Draft 9/11/08
Personal versus Situational Dynamics: Implications of Barry
Richmond’s Models of Classic Experiments in Social Psychology*
James K. Doyle, Khalid Saeed, Jeanine Skorinko
Department of Social Science and Policy Studies
Worcester Polytechnic Institute
ABSTRACT
There is a long-standing debate in the field of social psychology as to which is the primary
determinant of behavior, the situation or system in which people act or the personalities of the
role players. Psychologists have long studied this problem with controlled experiments on human
subjects, and have now come to a general resolution of the debate. However, the field of
psychology still lacks an efficient method for teasing apart the relative contributions of personal
and situational variables in applied domains. An alternative to human subjects experiments is to
employ system dynamics models of role systems, as was demonstrated by Barry Richmond when
he attempted to model two classic experiments in social psychology: the Milgram and Stanford
Prison experiments. In this paper, we replicate and discuss Barry Richmond’s models to present
them to a new audience. In addition, we use the models as a springboard to explore the
relationship between social psychology and system dynamics and the potential for useful
collaboration between the two fields.
1. Introduction
The disciplines of system dynamics and social psychology would appear to have a natural
affinity for each other. Despite their widely varying methodologies (computer simulation versus
experimentation on human subjects), both disciplines offer similar explanations for human
decision making and behavior. In system dynamics modelers constantly make the claim that
“structure drives behavior,” meaning that the physical structure of the system, how the stocks
“ Based on an essay written by the authors for a volume in memory of Barry Richmond to be
published by isee systems, inc.
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and flows are interconnected, is often a stronger determinant of system behavior over time than
the specific values of parameters. Similarly, in social psychology experiments often reveal that
the situation or role structure in which behavior occurs is a stronger predictor of cognition and
behavior than the precise makeup of an individual’s character, personality, or habits of thought.
Thus, both fields conceive of the individual decision maker as being embedded in an external
system whose properties can have a strong influence over behavioral outcomes.
But despite the similarity in theoretical approach, there has historically never been much
interaction between the two fields. Few psychologists have made the effort to learn the system
dynamics approach and apply it to the understanding of social behavior. Social psychologists, in
fact, only rarely use any form of computer simulation to develop and test their theories. At the
same time, few system dynamicists have attempted to apply the system dynamics method to such
socially relevant topics as the nature of obedience, group dynamics, persuasion, aggression, or
prejudice, that is, to the standard topics of social psychological inquiry. When such topics are
included in system dynamics models, they are often done so without reference to the large
experimental literature in social psychology.
There has, however, been one particularly notable exception to this lack of synergy between the
two fields: Barry Richmond’s attempt to replicate classic experiments in social psychology
using system dynamics. Barry joined the system dynamics doctoral program at MIT in 1975
and, along with his fellow doctoral students in the Sloan School of Management (including one
of the present authors), took a mandatory seminar in behavioral science. A particularly
fascinating part of this seminar was the presentations by Professor Edgar Schein of two highly
influential and somewhat disturbing social psychological studies: Stanley Milgram’s obedience
experiment (Milgram, 1963, 1974) and Philip Zimbardo’s prison simulation study, known as the
Stanford Prison Experiment (Haney et al, 1973; Haney and Zimbardo, 1976). [Readers
interested in learning more about the Milgram obedience studies would do well to begin with the
work of Thomas Blass, a Milgram scholar who maintains a website on Milgram and his work at
http:/Avww.stanleymilgram.com and who has published the definitive biography of Milgram,
The Man Who Shocked the World (Blass, 2004). Philip Zimbardo maintains a website on the
Stanford Prison Experiment at http://www.prisonexp.org/ and has recently for the first time
published his personal recollections of the experiment in his book, The Lucifer Effect (Zimbardo,
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2007a).] These two studies are often cited as the prototypical examples of a widespread
phenomenon in social behavior that psychologists refer to as “the power of the situation,” that is,
the ability of circumstantial or situational factors external to the individual to overwhelm the
influence of individual differences and personality factors, resulting in identical behavior from
very different people. Both experiments placed their human subjects in a difficult situation and
set up a conflict between the values of the individual subjects and the demands of the situation.
In the Milgram obedience studies, subjects were asked to obey the instructions of the
experimenter to deliver painful electric shocks to a fellow subject. In the Zimbardo experiment,
subjects were asked to play the role of prison guard in a simulated prison environment. Which
would matter more? The personal traits of the individuals or the situational pressures created by
the roles they were asked to assume? Would the subjects follow their individual values or adapt
their behavior to fit the demands of the experimenter or the role they were asked to play? The
surprising and disturbing result in both cases was that a majority of subjects took actions to harm
or denigrate others that prior to the experiment they would never have dreamed they were
capable of doing.
Barry, who also held a Master’s degree in psychology, walked away from these presentations
with what, for the time, was a very radical idea, namely, that the experiments could conceivably
be conducted on a computer using system dynamics modeling rather than employing real human
subjects. Despite being new to the field, Barry took on the challenge of building a system
dynamics model of the Milgram experiment, and produced a fascinating technical report
describing the model and his experimentation with it (Richmond, 1977). Later in his career, with
more experience under his belt, Barry also built a more elegant model of the Zimbardo
experiment. This model was never fully written up but was made available to the authors with
the kind assistance of isee systems. It is briefly described in a paper published by Barry in the
System Dynamics Review (Richmond, 1993).
This paper attempts to bring these two previously unpublished social psychological models to
light and evaluate their potential for guiding future research and education in
socialpsychology. Toward that end the models have been translated from the original Dynamo to
iThink, updated according to current system dynamic practice, and modified to allow easier
experimentation with parameters. For both the Milgram experiment and the Stanford Prison
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Experiment, an introduction, focusing on the experiences of the subjects involved, is provided
for readers who are unfamiliar with the details of the studies. Each introduction is followed by a
presentation of Barry Richmond's system dynamic model of the experiment, along with sample
computer simulation runs. Finally, in the concluding sections the models are used as a
springboard to address several important questions at the interface of system dynamics and social
psychology of current relevance, including: Why has there historically been such little
interaction between the two fields? What would be the benefits of more interaction in the future?
How suitable is the system dynamics methodology for exploring social psychological topics,
compared to other modeling paradigms?
2. The Milgram Experiment
After World War II, the world, shocked by the atrocities committed by Nazi soldiers onto the
German Jews, wondered what could make the Nazis such an evil group of people. In the midst
of this outrage against Nazi Germans, Stanley Milgram, interested in the influence of the
situation on individuals, wondered if it was that the Nazi’s were naturally evil people or whether
anyone, given the right situation, might commit similar acts. It was from this question that he
designed his now-famous obedience experiments.
In the first experiment, Milgram advertised in the local New Haven, Connecticut newspaper,
inviting individuals to be paid to participate in an experiment on learning. Interested participants
arrived at the Yale University lab, and were greeted by the Experimenter (dressed in a laboratory
coat), and met another “participant”, Mr. Wallace. Unbeknowst to the participant, Mr. Wallace
actually worked for the experimenter and was only pretending to be another participant (called a
confederate).
After the introductions, the Experimenter informed both the participant and Mr. Wallace that the
study is about learning and punishment. The experimenter also informed them that one of them
would be randomly assigned to be the Teacher and the other the Learner. While the participant
and Mr. Wallace drew sticks to see who would play each role, the experiment was set up such
that the participant always ended up being the Teacher and Mr. Wallace ended up as the Learner.
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The Experimenter then explained that the Teacher would be teaching the Learner word-pairs, and
the Learner would need to accurately recall the word pairs or they would be punished via electric
shocks. With each incorrect response, the intensity of the shocks increased by 15 volts.
After explaining the tasks, the Learner took a seat, and the Experimenter strapped electrodes onto
the Learner. While being strapped in, the Learner informed both the Experimenter and the
Teacher that he had a heart condition, and the Experimenter assured the Learner that while he
would feel pain from the shocks that his heart would experience no adverse effects. To ensure
that the Teacher understood the intensity of the shocks (and to provide the Teacher with a mental
cue of the pain the Learner would be withstanding), the Experimenter gave the Teacher a sample
low-intensity shock (that was still quite painful).
After getting the Learner set up in their room, the Experimenter showed the Teacher into another
room to see the “shock generator” (Kassin, Fein, & Markus, 2008). The generator had switches
that increased in 15 volt increments from 15-450 volts, and the highest voltage (450 volts) was
labeled “XXX”. The Teacher was reminded to increase the shocks by 15 volts each time the
Learner incorrectly answers a word-pair. Then the experiment began.
At first, the experiment went smoothly, as the Learner recalled the word-pairs correctly, and the
Teacher probably felt little if any anxiety. But as time went on, the Learner’s performance
declined, and the shock intensity needed to be increased, and the anxiety felt by the participant
(the Teacher) most likely increased as well. By observing the behavior of the Teacher and
measuring the maximum voltage that the Teacher would give the Learner before stopping the
experiment, Milgram hoped the experiment would enlighten him on how far would be too far to
go when administering the shocks, or when might the anxiety of doing something harmful to
another person override obeying an authority figure.
To aid in the reality of the situation (and make the harm on the other person more apparent), the
Teacher began to hear reactions from the Learner based on the shock’s intensity. When the
voltage ranged from 75-135, the Teacher heard the Learner yell, “Ugh”. When the intensity
increased to 150 volts, the Learner screamed “Ugh! Experimenter! That’s all. Get me out of
here. I told you I had heart trouble. My heart’s starting to bother me now. Get me out of here,
please. My heart’s starting to bother me. I refuse to go on. Let me out” (Milgram, 1963).
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And, at 330 volts, the Learner yelled, “Let me out of here” repeatedly. After 330 volts, the
Learner went silent. Thus, the Teacher most likely began to feel two types of increasing anxiety:
one over the fact they had to administer increasingly powerful shocks to the Learner, and two
over the reactions and screams given by the Learner to the increased intensity of the shocks. It is
important to point out that after the Teacher and the Experimenter left the Learner in the room,
the Learner (Mr. Wallace), removed himself from the shocking machine and played a tape
recording of his reactions given the voltage being administered.
Often after the first few reactions by the Learner and most likely due to increased felt anxiety
due to both the reactions and the increasing intensity of shocks needing to be administered, the
Teacher would look to the Experimenter for guidance or advice on what to do, especially after
the Learner asked to be let out of the experiment (at 150 volts). If the Teacher looked to the
Experimenter for guidance, the Experimenter responded in one of four scripted responses:
“Please continue”, “The experiment requires you continue”, “It is absolutely essential that you
continue”, or “You have no other choice, you must go on”. The Experimenter did nothing more
than make one of those four statements. Yet, the insistence by the Experimenter to continue the
experiment provided the participant (the Teacher) with one additional avenue for feeling
increased anxiety. The Teacher needed to weigh the anxiety they felt for simply administering
painful shocks, the anxiety they felt for the pain they were clearly inducing on the Learner, the
anxiety they felt for obeying an authority figure (the Experimenter) who stated that no real harm
was being done, and the anxiety they felt for not letting the Experimenter down and helping them
conduct their experiment.
What happened? Twenty-six out of 40 men (or 65 percent of the participants) “shocked” the
Learner to the maximum 450 volts. Were there any limits to these findings? Milgram (1974) ran
several replications to this original study. One key factor that did not play a role was gender. In
one subsequent study he found that sixty-five percent of the female participants shocked to the
maximum voltage—replicating the results when using male participants.
But, several other factors did result in lowered obedience by participants. First, the proximity to
the victim slightly reduced compliance. When the Learner (or victim of the shocks) was simply
in the same room as the Teacher, 40% of the participants gave the maximum shock. And, if the
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Teacher had to physically touch the Learner, and place the Learner’s hand on the shock plate,
then 30% of the participants continued to the maximum 450 volts. Felt anxiety may explain these
results. The more the Teacher had to face the victim (the Learner) and the pain they were
administering, then the more anxiety they felt and the more likely they were to want to witness
the harm they were inflicting—regardless of the presence of the Experimenter and anxiety felt
for trusting and keeping the Experimenter happy.
In addition, factors relating to the authority figure also contributed to reductions in obedience.
First, the presence of an authority figure played a key role. If the Experimenter left the room to
leave an ordinary member of their staff to run the experiment, then only 20% of the participants
shocked all the way. Likewise, the proximity of the Experimenter played a key role as well. If
the Experimenter administered the experiment from a different room, then again only 20% of the
participants obeyed and shocked to 450 volts. And, if the Experimenter never gave any of the
four prods (or commands described above), than very few (less than5%) of the participants
administered the maximum shock. Again, felt anxiety may help explain these results, as less
anxiety would be felt if the participant did not have to face the disappointed Experimenter.
And, the presence of other dissenting/rebelling participants led to increased rebellion on behalf
of the participant. If the experiment was run such that confederates pretending to be other
participants refused to continue shocking, then less than 10% of the participants would continue
shocking (especially to 450 volts) as well. In this case, the social influence of seeing someone
else refuse to continue provided the participant with an excuse to stop for both normative and
informational reasons. First, they may not have wanted to be the only ones not to stop running
the study. And, second, they may have believed that the other participants who were refusing to
continue had a reason to do so, or knew something about the situation that they did not know.
In conclusion, Milgram’s obedience studies have had important implications for a variety of
social science disciplines and remain “the most famous series of experiments in social
psychology” (Brown, 1985). First, the findings raised awareness of the importance of the
situation in possibly overriding personality traits. Second, it also raised the issue of ethics in
conducting research and raised questions about the delicate balance between the risks to
participants (e. g, the emotional distress they felt at harming another individual) and the benefits
Page 7 of 34
gained from the empirical exploration. In reaction to the findings, the Milgram study has been
replicated investigating many different factors (many explained above) in many different
countries, and at many different times, and each time the results are replicated. For instance,
ABC primetime (2007) replicated the original Milgram study (but stopped the study at 150
volts), and found similar results to Milgram. Sixty-five percent of men and 73 percent of women
administered painful shocks to the Learner. And, surprisingly, even when they ran a version of
the study where a confederate refused to continue the experiment, 63 percent of the participants
continued to administer painful shocks. In addition, Meeus & Raaijmakers (1995) replicated the
original Milgram study, but instead of relying on administering physical pain on an ostensible
other participant, they were instructed to administer psychological pain. In this study, the
participants were told that the researchers were interested in the effects of stress on test taking.
Therefore, the participants were instructed to distract a test-taker with harassing remarks.
Ninety-two percent of the participants made all 15 harassing statements--even with protests and
pleas from the applicant to stop. Thus, the take home message is that given the right situation,
any individual might do things that even they could not imagine they would do.
3. The Milgram Model
Barry originally formulated the dynamic hypothesis underlying the decision process in
Milgram’s experiment as shown in Figure 1. It consisted of two major negative feedback loops
that assured delivery of the voltage up to the implicit goal of the system as determined by the
personality-related parameters of the subject and the specification of the experimenter.
Level. of + Subjects Reluctance
Punishment Administered’ So to Continue Administering
by the Subject ft Punishment
5 +
Subject'e Willingness Insistence
oop z to Continue Adninistering by Authority
aDaxistnent rogee8
+ +
Resistance Exhibited Subject's Maxime Aecept-
by Véetin able Level of Pantehment
Fig. 1. Barry Richmond’s original causal loop diagram describing behavior
in the Milgram experiment. From Richmond (1977).
Page 8 of 34
We have reformulated the model in four sectors using the ‘Think hierarchy: Punishment
delivered, Decision to Continue, Anxiety, and Termination of the Experiment. The structure
and information relationships among the Punishment Delivered and Decision to Continue sectors
are shown in Fig. 2. The experiment is terminated when the total punishment delivered to the
victim exceeds a value
oo punishment Ad
total punishment
delivered to victim
time to delive
punishment
rate of punishfaent
delivered to victl
effect of resistence
by victim
anxiety from
voltage
l L 1 1
ee] decision to continue aX 8
fe
subject willingness to resistence
termination continue delivering by victim
multiplier punishment
max acceptable
level of punishment
resistence.
by subject
rate of decrease
in max acceptable
‘el of punishment
rate of increas
max acceptable lev
insistence by of punishment _ mara
authority effect of insistence ;
a resistance
by authority sw
Fig. 2. Punishment Delivered and Decision to Continue sectors of the Milgram model.
Page 9 of 34
set by the experimenter. It can also be terminated due to the anxiety level of the subject or
his/her willingness to continue to inflict punishment. Termination, in turn, ends anxiety,
punishment, and the decision to continue. Both punishment and the decision to continue fuel
anxiety. The instantaneous rate of punishment delivered to the victim is measured in volts/unit
time. This punishment is accumulated into a stock for driving the experimenter’s termination
process. Volts increase over time and are an exogenous input to the system as the experiment
continues. Volts create anxiety on the part of the subject, while also invoking resistance by the
victim and together with the criterion “ max acceptable level of punishment” determine the
willingness of the subject to continue punishment. Anxiety from voltage is eliminated when the
subject decides to terminate the process. The maximum acceptable level of punishment is a
stock whose increase is determined by insistence by authority, and can also change when the
subject resists or his willingness to continue wanes. The maximum acceptable level of
punishment also drains as the victim pretends to show resistance. We have added to Barry’s
original model a “moral resistance switch” that slows down the rate of increase of the maximum
acceptable level of punishment. This allowed us to change the intrinsic value of the moral
resistance a subject brings into the experiment. Barry probably would have approved of this
alteration since his model of the Stanford Prison Experiment, which he developed much later,
has built-in switches that allow a user to change personality factors in the role system the model
portrays.
Fig. 3 shows the anxiety sector of the model. The growth in the level of anxiety is driven by the
existing level of anxiety, the rising voltage, the resistance shown by the victim, and the insistence
by the authority. Anxiety decays as a first order function of the anxiety stock, but is drained
rapidly when the subject terminates the experiment. We have added to the original model an
“empathy switch” that allows us to specify another personality factor -- the empathetic nature of
a subject. We assume that anxiety will grow faster in case of a more empathetic subject.
Additional personality factors could be added to the model in terms of parameters that can be
exogenously changed, although we restricted our current experiments to changes only in
empathy and moral resistance levels of the subjects.
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Figure 4 shows how the experiment might end -- through anxiety and unwillingness to continue
by the subject or when the experimenter has determined that the maximum level of punishment
has been reached.
The model equations are placed at Annex A.
0 [) anxiety azaRX a |
insistence by maximum .
authority anxiety ®———* normal anxiety
growth fraction
anxiety from anxiety
insistence by decrease
authority rate
resistence
by victim @
anxiety from
resistence anxiety decrease
rate termination coefficient
heey multiplier
from voltage
Fig. 3. Anxiety sector of the Milgram model.
Page 11 of 34
a] termination aA~a
subject termination, willingness to
continue delivering
punishment
subject
termination anxiety termination
multiplier —— llevel-or
anxiety,
maximum
anxiety
total punishment
experimenter . __ delivered to
termination
maximum volts
Fig. 4. Termination of the Experiment sector of the Milgram model.
Figure 5 shows a computer simulation run of the experiment. An exogenous growth in volts
delivered drives the system. The level of anxiety, the maximum acceptable level of punishment,
the total punishment delivered to the victim, the resistance by the victim and the insistence by the
authority grow concomitantly until the experiment is terminated. The graph representing
insistence by the authority has a peculiar pattern that results from three nonlinear graphical
functions operating in tandem that create a complex net shape. Barry as a mature practitioner of
system dynamics would probably frown upon such a structure, but remember that this model was
developed during his first year at MIT!
Figure 6 shows the relationship between anxiety and maximum acceptable level of punishment,
which grows concomitantly because insistence by authority mitigates the resistance created by
anxiety. Three
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Ss 1: level of anxiety 2: max ...nishment 3: total... to victim 4: resis...by victim 5: insis... authority
b 500 4 = a
3 6000 Resistance
qj 1 By/victim 2: 7 2:
5
7 Max acceptable
punishment]
Insistence
1: 30
2: 300 By authority
3 30005
4
5 1
4 Level of anxiety
iy te)
2: 100 Total punishment
: Q delivered
‘| 07 T T 4 t 4
0.00 12.50 25.00 37.50 50.00
Page 1 Time 2:54 PM Thu, Jun 12, 2008
Figure 5: Simulation run of the Milgram model.
cases are shown: a subject with an “average” personality, a subject that is more empathetic than
average, and a subject with an above average level of moral resistance. As would be expected, a
moral subject terminates the experiment at a low level of punishment; however, an empathetic
subject does not terminate the experiment, but only takes longer to get to the design level of
maximum punishment. In the latter case, the insistence by the authority mitigates empathetic
behavior while in the former case, moral resistance effectively works against the rise in the
acceptable level of punishment.
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Ss max a...shment v. level ...anxiety: 1 - 2 - 3
5004
Baseline
behavior
Empathetic
behavior
3004
max acceptable level of punishment
Moral behavior
T T ]
oO 30 60
Page 3 level of anxiety 3:22 PM Wed, Jun 11, 2008
NdeBF ? Untitled
Fig. 6. Relationship between anxiety and maximum acceptable level of punishment in the
Milgram model.
4. The Stanford Prison Experiment
Also interested in the effect the social situation has on individuals, Philip Zimbardo and
colleagues (1973) decided to try to understand prison behavior. Unable to put participants inside
a real prison, Zimbardo created his own prison in the basement of Jordan Hall (the psychology
building) at Stanford University. Like Milgram, Zimbardo advertised in newspapers to solicit
participants. Interested participants were screened for mental illness and proclivity towards
violence, to ensure neither of these variables would influence the results of the study. Those
participants who passed these tests were then randomly assigned (by flipping a coin) to be either
a prisoner or a guard.
On the first day of the study, the guards reported to Jordan Hall and were briefed. They were
Page 14 of 34
informed that there could be no violent acts towards the prisoners, they must call them by their
Prisoner ID number, they had to conduct lineups and count the prisoners to ensure no one had
escaped, and they were allowed three bland meals and three toilet visits per day. Meanwhile, the
prisoners were unexpectedly arrested at their residences by the local police department. On
coming into Jordan Hall, the prisoners were then officially booked, strip searched, given a
Prisoner ID number (the only way they would be referred to throughout the experiment), given
prisoner apparel (looking similar to a smock worn during doctors visits), and had a chain placed
around their ankle.
At first, the scene was mundane as the prisoners and guards got situated to the new surroundings
and the experiment. But, as time went on, even on that first day, both the prisoners and guards
got used to their roles and acted accordingly. The guards started seeing the power they had in
the situation and some started taking advantage of their power. They started being cruel and
unjust with the prisoners, they would wake the prisoners in the middle of the night to do a lineup,
they started making the prisoners do manual labor (e.g., scrubbing the floors). On seeing other
guards taking advantage of their power, more guards felt compelled to follow suit, whether to fit
in with their fellow guards (normative influence, Kassin, Fein, & Markus, 2008) or because they
felt that the other guards must know something more about how to act in the situation then they
did (informational influence, Kassin, Fein, & Markus, 2008). One guard, in particular, used the
power he had by being a guard to punish and abuse the prisoners much more than the other
guards, and for his cruel behavior he earned the nickname “John Wayne”.
In response to the treatment by the guards, the prisoners started at first started to rebel. They
refused do the mandated manual labor, and ignored requests to wake up in the middle of the
night. As long as one prisoner rebelled, then the other prisoners felt as if they too could rebel.
But, as the rebellions increased and the number of prisoners rebelling increased, the guards
started to retaliate, especially “John Wayne”. They increased the cruelty in their language and
treatment of the prisoners, they woke the prisoners more frequently in the middle of the night,
increased the manual labor, and started placing the rebels in solitary confinement. The rebellions
and retaliations went back and forth. Ifthe initial retaliation by the guards did not work (e.g., it
was not cruel, repressive, or “John Wayne” enough), then they increased the cruelty to squash
the rebellion. For example, the leader of the rebellion was Prisoner #416. He objected to the
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treatment by the guards onto the prisoners and his complaints were received with more abuse by
the guards. In rebellion against this treatment, Prisoner #416 announced a hunger strike and
refused to eat his meals. In retaliation, the guards locked him in solitary confinement, and
attempted to turn the other prisoners against him by announcing that all the prisoners would need
to give up their blankets and sleep on a cold floor in order for Prisoner #416 to be released from
the solitary confinement.
With each failed rebellion, the prisoners started to feel a sense of learned helplessness (Seligman
& Maier, 1967), or that no matter what they did in reaction to the guards’ treatment there was
nothing they could do to remedy or escape the situation. Eventually, after enough failed
rebellions and with excessive increases in the cruelty from the guards, the prisoners stopped
rebelling and started to become more reticent, more passive, and more and more unhappy. And,
after 36 hours as a prisoner, one prisoner participant was released from the study because he was
exhibiting signs of severe depression and anxiety. Several more prisoners left for similar reasons,
and after 6 days Zimbardo ended the study. Ironically, the prisoners forgot, most likely due to
the situational demands and the effects of repeated failure in the rebellions, that they could have
escaped the treatment by asking to leave the study.
Thus, Philip Zimbardo, like Stanley Milgram, conducted research that forever shaped the field of
social psychology. Like the Milgram experiments, Zimbardo’s prison study raised awareness of
the importance of the situation. This research demonstrated that taking innocent, mentally
healthy, and non-violent individuals, and putting them into even an artificial setting where social
roles and expectations prevail can lead to serious ramifications in how people treat each other—
regardless of one’s personality traits. While not as many replication studies have been conducted
on the Zimbardo study, most likely due the complex nature of creating a mock-prison or finding
a less complex proxy, Zimbardo (2004) recently argued that the results from his Prison Study
predicted, or could have foretold, the atrocities that occurred at Abu Ghraib towards Iraqi
prisoners (Stannard, 2004). In conclusion, the Zimbardo prison study, like the Milgram study,
was pivotal in the history of social psychology as being some of the first research to demonstrate
the power of the situation over personality traits. In addition, the results of both the Milgram and
Zimbardo studies have stood the test of time and replication.
Page 16 of 34
5. The Stanford Prison Experiment Model
Barry’s original formulation of the Stanford Prison Experiment model has three main stocks
representing Prisoner resistance, Prisoner Fear, and Repression by Guards. A fourth stock named
Perceived Resistance by Guards is a complex exponential average of the Prisoner Resistance,
with perception time also varying with the level of Prisoner Resistance. This means that while it
would take the guards some time to perceive the actual prisoner resistance level, low levels of
resistance will go undetected and high levels will be quickly detected.
Prisoner ~
increase Resistance
in resistance
PY —~“decreasd
aback in resistance
experiment teouedssee
frac increase
in resistance
frac decrease
from fear
a
frac increase iris change in p fear
Homigpression of fear -} Prisoner \
Fear frac decrease
from repression |
indic fear
from repression Resistance
Perceived
by Guards
Repression by
Sie perception
Ei time
‘change it
__ 4 a perception
change in
repressiveness
fhe
Jonn Wayne Switch @,
Indicated Level of
Repression by Guards
Fig. 7. Structure of Barry Richmond’s model of the Stanford Prison Experiment.
Page 17 of 34
Perceived Resistance leads to Repression, which invokes more resistance, creating an escalating
process. At the same time, Repression also fuels Prisoner Fear. Both Repression and Fear decay
Resistance, thus creating major balancing feedback loops. While a major balancing feedback
loop alone can create an overshoot and instability, a positive feedback loop coupled with this
process will exacerbate such behavior. Hence, the structure of this system is bound to create
escalation of hostilities between the prisoners and guards, irrespective of the personalities of the
two parties.
The model includes a “Remove John Wayne Switch” which, when thrown, constrains the growth
in repression by the guards. With this switch, the model can be tested with different guard
personalities. In fact, the graphical functions representing Indicated Level of Repression by
Guards, Perception time for guards to detect Prisoner Resistance, Impact of fear on fractional
increase and decrease in resistance, and indicated fear from repression, all represent personality
related behavioral responses. Changing the slopes of these functions implies bringing in actors
with different personalities. The model equations are placed at Annex B.
Figure 8 compares changes in prisoner resistance with normal and John Wayne behavior. Figure
9 compares repression by guards with the two guard personality profiles.
Page 18 of 34
s Prisoner Resistance: 1 - 2 -
1 19 2
John Wayne behavior
By guards
Normal behavior
1: 14 By guards ;
2
1 |
1: -——————
0.00 1.20 2.40 3.60 4.80 6.00
Page 1 Days
NX ? Resistance and Hostility
Figure 8: Changes in prisoner resistance with normal and John Wayne behavior by guards.
® Repression by Guards: 1 - 2
1 14
Normal behavior
By guards ———_——_|
| | a
1: 1 f
1
| 2
7 John Wayne behavior
Ae By guards
1: oF l—2 , r t
0.00 1.50 3.00 4.50 6.00
Page 2 Days
epression by Guards
? R by Guard
Figure 9: Changes in repression by guards with normal and John Wayne attitude
Page 19 of 34
John Wayne behavior amplifies the repressive response on the part of guards. Normal behavior is
John Wayne behavior, with indicated repression of 100%. When the Remove John Wayne switch
is turned on, indicated repression is reduced to 70% of the normal value. When guards act like
John Wayne, prisoner resistance is broken down more quickly, hence repression by the guards
does not rise as much. When guards are more benign, prisoner resistance takes longer to break
and rises to a higher peak, and hence, repression rises too.
Many other experiments can be performed with this model by changing the slopes of the
graphical functions that represent personal behavioral characteristics of the subjects. Such
experimentation can help to further clarify the contribution of the personal and situational factors
to generating the dynamics observed. While we have explored some of these experiments, we
have not documented them in this article.
6. System Dynamics and Social Psychology: Unrealized Potential
Barry Richmond’s attempt to model the underlying dynamics of subjects’ behavior in the
Milgram obedience experiments and the Stanford Prison experiment demonstrates the feasibility
of combining the study of system dynamics and social psychology and the valuable insights that
can be gained by doing so. Yet 30 plus years later, it remains a rare example of such
interdisciplinary work. To our knowledge, in the intervening years only one other effort has been
made to build a dynamic simulation model of behavior in either of these two classic experiments
(see Rochat et al., 2000).
In the field of system dynamics, the psychological literature on judgment and decision making
has made its way into modeling practice, but other subdisciplines of psychology have generally
been overlooked. In the system dynamics literature the social psychology of group behavior is
widely used in the design of group model building interventions (see Vennix, 1996), but models
designed to explain experimental results in social psychology or models that incorporate those
results in addressing social or business problems are few and far between [however, see
Page 20 of 34
Repenning and Sterman (2000) for an example of a model that incorporates a classic social
psychological result called the “fundamental attribution error”].
In social psychology, the dynamic perspective has been an important part of the field since at
least the appearance of Kurt Lewin’s book The Dynamic Theory of Personality (1935), and can
even be traced back to William James (1890). And, many current social psychologists realize
that the outcomes of their experiments have dynamic implications, and have started to rely on
Structural Equation Modeling (SEM) to better understand how and to what extent the
independent variables influence the dependent variables (see Kenny, 2008; Maydeu-Olivares,
McArdle, 2005; and Ridgon, 2008). In other words, social psychologists use SEM to determine
if a model is valid based on the results and also to determine which model best fits the data.
However, the use of computer simulation modeling to build and test theories has not become part
of mainstream social psychology — even though there have been arguments for more
widespread use of dynamic simulation modeling in social psychology, particularly in recent
years (see, e.g., Palys, 1979; Vallacher et al., 2002; Mason et al., 2007; and Smith and Conrey,
2007). And surprisingly, the most influential book on the topic, Dynamical Social Psychology
(Nowak and Vallacher, 1998), does not discuss or demonstrate any awareness at all of Forrester-
style system dynamics modeling.
The lack of communication and interaction between social psychology and system dynamics is
striking. On the one hand is a field, system dynamics, which has for decades developed and
improved a technique for modeling economic, policy, and business problems that are inherently
social but has never fully taken advantage of the enormous empirical literature on human social
behavior. On the other is the field of social psychology, which has a long tradition of
constructing theories of behavior that are inherently dynamic, but generally resists the use of
computer simulation as an aid to theory building and seems almost completely unaware of the
system dynamics modeling tradition. How did this happen?
The answer, we believe, lies mainly in the fact that researchers and practitioners in the two fields
go about their business very differently. Social psychologists focus on conducting controlled
experiments that change one variable at a time and employ random assignment of subjects in
order to allow causality to be unambiguously determined. For example, in Milgram’s replications
Page 21 of 34
of his original obedience study, he systematically varied such factors as proximity to the victim
while keeping all other aspects of the experiment (e.g., the instructions, the sequence of events,
the experimenter’s prompts, the location, the personnel) the same. In Zimbardo’s prison
experiment, subjects were randomly assigned to the play the role of guard or prisoner. To a
social psychologist, verifying the nature and magnitude of the relationships in a system dynamics
model would represent a lifetime of work. In fact, many social psychologists have devoted their
entire careers to trying to definitively pin down the relationship between two variables (e.g., does
watching televised violence cause aggressive behavior?, or does contact with outgroup members
reduce prejudice?). Furthermore, the amount of time, effort, and expensive involved in
conducting experiments on human subjects means that the kind of time series data that would
lend itself to modeling is not often collected; most social psychology experiments are one-time
snapshots of behavior or, at best, two snapshots (one before the experimental task, and one after).
System dynamicists, by contrast, set aside the question of precise values for parameters and skip
right to the big picture task of identifying the structure of the system in which behavior takes
place. Since they theorize that it is primarily structure that drives system behavior, they believe it
is unnecessary to identify the precise magnitude of relationships between variables up front; in
fact, sensitivity analyses may ultimately show that system behavior is unchanged even with
widely varying assumptions about parameter values.
Thus, system dynamicists would suggest that social psychologists are probably collecting a lot of
unnecessary data. To which social psychologists would respond with the common argument that
system dynamics is “measurement without data.” With a long history within the field of
combating “common sense” assumptions about human behavior that controlled experimentation
proves to be false, the system dynamics attitude of “model first, measure later” would be viewed
as counterproductive and potentially harmful by many social psychologists.
Another important difference between the two fields is in the relative importance assigned to
different types of data for input to theories and/or models. Controlled experiments are held in
high esteem by social psychologists for their ability to determine causality. However, external
validity (whether results obtained in the lab also apply in real life) is an important concern as
well, and thus social psychologists employ a variety of additional data gathering techniques that
Page 22 of 34
vary in the degree to which they offer experimental control versus external validity, including
survey research, naturalistic observation, field and case studies, and interviewing techniques.
However, no matter the technique there is always an overriding concern for systematicity in data
collection and representativeness in the human subjects under study. System dynamicists, by
contrast, often display little interest in formal or systematic methodologies or the empirical
psychological literature and simply go straight to the managers or decision makers who have the
information they need and ask them for it. The modeling process determines the need for
information, and the pressure to solve a practical policy problem often does not leave time to
consult the empirical psychological literature. This approach suggests a high level of confidence
in the ability of people to accurately remember and report on their own thinking and behavior;
however, psychologists, based on decades of uncovering counterexamples in their experiments,
are not as confident in this type of approach. To a psychologist, the chance that information
collected so informally will turn out to be inaccurate or misleading is simply too high.
A third difference between the two fields is the relative emphasis placed on theoretical versus
applied work. Social psychologists conduct applied research on a wide variety of socially
important topics, but the emphasis is on developing and testing theories of human social
behavior. The applied work that is done is not primarily conducted in corporate or management
settings. In comparison, system dynamics modelers are concerned almost exclusively with social
problem solving as opposed to theory, and most of this work is done in collaboration with, or in
consultation for, businesses and other large organizations. Hence, another reason for lack of
collaboration between social psychologists and system dynamicists is simply that their paths do
not cross very often. In addition, neither field is a typical (or even atypical) component of
academic training in the other: there is a profound, mutual lack of awareness between the two
fields.
To fully realize the potential for productive interaction between system dynamics and social
psychology, social psychologists will need to a) become more open to the advantages of the
more wholistic approach that system dynamicists can provide, b) start applying the research they
have already conducted and associated findings to many different models of human behavior,
and c) begin to be more willing to leap into the modeling enterprise without waiting for data that
Page 23 of 34
may take years, if ever, to materialize. Even to date, social psychologists may use bootstrapping
simulations (see Efron &Tibshirani, 1993) in order to determine whether increasing the sample
size may increase statistical power and the likelihood of significant effects, but they rarely use
computer simulations based on their own data for any other purpose.
System dynamicists, following Barry Richmond’s example, will need to learn to find value in
exploring and applying the empirical literature in social psychology and to discover the
advantages of more systematic and representative data collection, and consequently more
complex (and possibly accurate) models. And of course researchers in both fields will need to
find ways to educate themselves about the methods and of the other domain.
The benefits of such interaction would in many ways be similar to the benefits offered by
dynamic modeling in any domain. The discipline imposed by modeling would doubtless
uncover errors, omissions, and inconsistencies in mental models of social psychological theories,
as it has in many other fields. It could also help strengthen the existing theories on human
behavior (e.g., Barry’s model on Milgram strengthened Milgram’s claim that the situation played
more of a role than personality). It would also help to make the theories less conceptual and
more operational. In addition, with the cognitive assistance provided by computer models, social
psychological theories could become more dynamic and complex. In addition to these general
benefits, there are some advantages to dynamic modeling that are unique to social psychology
(and other experimental disciplines within psychology). Given the time-consuming, labor-
intensive nature of each empirical test of a relationship in a psychology research program, use of
simulation runs to test alternate hypotheses before running human subjects would greatly aid in
preserving limited resources for use in the most promising live experiments. It could also
enhance understanding of human behavior theories by being able to combine many theories and
variables at one time that could not be included in one parsimonious experimental design. In
addition, as Barry Richmond (1977) suggested in his Milgram model manuscript, the simulation
model could be used to test experimental conditions that would be difficult or impossible to
reproduce in the laboratory or to put simulated subjects through procedures that would be
unethical to duplicate in real life.
Page 24 of 34
Of course, any of several different modeling paradigms might potentially offer the same list of
benefits to the field of social psychology. And for certain social psychological topics, other
modeling techniques seem to be obviously better suited than system dynamics (e.g., modeling
crowd or large group behavior seems to call for an agent-based modeling approach). Is there
anything that makes system dynamics particularly well-suited to the study of social psychology?
Certainly the emphasis in the system dynamics paradigm on the inclusion of so-called “soft”
variables, and the techniques that have been developed for incorporating them into models, is an
advantage for studying social psychology, where concepts such as anxiety, obedience, prejudice,
aggression, conformity, perception, and judgment may be the main topics of investigation [an
interesting example of modeling soft variables in an organizational context is in Saeed (1998),
where he attempts to track changes in role autonomy, citizenship and professional competence in
an innovation organization]. It would also allow the merging of theories and concepts from
many different domains with social psychology, psychology, and other disciplines (e.g.,
anthropology, economics, law, sociology). And other central aspects of the system dynamics
tradition, including the emphasis on feedback relationships and the operational emphasis, and the
ideas that the main purpose of modeling is for learning rather than prediction and that models are
most effective when they are designed to help solve problems rather than exhaustively replicate
systems, certainly offer an alternative to other modeling paradigms.
However, the best reason to choose a system dynamics approach for the study of social
psychology might be its suitability to study a long-standing problem at the heart of the field (and
of central importance to an understanding of the Milgram and Stanford Prison studies as well):
the relative contribution of the person versus the situation in determining behavior. For many
years a lively debate raged between the situationist camp, who emphasized the ability of
situational variables to overwhelm individual differences, and the personality camp, who
emphasized the important role of enduring character traits in explaining behavior. Today this
debate is largely concluded, with the majority of social psychologists supporting the view that
the person and situation are roughly equal in importance, and in addition can interact with each
other in interesting and sometimes counterintuitive ways (see, e.g., Fleeson and Noftle, 2008).
Even the modern interpretations of the Milgram and Stanford Prison experiments have evolved
from an almost exclusively situationist perspective to a more balanced view that recognizes the
important role of individual differences in providing a comprehensive explanation of the results
Page 25 of 34
[see Blass, 1991, for a more modern interpretation of the Milgram experiment; and Donnellan et
al. (2007) and Zimbardo (2007) for a discussion of person-situation interactionism in the
Stanford Prison Experiment].
However, for any given topic of study or experimental situation, it is still not easy to predict or to
tease apart the relative contributions of the person and the situation, how they may interact, and
how that interaction may unfold over time. System dynamics modeling could be a very valuable
tool to help simplify and systematize this effort. In fact, among the various modeling
alternatives, system dynamics seems ideally suited for the task. In system dynamics situational
variables can be incorporated into the model structure or constants. Individual difference or
personality variables can be represented as adjustable parameters. The test of the relative strength
of situational versus personality factors thus reduces to the standard practice of parameter
sensitivity analysis. This is in fact precisely the approach that Barry Richmond took in his
experiments with the Milgram and Stanford Prison Experiment models. In the case of the models
replicated in this chapter, these analyses confirm that the models are relatively insensitive to
changes in personality variables, supporting the situationist views espoused by Milgram and
Zimbardo.
7. Conclusion
It has been inspiring for the present authors (one system dynamicist and two social
psychologists) to have the opportunity to examine and reflect upon Barry Richmond’s early
effort to combine his knowledge and interest in social psychology and system dynamics. This
exercise has greatly aided our thinking about the need for and benefits of productive
collaboration between the two fields, and improved our understanding of the obstacles that will
need to be overcome to increase such collaboration in the future. We hope other modelers with
an interest in psychology will be inspired to follow up or expand upon Barry Richmond’s work
and, perhaps, explore other theories and applications of social psychology using the powerful
tools of system dynamics.
Page 26 of 34
We also hope Barry’s models will gain some use in psychological education. The concept of “the
power of the situation” is contrary to the mental models people form about human behavior
through their life experience. For example, when people hear about the Milgram experiment,
everyone thinks they would be one of the ones to resist authority. But the experiment, and its
many replications with diverse subjects, prove otherwise. Allowing students to experiment with
the simulation model themselves and see the effects of changing personality variables may be an
effective way to drive home the point that in certain situations personality just does not matter
that much.
We believe there are also larger lessons to be learned from Barry’s work. Certainly, it paves the
way for system dynamics modelers to make better use of an underutilized information source,
namely, the results of controlled experiments on human subjects. In addition, as there are still
those in the system dynamics community that are reluctant to model so-called “soft” or
psychological variables, Barry’s work serves as a reminder that such work, while challenging,
can, and must, be done. And, finally, the topics of the Milgram and Stanford Prison Experiment
models themselves serve as a useful reminder that the field of system dynamics began by
addressing, and still can address, the great problems of society.
Page 27 of 34
Annex A
Equations for Milgram model
anxiety
level_of_anxiety(t) = level_of_anxiety(t - dt) + (anxiety_growth_rate - anxiety_decrease_rate) *
dt
INIT level_of_anxiety = 5
INFLOWS:
anxiety_growth_rate =
normal_anxiety_growth_fraction_fraction*level_of_anxiety*anxiety_from_insistence_by_author
ity*anxiety_from__resistence_by_victim*anxiety_from_voltage*subject_termination_multiplier
OUTFLOWS:
anxiety_decrease_rate =
level_of_anxiety*subject_termination_multiplier*anxiety_decrease_coefficient
anxiety_decrease_coefficient = .03
maximum_anxiety = 50
anxiety_from_insistence_by_authority = GRAPH(insistence_by_authority)
(0.00, 1.00), (0.2, 1.05), (0.4, 1.20), (0.6, 1.45), (0.8, 1.60), (1.00, 1.70)
anxiety_from__resistence_by_victim = GRAPH(resistence_by_victim)
(0.00, 1.00), (0.2, 1.10), (0.4, 1.30), (0.6, 1.60), (0.8, 2.00), (1.00, 2.50)
normal_anxiety_growth_fraction_fraction = GRAPH{(level_of_anxiety/maximum_anxiety)
(0.00, 0.06), (0.25, 0.03), (0.5, 0.015), (0.75, 0.01), (1.00, 0.008)
decision to continue
max_acceptable_level_of_punishment(t) = max_acceptable_level_of_punishment(t - dt) +
(rate_of_increase_in_max_acceptable_level_of_punishment -
rate_of_decrease_in_max_acceptable_level_of_punishment) * dt
INIT max_acceptable_level_of_punishment = 150
INFLOWS:
rate_of_increase_in_max_acceptable_level_of_punishment =
effect_of_insistence_by_authority*subject_termination_multiplier
Page 28 of 34
OUTFLOWS:
rate_of_decrease_in_max_acceptable_level_of_punishment = GRAPH(resistence_by_victim)
(0.00, 0.00), (0.2, 0.25), (0.4, 1.00), (0.6, 2.50), (0.8, 4.50), (1.00, 7.00)
resistence_by_victim = effect_of_resistence_by_victim*subject_termination_multiplier
effect_of_insistence_by_authority = GRAPH(insistence_by_authority)
(0.00, 0.00), (0.2, 7.00), (0.4, 17.0), (0.6, 19.0), (0.8, 12.0), (1.00, 7.00)
insistence_by_authority = GRAPH(resistence_by_subject)
(0.00, 0.00), (0.2, 0.4), (0.4, 0.7), (0.6, 0.9), (0.8, 0.95), (1.00, 1.00)
resistence_by_subject = GRAPH(willingness_to__continue_delivering_punishment)
(0.00, 1.00), (0.1, 0.98), (0.2, 0.97), (0.3, 0.95), (0.4, 0.85), (0.5, 0.7), (0.6, 0.45), (0.7, 0.25),
(0.8, 0.05), (0.9, 0.00), (1, 0.00)
willingness_to__continue_delivering_ punishment =
GRAPH(max_acceptable_level_of_punishment-volts)
(-25.0, -0.1), (0.00, 0.00), (25.0, 0.05), (50.0, 0.2), (75.0, 0.65), (100, 0.75), (125, 0.9), (150,
0.95), (175, 0.98), (200, 1.00)
punishment
total_punishment_delivered_to_victim(t) = total_punishment_delivered_to_victim(t - dt) +
(rate_of_punishment_delivered_to_victim) * dt
INIT total_punishment_delivered_to_victim = 0
INFLOWS:
rate_of_punishment_delivered_to_victim =
(volts/time_to_deliver_punishment)*subject_termination_multiplier
time_to_deliver_punishment = |
volts = (TIME+1)*15
anxiety_from_voltage = GRAPH{(volts*subject_termination_multiplier)
(45.0, 1.00), (105, 1.10), (165, 1.20), (225, 1.30), (285, 1.40), (345, 1.50), (405, 1.60), (465,
1.70)
effect_of_resistence_by_victim = GRAPH(volts)
(0.00, 0.01), (75.0, 0.05), (150, 0.15), (225, 0.5), (300, 0.9), (375, 1.00)
Page 29 of 34
willingness_to_continue_to_deliver_punishment =
GRAPH(max_acceptable_level_of_punishment-volts)
(-25.0, -0.1), (3.12, 0.00), (31.2, 0.05), (59.4, 0.2), (87.5, 0.65), (116, 0.75), (144, 0.9), (172,
0.95), (200, 0.98)
termination
anxiety_termination = [F(maximum_anxiety-level_of_anxiety) >0 THEN(1) ELSE(0)
experimenter_termination = IF(maximum_volts-total_punishment_delivered_to_victim) > 0
THEN(1) ELSE(0)
maximum_volts = 11475
subject_termination = IF(willingness_to__continue_delivering_ punishment) > 0 THEN(1)
ELSE(0)
subject_termination_multiplier =
anxiety_termination*experimenter_termination*subject_termination
Annex B
Equations for Zimbardo Model
Prisoner_Fear(t) = Prisoner_Fear(t - dt) + (change_in_p_fear) * dt
INIT Prisoner_Fear = 0
INFLOWS:
change_in_p_fear=(indic_fear_from_repression-Prisoner_Fear)/.5
Prisoner_Resistance(t) = Prisoner_Resistance(t - dt) + (increase_in_resistance -
decrease_in_resistance) * dt
INIT Prisoner_Resistance = 0
INFLOWS:
increase_in_resistance = (Prisoner_Resistance*frac_increase_in_resistance)
+ PULSE(.1,start_of_experiment,100)
OUTFLOWS:
decrease_in_resistance = Prisoner_Resistance*frac_decrease_in_resist
Repression_by_Guards(t) = Repression_by_Guards(t - dt) + (change_in__repressiveness) * dt
Page 30 of 34
INIT Repression_by_Guards = 0
INFLOWS:
change _in__repressiveness = IF Remove_John_Wayne_Switch = 0 THEN
((Indicated_Level_of_Repression_by_Guards-Repression_by_Guards)/.5)
ELSE (((Indicated_Level_of_Repression_by_Guards*.7)-Repression_by_Guards)/.5)
Resistance_Perceived_by_Guards(t) = Resistance_Perceived_by_Guards(t - dt) +
(change_in_perception) * dt
INIT Resistance_Perceived_by_Guards = Prisoner_Resistance
INFLOWS:
change_in_ perception = (Prisoner_Resistance-
Resistance_Perceived_by_Guards)/perception_time
frac_decrease_from_fear = GRAPH(Prisoner_Fear)
(0.00, 0.00), (0.1, 0.02), (0.2, 0.065), (0.3, 0.23), (0.4, 0.445), (0.5, 1.00), (0.6, 1.33), (0.7, 1.50),
(0.8, 1.50), (0.9, 1.50), (1.00, 1.50)
frac_decrease_from_repression = GRAPH(Repression_by_Guards)
(0.00, 0.00), (0.1, 0.01), (0.2, 0.01), (0.3, 0.02), (0.4, 0.03), (0.5, 0.08), (0.6, 0.24), (0.7, 2.83),
(0.8, 3.00), (0.9, 3.00), (1.00, 3.00)
frac_decrease_in_resist = frac_decrease_from_fear+frac_decrease_from_repression
frac_increase_from_repression = GRAPH(Repression_by_Guards)
(0.00, 0.00), (0.1, 0.285), (0.2, 0.605), (0.3, 0.82), (0.4, 0.92), (0.5, 0.97), (0.6, 0.985), (0.7,
1.00), (0.8, 1.00), (0.9, 1.00), (1.00, 1.00)
frac_increase_in_resistance = (frac_increase_from_repression*impact_of_fear)
impact_of_fear = GRAPH(Prisoner_Fear)
(0.00, 1.00), (0.1, 1.00), (0.2, 0.99), (0.3, 0.98), (0.4, 0.915), (0.5, 0.765), (0.6, 0.65), (0.7,
0.445), (0.8, 0.275), (0.9, 0.16), (1.00, 0.00)
Indicated_Level_of_Repression_by_Guards = GRAPH(Resistance_Perceived_by_Guards)
(0.00, 0.00), (0.1, 0.27), (0.2, 0.485), (0.3, 0.63), (0.4, 0.74), (0.5, 0.85), (0.6, 0.925), (0.7, 0.95),
(0.8, 0.975), (0.9, 0.985), (1, 1.00)
indic_fear_from_repression = GRAPH(Repression_by_Guards)
(0.00, 0.02), (0.1, 0.03), (0.2, 0.045), (0.3, 0.055), (0.4, 0.08), (0.5, 0.225), (0.6, 0.45), (0.7,
0.645), (0.8, 0.77), (0.9, 0.9), (1, 0.97)
Page 31 of 34
perception_time = GRAPH( Prisoner_Resistance/(Resistance_Perceived_by_Guards+.001))
(0.9, 30.0), (0.92, 30.0), (0.94, 30.0), (0.96, 22.1), (0.98, 10.7), (1.00, 0.25), (1.02, 0.25), (1.04,
0.25), (1.06, 0.25), (1.08, 0.25), (1.10, 0.25)
Remove_John_Wayne_Switch = 0
start_of_experiment = |
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