AGENT-BASED SIMULATION OF SOCIAL LEARNING

IN CRIMINOLOGY

Tibor Bosse, Charlotte Gerritsen and Michel C. A. Klein

Vrije Universiteit Amsterdam, Department of Artificial Intelligence

de Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands

Keywords: Agent-based simulation, Social learning, Delinquent behaviour.

Abstract: Criminal behaviour exists in many variations, each with its own cause. A large group of offenders only

shows criminal behaviour during adolescence. This kind of behaviour is largely influenced by the

interaction with others, through social learning. This paper contributes a dynamical agent-based approach to

simulate social learning of adolescence-limited criminal behaviour, illustrated for a small school class. The

model is designed in such a way that it can be compared with data resulting from a large scale empirical

study.

1 INTRODUCTION

Within Criminology, the analysis of the emergence

of criminal behaviour is one of the main challenges

(Gottfredson and Hirschi, 1990). An important

mechanism behind the emergence of criminal

behaviour is social learning (Burgess and Akers,

1966). To analyse this mechanism, this paper

presents an agent-based approach to simulate social

learning, which specifically addresses the mutual

influence of peers, parents and school, with respect

to delinquent behaviour.

To formalise and analyse the emergence of

criminal behaviour through social learning, an

artificial society has been modelled to represent a

small school class. The models for the agents have

been formally specified by executable

temporal/causal logical relationships, using the

modelling language TTL (Bosse et al., 2006) and its

executable sublanguage LEADSTO (Bosse et al,

2007). This language allows the modeller to

integrate both qualitative, logical aspects as

quantitative, numerical aspects. Moreover, since the

language has a formal logical semantics, simulation

models created in TTL and LEADSTO can be

formally analysed by means of logical analysis

techniques.

In the field of Criminology, it is often quite

difficult to perform experiments that involve

changes in the real world. A model as the one

presented in this paper can be used to study general

patterns in the development of criminal behaviour.

Simulation can help to answer what-if questions and

to verify theories about the relation between

different processes. Discussions with a team of

criminologists taught us that the evidence provided

by simulation models is already considered as useful

knowledge about the relevance of criminological

theories such as the differential association theory,

which will be discussed below.

In a next step of the research, we plan to validate

the model using data of an existing empirical study

e.g. (Weerman and Bijleveld, 2007). In that study,

the social networks of 1730 non-delinquent, minor

delinquent and serious delinquent

pupils at lower-

level secondary schools in the Netherlands were

analysed. This paper only reports about the first step,

the model and simulations.

In Section 2 a summary from the literature on

social learning is presented. Section 3 discusses the

chosen modelling approach. The simulation model is

presented in Section 4, and Section 5 discusses

simulation results. In Section 6, these results are

analysed using formal techniques. Section 7 presents

related work. Finally, Section 8 concludes the paper.

2 SOCIAL LEARNING

According to (Moffitt, 1993), two types of

delinquents can be distinguished: life-course-

persistent offenders, who stay criminal throughout

their entire life and adolescence-limited offenders,

who only show antisocial behaviour during

Bosse T., Gerritsen C. and C. A. Klein M. (2009).

AGENT-BASED SIMULATION OF SOCIAL LEARNING IN CRIMINOLOGY .

In Proceedings of the International Conference on Agents and Artiﬁcial Intelligence, pages 5-13

DOI: 10.5220/0001512000050013

 SciTePress

adolescence. Life-course-persistent anti-social

behaviour is caused by neuropsychological problems

during childhood that interact cumulatively with

their criminogenic environments across

development, which leads to a pathological

personality. Adolescence-limited antisocial

behaviour is caused by the gap between biological

maturity and social maturity. It is learned from

antisocial models that are easily mimicked, and it is

sustained according to the reinforcement principles

of learning theory. They peak sharply at about age

17 and drop fast in young adulthood. In the current

paper, we explicitly focus on the adolescence-

limited offenders.

An influential theory on the emergence of

adolescence-limited criminal behaviour is the

differential association theory, which was first

proposed by Sutherland and Cressey (1966) and later

expanded by Burgess and Akers (1966). In short,

this (informal) theory states that behaviour is learned

through interaction with others. We learn most from

the people we are in close contact with, like parents

and peers. There are two basic elements to

understanding the differential association theory.

First, the content of what is learned is important

(e.g., motives, attitudes and evaluations by others of

the meaningful significance of each of these

elements). Second, the process by which learning

takes place is important, including the intimate

informal groups and the collective and situational

context where it occurs. Criminal behaviour itself is

learned through assigning meaning to behaviour,

experiences, and events during interaction with

others.

According to Sutherland and Cressey (1966), the

extent to which delinquent behaviour is imitated is

influenced by the frequency, duration, and intensity

of the contact. Frequent, long and important or

prestigious contacts have a larger influence. In

addition, the priority of learning influences the

social learning process: the earlier behaviour is

learned, the more influential it is.

3 MODELLING APPROACH

To formalise and analyse the emergence of criminal

behaviour through social learning from an agent

perspective, an expressive modelling language is

needed. On the one hand, qualitative aspects have to

be addressed, such as certain characteristics about

the agents (e.g., their age), their social relationships

(e.g., who are their parents and friends). On the other

hand, quantitative aspects have to be addressed. For

example, an agent’s level of delinquency, which is

the extent to which an agent exhibits delinquent

behaviour, can best be described by a real number.

The change of this delinquency can best be

described by a mathematical formula. Another

requirement of the chosen modelling language is its

suitability to express on the one hand the basic

mechanisms of social learning (for the purpose of

simulation), and on the other hand more global

properties of social learning (for the purpose of

logical analysis and verification). For example, basic

mechanisms of social learning involve decisions of

individual agents to attach to their peers, whereas

global properties are statements that consider the

learning process over a longer period, like

“eventually the delinquent pupils become less

delinquent”.

The predicate-logical Temporal Trace Language

(TTL) (Bosse et al., 2006) fulfils all of these

desiderata. It integrates qualitative, logical aspects

and quantitative, numerical aspects. This integration

allows the modeller to exploit both logical and

numerical methods for analysis and simulation.

Moreover it can be used to express dynamic

properties at different levels of aggregation, which

makes it well suited both for simulation and logical

analysis.

TTL is based on the assumption that dynamics

can be described as an evolution of states over time.

The notion of state as used here is characterised on

the basis of an ontology defining a set of physical

and/or mental (state) properties that do or do not

hold at a certain point in time. These properties are

often called state properties to distinguish them

from dynamic properties that relate different states

over time. A specific state is characterised by

dividing the set of state properties into those that

hold, and those that do not hold in the state.

Examples of state properties are ‘agent 1 has a

delinquency level of 0.35’, or ‘agent 2 has an

attachment to agent 3 of 0.5’.

To formalise state properties, ontologies are

specified in a (many-sorted) first order logical

format: an ontology is specified as a finite set of

sorts, constants within these sorts, and relations and

functions over these sorts (sometimes also called

signatures). The examples mentioned above then can

be formalised by n-ary predicates (or proposition

symbols), such as, for example,

has_delinquen-

cy(agent1,0.35)

or has_attachment_to(agent2, agent3,

0.5)

. Such predicates are called state ground atoms

(or atomic state properties). For a given ontology

Ont, the propositional language signature consisting

of all ground atoms based on

Ont is denoted by

APROP(Ont). One step further, the state properties

based on a certain ontology

Ont are formalised by the

ICAART 2009 - International Conference on Agents and Artificial Intelligence

propositions that can be made (using conjunction,

negation, disjunction, implication) from the ground

atoms. Thus, an example of a formalised state

property is has_delinquency(agent1,0.35) & has_delin-

quency(agent2,0.45)

. Moreover, a state S is an

indication of which atomic state properties are true

and which are false, i.e., a mapping

S: APROP(Ont) →

{true, false}

. The set of all possible states for ontology

Ont is denoted by STATES(Ont).

To describe dynamic properties of complex

processes such as the development of criminal

behavior, explicit reference is made to time and to

traces. A fixed time frame

T is assumed which is

linearly ordered. Depending on the application, it

may be dense (e.g., the real numbers) or discrete

(e.g., the set of integers or natural numbers or a

finite initial segment of the natural numbers).

Dynamic properties can be formulated that relate a

state at one point in time to a state at another point in

time. A simple example is the following (informally

stated) dynamic property about the delinquency of

agents:

For all traces γ,

there is a time point t such that

all agents have a delinquency that is lower than d.

A trace γ over an ontology Ont and time frame T

is a mapping γ : T → STATES(Ont), i.e., a sequence of

states

(t ∈ T) in STATES(Ont). The temporal trace

language TTL is built on atoms referring to, e.g.,

traces, time and state properties. For example, ‘in

trace

γ at time t property p holds’ is formalised by

state(γ, t) |= p. Here |= is a predicate symbol in the

language, usually used in infix notation, which is

comparable to the

Holds-predicate in situation

calculus. Dynamic properties are expressed by

temporal statements built using the usual first-order

logical connectives (such as ¬, ∧, ∨, ⇒) and

quantification (∀ and ∃; for example, over traces,

time and state properties). For example, the

informally stated dynamic property introduced

above is formally expressed as follows:

∀γ:TRACE ∃t:TIME ∀a:AGENT ∃x:REAL

state(γ, t) |= has_delinquency(a, x) & x≤d

In addition, language abstractions by introducing

new predicates as abbreviations for complex

expressions are supported.

To be able to perform (pseudo-)experiments, only

part of the expressivity of TTL is needed. To this

end, the executable LEADSTO language (Bosse et

al., 2007) has been defined as a sublanguage of TTL,

with the specific purpose to develop simulation

models in a declarative manner. In LEADSTO,

direct temporal dependencies between two state

properties in successive states are modelled by

executable dynamic properties. The LEADSTO

format is defined as follows. Let α and β be state

properties as defined above. Then, the notation α →→

e, f, g, h β means:

If state property α holds for an interval with duration g,

then after some delay between e and f

state property

will hold for an interval with duration h.

As an example, the following executable dynamic

property states that “if during 1 time unit the

attachment between agent a1 and a2 is x1, and the

difference in delinquency between both agents is x2,

then for the next 5 time units (after a delay between

0 and 0.5 time units) the attachment between both

agents will be

β*x1+(1-β)*|x2|”:

∀a1,a2:AGENT ∀x1,x2:REAL

has_attachment_to(a1,a2,x1) ∧

delinquency_difference(a1,a2,x2) →→

0, 0.5, 1, 5

has_attachment_to(a1,a2,β*x1+(1-β)*|x2|)

Based on TTL and LEADSTO, two dedicated

pieces of software have recently been developed.

First, the LEADSTO Simulation Environment

(Bosse et al., 2007) takes a specification of

executable dynamic properties as input, and uses this

to generate simulation traces. Second, to

automatically analyse the resulting simulation traces,

the TTL Checker tool (Bosse et al., 2006) has been

developed. This tool takes as input a formula

expressed in TTL and a set of traces, and verifies

automatically whether the formula holds for the

traces. In case the formula does not hold, the

Checker provides a counter example, i.e., a

combination of variable instances for which the

check fails.

4 SIMULATION MODEL

To study the influence of social learning on

delinquent behaviour, we modelled a school class

with 10 pupils. There are three groups that influence

the process of social learning, namely parents,

school and peers. Therefore, each pupil is

represented as an agent; the parents of the pupils and

the school are modelled as groups. Each pupil is

related to one parent group. The agents have a

number of characteristics in our model (determined

based on discussions with experts). We restricted

our study to the characteristics that are collected in

the empirical study (Weerman and Bijleveld, 2007).

The first property of an agent is its age. In our model

the age is restricted to values between 12 and 17.

The age is relevant for influence of peers on each

other. The older an adolescent is (up to 17) the more

AGENT-BASED SIMULATION OF SOCIAL LEARNING IN CRIMINOLOGY

his behaviour is influenced by peers. In addition, the

age difference between peers is relevant, since older

people are often more dominant in the relationship.

The influence of school and parents tends to

decrease as the adolescent gets older.

In addition, agents have a basic level of

influenceability: this represents how easily they can

be influenced. Oppositely, agents and groups have a

level of dominance: this represents how easily they

can influence others. For persons this is a character

trait. Schools can also have a level of dominance. A

dominant school can be seen as a strict school, while

a school that is less strict could be considered to be

less dominant.

The social relations between pupils in a school

class are modelled via attachment relations. All

agents are attached to each other with a specific level

of attachment, representing the intensity of the

contact as defined by Sutherland and Cressey

(1966). The attachment relation is also used to

model the attachment of pupils to their parents and

to their school. We assume that a high attachment

results in a higher influence of the attached agent or

group on the behaviour of the pupil.

Finally, we model a level of delinquency for all

agents and groups, also for parents and schools. The

initial value for the delinquency of an agent could be

based on a measurement of the number of delinquent

acts of a pupil in the past. The interpretation of the

delinquency of a school is indirect: the school has a

low level of delinquency if it is a good school, i.e.

teachers and other staff members have a low level of

delinquency. When the atmosphere in the school is

less positive, then it has a higher level of

delinquency.

During the simulation, the levels of delinquency

of the pupils change because of the influence of

others. This process is depicted in Figure 1, where

the circles denote state properties and the arrows

denote dynamic properties (relationships) between

them. The age of each agent increases every year.

Every agent starts with a basic influenceability;

together with the age of the agent and the attachment

to a specific group or agent, the effective

influenceability of the agent by that agent or group is

determined (denoted by

has_influenceability in Figure

1).

This effective influenceability is combined with

the level of dominance of the other party, the

difference in delinquency between the agent and the

other party, and - in case the other party is an agent -

the age difference between two agents. This leads to

the so-called delta delinquency. The delta

delinquency represents all factors that influence the

level of delinquency of an agent. In order to

calculate the new delinquency of an agent, the delta

delinquencies of all agents and groups in its

environment are combined with the old delinquency

(the delinquency the agent started out with).

In addition, the model is able to adapt the

attachment between the agents. The idea behind this

is that the strength of a relation is influenced by the

overlap in values. If the difference in the level of

delinquency is very high, then the attachment will

decrease. However, because there are many other

factors that influence the attachment as well, the

difference in delinquency only causes a minor

change in attachment.

In the model, the concepts of influenceability,

dominance, attachment, and delinquency are

modelled as a real number between 0 and 1.

Furthermore, the age is modelled as an integer

between 12 and 17, and the delta delinquency as a

real number between -1 and 1. The relationships

between the concepts have been modelled in

LEADSTO. Two example relationships (to

determine the delta delinquency of groups, and the

new delinquency, respectively) are stated below.

Here, the β’s are decay factors, and the w’s are

weight factors. Note that these relationships

correspond to (conjunctions of) arrows in Figure 1.

The complete set of LEADSTO relationships is

shown in the online appendix

Delta Delinquency Determination (for Groups)

∀a:AGENT ∀g:GROUP ∀x1,x2,x3:REAL

delinquency_difference(a,g,x1) ∧ has_influencability(a,g,x2) ∧

has_dominance(g,x3) →→

has_delta_delinquency(a,g,β2*(β1*x1+(1-β1)*x1*

(w4*x2+w5*x3)))

New Delinquency Determination

∀a1:AGENT ∀g:GROUP ∀d,s,p,x1,...,x10:REAL

has_old_delinquency(a1,d) ∧

has_delta_delinquency(a1,school,s) ∧

has_delta_delinquency(a1,g,p) ∧ are_parents_of(g,a1) ∧

has_delta_delinquency(a1,agent1,x1) ∧ ...

has_delta_delinquency(a1,agent10,x10) →→

has_delinquency(a, d+ (s+p+x1+...+x10)/12))

5 SIMULATION RESULTS

A number of simulation experiments have been

performed to see whether the behaviour of the model

was as expected for some common scenarios. A

thorough evaluation will be performed later when

the results will be compared with data of an

empirical study. A longer description with more

scenarios and details can be found in the appendix.

http://human-ambience.few.vu.nl/docs/ICAART09.pdf

ICAART 2009 - International Conference on Agents and Artificial Intelligence

has_basic_

influenceability(a,x)

has_influenceability

(a,gr,x)

has_dominance

(gr,x)

has_attachment_to

(a,gr,x)

has_delinquency

(gr,x)

has_delinquency

(a,x)

has_delta_

delinquency

(a,gr,x)

has_age(a,x)

delinquency_

difference(a,gr,x)

age_difference

(a,a2,x)

has_age(a2,x)

Figure 1: Concepts and relations in the simulation model.

In the first scenario there is one bad guy with

criminal parents in an otherwise reasonable school

class. We are interested in the question whether the

criminal boy makes the other boys bad or whether

the group is able to straighten out the delinquent. In

this scenario agent 1 has a delinquency of 0.8 while

the other agents have a delinquency of 0.3. All

agents are male2 and are 12 years old at the start of

the simulation. They have a basic influenceability

with a value of 0.4, a level of dominance of 0.6 and

a mutual attachment of 0.3. The attachments are

stable in this simulation. Every agent has parents

with a dominance of 0.7 and a delinquency of 0.2,

except for agent 1, whose parents have a

delinquency of 0.8.

The resulting trace is shown in Figure 2 (this and

the following figures can be found at the last page of

the paper). Here, time is on the horizontal axis and

the level of delinquency is on the vertical axis. The

three graphs show the combined delinquencies of all

pupils, the delinquency of agent 1 and the

delinquency of the other agents (that all show the

same behaviour; agent 10 is just taken as an

example), respectively. The two lines in the first

graph correspond to the lines in the second and third

graph, respectively, where a more detailed scale is

Note that the model does not incorporate a direct influence of

gender. Difference between male and female pupils can be

modeled indirectly by giving the males higher initial

delinquencies.

used. The results show that the interaction between

the agents leads to a decreased delinquency of agent

1. The delinquency of the other agents increases

slightly to 0.31 and from this point on it decreases to

0.255 at time point 100. From time point 70 on,

there is a more or less stable difference in

delinquency between the agent with criminal parents

and the others.

In a second scenario (Figure 3), the influence of

the school is examined by increasing its delinquency

to 0.8. The level of delinquency of the agents and

their parents were identical to the settings in the

previous scenario. The results show that the

increased delinquency of the school causes an

increased level of delinquency of all the agents. This

influence appeared to be larger than the influence of

individual agents, because it propagates through to

pupils, who again influence each other.

In the third scenario, half of the pupils (and

their parents) have a high delinquency. The other

pupils (and their parents) have the same level of

delinquency as in scenario 1. In this case all agents

influence each other and their delinquencies grow

towards each other, while a difference remains

because of the influence of the parents (see Fig. 4).

Finally, the fourth scenario represents a school

class with two groups (3 delinquent pupils with a

high mutual attachment, 3 extremely non-delinquent

pupils with a high mutual attachment) and 4

individuals with a high basic influenceability. One

of these ‘group-less pupils’ has a high attachment to

AGENT-BASED SIMULATION OF SOCIAL LEARNING IN CRIMINOLOGY

a person in the criminal group, one to a person in the

non-criminal group, and the others had no specific

relations. The attachments can change over time.

The goal of this scenario is to see whether a pupil

will be incorporated in a group if he has a strong

relationship with one of them. Figure 5 shows the

resulting delinquencies.

Interestingly, we see that all group-less pupils

reach a level of delinquencies that is close to that of

the pupils in the ‘good group’, even for the pupils

that have a strong relation to a pupil in one of the

groups. This observation can be explained by the

fact that the delinquency of the parents of the group-

less pupils is close to the delinquency of the parents

in the good group. However, if we look closely at

the delinquencies of the group-less people (lower

graph in Figure 5), we see that they develop slightly

differently (notice the different scale). Apparently,

the delinquency of the pupil with a friend in the bad

(good) group initially grows faster (slower), but

eventually it reaches the same level as the other

group-less pupils.

6 FORMAL ANALYSIS

The detailed settings and results of ten simulation

experiments (including the ones described in Section

5) are shown in the appendix. Among the different

experiments, various parameter settings were varied,

in particular the initial delinquencies of agents,

parents, and school, the initial attachment between

agents, and several weight factors.

To analyse the resulting simulation traces in

more detail, the TTL Checker tool (Bosse et al.,

2006) has been used. As mentioned earlier, this tool

takes as input a TTL formula and a set of traces, and

verifies automatically whether the formula holds for

the traces. For the current domain, a number of

hypotheses have been expressed as dynamic

properties in TTL, which were inspired by relevant

questions in Criminology (see Sections 1 and 2). To

give a simple example, consider the following

dynamic property (P1), which expresses that the

delinquency of an agent keeps on decreasing over

time:

P1 Strict Monotonic Decrease of Delinquency

For all time points t1 and t2, if t2 is later than t1, then the

agent’s delinquency at t2 is lower than at t1.

P1(γ:TRACE, a:AGENT) ≡

∀t1,t2:TIME ∀d1,d2:REAL

[ state(γ, t1) |= has_delinquency(a, d1) &

state(γ, t2) |= has_delinquency(a, d2) & t1<t2 ] ⇒ d1>d2

Note that this formula comprises two free

variables (the trace

γ and the agent a), for which

different values can be instantiated. For example, in

order to check whether agent 1 satisfies the criterion

of strict monotonic decrease of delinquency in

simulation trace 5, the formula

P1(trace1, agent1)

should be checked. Similarly, it is possible to check

whether the property holds for all agents and all

traces, or for a certain percentage of them.

Besides checking whether the delinquency of

agents keeps on decreasing, also other properties can

be verified. A relevant question in Criminology is

what the relative influences of (respectively) parents,

peers, and school on the development of a person’s

delinquency are. For example, might it be the case

that the biggest contribution is provided by parents

and school only, and that the influence of classmates

can almost be neglected? To analyse these kinds of

hypotheses, properties like the following have been

established:

P2 Agent Converges to Parents and School

At the end of the trace, the delinquency of agent a lies within

a margin δ of the average of the delinquencies of its parents

and the school at the start of the trace.

P2(γ:TRACE, a:AGENT) ≡

∀d1,d2,d3:REAL ∀p:AGENT

[ state(γ, start_time) |= has_delinquency(p, d1) &

state(γ, start_time) |= has_delinquency(school, d2) &

state(γ, end_time) |= has_delinquency(a, d3) &

are_parents_of(p,a) & ]

⇒ d3-δ < (d1+d2)/2 < d3+δ

If this property were true (for a small δ), this

would indicate that the development of a pupil could

be predicted by taking into account the delinquency

of the parents and the school only. Some initial

checks have pointed out that the lowest δ for which

the property satisfies all generated traces is 0.22. In

other words, for all of the traces the influence of

parents and school was relatively high. In addition to

P2, a property was created to compare the change in

delinquency between two agents a1 and a2.

P3 Bigger Change in Delinquency

During the whole trace, agent a1 made a bigger change in

delinquency than agent a2.

P3(γ:TRACE, a1,a2:AGENT) ≡

∀d1,d2,d3,d4:REAL

[ state(γ, start_time) |= has_delinquency(a1, d1) &

state(γ, start_time) |= has_delinquency(a2, d2) &

state(γ, end_time) |= has_delinquency(a1, d3) &

state(γ, end_time) |= has_delinquency(a2, d4) ]

⇒ |d1-d3| > |d2-d4|

This property can be used, for example, to find

out whether in a school class with many “good”

pupils and one “bad” guy (see scenario 1), the bad

pupil tends to move towards the good ones, or vice

versa. In our simulation traces, such a bad pupil

ICAART 2009 - International Conference on Agents and Artificial Intelligence

indeed turned out to converge towards his

classmates.

To summarise, a number of TTL properties have

been checked against the generated simulation

traces, as a first pilot study of the applicability of the

approach. Although no real conclusions can be

drawn as yet, these checks pointed out that the traces

satisfy basic properties that were inspired by

criminological theories, such as property P2 and P3.

Finally, it is important to note that, in addition to

simulated traces, the TTL Checker can also take

empirical traces as input. In future work, several

properties as those introduced here will be verified

against empirical traces that are constructed on the

basis of experiments in real classrooms

7 RELATED WORK

With respect to related work, the research presented

in this paper on the one hand has commonalities

with literature from the social and behavioural

sciences (in particular, the area of Criminology), and

on the other hand with literature in AI and Computer

Science (among others, agent-based simulation).

Concerning the criminological and psychological

area, first of all the current paper is related to early

articles from the 60’s and 70’s such as Bandura

(1977), Burgess and Akers (1966) and Sutherland

and Cressey (1966), which were the first to

formulate (different variants of) the social learning

theory. Here, the theory put forward by Bandura

(1977) is more generic, whereas the other two focus

specifically on social learning in Criminology. For

an overview of these theories, see Lanier and Henry

(1998), Chapter 7. In fact, these theories formed the

basis of the research questions addressed in this

paper. Based on these theories, Opp (1989)

identified a number of (informal) properties that are

expected to hold for social learning in Criminology,

such as “the more frequently persons show deviant

behaviour, the more frequently they will have

contact with patterns of deviant behaviour”.

Although a detailed verification (using larger-scale

experiments and statistical techniques) is left for

future work, an initial analysis provides evidence

that our model indeed satisfies these properties.

Next, a number of papers in Criminology propose

more refined models for social learning, often

focusing on specific aspects of the learning. For

example, Thornberry et al. (1994) compared three

theoretical models of the interrelations among

associations between delinquent peers, delinquent

beliefs, and delinquent behaviour. A main difference

with our work is that these models are not

computational. Nevertheless, their conclusions are in

agreement with the initial results found in this paper.

Finally, several authors have performed empirical

studies on social learning of delinquent behaviour in

schools (Bruinsma, 1984) and Weerman and

Bijleveld, 2007). Our model was designed explicitly

with the purpose of reproducing such data.

Concerning the literature in AI and Computer

Science, we are not aware of approaches using

multi-agent technology to simulate delinquent

behaviour of individuals in a group. However,

various papers have similarities to the work

proposed here. First, Van Dijkum and Landsheer

(2000) present a model that is rather similar to ours,

but which uses differential equations to describe the

development of juvenile criminal behaviour.

Another difference with our model is that they aim

for an integration of multiple criminological theories

(namely social learning theory, career theory, and

rational choice theory), whereas we focus (in more

detail) on the former only. Moreover, several authors

have created models that address social learning and

criminal behaviour at a more global level. For

example, Chamley (2003) presents an economic

model for social learning, although not explicitly

focussed on learning of delinquent behaviour.

Similarly, Winoto (2002) presents an agent-based

economic model for the market for offenses. This

model addresses the global development of

delinquency in a population. These models differ

from our model in the sense that they are situated at

a macroscopic level, thereby abstracting from

differences between individuals. An approach that

does consider individual differences, but that

addresses a different domain, is presented by

Tsvetovat and Carley (2005). They present a

simulation model of the dynamics of terrorist

networks, based on networks of non-deterministic

finite automata. Furthermore, a large number of

approaches address simulation of the environmental

aspects of criminal behaviour, such as the

displacement of crime and the emergence of “hot

spots”, e.g., Liu et al. (2005) and Bosse and

Gerritsen (2008). Finally, relevant work is put

forward by Conte and Paolucci (2001). They

identify a number of (cognitive) factors that are

relevant in social learning in general. However, in

contrast to our work, they do not provide a

computational model.

8 CONCLUSIONS

This paper presented an agent-based approach to

simulate and formally analyse the process of social

AGENT-BASED SIMULATION OF SOCIAL LEARNING IN CRIMINOLOGY

learning of delinquency during adolescence. The

general mechanism of change by influences of peers

is possibly also useful in other domains in which

social learning is relevant. In this paper, however,

we focused on learning of delinquent behaviour.

Inspired by criminological literature, the approach

incorporates the influences of three types of groups,

namely peers, parents, and school. Various relevant

factors were identified, such as influenceability,

dominance, and attachment, and their mutual

relationships were formalised by means of the

hybrid modelling language LEADSTO. Moreover, it

was shown how the approach can be used to

generate simulation traces, and how such traces can

be automatically verified against relevant properties,

expressed in the language TTL. Although

preliminary, the first results are promising. Firstly,

they provide evidence that the proposed model is a

useful experimental tool to give insight in social

learning processes as described in the criminological

literature. Secondly, some interesting patterns have

already been found. For example, the simulation

results suggest that the influence of the school on

delinquency is relatively high (scenario 3), that the

impact of attachment is relatively low (scenario 4),

and that every individual learning process

approaches a final delinquency near the average of

the delinquencies of parents, school, and peers.

In the current paper, no detailed empirical

validation of the model has been presented.

However, as mentioned in the introduction, various

empirical studies have been performed, of which

large data sets are available (Bruinsma, 1985) and

Weerman and Bijleveld, 2007). The model has been

explicitly designed with the objective of using such

data sets for validation in the future. Currently, some

initial steps in this direction are taken. During such a

validation, several questions are addressed, such as

“is it realistic that the average delinquency almost

always decreases?”, or “is it realistic to have a

relatively stable delinquency for school and

parents?”. When these questions are solved, the

model can be further fine-tuned, in particular by

choosing realistic values for all parameter settings

and weight factors involved.

REFERENCES

Bandura, A. (1977). Social Learning Theory. Englewood

Cliffs, NJ, Prentice-Hall.

Bosse, T., and Gerritsen, C., Agent-Based Simulation of

the Spatial Dynamics of Crime: On the Interplay

between Criminal Hot Spots and Reputation. In:

Proceedings of the 7

International Joint Conference

on Autonomous Agents and Multi-Agent Systems,

AAMAS’08. ACM Press, 2008, pp. 1129-1136.

Bosse, T., Jonker, C.M., Meij, L. van der, and Treur, J.

(2007). A Language and Environment for Analysis of

Dynamics by SimulaTiOn. International Journal of AI

Tools, vol. 16, issue 3, pp. 435-464.

Bosse, T., Jonker, C.M., Meij, L. van der, Sharpanskykh,

A., and Treur, J. (2006). Specification and Verification

of Dynamics in Cognitive Agent Models. In:

Proceedings of the 6

International Conference on

Intelligent Agent Technology, IAT’06. IEEE Computer

Society Press, 2006, pp. 247-254.

Bruinsma, G.J.N. (1985). Crime as Social Learning

Process. A Test of the Differential Association Theory

in the version of K.-D. Opp (in Dutch). Gouda Quint,

Arnhem.

Burgess, R., and Akers, R.L. (1966). A Differential

Association-Reinforcement Theory of Criminal

Behavior. Social Problems, vol. 14, pp. 363-383.

Chamley, C.P. (2003). Rational Herds: Economic Models

of Social Learning. New York: Cambridge University

Press.

Conte, R., and Paolucci, M. (2001). Intelligent Social

Learning. Journal of Artificial Societies and Social

Simulation, vol. 4, issue 1.

Dijkum, C. van, and Landsheer, H. (2000). Experimenting

with a Nonlinear Dynamic Model of Juvenile Criminal

Behavior. Simulation & Gaming, vol. 31, pp. 479-490.

Gottfredson, M. and Hirschi, T. (1990). A General Theory

of Crime. Stanford University Press.

Lanier, M.M., and Henry, S. (1998). Essential

Criminology. Boulder, CO: Westview Press.

Liu, L., Wang, X., Eck, J., and Liang, J. (2005).

Simulating Crime Events and Crime Patterns in

RA/CA Model. In F. Wang (ed.), Geographic

Information Systems and Crime Analysis. Singapore:

Idea Group, pp. 197-213.

Moffitt, T.E. (1993). Adolescence-Limited and Life-

Course-Persistent Antisocial Behavior: A

Developmental Taxonomy. Psychological Review, vol.

100, no. 4, pp. 674-701.

Opp, K.D. (1989). The Economics of Crime and the

Sociology of Deviant Behaviour - A Theoretic

Confrontation of Basic Propositions. Kyklos, vol. 42,

issue 3, pp. 405-430.

Sutherland, E.H., and Cressey, D.R. (1966). Principles of

Criminology, 7

edition. Philadelphia: J.B. Lippincott.

Thornberry, T.P., Lizotte, A.J., Krohn, M.D., Farnworth,

M., and Jang, S.J. (1994). Delinquent Peers, Beliefs,

and Delinquent Behavior: A Longitudinal Test of

Interactional Theory. Criminology, vol. 32, pp. 47-83.

Tsvetovat, M., and Carley, K.M. (2005). Structural

Knowledge and Success of Anti-Terrorist Activity:

The Downside of Structural Equivalence. Journal of

Social Structure, vol. 6.

Weerman, F.M., and Bijleveld, C.C.J.H. (2007). Birds of

Different Feathers. European Journal of Criminology,

vol. 4, issue 4, pp. 357-383.

Winoto, P. (2002). An Agent-Based Simulation of the

Market for Offenses. In: AAAI Workshop on Multi-

Agent Modeling and Simulation of Economic Systems.

Edmonton, Canada.

ICAART 2009 - International Conference on Agents and Artificial Intelligence

Figure 2: Delinquency in a school class with one bad guy.

Figure 3: Influence of a bad school.

Figure 4: Delinquency in a school class with half of the pupils being criminal.

Figure 5: Delinquencies in school class with two groups.

AGENT-BASED SIMULATION OF SOCIAL LEARNING IN CRIMINOLOGY