Fraud dynamics and controls in organizations

Description
This paper develops an agent-based model to examine the emergent dynamic characteristics
of fraud in organizations. In the model, individual heterogeneous agents, each of whom
can have motive and opportunity to commit fraud and a pro-fraud attitude, interact with
each other. This interaction provides a mechanism for cultural transmission through which
attitudes regarding fraud can spread. Our benchmark analysis identifies two classes of
organizations. In one class, we observe fraud tending toward a stable level. In the other
class, fraud dynamics are characterized by extreme behaviors; organizations with mostly
honest behavior suddenly change their state to mostly fraudulent behavior and vice versa.
These changes seem to occur randomly over time. We then modify our model to examine
the effects of various mechanisms thought to impact fraud in organizations. Each of these
mechanisms has different impacts on the two classes of organizations in our benchmark
model, with some mechanisms being more effective in organizations exhibiting stable
levels of fraud and other mechanisms being more effective in organizations exhibiting
unstable extreme behavior.

Fraud dynamics and controls in organizations
Jon S. Davis
?
, Heather L. Pesch
1
Department of Accountancy, University of Illinois at Urbana–Champaign, 1206 S. Sixth Street, Champaign, IL 61821, USA
a b s t r a c t
This paper develops an agent-based model to examine the emergent dynamic characteris-
tics of fraud in organizations. In the model, individual heterogeneous agents, each of whom
can have motive and opportunity to commit fraud and a pro-fraud attitude, interact with
each other. This interaction provides a mechanism for cultural transmission through which
attitudes regarding fraud can spread. Our benchmark analysis identi?es two classes of
organizations. In one class, we observe fraud tending toward a stable level. In the other
class, fraud dynamics are characterized by extreme behaviors; organizations with mostly
honest behavior suddenly change their state to mostly fraudulent behavior and vice versa.
These changes seem to occur randomly over time. We then modify our model to examine
the effects of various mechanisms thought to impact fraud in organizations. Each of these
mechanisms has different impacts on the two classes of organizations in our benchmark
model, with some mechanisms being more effective in organizations exhibiting stable
levels of fraud and other mechanisms being more effective in organizations exhibiting
unstable extreme behavior. Our analysis and results have general implications for design-
ing programs aimed at preventing fraud and for fraud risk assessment within the audit
context.
Ó 2012 Elsevier Ltd. All rights reserved.
Introduction
Fraud
2
has become a popular area of inquiry among
accounting academics because of the magnitude of losses
(estimated by the Association of Certi?ed Fraud Examiners
in 2010 to be US$2.9 trillion worldwide) and requirements
imposed on auditors to explicitly address the problem (AIC-
PA, 2002). Research has addressed fraud risk assessment by
auditors (e.g., Bell & Carcello, 2000; Carpenter, 2007; Wilks
& Zimbelman, 2004), fraud detection (e.g., Cleary & Thibo-
deau, 2005; Hoffman & Zimbelman, 2009; Matsumura &
Tucker, 1992), fraud incentives (e.g., Erickson, Hanlon, &
Maydew, 2006; Gillett & Uddin, 2005), and the correlation
of fraud with ?nancial statement reporting choices and cor-
porate governance variables (e.g., Beasley, 1996; Jones,
Krishnan, & Melendrez, 2008; Sharma, 2004).
In light of the high cost of corporate fraud, one might
expect considerable research activity investigating the ef?-
cacy of mechanisms designed to prevent or reduce fraud.
However, despite its potential importance, a review of re-
search reveals a striking dearth of work examining the
effectiveness of various prevention mechanisms, except
for the deterring role of audits (e.g., Finley, 1994; Schneider
& Wilner, 1990; Uecker, Brief, & Kinney, 1981). This lack of
work on prevention is likely due to fraud being a hidden
crime. Because the extent of fraud is usually unknown in
an organization, measuring the effectiveness of prevention
mechanisms is dif?cult using traditional empirical
methods.
Research on fraud in organizations tends to focus on
either the individual or the organization (Holtfreter,
2005; Pinto, Leana, & Pil, 2008). To date, very little work
has attempted to explicitly link individual behaviors in
0361-3682/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.aos.2012.07.005
?
Corresponding author. Tel.: +1 217 300 0489; fax: +1 217 244 0902.
E-mail addresses: [email protected] (J.S. Davis), [email protected]
(H.L. Pesch).
1
Tel.: +1 217 300 0514; fax: +1 217 244 0902.
2
For the purposes of our model, we de?ne fraud as all forms of
occupational fraud, including asset misappropriation, corruption, and
?nancial statement fraud.
Accounting, Organizations and Society 38 (2013) 469–483
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the organization to organizational outcomes within the
fraud context.
3
Understanding the individual–organization
link is important because a focus on either individual behav-
ior or the organization in isolation turns a blind eye to the
social process through which individuals’ behaviors are
in?uenced by the organization as a whole and vice versa.
In other words, a narrow focus on individual behaviors or
on the organization ignores the organization’s sociology,
which can have profound effects on fraud outcomes and
the ef?cacy of fraud prevention mechanisms.
We develop a model of fraud in organizations that al-
lows an evaluation of the relative ef?cacy of mechanisms
designed to prevent fraud while explicitly recognizing
the social processes underlying the formation of organiza-
tional norms. To develop our model, we use a method that
is relatively new in accounting research: agent-based mod-
eling (ABM). Designed to study the emergence of macro-le-
vel phenomena from micro-level interactions, ABM is well
suited to address questions involving organizational out-
comes (e.g., a culture of fraud) resulting from the interac-
tions between individuals within an organization and
organizational variables. The use of ABM confers an addi-
tional advantage: It allows us to gain insights into fraud
even when data in organizations are censored.
Our model is comprised of an organization represented
by 100 independent, heterogeneous agents (employees)
and a set of simple interaction rules. Following Cressey’s
(1953) characterization of occupational fraud (known as
the fraud triangle hypothesis), any agent in our model pos-
sessing motive, opportunity, and an attitude that frames
the fraudulent act as acceptable will commit fraud. We al-
low agents to repeatedly interact, with an eye toward
emergent aggregate fraud levels and the dynamics of fraud
over time. We begin with a benchmark model in which all
agents have opportunity and motive. We then modify our
model to investigate the impact of mechanisms to prevent
or detect fraud. We ?rst investigate the impact of modify-
ing the likelihood that agents perceive the opportunity to
commit fraud. Next, we consider a hierarchy in which
higher-level honest employees exert greater in?uence than
lower-level employees (i.e., ‘‘tone at the top’’). Then we
consider the impact of asymmetric in?uence exerted by
fraudsters relative to honest employees (which can arise
as a result of ethical training, the implementation of a code
of ethics, or a variety of other interventions). Finally, we
consider the impact of detection and termination efforts.
Two patterns emerge from the analysis of our bench-
mark model, depending upon how susceptible individual
agents are to social in?uence. When average susceptibility
is low, the number of fraudsters in the organization tends
toward a speci?c level and remains relatively stable over
time. When average susceptibility is moderate to high we
observe a very different pattern in which the number of
fraudsters in the organization vacillates over time between
extremes; either virtually no one in the organization is a
fraudster or virtually everyone is.
When we consider mechanisms to prevent or eliminate
fraud, we ?nd that their impact is contingent on average
susceptibility to social in?uence within the organization.
A reduction in perceived opportunity or the introduction
of in?uential, honest managers (tone at the top) reduces
the number of fraudsters, but neither change to our model
is effective in eliminating outbreaks of fraud when suscep-
tibility is moderate or high. Allowing honest employees to
be more in?uential than fraudsters has no qualitative ef-
fect when susceptibility is low; however, it transforms
behavior when average susceptibility is moderate to high,
reducing the number of fraudsters to near zero and elimi-
nating fraud outbreaks. The contingent nature of this effect
may prove important in fraud risk assessments performed
by auditors. We also ?nd that efforts to remove fraudsters
can effectively reduce the number of fraudsters to near
zero regardless of the level of susceptibility, but such ef-
forts do not eliminate fraud outbreaks when susceptibility
is moderate to high.
This paper continues with a brief introduction to ABM.
This methodological introduction is followed by the devel-
opment of a benchmark model of an organization with no
interventions to prevent fraud. We then modify the bench-
mark model to examine the effect of anti-fraud interven-
tions. This paper ends with our conclusions and a
discussion of the implications of our analysis.
Agent-based models
We use ABM to address our research question because
it confers several advantages. As noted by Epstein (2006),
the method avoids several shortcomings in traditional the-
oretical work in the social sciences. When aggregate
behavior is the research subject in traditional theory,
heroic assumptions about individual behavior and the pop-
ulation being modeled are typically required to maintain
tractability (e.g., the perfect rationality and homogeneity
of individual actors). While these assumptions bear little
resemblance to human behavior, it is often argued that
such simpli?cations are necessary because no rigorous
method exists that would allow their relaxation. Similarly,
in traditional theory, the notion of equilibrium plays a pre-
dominant role as a solution concept; models attempt to ex-
plain social phenomenon by identifying the behavior of
interest as an equilibrium. While this approach can yield
valuable insights, there are limits. In many cases, phenom-
ena of interest may involve disequilibrium dynamics or the
identi?ed equilibria may be unattainable either outright or
within acceptable time scales (Epstein, 2006, p. 72). Exper-
imental research in the social sciences that attempts to test
hypotheses linking heterogeneous individual behaviors to
aggregate behavioral outcomes is also challenging because
of an exiguity of theoretical work linking realistic individ-
ual behaviors to aggregate phenomena. Finally, the stove-
pipe structure of the social science disciplines (e.g.,
sociology, economics, psychology, anthropology) tends to
3
Pinto et al. (2008) discuss the ways in which corruption can exist in an
organization, with a particular focus on how individual corruption can
spread to the point where it becomes an organizational phenomenon.
Chang and Lai (2002) use econometrics to model corrupt organizations as a
pandemic arising from individual interactions. Kim and Xiao (2008)
examine the link between individual behaviors and aggregate outcomes
in the context of fraud in a public health care delivery program. In a broader
context, Davis, Hecht, and Perkins (2003) develop a model that links
individual behaviors to societal outcomes related to tax evasion.
470 J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483
limit the perspective that each discipline develops (much
like the parable of the blind men and the elephant).
4
The approach taken by ABM promises a solution to
many of the shortcomings identi?ed in traditional social
science research. The method allows for the speci?cation
of heterogeneous actors who follow simple and realistic
(boundedly rational) behavioral rules. It focuses on the
emergence of macro-level phenomena from micro-level
behavior and is therefore well suited for the study of social
phenomena (including the emergence of fraud outbreaks
in organizations).
5
Because ABM is dynamic, the natural fo-
cus of the research is on changes in behavior over time
rather than on equilibria that may never be achieved. Final-
ly, ABMs naturally cross the boundaries of the various social
sciences because of the requisite focus on modeling individ-
ual behaviors (e.g., psychology), spatial and ecological con-
siderations (e.g., anthropology), social interaction (e.g.,
sociology), and a wide range of other potential cross-disci-
plinary considerations.
A fully speci?ed agent-based model consists of agents
(e.g., individuals in an organization, traders in a market,
organizations in an economy, or trees in a forest), an envi-
ronment in which the agents ‘‘live,’’ and a set of rules that
govern agent interactions with other agents and their envi-
ronment. Agents are characterized by a collection of inter-
nal states, endowments (knowledge and assets), and
behaviors that may recognize the existence of bounded
rationality. Some of these characteristics are static, while
others can change in response to interactions with the envi-
ronment or with other agents. Similarly, environments can
be static or can change on the basis of rules or as a result of
interactions with agents. Environments can be represented
in a variety of ways. When location or resource placement
is important in a model (an issue in anthropological or eco-
logical research), the environment can be represented spa-
tially, using a lattice or a landscape developed from a
geographic information system. In economics, the environ-
ment of choice is a market (e.g., Gode & Sunder, 1993). In
research examining sociological or sociopsychological phe-
nomena (the development of a culture of fraud in organiza-
tions, in our instance), a social network may be favored
(e.g., Breiger & Carley, 2003). Finally, a set of institutional
rules is speci?ed that de?nes howagents interact with each
other and with their environment. As with agent and envi-
ronmental characteristics, these rules can be static, dy-
namic, or adaptive. A simple rule for an agent might be to
sell to another agent if the offer price is less than the bid
price or, in the context of our fraud model, to commit fraud
if the agent believes that it is acceptable behavior and if
both motive and opportunity are present.
Once the elements of the agent-based model have been
developed (usually instantiated in a computer program
6
),
agents are allowed to repeatedly interact with each other
and with the environment. As interactions occur, the re-
search focuses on the spontaneous emergence of aggregate
or group behaviors resulting from interactions at the micro
(agent) level. Epstein and Axtell (1996) characterize this ap-
proach as attempting to ‘‘grow’’ social phenomena from the
bottom up (modeling individual behavior) rather than from
the top down (directly modeling aggregate phenomena).
Thus, ABM does not involve macro models but, rather, mod-
els of individual behavior and social interaction that produce
macro-level outcomes.
Since agent-based models are simulations, they rely on
both deduction and induction. While each such model is a
strict deduction and constitutes a suf?ciency theorem(that
proves existence but not uniqueness), multiple simulations
can be thought of as a distribution of theorems that to-
gether are used to inductively test a proposition (Epstein,
2006). Thus, the ?avor of ABM research is more similar to
laboratory experimentation than to deductive proofs.
7
That
is, each instantiation of an agent-based model can be used as
an empirical observation; theoretical support can be gar-
nered for a theory through induction, but no deductive proof
obtained.
In the context of scienti?c inquiry, ABM has been em-
ployed as a tool for both prediction (akin complex econo-
metric models) and understanding and explanation (akin
to analytical models). When models are used for predic-
tion, researchers typically focus on incorporating as much
realism as possible. When models are used as a tool for
improving understanding, researchers strive for simplicity,
with the ultimate goal of incorporating only the features
necessary to generate the phenomenon of interest (Axel-
rod, 1997; Grimm et al., 2005; Miller & Page, 2007; Ragan,
2010; Tesfatsion & Judd, 2006). Because the goal of this pa-
per is to improve understanding and to provide insights
into the effects of various interventions on fraud, we adopt
the latter approach.
Benchmark model
Most (if not all) organizations face some level of fraud.
There is also anecdotal evidence of fraud outbreaks in orga-
nizations where fraud becomes institutionalized as accept-
able behavior. Consider the case of bribery at Siemens. A
newspaper article (Schubert & Miller, 2008) reports that
illegal bribe payments were so widely accepted at Siemens
that they were treated as any other line itemin the ?nancial
statements. The authors note that ‘‘bribery was Siemens’s
4
In the parable of the blind men and the elephant, a group of blind men
touch an elephant to learn what it is like. Each one feels a different part, but
only one part (e.g., the elephant’s tail, tusk, leg, etc.). The blind men
compare notes and ?nd themselves in disagreement.
5
The micro-level focus of agent-based models confers another bene?t: It
avoids the problematic representative agent assumption that is common in
macro-level models (for a discussion of the shortcomings of the represen-
tative agent assumption, see Kirman, 1992).
6
Our model employs Mathematica 7.0 (Wolfram Research Inc., 2008) as
the programming platform.
7
Epstein (1999) observes that ABM represents a new approach to
science that can be used as an instrument for either theory development or
theory testing. Rather than ?tting neatly into inductive or deductive realms,
ABM is more appropriately thought of as a generative form of science. To
explain a macroscopic social phenomenon, the generativist asks, ‘‘How
could decentralized local interactions of heterogeneous autonomous agents
generate the given regularity?’’ (Epstein, 1999, p. 41), Put another way, the
generativist’s motto is ‘‘If you didn’t grow it, you didn’t explain its
emergence’’ (Epstein, 1999, p. 46).
J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483 471
business model . . . Siemens had institutionalized corrup-
tion.’’ Organizational level fraud (or fraud outbreaks) can
arise fromthe creation of a culture of fraud in the organiza-
tion, wherein fraud grows from the bottom up, as individ-
ual employees spread a culture of fraud to others through
socialization or other means (e.g., see the discussion of
organizations of corrupt individuals by Pinto et al.
(2008)). Alternatively, organization-level fraud can be engi-
neered by the organization’s leaders and pushed from the
top down, using powerful mechanisms such as obedience
to authority (Milgram, 1963).
8
Consistent with the land-
scape of fraud observed in the natural ecology, our modeling
goal is to identify a minimal set of plausible assumptions suf-
?cient to generate organizations that experience both fraud
outbreaks and stable levels of fraud. This goal guides our
modeling choices, described below.
We base our model on Cressey’s (1953) fraud triangle
hypothesis, which still prevails as a popular view of the
necessary and suf?cient conditions for an individual’s deci-
sion to commit fraud.
9
Cressey’s characterization identi?es
three key determinants of fraud. When the conjunction of
these determinants exists, an individual will commit fraud.
The determinants are a perceived non-sharable ?nancial
need (or, more generally, a motive), a perceived opportunity
to commit fraud, and an attitude or belief that frames the
fraudulent act as acceptable behavior. In our model, agents
become fraudsters if they face a conjunction of perceived
opportunity (O), motive (M), and an attitude (A) that fraud
is an acceptable behavior, or
O ^ M ^ A $ F:
Conversely, over time, if a fraudster no longer has opportu-
nity, motive, or attitude, then he or she will reform to
become an honest agent.
10
For simplicity, we assume
that each of these variables is binary (either present or
absent).
11
Each of the agents in our model may or may not
have a motive for fraud (determined randomly with
some predetermined agent-speci?c probability at each
step of the simulation).
12
Implicit in motive is some form
of mental calculus performed by individual agents evalu-
ating the perceived costs and bene?ts of committing
fraud.
13
Over time, an agent’s motive to commit fraud
can change in response to her personal situation (e.g.,
unexpected medical bills or loss of employment by a
family member).
Opportunity is an organization-level variable that
proxies for the overall strength of a system of internal
controls. It is represented as the probability that each
agent will perceive an opportunity to commit fraud. For
example, a 20% opportunity implies that each agent inde-
pendently has a 20% chance of perceiving an opportunity
to commit fraud at each point in the simulation. An agent
might perceive such an opportunity when a loophole is
discovered in the control system (e.g., a fellow employee
fails to log off his computer or a manager ‘‘turns her
back’’).
Finally, an individual’s ability to rationalize fraud in
our model is a function of both in?uence by others within
the organization and factors exogenous to this in?uence
(i.e., events not related to the work environment, for
example, shifts in the attitudes of other reference groups
such as family and friends). The plasticity of attitude in
response to in?uence by others in the organization
(whether through socialization among rank and ?le
employees or through the command of organizational
leadership) is central to the potential for fraud outbreaks
in our model.
Characterizing agents
We begin developing our model of fraud in organiza-
tions by characterizing individual agents. In particular,
each agent is a vector whose elements indicate the
agent’s attributes (endowments and individual behavioral
rules). Each attribute is a number or a list of numbers. In
our benchmark model, agent attributes include the
following:
8
Social in?uence may also play a part in top-down fraud as more
employees participate in the activity.
9
Wolfe and Hermanson (2004) expand the fraud triangle to a fraud
diamond, suggesting capability as a fourth condition required for fraud. We
elect to build on Cressey’s original approach for two reasons. First, the
original fraud triangle has the advantage of simplicity: Capability is already
included in the hypothesis as part of opportunity. Second, the fraud triangle
remains the dominant characterization in the professional literature. For
example, it is incorporated in a discussion of the characteristics of fraud in
the AICPA’s 2002 Statement on Auditing Standards (SAS) 99, which addresses
the auditor’s responsibilities relating to fraud in an audit of ?nancial
statements.
10
Our model allows for free ?ow between the honest and fraudster
classes. In the natural ecology, such a free ?ow is not always observed. In
some cases individuals commit one fraud or a series of frauds to meet a
particular goal and then reform. As an example, a sales manager may
fraudulently record a large sale as occurring before year-end to meet his
forecast in one year but then report properly in future periods when he is
able to meet his forecast honestly. In other cases, the fraudster continues to
commit fraud in perpetuity or until discovered. This can occur when the
fraud is committed to solve an ongoing problem (e.g., living beyond one’s
means or hitting unrealistic growth expectations year after year) or if the
decision to commit fraud in one period requires future fraud to keep the
original fraud hidden. Because fraud is censored, we have no sense of the
relative frequencies of one-shot versus continued fraud. Our model permits
either type.
11
It is possible that the levels of these variables are a matter of degree in
organizations and that a high value of one variable (e.g., motivation)
compensates for the low value of another (opportunity or attitude). To
model continuous values of O, M, and A, one would likely employ a
threshold rule (where fraud occurs when the combination of the three
factors exceeds some level). We conjecture that the use of a threshold rule
in our model could lead to unanticipated responses to changes in
parameters such as the phase transition observed in the threshold model
in Davis et al. (2003).
12
At the outset, for simplicity, we assume that every agent has a motive
for fraud but the model admits the possibility of heterogeneity in motives
across individual agents.
13
Our model subsumes both fraud committed on behalf of individual
agents and fraud committed on behalf of the organization. Underlying the
mental calculus noted here, the bene?ts could accrue to the individual
committing the fraud or to the organization. Similarly, the costs arising
from the fraud could be imposed on either the individual or the
organization (see Pinto et al. (2008) for a discussion).
472 J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483
A unique integer that identi?es the agent (a ‘‘name’’).
Four independent probabilities, each drawn from a
bounded uniform distribution. The ?rst two represent
the likelihood of the agent taking on a particular
characteristic (motive for fraud and perceived oppor-
tunity to commit fraud) and the second two repre-
sent (i) the likelihood (q) of one’s attitude toward
fraud changing as a result of interacting with other
agents and (ii) the likelihood (p) of one’s attitude
toward fraud changing as a result of factors
unrelated to interactions with other agents. These
probabilities are static and, with the exception of
the opportunity likelihood, randomly determined for
each agent. The opportunity likelihood is a static
organization-level variable.
Four binary variables indicating whether a motive for
fraud is present, whether perceived opportunity is pres-
ent, whether a pro-fraud attitude is present, and, ?nally,
whether the agent is committing fraud. The presence of
motive, opportunity, and attitude is determined at each
step in the simulation for each agent, based on the
assigned probabilities above. Fraud exists if motive,
opportunity, and attitude co-exist.
The organization
To create an organization,
14
we develop a matrix. Each
row in the matrix is an agent vector. To allow for interac-
tions between agents, we represent a social network (a set
of co-workers) for each agent by adding a list to each
agent’s vector, where each element in the list is an integer
referring to another agent’s name. In our social network,
agent relationships are symmetric (if agent 1 is included
in agent 3’s social network, then the reverse is also true).
The list of co-workers assigned to each agent is randomly
determined (subject to the symmetry constraint) and re-
mains static.
Observing the organization over time
After establishing a starting population in the organi-
zation, we allow agents to repeatedly interact and up-
date agent states. Interactions between agents are
accomplished by repeatedly and randomly pairing each
agent with a member of his or her social network.
15
The pairing allows each agent to observe another. As
noted previously, the observing agent will emulate the
attitude
16
of the observed with probability q. Consider,
for example, a situation in which an agent goes to lunch
with co-workers and is told that one of them believes it
is acceptable to claim a personal meal as a reimbursable
business expense. We assume that the more often this oc-
curs, the more likely the agent will begin to rationalize
committing similar behavior. We also allow for the possi-
bility that one’s attitude toward fraud can change (with
probability p) independently of observing others inside
the organization.
In the model, agents’ attitudes about the acceptability
of fraud change according to their particular experiences
with other agents and their personal proclivities. At any
given time, agent attitudes may be heterogeneous be-
cause each agent has a unique set of characteristics and
different experiences in the organization. One particular
agent can be a fraudster at a given time while other
agents may be honest. When interacting with an honest
agent in the organization, the fraudster can trigger a
pro-fraud attitude in the honest agent (and possibly con-
vert the honest agent into a fraudster, if both motive and
perceived opportunity exist) or the honest agent can con-
vert the fraudster into an honest agent. In the case of two
honest agents interacting, one or both agents may begin
to view fraud as acceptable because of factors exogenous
to their interactions. These rules for interaction and
behavior de?ne a social dynamic. The culture changes
dynamically in response to both agent interactions and
their spontaneous behavior. The model is ‘‘bottom up,’’
in that a culture of fraud can emerge spontaneously in
the population as a result of the interactions of individual
agents with each other.
An example
Recall that our model begins with an initial organiza-
tion represented by a matrix in which each row represents
an agent and each element in a row represents an agent
attribute. For clarity, we present an example of a matrix
with a population size of ?ve:
ID pðMÞ M p q A pðOÞ O F E S SN
1 0:00449253 0 0:0242858 0:90035 0 0:95 1 0 0 1 f4g
2 0:426662 0 0:0292374 0:585986 0 0:95 1 0 0 0 fg
3 0:354574 0 0:0322799 0:511431 0 0:95 1 0 0 2 f4; 5g
4 0:0897837 0 0:036227 0:525595 0 0:95 1 0 0 2 f1; 3g
5 0:496052 0 0:0205544 0:892721 0 0:95 1 0 0 1 f3g
0
B
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
C
A
:
The elements in each column represent the following agent
attributes:
ID = agent’s unique identi?er,
p(M) = likelihood of an agent’s motive to commit fraud
changing,
M = binary variable indicating the presence of motive,
p = likelihood of an agent changing attitude as a result
of factors exogenous to agent interactions,
q = likelihood of an agent changing attitude as a result
of interactions with other agents,
A = binary variable indicating the presence of an atti-
tude supporting fraud,
14
In our model, the term ‘‘organization’’ can apply to an entire business
entity, a branch, a division, an of?ce, or even a department within an of?ce.
15
We employ an algorithm developed by Gaylord and Davis (1999) to
accomplish this pairing.
16
The model presented in this paper assumes that agent attitude is
in?uenced by other agents’ attitudes. We also evaluated an alternative
model where agent attitude is in?uenced only by other agents’ actions. The
only qualitative difference observed was in the conditions under which
perceived opportunity to commit fraud is reduced. In this instance,
organizations with moderate to high levels of social in?uence respond to
reduced opportunity in a fashion similar to that observed in our
asymmetric in?uence condition (i.e., fraud outbreaks are eliminated and
the mean level of fraud is reduced).
J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483 473
p(O) = likelihood of an agent perceiving an opportunity
to commit fraud,
O = binary variable indicating the perceived opportu-
nity to commit fraud,
F = binary variable indicating whether an agent is com-
mitting fraud,
E = binary variable to be used later when agent removal
is considered,
S = social network size, and
SN = list of an agent’s social network.
In the sample matrix above, agent 3’s likelihood of a
change in motive is 0.354574, opportunity is currently
perceived as present, no fraud is being committed,
the termination variable is set to zero, the agent’s so-
cial network size is two, and the social network con-
sists of agents 4 and 5. The matrix represents the
organization’s and agents’ characteristics for one period
in time.
As noted previously, agents are iteratively paired and
allowed to interact over time. For example, moving for-
ward one interaction period from the initial matrix above,
if agent 1 begins to rationalize fraud as a result of factors
exogenous to agent interaction, his attitude variable will
change from zero to one. Further, if we assume agent 4 is
subsequently paired with agent 1 during this period and
is in?uenced by agent 1, agent 4 will also adopt an attitude
supportive of fraud, with a consequent change in his atti-
tude variable (from zero to one). The following matrix
illustrates the result:
ID pðMÞ M p q A pðOÞ O F E S SN
1 0:00449253 0 0:0242858 0:90035 1 0:95 1 0 0 1 f4g
2 0:426662 0 0:0292374 0:585986 0 0:95 1 0 0 0 fg
3 0:354574 0 0:0322799 0:511431 0 0:95 1 0 0 2 f4; 5g
4 0:0897837 0 0:036227 0:525595 1 0:95 1 0 0 2 f1; 3g
5 0:496052 0 0:0205544 0:892721 0 0:95 1 0 0 1 f3g
0
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
A
:
In the matrix we can see that although agents 1 and 4 now
hold a pro-fraud attitude (A = 1) and both perceive the
opportunity to commit fraud (O = 1), neither has motive
(M = 0) and therefore neither commits fraud.
Benchmark model design
We use 10 unique starting organizations to investigate
our model.
17
To establish a benchmark, we initially assume
that every agent has a motive for fraud and perceives oppor-
tunity. We set the size of the population to 100 agents and
observe 15,000 interaction periods. Each agent is initially as-
signed (with a 50% probability) to either a pro-fraud or an
anti-fraud attitude.
18
Finally, we begin by allowing agents
to have a very small but heterogeneous likelihood of chang-
ing their attitude toward fraud as a result of factors exoge-
nous to agent interaction (probability p drawn
independently for each agent from a uniform distribution
from 0 to 0.005).
19
The design of our benchmark analysis
(and subsequent analysis of anti-fraud interventions) is de-
scribed in Table 1.
Table 1
Summary of model analysis.
Starting population attitude Random (n = 10) All pro-fraud (n = 5) All anti-fraud (n = 5)
Model variant
Benchmark q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95}
Opportunity q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95}
p(O) = {0.9, 0.8, . . ., 0.5} p(O) = {0.9, 0.8, . . ., 0.5} p(O) = {0.9, 0.8, . . ., 0.5}
Tone at top q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95}
Managers = {1, 2, 4, 6} Managers = {1, 2, 4, 6} Managers = {1, 2, 4, 6}
Asymmetric q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95}
In?uence c = {99, 19, 9, 5.7, 4, 3} c = {99, 19, 9, 5.7, 4, 3} c = {99, 19, 9, 5.7, 4, 3}
Termination q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95} q = {0.05, 0.10, . . ., 0.95}
e = {0.05, 0.10, . . ., 0.20} e = {0.05, 0.10, . . ., 0.20} e = {0.05, 0.10, . . ., 0.20}
For all model variants, 10 starting organizations were used. Attitude regarding fraud was either randomly assigned to agents (for all 10 organizations) or set
to anti-fraud or pro-fraud for a subset of ?ve organizations. For all model variants, average emulation likelihood (q) was varied from 0.05 to 0.95 in 5%
increments. Within each value of q, the model variant parameters (i.e., perceived opportunity, number of managers, in?uence scalar, and termination
likelihood) were evaluated at the levels indicated.
17
Our design and analysis were constrained by computational power and
practicality (approximately 5000 hour of computing time were expended).
We chose fewer organizations and more interaction periods because
additional interaction periods were low cost relative to examining
additional organizations (due to the extensive analysis required for each
organization across the range of parameters that we examine). Similarly,
additional agents (beyond 100) placed excessive demands on our compu-
tational resources and we felt that the additional insight provided was
likely to be limited.
18
For a subset of ?ve of the organizations, we examined alternative
starting conditions, where all agents start with a pro-fraud attitude or all
agents start with an anti-fraud attitude. As these starting populations
evolved, the patterns of behavior converged to match those observed in
populations where agents were initially assigned to either pro-fraud or
anti-fraud attitudes with equal likelihood. We consequently conclude that
assignment of attitudes in the starting population has no effect on
outcomes over time.
19
Our choice of a small probability here is consistent with a belief that
individuals’ attitudes regarding the acceptability of fraud are relatively
stable in response to non-organizational factors. As noted by the AICPA
(2002) in SAS 99, the ability to rationalize can be affected, in part, by one’s
attitude, character, and set of ethical values (which we believe to be stable
with only a small likelihood of change over time). This is the aspect of
rationalization captured by our small exogenous probability p. In contrast,
the likelihood of being in?uenced via interactions in the organization, q,
captures a second source of rationalization noted in SAS 99, the organiza-
tional environment.
474 J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483
Emergence: Two states
The benchmark analysis studies the effect of a system-
atic change in individuals’ tendencies to be impacted by
the behavior of others in the organization (emulation like-
lihood, q). We explore the entire parameter range by vary-
ing the average emulation likelihood in increments of 5%,
from q = 0.05 to 0.95.
20
Each agent is initially assigned an
independent probability drawn from a uniform distribution
between a minimum and a maximum value for q. The as-
signed probability is static for each agent. Since the likeli-
hood is bounded, as we approach the extremes we
manipulate either the minimum or the maximum to reach
the desired average.
21
Our analysis focuses on both state distributions in the
form of histograms illustrating the number of fraudsters
in the population that emerge and on time series graphs
illustrating the change in the number of fraudsters over
time, with an eye toward the periodic existence of fraud
outbreaks. Each histogram shows the number of periods
during which n agents are fraudsters, where n ranges from
0 to 100 (the entire organization). In Fig. 1, Panels A and B,
for example, the y-axis represents the number of periods in
which a speci?c number of fraudsters is observed, while
the x-axis represents the number of fraudsters. Panels C
and D of Fig. 1 illustrate changes in the number of fraud-
sters over time. In each time series, the y-axis represents
the number of fraudsters in a given period and ranges from
0 to 100 and the x-axis represents time (or interaction peri-
ods) and ranges from 1 to 15,000.
Two state distributions emerge in our analysis. At mod-
erate and high emulation likelihoods, the majority of peri-
ods exhibit extreme behavior in all 10 organizations,
where either virtually every agent is a fraudster or virtually
no agents are fraudsters. We call this distribution U shaped
after the appearance of its associated histogram, shown in
Fig. 1, Panel A. A typical time series associated with U-
shaped distributions is illustrated in Fig. 1, Panel C. The
time series is characterized by rapid swings between ex-
tremes. For example, in Panel C, at approximately the
11,000th pairing, a rapid shift occurs from a period in
which few agents are fraudsters to a period in which virtu-
ally everyone is a fraudster. We ?nd that the characteristic
U shape and sudden shifts between extreme states persist
across conditions ranging from very high average emula-
tion probabilities down to approximately 30%.
22
The dra-
matic shifts in behavior arise from the overwhelming
effect of emulation relative to the random effects introduced
by other parameters in the model.
At low average emulation likelihoods (30% and below),
a very different state distribution emerges in every organi-
zation that we observe. Instead of tending toward ex-
tremes, the population tends toward a speci?c level of
fraud. The shape of the associated histogram is an inverted
U, as illustrated in Fig. 1, Panel B. Notice in this example,
roughly half of the population in the majority of periods
are fraudsters. When we consider the change in fraud
behavior over time in Fig. 1, Panel D, we see that the rapid
extreme shifts in the number of fraudsters found in the U-
shaped distribution disappear for the most part. Instead,
we see smaller (noisy) movements around a speci?c num-
ber of fraudsters.
We perform additional analysis at parameter values
around the transition from a U-shaped organization to an
inverted U-shaped organization to evaluate whether the
change in state is gradual or a bifurcation point exists.
Our analysis indicates that the change is gradual. As q de-
creases, the population spends less time at the extremes
and more time at moderate levels of fraud; the height of
the upper and lower supports of the U shape in the histo-
gram decrease and the middle range becomes thicker until
organizations reach a point where the state distribution is
?at (all fraud outcomes are equally likely over time). As q
continues to decrease, the population tends toward a spe-
ci?c number of fraudsters, leading to an inverted U shape
in the histogram. The location of the transition from U to
inverted U differs slightly across different organizations
and depends on the relative values of p (likelihood of
changing attitude in response to exogenous factors) and
q (likelihood of emulating the attitude of others in the
organization). As p increases, increasingly large values of
q are required to generate a U-shaped state distribution.
High emulation likelihoods within the organization rela-
tive to external in?uences on attitude facilitate cascades
from mostly honest to mostly fraudster populations and
vice versa.
In Table 2 we provide descriptive statistics (mean and
standard deviation) to illustrate the impact of interven-
tions on the statistical properties of fraud in our models.
For the benchmark analysis, the table shows a reduction
in the average standard deviation across organizations as
q is reduced, while the mean remains relatively constant.
This pattern is consistent with the change in state distribu-
tions noted previously.
The possibility of two states of fraud dynamics observed
in our benchmark model raises an additional question: Do
efforts to prevent or detect fraud have differential effects
on the two fraud dynamics observed? We now turn our
20
While we have no direct evidence regarding the level of q in real world
organizations, research by Milgram (1965) suggests that the level of q
across organizations may vary. In the study, the extent of obedience to
authority (one aspect of emulation likelihood) was investigated at Yale and
at an of?ce building in Bridgeport, Connecticut. Subjects were more
obedient at Yale; 65% were fully obedient versus 48% at the of?ce in
Bridgeport. The study (and others conducted by Milgram) suggests that the
effectiveness of efforts to recruit (q) in our model may depend in important
ways on the organizational setting (e.g., background authority inherent in
the organization, etc.).
21
For example, if the maximum likelihood is set at 100% and the
minimum at zero, the average likelihood is 50%. Holding the ?oor constant
at zero as the ceiling is reduced from 100%, the average will drop below
50%. To examine the parameter space where averages exceed 50%, we
increase the ?oor and hold the ceiling constant at 100%. Since this approach
to manipulating the mean value of q also varies the range from which the
value of q is drawn, we performed additional analysis using a variety of
mean-preserving ranges. Our results are qualitatively similar (both time
series patterns and state distributions of fraud over time are consistent) in
both the mean-preserving and mean-shifting analyses, with the exception
that a U-shaped distribution is observed more frequently when mean-
preserving ranges are reduced.
22
Unless noted otherwise, the results are consistent and clearly
observable across all organizations and all initial fraud distributions in
the populations.
J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483 475
attention to the impact of attempts to prevent or eliminate
fraud in the organization.
Perceived opportunity
We begin our investigation into the effectiveness of
fraud prevention mechanisms by systematically manipu-
lating perceived opportunity. Our analysis examines
opportunity likelihood parameter values from 90% to 50%
in 10% increments. For each value of p(O), we investigate
the entire emulation likelihood (q) range, focusing our
attention on the two state outcomes (U-shaped and in-
verted U-shaped distributions) identi?ed during the
benchmark analysis.
When we evaluate the effect of reducing opportunity in
U-shaped organizations (with moderate and high average
emulation levels), most of the time series characteristics
are unchanged. We observe the same extreme changes be-
tween honesty and fraud at the same points in time within
an organization. The frequency of the peaks and valleys are
the same relative to the benchmark time series for each
organization, as is the duration spent in each state. How-
ever, as indicated in Table 3, when perceived opportunity
is reduced, we observe a reduction in the maximum level
of fraud (e.g., in the q = 0.95 condition, the maximum level
of fraud changes from 100% when p(O) = 1.0 to 68 percent
when p(O) = 0.50). The effect on the time series is illus-
trated by comparing the benchmark time series in Fig. 1,
Panel C to the time series in Fig. 2, Panel A. The associated
state distribution histogram is illustrated in Fig. 2, Panel B.
As opportunity decreases, the upper support of the U shape
is lowered in the histogram.
The same result emerges when we consider low emula-
tion likelihood organizations. Relative to the benchmark
analysis, the qualitative characteristics of each organiza-
tion’s time series (the frequency, duration and location of
peaks and valleys) are unchanged, but the maximum fraud
level drops as p(O) is reduced (in Table 3, for organizations
where q = 0.05, the maximum level of fraud drops from
91% in the benchmark model to 58% when p(O) = 0.5). A
time series for a representative organization is illustrated
in Fig. 2, Panel C. In Table 2, both the mean and the stan-
dard deviation of fraud are reduced as perceived opportu-
nity is reduced. The inverted U state distribution retains its
basic shape, but it is shifted to the left and becomes more
peaked (consistent with the reduced mean and standard
deviation). An illustrative histogram is presented in
Fig. 2, Panel D.
Thus, overall, we ?nd that reducing opportunity in the
organization shifts the average fraud level closer to zero
and reduces the standard deviation of fraud, but it does
not otherwise affect the shape of the distribution of fraud
over time or the nature of fraud dynamics. The two emer-
gent states observed in our benchmark model persist and
P
e
Pane
emu
el C:
ulatio
: Tim
on li
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ikelih
serie
hood
es of
d (q
f agg
) is 0
grega
0.95
ate f
5 (U-
fraud
-sha
d wh
aped
hen a
org
aver
aniz
rage
zatioon).
Pa
is
anel
0.05
B: H
5 (in
Histo
nvert
ogra
ted U
am w
U-sh
when
hape
n ave
ed or
erag
rgan
ge em
nizati
mula
ion)
ation
.
n likeelihoood (q)
Pa
lik
anel
kelih
D: T
hood
Time
d (q)
e ser
) is 0
ries
0.05
of a
(inv
aggre
verte
egat
ed U
te fra
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aud
aped
whe
d org
en av
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emullation
PPane
i
el A
s 0.9
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istog
U-sh
gram
hape
m wh
ed or
hen a
rgan
aver
nizat
rage
ion)
emu
).
ulatiion llikellihoood ((q)
Fig. 1. Illustrative results from analysis of a single organization in the benchmark model, including histogram of number of fraudsters and associated time
series. Panel A: Histogram when average emulation likelihood (q) is 0.95 (U-shaped organization). Panel B: Histogram when average emulation likelihood
(q) is 0.05 (inverted U-shaped organization). Panel C: Time series of aggregate fraud when average emulation likelihood (q) is 0.95 (U-shaped organization).
Panel D: Time series of aggregate fraud when average emulation likelihood (q) is 0.05 (inverted U-shaped organization).
476 J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483
the extreme swings between honesty and widespread
fraud in U-shaped organizations remain. The results of
our analysis suggest that, while reducing opportunity can
limit the extent of fraud in an organization, ?rm culture
and individual susceptibility to in?uence continue to play
an important role in the nature of fraud dynamics.
Tone at the top
Tone at the top is often noted as an important charac-
teristic in organizations for controlling fraud (Association
of Certi?ed Fraud Examiners, 2007). To better understand
the impact of tone at the top on dynamics in our model,
we begin by extending our benchmark analysis to create
a hierarchical organization with two levels of employees:
managers and staff. We assume that managers are more
likely than staff to in?uence the attitudes of others.
We introduce a hierarchy by adding a status identi?er
to each agent vector in the benchmark model. Agents are
randomly identi?ed as managers in the organization prior
to the ?rst period of agent interaction. Agents identi?ed as
managers are assigned a hierarchical status identi?er equal
to two (resulting in twice the impact on emulation likeli-
hood),
23
while the remaining agents are considered staff
and assigned a hierarchical status identi?er equal to one.
We use this identi?er to scale emulation likelihoods during
Table 2
Mean percentage (standard deviation) of agents who commit fraud within 10 organizations, where agent attitude (pro-fraud versus anti-fraud) is randomly
assigned in the initial time period.
Mean emulation likelihood (q) 0.05 0.25 0.50 0.75 0.95
Benchmark 50.4 (13.5) 48.1 (22.9) 52.4 (26.6) 47.8 (34.8) 51.0 (35.3)
Opportunity (p(O))
0.90 45.4 (12.4) 43.3 (20.1) 47.2 (24.1) 43.0 (31.4) 45.9 (31.8)
0.80 40.3 (12.4) 38.5 (15.9) 41.0 (20.4) 38.3 (28.0) 40.8 (28.4)
0.70 40.3 (11.2) 33.7 (15.9) 36.7 (19.0) 33.5 (24.6) 35.7 (24.9)
0.60 30.2 (8.8) 28.9 (13.8) 31.5 (16.4) 28.7 (21.0) 30.6 (21.5)
0.50 25.2 (7.6) 24.1 (11.6) 26.2 (13.8) 23.9 (17.7) 25.5 (18.0)
Tone at top
1 manager 42.5 (12.8) 33.6 (17.8) 30.1 (20.2) 15.2 (17.5) 15.4 (18.2)
2 managers 38.5 (11.6) 25.8 (14.8) 21.3 (15.8) 8.8 (11.2) 9.3 (12.1)
4 managers 32.3 (10.4) 17.2 (10.9) 13.2 (11.0) 5.0 (7.0) 4.9 (7.0)
6 managers 27.1 (9.4) 13.7 (8.9) 9.9 (8.7) 3.4 (5.0) 3.4 (5.2)
Asymmetric in?uence (c/(c + 1))
0.99 47.0 (13.0) 43.9 (22.3) 44.3 (26.6) 33.7 (32.4) 27.9 (30.1)
0.95 44.4 (12.3) 33.0 (19.5) 23.5 (19.0) 7.5 (10.7) 5.5 (8.2)
0.90 37.9 (12.0) 20.4 (13.2) 12.7 (11.3) 3.3 (5.2) 2.4 (4.0)
0.85 31.6 (10.5) 14.7 (10.4) 8.6 (8.0) 2.1 (3.5) 1.5 (2.8)
0.80 27.0 (9.6) 10.7 (8.0) 6.5 (6.1) 1.5 (2.7) 1.1 (2.1)
0.75 24.6 (8.9) 8.6 (6.3) 5.3 (4.9) 1.2 (2.1) 0.8 (1.7)
Termination likelihood (e)
0.01 28.4 (11.0) 31.9 (19.8) 33.2 (25.4) 39.2 (34.0) 36.6 (33.8)
0.05 7.4 (4.7) 8.7 (7.9) 9.2 (10.3) 11.7 (17.0) 12.4 (17.4)
0.10 3.7 (3.0) 4.2 (4.5) 4.5 (5.7) 5.3 (7.8) 5.3 (8.2)
0.15 2.3 (2.4) 2.8 (3.3) 2.9 (4.1) 3.5 (5.5) 3.7 (5.8)
0.20 1.7 (1.9) 2.1 (2.7) 2.2 (3.2) 2.6 (4.2) 2.7 (4.4)
Table 3
Maximum (minimum) fraud level observed across all organizations in the ?nal 10,000 time steps by level of emulation likelihood for the benchmark and model
variants most likely to impede fraud.
Mean emulation likelihood (q) 0.05 0.25 0.50 0.75 0.95
Benchmark 91 (9) 100 (0) 100 (0) 100 (0) 100 (0)
Opportunity (p(O))
0.50 58 (1) 68 (0) 67 (0) 68 (0) 68 (0)
Tone at top
6 managers 64 (2) 60 (0) 64 (0) 52 (0) 70 (0)
Asymmetric in?uence (c/(c + 1))
0.75 68 (0) 48 (0) 44 (0) 25 (0) 20 (0)
Termination likelihood (e)
0.20 13 (0) 33 (0) 38 (0) 50 (0) 65 (0)
23
We tested the sensitivity of the emulation likelihood scalar introduced
when interacting with a manager by increasing it from two to four. No
qualitative effect was observed on aggregate outcomes.
J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483 477
agent interactions. For example, assume agent 1 is assigned
an emulation likelihood of 0.15 when the organization is
formed. In our benchmark model, when agent 1 observes an-
other agent, agent 1 will change her attitude to match the
observed agent’s attitude with a 15% probability. However,
in our hierarchical model the likelihood of emulating an-
other agent is doubled, to 30%, when the agent observed is
a manager.
24
The notion of tone at the top incorporates more than a
hierarchical organization with in?uential management. It
is usually characterized as a management team with a con-
sistent message regarding ethical values and appropriate
behavior. To capture this idea, all of the managers in the
model are identical. Each is assigned an anti-fraud attitude
in the initial period of the simulation. To ensure their atti-
tudes do not change, the managers’ likelihood of emulating
another agent (q) and likelihood of spontaneous attitude
change (p) are both set to zero.
25
For the purposes of our
analysis, we make no other modi?cations relative our
benchmark. Motive and opportunity remain constant, at
100%. We systematically vary the number of managers in
the organization (span of control) and investigate the impact
of this manipulation over the range of emulation likelihood
(q) values (as in the benchmark model).
We ?nd that a monolithic, honest management team in
a U-shaped organization changes the characteristic shape
of the state distribution. With even one honest manager,
we see the tendency to achieve maximum levels of fraud
with high frequency disappear (the upper tail in the U
shape is gone, as illustrated in Fig. 3, Panel A).
26
A clearer
picture of the qualitative effect of the manipulation is pro-
vided by an examination of the dynamics of fraud over time.
While there is an overall tendency toward honesty in orga-
nizations with a positive tone at the top, the time series
exhibits short-lived outbreaks of fraud in the organization
(see Fig. 3, Panel B). This remains the case regardless of
the number of managers we examined. The large in?uence
exerted by management in U-shaped organizations can be
attributed to both the consistent behavior exhibited by man-
agement and the high level of susceptibility to in?uence
exhibited in the agent population.
To complete our analysis of a monolithic, honest man-
agement team, we consider its impact on the aggregate
fraud outcomes and dynamics when average emulation
(q) levels are low (i.e., inverted U-shaped organizations).
Fig. 2. Representative histograms and time series of aggregate fraud levels when perceived opportunity, p(O), equals 0.50. Panel A: Time series when
average emulation likelihood (q) is 0.95 (U-shaped organization). Panel B: Histogram when average emulation likelihood (q) is 0.95 (U-shaped
organization). Panel C: Time series when average emulation likelihood (q) is 0.05 (inverted U-shaped organization). Panel D: Histogram when average
emulation likelihood (q) is 0.05 (inverted U-shaped organization).
24
Since q is bounded (q 6 1), managers can only increase another agent’s
emulation likelihood parameter to 1, but no higher.
25
We also evaluated a hierarchical model using non-identical managers
with attitudes that can change to investigate the effect of introducing a
hierarchy. The introduction of a hierarchy by itself had no qualitative
impact relative to the benchmark model.
26
Notably, when a monolithic, dishonest management team is introduced
into the model, the mirror image of the behavior exhibited here is observed.
The lower support is eliminated and fraud becomes the prevalent behavior.
478 J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483
We ?nd that, while introducing a monolithic, honest man-
agement team reduces mean fraud level and its associated
standard deviation (as can be seen in Table 2), it has no
other effect on either the inverted-U shape of the histo-
gram or characteristics of the related time series. Further-
more, increasing the relative size of the management team
does not alter this general ?nding.
Asymmetric in?uence
Some interventions are aimed at enhancing the ethical
tendencies of employees. For example, organizations may
engage in ethical training or encourage personal adherence
to a code of ethics. A clearly communicated emphasis on
ethical behavior could have effects on both fraudsters
and others in the organization. Non-fraudsters would be
better informed about what actions constitute fraud and
engage in more careful thought before conforming with
undesirable norms (rather than thoughtless conformity to
norms). Fraudsters would feel less comfortable in their
recruitment efforts and less likely to reveal their attitudes
to others. To model these effects, we allow asymmetric
in?uence, where honest employees exert more in?uence
on their peers than fraudsters. To achieve asymmetry, we
add a scalar (c) to our benchmark model. The scalar is con-
stant across all agents because we assume that the inter-
vention would be applied across the entire population.
During agent interaction, the scalar changes the likelihood
of emulating a fraudster relative to an honest agent in the
following manner:
Q ¼ qc=ðc þ1Þ when the agent observes another agent
with a pro-fraud attitude and
Q ¼ q otherwise;
where Q is the emulation likelihood in the asymmetric
in?uence model and q is the emulation likelihood in the
benchmark model. To illustrate the application of this rule
set, assume agent A’s emulation likelihood (q) is 0.50 and
the scalar (c) is 9 in the organization. When agent A ob-
serves another agent with a pro-fraud attitude, he will
have a 45% likelihood of emulating the attitude. However,
if agent A observes an anti-fraud attitude in another agent,
he will have a 50% likelihood of emulating the attitude.
Thus, the smaller the value of c, the higher the likelihood
that an agent will emulate an honest agent relative to a
fraudster, and the more effective the ethics intervention.
To evaluate this version of our model, we systematically
vary c at six levels (99, 19, 9, 5.7, 4 and 3)
27
for every
Panel A: Histogram for U-shaped organizations illustrating Panel B: Time series for U-shaped organizations illustrating
loss of upper support in tone at the top, asymmetric fraud outbreaks under tone at the top and termination
influence, and termination model variants. model variants.
Panel C: Time series of aggregate fraud levels exhibiting no fraud outbreaks in U-shaped organizations in the asymmetric influence
model variant and in inverted U-shaped organizations in the termination model variant.
Fig. 3. Other histograms and time series of aggregate fraud levels observed in the analysis of model variants. Panel A: Histogram for U-shaped organizations
illustrating loss of upper support in tone at the top, asymmetric in?uence, and termination model variants. Panel B: Time series for U-shaped organizations
illustrating fraud outbreaks under tone at the top and termination model variants. Panel C: Time series of aggregate fraud levels exhibiting no fraud
outbreaks in U-shaped organizations in the asymmetric in?uence model variant and in inverted U-shaped organizations in the termination model variant.
27
The levels of c were chosen to scale the in?uence of pro-fraud relative
to anti-fraud attitudes to 99%, 95%, 90%, 85%, 80% and 75%, respectively.
J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483 479
emulation likelihood level used in the benchmark model so
that the effect of asymmetric in?uence can be assessed
across both U-shaped (moderate to high emulation likeli-
hood) organizations and inverted U-shaped (low emulation
likelihood) organizations. We compare the results of these
parameter sweeps to matched (identical) starting organiza-
tions examined in our benchmark model.
For U-shaped organizations, asymmetric in?uence dra-
matically affects both the shape of the state distribution
and the dynamics of fraud behavior over time. As the asym-
metry in in?uence is increased (by decreasing the scalar c),
the upper support of the U shape rapidly disappears. The
resulting state distribution resembles that observed in the
tone at the top condition, in Fig. 3, Panel A.
28
However,
the periodic fraud outbreaks observed in the tone at the
top condition are completely eliminated. As can be seen in
Table 3, the maximum level of fraud observed when
q = 0.95 is 20 at the highest level of asymmetric in?uence,
compared to 100 in the benchmark model. The resulting time
series is illustrated in Fig. 3, Panel C. Intuitively, when emu-
lation likelihoods are high and asymmetric, the number of
honest agents in the population will continue to grow until
there are a suf?cient number of honest agents to prevent
an outbreak. A very different result emerges when we ob-
serve the impact on the inverted-U distribution found in
organizations with low average emulation likelihoods. As
asymmetry in in?uence increases, the mean level and stan-
dard deviation of fraud decreases, but the inverted-U shape
of the state distribution and the qualitative characteristics
of the time series in the benchmark model are preserved.
The results suggest that the role of ethical interventions in
fraud prevention is contingent on the nature of the organiza-
tion, a relation not previously recognized in the literature
that could prove important in fraud risk assessment.
Removing fraudsters from the organization
Our investigation so far has focused on organizational
interventions associated with fraud prevention. We now
turn our attention to the effect of detecting and eliminat-
ing fraud in the organization through the termination of
fraudsters. To model termination, we assume that fraud-
sters will be detected with some probability t(e). Once de-
tected, agents are removed from the organization
(‘‘terminated’’) and replaced with a new agent.
We expect the existence of budget constraints with re-
gard to termination efforts. As a result, we assume fraud
detection and termination programs will be more success-
ful in organizations with lower levels of fraud. At higher
fraud levels, we anticipate that collusion among employees
will impede such efforts. Therefore, in each period, we
determine the likelihood of detection and termination as
tðeÞ ¼ eððN À f Þ=NÞ;
where t(e) is the likelihood of detection and termination, e
is the likelihood of detection and termination unadjusted
for the number of fraudsters in the organization, N is the
number of agents in the organization (N = 100), and f is
the number of fraudsters in the organization at the start
of the simulation period.
29
When a fraudster is discovered and replaced, our termi-
nation model assigns new values for all agent attributes
(using the process described in the benchmark model),
with the exception of the agent identi?er (ID), social net-
work (SN), and social network size (S).
30
These three attri-
butes remain unchanged under the assumption that when
an agent is replaced, the new agent will interact with the
same individuals as the previous one. Our analysis of the ter-
mination model evaluates the effect of a change in detection
and termination likelihood (e) over the entire range of emu-
lation likelihood values examined in the benchmark model
to investigate the impact of termination on our two classes
of organizations (U shaped and inverted U shaped). In our
analysis, e is examined at ?ve levels: 0.01, 0.05, 0.10, 0.15
and 0.20.
When we consider organizations with moderate to high
average emulation likelihoods (U-shaped organizations),
we ?nd that the introduction of a termination regime leads
to results similar to those observed in the tone at the top
model. The upper support of the U-shaped state distribu-
tion is gone (a tendency toward low levels of fraud), while
periodic fraud outbreaks persist in the time series (see Pan-
els A and B of Fig. 3). For organizations with low emulation
likelihoods, we ?nd the ?rst instance of an intervention
triggering a dramatic change in the inverted-U shape of
the state distribution. As the likelihood of detection and
termination increases, the level of fraud approaches zero
(the state distribution resembles Fig. 3, Panel A) and fraud
outbreaks are not observed in the time series (see Fig. 3,
Panel C). Our analysis suggests that detection and termina-
tion efforts can be effective at reducing average fraud lev-
els to near zero in both types of organizations (U and
inverted U shaped). However, the effectiveness of such ef-
forts at preventing widespread fraud outbreaks appears
contingent on the type of organization and related individ-
ual susceptibilities to fraud.
Discussion and conclusions
We use an ABM to investigate the dynamics of fraud
within organizations and the impact of fraud prevention
and detection mechanisms. Our model consists of an orga-
nization, agents (employees), and a set of simple social
interaction rules. In accordance with Cressey’s (1953)
occupational fraud model, any agent within our model
possessing the conjunction of motive, opportunity, and a
pro-fraud attitude commits fraud. We allow agents to
repeatedly interact, resulting in changes in agent attitudes
28
If our asymmetric in?uence model were re-conceptualized to examine
a setting where fraudsters have more in?uence that honest agents, the
lower support in U-shaped organizations would be eliminated, with fraud
becoming the dominant behavior.
29
Presumably, the introduction of a termination regime might also
decrease agents’ perceived opportunity or motivation to commit fraud.
However, for the purposes of our analysis, we investigate effects indepen-
dently as an initial step toward understanding our model.
30
While we assume newly hired agents are randomly selected from the
general population, one could also model an organization where hiring is
biased toward a particular type of agent. For example, an organization of
fraudsters might be more likely to hire another fraudster (or someone who
believes fraud to be acceptable behavior).
480 J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483
toward fraud (via cultural transmission). We ?nd that two
types of organizations emerge, depending on how suscep-
tible individual agents are to social in?uence. When aver-
age susceptibility to in?uence is low, a state distribution
emerges where aggregate fraud levels tend toward a spe-
ci?c level of fraud. When average susceptibility is moder-
ate to high, we observe an outcome characterized by
extreme swings in behavior from an overall honest organi-
zation to an overall fraudulent one.
After identifying these two types of organizations, we
turn our attention to the effect of mechanisms to prevent,
detect, and eliminate fraud. We examine the effects of
decreasing perceived opportunity to commit fraud, tone
at the top, asymmetric in?uence (resulting from ethical
interventions), and the removal of fraudsters from the
organization. We ?nd the effectiveness of these mecha-
nisms is contingent on the type of organization. Our ?nd-
ings are summarized in Table 4.
The model suggests that ethical interventions aimed at
increasing the in?uence of honest employees relative to
fraudsters are particularly effective for moderate to high
average emulation likelihood organizations. However, eth-
ical interventions are observed to be much less effective for
organizations with low emulation likelihoods. A different
result emerges when we consider the impact of efforts to
detect and remove fraudsters from the organization. Fraud
is reduced to near zero in both types of organizations when
the likelihood of terminating fraudsters is increased to
0.20. However, increasing the likelihood of termination
does not prevent occasional outbreaks of widespread fraud
in U-shaped organizations. The introduction of a mono-
lithic, honest management team (tone at the top) effec-
tively reduces the amount of fraud in both types of
organizations. Furthermore, while it eliminates the ten-
dency to achieve maximum levels of fraud with high fre-
quency in U-shaped organizations, it does not eliminate
sporadic, short-lived fraud outbreaks. Reducing opportu-
nity (e.g., through stronger internal controls) merely re-
duces the average mean level of fraud and associated
standard deviation within an organization. In our model,
reduced opportunity does not affect other aspects of fraud
dynamics, regardless of emulation likelihood levels.
The intuition behind these results lies in the relation be-
tween each intervention and the emulation likelihood, q.
Reduced opportunity has no impact on q in our model
and fraud dynamics are not affected under the interven-
tion.
31
Every other intervention affects the dynamics of
fraud. In every case, the effects on dynamics can be traced
to the interaction of each intervention with q. Ethical inter-
ventions (asymmetric in?uence) directly impact the value of
q. Tone at the top affects q for some interactions (those be-
tween a manager and staff) and termination introduces new
agents (each with a new q) into the organization. Since each
intervention affects q differently, they each have a different
impact on fraud dynamics.
Our ?ndings have important implications for auditors
and other individuals responsible for assessing fraud risk
and detecting and preventing fraud. First, for certain types
of organizations aggregate fraud levels can vary tremen-
dously over time. Furthermore, the effectiveness of mech-
anisms to prevent and detect fraud can be contingent on
the type of organization and related individual susceptibil-
ities to social in?uence. Therefore, it may be inappropriate
for auditors to evaluate fraud prevention and detection
mechanisms in a uniform manner. Our results suggest that
the same fraud prevention and detection mechanisms
implemented in a similar manner in two different organi-
zations cannot be expected to be equally effective without
considering the average susceptibilities to social in?uence
of the individuals therein.
32
Similarly, some mechanisms
can appear effective most of the time but still be ineffective
at preventing outbreaks of fraud. In general, there is no one-
size-?ts-all fraud prevention (and/or detection) mechanism
and fraud risk may be contingent on individual susceptibil-
ities to social in?uence in the organization.
Table 4
Summary of ?ndings.
Intervention Effect on U-shaped organization Effect on inverted U-shaped organization
Perceived opportunity Upper support lowered Average fraud level reduced
Dynamics preserved Dynamics preserved
Spontaneous outbreaks persist
Tone at the top Upper support removed Average fraud level reduced
Spontaneous outbreaks persist Dynamics preserved
Asymmetric in?uence Highly effective Average fraud level reduced
Upper support removed Dynamics preserved
Stops spontaneous outbreaks
Termination Upper support removed Highly effective
Spontaneous outbreaks persist Fraud reduced to near zero
No spontaneous outbreaks
31
The behavioral response to varying motivation in agents is the same as
the behavioral response to changes in opportunity because, like opportu-
nity, motivation is independent of q. Consequently, decreasing motivation
decreases the average level of fraud. In the case of U-shaped organizations,
the decrease is exhibited through a reduction in the maximum level of the
upper support in the histogram. In the case of inverted U-shaped
organizations, the distribution is simply shifted toward the origin. Because
both motivation and opportunity are independent of q, we do not expect
interaction effects between these variables and our model variants that do
affect q.
32
We conjecture that it might be possible to develop an instrument to
measure differences in q across organizations (e.g., see Bearden, Netemeyer,
& Teel, 1989) and that such an instrument might be useful to auditors in
their assessment of fraud risk and the relative effectiveness of anti-fraud
interventions.
J.S. Davis, H.L. Pesch/ Accounting, Organizations and Society 38 (2013) 469–483 481
While the ABM method used in our investigation con-
fers a number of advantages over traditional models in
the social sciences, it presents limitations as well. First,
seemingly innocuous assumptions have sometimes been
shown to have unexpected consequences that are not yet
fully understood (e.g., Huberman & Glance, 1993). In the
context of our model, additional research might examine
alternative updating rules (e.g., one alternative model
might randomly select an agent and then randomly deter-
mine whether the agent will interact with another agent or
make a decision about committing fraud). The results we
report may also be sensitive to other modeling choices.
For example, we use Cressey’s (1953) fraud triangle to rep-
resent the agent’s decision to commit fraud. Other formu-
lations are possible, such as the fraud diamond (Wolfe &
Hermanson, 2004) or perhaps a utility-maximizing ap-
proach. Our characterization of a social network assumes
a static organization with uniform mixing for the sake of
simplicity. An alternative model might assume a dynamic
network with local mixing or local mixing together with
random connections among agents. Other characteriza-
tions of social in?uence (e.g., normative social in?uence
in lieu of paired recruitment) could also have an impact.
The second limitation associated with ABMis that the solu-
tion concepts employed tend to be relatively weak and, to
date, there has been little formal work on the replicability
of results using different models (but see Axtell, Axelrod,
Epstein, and Cohen (1996) for an exception). Finally, ABM
still lacks a set of standard, generally accepted practices.
Our initial investigation of fraud leads to a variety of
additional opportunities for future research. Our analysis
examines speci?c changes to our model in isolation. Our
design choice was driven by a desire to develop a deeper
understanding of the effects of various approaches taken
to control fraud; however, in organizations, speci?c inter-
ventions are seldom implemented alone. The relative ef?-
cacy of combining different interventions could be
investigated.
A more detailed examination of each leg of the fraud tri-
angle could be undertaken. Future research might re?ne
our characterization of motivation by explicitly consider-
ing social psychological factors in the organization. Equity
theory (Adams, 1965) suggests that an honest individual in
an organization replete with fraudsters would be more
likely to have a motivation to commit fraud in order to
reestablish fairness in their relationships with co-workers
and the organization. Our model could be modi?ed to
incorporate this effect by making motivation a function
of the number of fraudsters in the agent’s social network.
Our model ignores ancillary changes in motive, oppor-
tunity, and attitude that might result from the interven-
tions that we investigate (or from social changes and
other forms of regulation). For example, our model’s repre-
sentation of the detection and removal (termination) of
fraudsters ignores the deterrent effect that can be gener-
ated by an active termination programand concomitant ef-
fects on motivation. Future research could extend our
study to incorporate these correlated effects. Our model
also ignores the magnitude of fraud (dollars lost). Instead,
we focus on the number of fraudsters in the organization.
Insights on the magnitude of fraud might be gained by
adding a ‘‘dollars available’’ variable to the model. Perhaps
this variable could be linked to one’s position in the orga-
nization (manager versus staff). Finally, while our model
allows for selection in the termination intervention, it does
not select on the basis of relative ?tness (allowing those
more skilled at fraud to avoid detection). Our model could
be extended to investigate fraud in this evolutionary
context.
Acknowledgements
The authors acknowledge ?nancial support provided
the American Institute of Certi?ed Public Accountants
(AICPA) Center for Audit Quality. The paper bene?ted from
comments provided by David Piercey and participants at
the Queens University Fraud Conference, the University
of Illinois Audit Symposium, and the Fraud in Accounting,
Organizations and Society Conference. We also acknowl-
edge comments from two anonymous reviewers.
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