would mean that their own precedent would be established.

Nowak and Latané have put forward a sophisticated model of influence as the product of several variables (see Nowak and Latané 1994). Their model is derived from Latané's theory of social impact. Latané defines "social impact" as "any change resulting from the real or imagined presence of others". He maintains that the social impact of other people on a given individual is determined by three classes of variables: "the 'strength' of the members of the group (how credible or persuasive they are), their 'immediacy' (a decreasing function of their social distance from the individual) and their number." (Nowak and Latané 1994, pp 63-64.)

The social actors in Nowak and Latané's model are assigned opinions at random. The model incorporates the first class of variables that affect social impact (the 'strength' of members of the group) by giving each actor a numerical value representing their power to influence others. It incorporates the second class (immediacy) by representing actors in a two-dimensional grid. The immediacy of two members is calculated by the distance between them on the grid. The third class of variables (the number of members holding a given opinion) can be calculated by totalling the number of members for or against a given opinion over given distances. Simulations begin by choosing a size for the grid and assigning values to the actors' attributes. They progress by recalculating the attitude of each individual according to a "change rule", which is a function of the variables.

Without going further, it is apparent that interesting parallels could be drawn with judicial behaviour. The system of precedent could be regarded as an example of social impact, with judges as the members of the group, their strength a product of their prestige, their immediacy a product of their position in the curial hierarchy, and their number being simply the number of judges who take a similar position on a point of law. From this, it would be possible to program different change rules and observe whether uncommitted or dissenting judges conform to the opinions of others. Since Latané's theory predicts changes in individual opinion and the formation of consensus in a system of influence, it produces the sort of results that would be useful to our project.

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2. Cultural Inheritance Models

Some models explore the phenomenon of cultural inheritance, which is the transmission of substantial body of knowledge regarding the environment from one generation to the next. There is clearly an immediate parallel with judicial behaviour, since precedent is a system of transmitting knowledge from one generation of judges to the next. In the broadest sense, this is the field investigated by Posner and Landes, as discussed above. Anthropologists focus on a different aspect of the debate: whether human evolution is the result of a combination of two independent and interacting inheritance systems, one genetic and one cultural (see generally Reynolds 1994, p. 223.) There is a rough analogy with the debates on the development of precedent within the curial system. The curial equivalent of the genetic factors in evolution might be found in the structural system of the courts, whereas the cultural equivalent might be found in the practices regarding ratio decidendi, the distinguishing of precedents, and the like. This is a very rough analogy, since the biological systems of genetic and cultural evolution are conceived of as independent sets of rules, but the legal equivalent of genetic and cultural rules can be described as a set of interrelated rules and meta-rules. Nevertheless, the idea of cultural inheritance seems so close to the legal inheritance of case-based knowledge that it is worth investigating further.

Models of cultural evolution use two methods of representing culture. One method is trait-based, whereby units of culture are observable in individuals. Reynolds reports that this method tends to be more successful with tracing changes in individual behaviour than it is with group behaviour. This might be useful in observing how different structures affect a judge's tendency to follow precedent. A second method is ideational, whereby culture is represented through 'cultural algorithms'. Reynolds demonstrates the use of cultural algorithms in his model of co-operation among llama-herders of Peru. This may prove useful in the legal context in tracing how individual preferences become expressed through more general rules regarding precedent and consistency.

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Criticisms of modelling the judicial system

The utility of a model depends upon how accurately it describes the system's social agents, their attributes, their relationships with other social agents and the events to which they react. The reduction of any one of these aspects of the model raises highly controversial points of legal theory. The issues cannot be explored fully in a preliminary study such as this, but they can be outlined briefly.

The first objection turns on the point that a programmable model uses a limited set of social actors who operate a decision function that is the product of a limited set of variables. One might object that curial consistency cannot be modelled by limited sets. There is considerable strength to this point, since neither the actors nor the variables appear to be limited. First, insofar as actors are concerned, it is true that there are only a certain number of judges who have the authority to set a precedent on any given point. However, one might argue that a judgment is not the product of a single judge but of a great many different actors. In order for a precedent to be created, litigants must decide that they can finance the trial, counsel must advise that a trial is worthwhile, the judge must decide that the case is important enough to warrant a full opinion, reporters must decide the case is worth reporting, and libraries and practitioners must decide that the report is worth reading. Even at that, there is considerable doubt amongst legal theorists that a binding precedent is in fact created. Julius Stone argues that the principle of a case is not known until another court uses it in subsequent litigation; indeed, the principle changes with each decision where it is considered (Stone 1964). To take it one step further, it could be argued that the principle cannot be defined at any point in time, since it changes with each reading and carries a different meaning for each reader. Secondly, insofar as the variables are concerned, the objection seems even stronger. Programmable models express decisions as functions of a defined and limited set of variables, but it is debatable whether any judge has such a list (whether or not acknowledged by the judge) in mind for any decision.

For some, this objection amounts to arguing that no definition of precedent is possible, that certainty of any concept is unattainable, and indeed that the study of curial consistency is pointless. For some modelling enthusiasts, these objections are answered by the observation that everyone 'knows' that there is some consistency in the system; for example, we 'know' that there can be no murder without a death. But, in our context, the criticism of anti-formalists is not that certainty is impossible but merely that any given list of actors or criteria cannot provide an accurate representation of the system. To put it in terms of set logic, the mathematics of infinite sets is significantly different than the mathematics of finite sets. Operations performed on finite sets cannot be expected to produce results that necessarily apply to infinite sets. The best description of human decision-making may involve infinite sets, whereas modelling only involves finite sets.

A second answer often made by modelling enthusiasts is that some actors and some criteria can be identified. Hence, it must be useful to study models based on these actors and criteria. However, there is no guarantee that such models would be useful. For example, if modelling legal decision-making is as complex as modelling the weather, then accuracy is possible only a very short term. In our case, the term may be so short that any information that is produced is not valuable. In addition, we do not know if legal decision-making is a system where slight variations in some criteria (identified or not) may produce such great variations in results, even over a short period, that the model is effectively worthless.

We are not prepared, at this point, to offer a full answer to the anti-formalist criticisms of modelling. However, our interest in modelling is itself a demonstration of our belief that the anti-formalists overstate the practical problems of uncertainty. On the other hand, we have some doubts that the solutions to judicial consistency that are usually proposed by lawyers are as effective as they seem to think. That is, a statement of law from a higher court or Parliament does not necessarily resolve legal inconsistency as felicitously as other methods. We believe that there is considerable merit in the belief that models of lawmaking tend to fail to incorporate criteria that are not already expressed in legal form.

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Conclusion

We are not prepared, at this point, to offer a final answer to the anti-formalist criticisms of modelling. However, our interest in modelling is itself a demonstration of our belief that the anti-formalists overstate the practical problems of uncertainty. On the other hand, we have some doubts that the solutions to curial inconsistency that are usually proposed by lawyers are as effective as they seem to think. That is, a statement of law from a higher court or Parliament does not necessarily resolve legal inconsistency as felicitously as other methods.

We believe that there is considerable merit in the belief that models of lawmaking tend fail to incorporate criteria that are not already expressed in legal form. The economic and game theory models attempt to introduce non-legal preferences as criteria in systems, and this is something that we would continue. It is central to our approach that we investigate the development and impact of these preferences. We doubt that this would ever satisfy the committed anti-formalists, but we believe that it may indicate alternatives to the approaches usually suggested by lawyers.

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BIBLIOGRAPHY

Audit Commission/HMI (1992) Getting in on the Act. Provision for Pupils with Special Educational Needs: the National Picture (HMSO, 1992)

Axelrod, R (1995) 'A Model of The Emergence of New Political Actors' in Gilbert, N and Conte, R (eds) Artificial Societies: The Computer Simulation of Social Life (London: UCL Press) p 19.

Landes, W and Posner, W (1976) 'Legal Precedent: A Theoretical and Empirical Analysis' 19 Journal of Law and Economics 249.

Nowak, A and Latané, B (1994) 'Simulating The Emergence of Social Order From Individual Behaviour' in Gilbert, N and Doran, J (eds) Simulating Societies: The Computer Simulation of Social Phenomena (London: UCL Press) p 63.

Rasmusen, E (1994) 'Judicial Legitimacy as a Repeated Game' 10 The Journal of Law, Economics, & Organization 63.

Reynolds, R (1994) 'Learning to Co-operate Using Cultural Algorithms' in Gilbert, N and Doran, J (eds) Simulating Societies: The Computer Simulation of Social Phenomena (London: UCL Press) p 223.

Stone, J (1994) Legal System and Lawyers' Reasonings (London: Stevens and Sons).

Footnotes

(1) Some participants do recoup the cost; for example, publishers of legal materials charge subscribers.