Model Building with Soft Variables: A Case Study on Riots
John Hayward, Rebecca A. Jeffs,
Leanne Howells and Kathryn S. Evans
University of South Wales
School of Computing and Mathematics, Pontypridd, CF37 1DL, Wales, UK
john.hayward@southwales.ac.uk
nd
Presented at the 32 International System Dynamics Conference, Delft, Netherlands, 2014
Abstract
A methodology for incorporating soft variables into system dynamics models is proposed.
Building on previous research, the methodology uses a systematic assessment to identify
soft variables, and concepts from software engineering to implement them. Data hiding is
used to separate the units and scale of a soft variable from its effect on other model ele-
ments. By encapsulating the soft variable in a module with well-defined inputs and out-
puts, it can be used from a knowledge of its parameters alone, and not its internal con-
struction, that is it is referentially transparent. The methodology is applied to an existing
population model on riot growth, extending it to include soft variables whose scales are
limited. The effects of the different soft variables on the populations are combined to-
gether using cognitive algebra. The extended model is compared to historical data and
found to give a richer explanation of the riot dynamics than the original model. The paper
is exploratory and intended to inspire further research
Key Words: Social diffusion, soft variable, riot growth, data hiding, referential transparency,
cognitive algebra
1 Introduction
The use of soft, or unquantified, variables is widespread in system dynamics, despite the
difficulties associated with such variables. By their very nature soft variables, or soft
concepts, are difficult or even impossible to measure; yet their inclusion in a model is
often a matter of necessity, as they are known to be a part of a chain of cause and effect.
For example in a public riot the size of that riot can encourage feelings of enthusiasm on
the part of the rioters, encouraging them to recruit more to the cause. The size of the
riot is easy to enumerate, but the enthusiasm of the riot is much harder to quantify. The
temptation is to leave candidates for soft variables out of a model, as calibration would
be difficult. However the much quoted comments of Jay Forrester (1961, p. 57) should
encourage anyone to resist such a temptation: “To omit such variables is equivalent to
saying they have zero effect - probably the only value that is known to be wrong!” Such
an approach would be in the words of Sterman (2002) “a sure route to narrow model
boundaries, biased results, and policy resistance”. The purpose of a model is to explain
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behaviour by theory and hypotheses, and thus if the concept is part of that explanation
it needs to be included in the model, however difficult it is to quantify.
System dynamics as a modelling methodology is not just an explanation of cause and
effect, it is also a simulation tool. As such there comes a point where a soft concept has
to be turned into a variable with numbers attached to enable a simulation, however
“unquantifiable” the concept may be. Indeed once the word “variable” is used, it is al-
most implied that a numeric equivalent of the concept has been constructed. A method-
ology as to how such concepts can be turned into simulation variables is more problem-
atic. In his review of the problems of qualitative modelling, Coyle (2000) raised re-
search questions with regard to soft variables, suggesting the need for procedures to
understand their identification, measurement, construction and validation. In reviewing
the work of authors both previous and subsequent to Coyle (2000), it will be convenient
to group them under those four headings.
A. Identification and Nature of Soft Variables
From a sociological perspective, Jacobsen & Bronson (1987) gave very helpful
guidelines for handling sociological variables, which can be carried over to soft
variables in system dynamics (Levine, 2000). Such a variable must be:
(i) Reliable - it must have units of measurement and have a meaning that can
be agreed by all;
(ii) Realistic - it must correspond to some concept in the real world;
(iii) Have face validity - it can be reasonably substituted by an indirect indica-
tor, that is a similar concept with a better defined means of measurement
and thus closer to a variable.
B. Scales and Units of Soft Variables
Levine (1983) noted that psychologists deal with soft variables and have used cor-
relation analysis to obtain stable and relevant measures of “fuzzy” concepts such as
anxiety and cognitive complexity. Levine (2000) also showed how psychological
concepts could be modelled using system dynamics, highlighting the conceptual
problems of allowing the soft variable to go infinite. Instead he proposed limiting
the scale to 0 to 100, to allow the use of percentage points, using a limits-to-growth
balancing loop to control the upper bound of the variable.
Nuthmann (1994) discussed four different scales of variables: nominal - used to de-
scribe characteristics that have no numerical value such as gender, ethnicity, which
unordered descriptive values; ordinal - where values can be place in rank order but
without a sense of inter-value distance; interval - where there is an additive inter-
value distance; and ratio where that distance is multiplicative. He argued for the in-
terval scale as the most natural. By contrast Levine (2000) puts a case for ratio
scales in soft variables, including how they can be related to a measurement of the
variable on an interval scale. In either case it is clear that soft variables have a sense
of order, i.e. they are at least ordinal.
C. Construction of Soft Variables
Levine & Doyle (2002) discussed types of soft variables using a variety of generic
structures. Initially looking for social archetypes they decided that a social psy-
chological molecule was more appropriate as they were attempting to “capture the
dynamics of small bits of social processes”, rather than a generic behaviour pattern.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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From this perspective a soft variable is no longer just a stock but includes appropri-
ate converters and connectors in order for it to respond to inputs in a particular
way. This suggests that a modular approach to soft variables could be developed.
Nuthmann (1994) discussed combinations of soft variables based on the cognitive
algebra of Anderson (1981). He identified three: addition, averaging and multiplica-
tion. McLucas (2003) took this further, developing a method of weighted variable
combinations according to their perceived importance (c.f. Sterman, 2000, Ch. 13).
Thus if a modular approach to soft variable construction is taken, thought is needed
as to how the outputs of such modules are combined.
D. Validation of Models with Soft Variables
Sterman (2002) stated that soft variables should be used in simulation when neces-
sary, providing the model is properly validated, including historical and statistical
fits, but not exclusively. He suggested modellers need to ask why soft concepts used
in modelling have not been measured, and gives examples of soft concepts for
which measures, albeit imperfect, have been obtained once their importance was
established. Roy & Mohapatra (2003) suggested a method of validating models
with soft variables using structural equation modelling.
The purpose of this paper is to put forward a possible methodology by which soft vari-
ables can be incorporated into a system dynamics model, using some of the insights
referenced above. The method is divided into three main stages: the identification, the
construction and the use of soft variables. Jn particular it is proposed that soft variables
are understood by their use, rather than by their internal construction; and that their
measure is dealt with separately to their effect. To achieve this understanding a modular
approach to their construction is taken, using ideas from software engineering.
The proposed method is both exploratory and tentative. It is intended to inspire discus-
sion and further investigation rather than enumerate a definitive set of guidelines. A
thorough discussion of model calibration and validation is beyond the scope of the pa-
per, though some comments will be made in the discussion.
To illustrate the proposed method, an existing model on the dynamics of riot growth by
Burbeck, Raine, & Stark (1978) is extended to include soft variables. The original model
used only hard variables in the form of population numbers, being modelled by analogy
with an SIR epidemic. However the problem description had causes that would have al-
lowed for the use of soft variables, producing a model with a richer explanatory power.
2 Model Description
2.1 Original Riot Model
In 1978 Burbeck, Raine, & Stark put forward a mathematical model for the dynamics of
the growth of a riot with specific application to the riots of Los Angeles 1965, Detroit
1967, and Washington DC 1968. The primary hypothesis was that rioters recruited
other rioters from the population by word of mouth. It was further hypothesised that
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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rioters left the riot after an average length of time either due to tiredness or arrest. As
such the model had the same structure as that of an SIR epidemic model.
Although there was no direct information on the number of rioters over time, the
authors had access to police, fire service and civil defence records that gave reports of
incidents during the progress of each riot, recorded by time of day, which they compiled
into a unified time series of reported events. They further assumed that a fixed percent-
age of rioters caused the damage, and were thus able to show that the reported inci-
dents followed the expected pattern of the infected of the SIR model. The duration of
each riot was about 5 days.
The model of Burbeck et. al. (1978) was entirely composed of quantified variables: po-
tential rioters, the susceptibles; rioters, the infected; dropouts, the removed, and riot
events, a normalised variable to represent the occurrence of reportable events. How-
ever they also referred to other factors that influenced the dynamics of the riot such as
the media reports and the contagiousness of the rioters. The former they ignored and
the latter they assumed was constant even though it would vary with the enthusiasm of
the rioters and the strength of the cause. Additionally they discussed the level of sympa-
thy among the potential rioters. Media reports, enthusiasm, sympathy and strength of
cause are of course much harder to quantify, but an attempt at their inclusion in the
model would make a useful illustrative test case for a possible methodology for model-
ling with soft variables.
The original model of Burbeck et. al. (1978) was written using differential equations.
However it can be re-expressed as the equivalent system dynamics model, figure 1.
events per rioter per day
— events Cummultative
per day
[ -—* LJ
. 7 join Lot f
, / joi Rioters \ /
PA - riot * /
fraction of a eZ
popuiston CK | moor iad
sympathisers \ 20) “toon per rioter
time in riot
VA / actual number
of contacts per
day per person probability of
Population succesful influence
potential number of
contacts per day per person
Figure 1: SIR Model of Riot Growth based on Burbeck, Raine, & Stark (1978)
The hypothesis that rioters recruit to the riot by word of mouth is expressed in the re-
inforcing loop R1. Their reduced effect on the sympathisers is expressed in the balan-
cing loop B1. The original model considered a single leaving rate of rioters from the riot.
The limited time rioters spend in riot activity, whether due to arrests or self action, is
modelled by the single loop B2, reflecting the hypothesis of Burbeck et. al. (1978). The
authors compared the reported events over time with events per day in the model show-
ing that the model could reproduce the observed pattern for certain parameter values.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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2.2 Model Extension
For the purpose of extending the Burbeck model to include soft variables, the following
additional concepts and hypotheses are considered:
1. The strength of the cause which originally sparked the riot;
2. The number of arrests due to the action of the police. This is assumed to be the
cumulative number rather than the arrest rate, as the impact of arrests on rioter
enthusiasm is more likely to be accumulative over the short period of the riots
being modelled;
3. The enthusiasm of the rioters. This enthusiasm will influence recruitment and
retention of rioters. Enthusiasm will be generated through the size of the riot
and the strength of the cause, but will be dampened according to the number of
arrests;
4. Media interest which creates sympathy for the riot, and also will increase the ef-
fectiveness of recruitment to the riot. Media interest will increase as the number
of reported events increases as such events measure both the size and serious-
ness of the riot;
5. The sympathy of the non-riot population towards the riot. That sympathy makes
recruitment to the riot more likely and is in turn affected by the media interest.
These concepts lead to potential soft variables: Strength of cause, enthusiasm of rioters,
media interest, sympathy of non-rioters, and events. Although events was a quantified
variable in the original model, its definition will be reconsidered as a candidate for a
soft variable.
3 Methodology
The methodology used to turn the concepts into soft variables is divided into three
stages: the identification of the variable; the construction of the variable; and the use of
the variable. It will be assumed that a causal loop diagram of the whole model has al-
ready been constructed so that the causes and effects of each potential soft variable
have been determined.
3.1 Identification of Soft Variable
The aim is to assess whether the concept can be thought of as a numerical variable.
General Description
How is the concept informally described? This should give an initial assessment or
description of the concept to be modelled and explain why it is needed. It can be
helpful to describe its causes and effects as this may shed light on the description.
This corresponds to the nominal variable definition of Jacobsen & Bronson, 1987.
Aggregation
Is the concept a single irreducible entity or is it a composite structure, a collection of
entities? The purpose is to give reasons why the concept or entity may be modelled
as a single variable or a number of variables. That is, is the entity one-dimensional
or multi-dimensional? The principle of Occam’s razor should be used, i.e. entities
must not be multiplied beyond necessity.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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Ordering
Does the concept have a clear ordering? The main purpose is to help justify why a
single variable could be used. If a sense of ordering were ambiguous it may imply
that a many variable, multi-dimensional model might be more appropriate. Identifi-
cation of an ordinal scale is necessary for the concept to be a single variable (Nuth-
mann 1994).
Potential Measures
How could the concept be potentially measured? Although the measurement will not
necessarily be built into the model this exercise helps clarify the variable.
At this stage it should be clear whether a concept is a candidate for a soft variable, i.e. it
should have reliability, realism and face validity (Levine, 2000). It is not necessary yet
to know how it will be modelled or used in a system dynamics model; that is the next
stage. From now on the concept will be referred to as a variable.
3.2 Construction of Soft Variable
Levine (2000) distinguished the use of a soft variable in a model from its measurement.
The latter could be seen as its effect on the observer, rather than on the model elements.
Thus it is proposed that the soft variable model is constructed in a modular fashion such
that its inner workings, including its measurement, are hidden from the other model
variables in its cause and effect chain. In software engineering this concept is referred
to as data hiding (Booch et. al., 2007) and enables modules to be tested prior to their
inclusion in a larger model. Once incorporated into the system dynamics model the soft
variable will be understood in terms of its input and output alone, a concept referred to
as referential transparency (Bird and Wadler, 1988). Such a modular approach for a soft
variable is an example of the social psychological molecules of Levine and Doyle (2002).
Thus the soft variable will be constructed so that both its numeric value and dimensions
are hidden from connecting elements. Its internal numerical value is not relevant, nor is
its unit of measure, only its response to stimuli and its effect on other variables. Thus
the effect of a soft variable on other el ts can be di ionless, enabling the effects
of different soft variables to be combined together without regard to their hidden units.
To complete the construction of the soft variable model the following stages are con-
sidered:
Scale
Does the soft variable have a minimum value? Does the variable have a maximum
value? That is, are there limits on the scale of the variable? If the answer is yes in
either case then the values of these limits are set. In the remainder of the paper dis-
cussion is confined to variables on a limited scale.
Units
Are there any suggested units of measure for the soft variable? A discussion of appro-
priate units naturally comes out of the previous discussion of scale. Although these
units will be hidden from connecting elements, for the sake of internal dimensional
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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consistency some units should be used. If no unit of measure is natural then an ab-
stract unit should be defined.
Nature
Is the soft variable a stock, converter or flow? A consideration of units will help dis-
tinguish a stock from a flow, as will the photograph test (Sterman, 2000). A con-
sideration of memory or delays can help distinguish a stock from a converter.
Inputs
What outside elements have an effect on the soft variable? I.e. what is the effect of its
causes? If the decision is to model the soft variable with a stock then is its growth
and decline mechanisms should be consider. It is suggested that endogenous
mechanisms are tackled first.
Outputs
What outside elements does the soft variable affect? There must be at least one out-
put otherwise the variable would not be required. Although different outside ele-
ments may be affected by the same internal element of the soft variable, the possi-
bility of more than one type of output should be considered. The output should be
constructed so that the internal units are hidden and that it follows any limits set
on the scale. For the remainder of the paper it is assumed the soft variables have an
output scale limited from 0 to 1.
As the identification of soft variables progresses it will be helpful to re-express the cau-
sal loop diagram into a modular diagram to help highlight the causes and effects of each
soft variable.
3.3 Use of Soft Variable
Once the model for the soft variable has been constructed (and tested) consideration is
given as to how it connects to the wider model. This will be subdivided into the effect of
the soft variable and the way different soft variables need to be combined. Reference
should be made to a modular version of the causal loop diagram.
Effect
How many different model elements does the soft variable affect? There will be a sepa-
rate model for each effect of the soft variable, which will allow it to have different im-
pacts on different elements. Essentially there is one effect model for each link from the
soft variable. These models can be modularised. If the soft variable has any scaling then
the scaling can be preserved in the effect.
Combinations
How are different soft variable effects combined before they influence another element?
Popular combinations are multiplication, addition and weighted averages, which may
be linear or non-linear (Sterman, 2000, Ch.13). Multiplication of effects is often as-
sumed, which can be problematic if there are many such combinations as the lowest
factor can dominate the result (Coyle, 2000). McLucas (2003) also warns of the dangers
of more esoteric combinations and advises that combinations are kept as simple and
natural as possible.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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Following the work on cognitive algebra of Anderson (1981) and Nuthmann (1994), the
number of combinations of two variables are limited to four, table 1, where it has been
assumed the variables in question have been limited to a scale of 0 to 1.
Description Mathematical Construct Formula f(x,y)
Strict Logical AND xy
Strict Compromise Harmonic Average {xy
Lenient Compromise Arithmetic Average x+y
2
Lenient Logical OR X+y-xy
Table 1: Combinations of Soft Variable Effects (0 s x,y <1)
The strict combination of soft variables x and y is the usual multiplication model, and is
the equivalent of the logical AND. That is, if the effect of one soft variable is switched off,
the other has no effect. If one is set to the maximum value of 1, the combined effect is
the full range of the second variable. Other combinations are shown in figure 2. This
case is referred to as strict as the output is less than the smallest input,
xX <y=>xy<x<y. This can be thought of as the most pessimistic approach to combi-
nation, as the one soft variable restricts the effect of the other.
‘£(x,0.5)
sree Lenient
=== Lenient Compromise
Strict Compromise
1) flx,0.2)
= = = Strict
s7 Lenient
= Lenient Compromise
Strict Compromise
Figure 2: Cognitive Algebra. Output as a function of one input x with second input 0.5 and 0.2.
There are two models of a compromise position between the two variables. The lenient
compromise combination is the familiar averaging. An un-weighted combination is used
as it is assumed that the effects of the two variables are already on comparative scales.
The level and response for two given inputs is higher than the strict case AND (figure 2).
A more tentative suggestion is made for a strict compromise combination using the
harmonic average. There will be a point where its response can match the lenient com-
promise, but at the extremes of one of the inputs being 0 the response matches the
strict case (figure 2). The comments of McLucas (2003) about this combination being
“an abuse of mathematical logic and system dynamics principles” are noted, but it is
hoped that the use of the dimensionless effects of the soft variables with a clear logic-
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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based methodology have avoided the issue. For both compromise combinations if the
effects of the two soft variables are the same the output matches that effect, f(x,x) =x.
In addition the output of both compromised combinations lies between the smallest and
x+y
2
largest inputs x < y => x <+xy < < y, which suggests the term compromise.
The final combination is based on the logical or cognitive OR, is referred to as the lenient
combination, and can be thought of as the most optimistic case. If one soft variable is
switched off the response follows the full range of the other variable (figure 2). If how-
ever one variable is at its maximum 1, the second variable can have no further effect.
The response of OR is higher than all the other combinations for the same inputs, and is
larger than its highest input x < y= x <y<x+y-vx,y. In this sense the one soft vari-
able enhances the effect of the other.
For all combinations the scale of 0 to 1 is preserved, and thus do not have the scaling
issues raised by Coyle (2000).
4 Model Construction
In this section the riot model of Burbeck et. al. (1978) is extended to include soft vari-
ables and used to illustrate the model construction methodology of section 3. Firstly a
causal loop diagram is produced in line with the existing model (figure 1) and the addi-
tional hypotheses (section 2.2), and is given in figure 3.
The population variables are indicated as stocks, as there is no intention to remodel
these. Solid connectors refer to the causal links of the original model, with the dashed
connecters coming from the new hypotheses. This is an initial causal loop diagram
pending the assessment of potential soft variables.
Feedback loops R2 and R3 are due to the effects of the media interest and rioter enthu-
siasm on recruitment. R4 is due the effect of the media in creating initial sympathy for
the riot. R5 is the effect of enthusiasm on riot retention resulting from the numbers of
rioters, whereas B6 is the opposing force on retention resulting in the drop of enthusi-
asm due to arrests. B3 is the balancing loop due to the loss of rioters due to arrests. B5 is
the effect of reducing enthusiasm through arrests in riot recruitment.
4.1 Identification of Soft Variables
The following variables are considered as potential soft variables: Media Interest, sym-
pathy in population towards rioters, Rioter Enthusiasm and events per day. In addition
strength of cause is also considered as a “soft constant’. Other model elements are popu-
lation numbers related entities; all easily countable and with clear measures.
Media Interest
General Description. The media in the 1960s included newspapers and broadcast-
ing. The media expresses its interest through its coverage of an event. If
something is reported, the media is interested, and that reporting will have
an effect on others.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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events per day
R4
Media Interest
/ sympathy in
_ piviaton te a .
~~ 8 +
v.
: a
\ join riot leave riot
\ :
\ 4 | \
R3 7 Aes Bs) \ B6 time in riot
\
~ 7 \ 7
~ 7 Arrested Rioters \ /
+ effectiveness in RS sae
reeruitment, +/ v™® : | /
4
SN. __Rioter Eniusiasm wo arrests per day A
os 7 F
ae ~N
strength of cause. — ~ #
~~ s
a “Pretention of rioters —
Figure 3: Initial CLD of the Extended Riot Growth Model
Aggregation. The media has different styles of reporting, in particular whether
they are sympathetic or not to the event. As the only effect of media interest
in this model is on a population of potential sympathisers for the riot and
the rioters themselves it is deemed that any reporting would only positively
affect sympathy and recruitment. The riots progressed so fast it was simply
the news that they were happening that prompted people to action, not a
more time-consuming weighing up the pros and cons. Thus a single variable
should suffice.
Ordering. Newspapers and broadcasters give more coverage to some news items
than others. A function of a newsroom each day is to prioritise news. Thus a
clear ordering is implied.
Potential Measures. For newspapers these include: the number of words in the
newspaper article; its position in the newspaper, e.g. main page, page 2 etc;
its appearance in the opinion column. For broadcast media there could be:
the duration of a broadcast report; its position in the running order; the
number of reporters on the ground.
Thus Media Interest is a candidate for a soft variable.
Rioter Enthusiasm
General Description. Enthusiasm is a quality of an individual person, a rioter in
this case. It describes an internal dedication to the riot at hand whose results
will be seen by their desire to remain in the riot, recruit others and partici-
pate in protest. The latter is quite visible and could provide a meaning that
others can agree with.
Aggregation. Enthusiasm can also be applied to the group of rioters. With individ-
ual enthusiasm dependent on external events such as riot size, strength of
cause and arrests, there would not be a wide variation between rioters at a
given point in time. Thus an average value of individual enthusiasm should
suffice for group enthusiasm, giving the latter a realistic real world concept.
Ordering. It is common to describe some people as more enthusiastic than others,
thus an ordered variable is reasonable.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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Potential Measures. Potential measures of enthusiasm could be the volume of
chanting by the crowd, verbal engagement with onlookers, people recruited
per person, skirmishes with police. Generally individual enthusiasm for a
cause can be measured by an amount of time in a given period spent on that
cause, in this case time spent in the riot. Two of the measures mentioned,
time in riot and people recruited per person, are effects of enthusiasm in the
model.
Thus Enthusiasm is a candidate for a soft variable.
Sympathy
General Description. Sympathy is a quality of an individual person, a non-rioter in
this case. It describes a positive engagement with any news reports about
the cause coming from an internal alignment with the cause. It may result in
positive verbal comments to others and an openness to join the cause. The
former could provide a reportable meaning that others could agree.
Aggregation. Sympathy can also be applied to the group of non-rioters. However
unlike enthusiasm, sympathy will have much wider variations over indi-
viduals at any one time; riots, and their causes, can invoke strong opinions
for and against. Thus it is decided to disaggregate Sympathisers, into 2
stocks: one who are strongly sympathetic, and the remainder who remain to
be persuaded. Although both could have a variety of thresholds of persua-
sions (Granovetter, 1978), to a first approximation each can be taken as a
rough average of two widely diverging degrees of sympathy to the riot.
Thus the soft concept of sympathy is modelled by two population stocks, rather
than a soft variable.
Strength of Cause
General Description. This is the strength of feeling in a person. It could be under-
stood in terms of group membership, willingness to sacrifice time and
money for the cause. There does not need to be a riot occurring for this to be
understood.
Aggregation. If a single issue dominates the cause then a single variable is suffi-
cient. The trigger for the riots was the deep feeling of racial bias in living
conditions. Although there were many complex issues, this one issue sum-
marised them all.
Ordering. Clearly some people will give more time and money to a cause than oth-
ers.
Potential Measures. As mentioned, time and money spent on the cause, perhaps as
a proportion of available time and money.
Thus Strength of Cause is a soft variable. As the riots progressed over short pe-
riods of time, a few days, it will be sufficient for it to be a constant in this
model
Events per day
General Description. These were the events caused by rioters that were deemed il-
legal behaviour, largely damage, or attacks on other people. As events these
are potentially countable and are only “semi-soft” because of their variety,
including their seriousness.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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Potential Measures. For each riot there are excellent measures of reported inci-
dents to the police, medical and other authorities. Thus it will be sufficient to
count these events, relying on the person who initiated the call to decide
that they were serious.
As such events per day will be treated as a non-soft, countable variable; a popula-
tion flow.
Now the potential soft variables have been identified, the causal loop diagram, figure 3
can be revised, figure 4. The two clear soft variables, Media Interest and Rioter Enthusi-
asm, are identified by stock notation. Sympathisers has been split into two stocks, with
Potential Sympathisers earlier in the chain. The different effects of the media on creating
sympathy R4, and enhancing recruitment to the riot R2, can now be seen more clearly.
+
_ = events per day
@
, effectiveness in ! /
VN Z ot +}
SX ssmpathy in ibe aN atest por ap /
i sino ais KB te rsh JU __ arrests per da 2
sis Z Enhusasm | — 2 g
N =
x ie cat ~ a
Figure 4: Revised CLD of Extended Riot Growth Model
4.2 Construction of Modular Structure
To assist the model construction, the causal loop diagram, figure 4, is re-expressed in
modular form. The population model becomes a single module, named Population with
Riot, which will contain all five population stocks. Loops, R1, B1, B2, B3 and B4 are in-
ternal to this module. The two soft variables become the other two modules, named En-
thusiasm of Rioters, and Media Interest, figure 5 (overleaf).
There are three inputs to the population module, created by:
i. The effect of media interest on sympathy for the riot R4;
iii The combined effect of media interest R2, and rioter enthusiasm R3 & B5, on re-
cruitment;
tii. The effect of rioter enthusiasm on rioter retention R5 & Bé.
The three effects, which are the interface between the soft variable models and the
population module, are themselves made modules.
The population module also has two outputs:
i. The negative effect of arrests on rioter enthusiasm B5 & B6;
ii. The positive effect of riot size on rioter enthusiasm R3 & R5, combined with the
exogenous strength of the cause. Additionally there is a positive effect of riot size
on media interest R2 & R4. This output is used twice.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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The three effects of the population are passed through interfaces to the two soft vari-
ables, again made modules to model those effects.
effect of rioters
on media
‘on enthusiasm,
effect of rioter:
effect of arrests
on enthusiasm
Population
with Riot
5 :
gs 7
25 88
eo Se
pet gc
$3 25
5B
Be 2 =
BS
3
‘effect of enthusiasm
and media on
riot recruitment
[effect of media
‘on sympathy
for riot
Figure 5: Modular CLD of Extended Riot Growth Model
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 14
4.3 Construction of Sub-Models
4.3.1 Population Sub-Model
The main population sub-model is straightforward, figure 6. The two outputs, Rioters
and Arrested Rioters, are indicated by double outline symbols. The three inputs are
given in bold, and contain the name of the connecting sub module “effect of ...”. The
three inputs are the fraction of the population influenced, the probability of successful in-
fluence (of the sympathisers) and time in riot. The three are exogenous parameters as
far as the sub-model is concerned, but endogenous in the overall model. If these param-
eters are set exogenously, e.g. by constants or time series, the sub-model can be tested
independently. There are two internal parameters, Potential Number of Contacts and
Arrest rate; and the five initial values.
Arrested Rioters
ArestRate
arrests
per day
Ec Riotar
Va
rita. sympathisars
= va
jon
Polenta ympatate / 2, / #
Sympathisers ~~ / @
peg seaseansosaasef ™ nurperiivenens \
sympahisers \ # i jin per soter ,
fraction of me / | mma
population / ‘
{ |infuenced per day (atiainummet 0) pray \
\ { ofcontacts par succesful influsnce
\ Free Popuation | dav Dar person s \
~@ S
effect of enusiasm on
effect ofmedia on sympathy for Potential Number of effect of enthusiasm andmedia on riot ot retontion.timo in riot
riot raction of population influenced per day contaets per day perp
Figure 6: Population Sub Model
4.3.2 Media Interest Sub-Model
As a soft variable the construction of Media Interest will require a consideration of scale,
units, nature, inputs and output.
Scale
There is a clear minimum value Media Interest, corresponding to no reporting by
the media. Since newspapers and broadcasters have a limited capacity then Media
Interest will be given a maximum value.
Units
If units are the number of words used as a fraction of the total in a paper, then the
minimum value is 0%, and the maximum is 100%. A similar argument follows if
the units are the percentage of the broadcast time.
Nature
Because reports can be hourly, or daily, it is possible to think of Media Interest as
a flow. However Media Interest is not just modelling the physical reporting of the
events, but the impact those events have on the editors. As such reports of events
will appear in subsequent news reports, often with diminishing importance, un-
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 15
less there has been new events of the same nature. Thus there is a group memory
effect of the editorial team, and thus the variable is best modelled as a stock.
Additionally Media Interest is also understood by its effect on a population. That
population will also have a memory of news items for some period. Thus a stock
is preferred.
In order to achieve a limited scale on a stock, a goal-seeking archetype is used, figure 7.
The balancing loop Bim controls the growth of the stock, limiting growth to the target,
maximum media interest. The loop B2m allows the Media Interest to decline if there are
no further events to stimulate interest, modelling the decline in reporting over time
when a news item becomes “old news”. The generic pattern will be referred to as a Soft
Variable on a Limited Scale (SVLS). Levine (2000) uses a similar goal-seeking construct
for soft variables.
ica
effect ofrioters on
‘on media
effect
on Media /
Media / | -—~
\
\ increase Interest! /
Effect of media
x
{4
Bim) / interest
s rate of losing Interest
reaction time of Media to Events available
‘media interest
maximum media interest
Figure 7: Media Interest Sub-Model
Inputs
Media Interest is only influenced by the effect of the rioters. This causes increased
interest from the media, and is connected to the inflow (shown in bold, figure 7).
Outputs
The output is related to the stock value. In order to hide both values and units the
stock value is divided by its maximum possible value. The output, indicated with a
double outline, figure 7, is now limited to a scale 0 to 1, regardless of the value of
the stock. Thus any potential measure of the soft variable is private, and does not
affect the use of the variable in the model.
4.3.3 Rioter Enthusiasm Sub-Model
This follows ina similar fashion to Media Interest.
Scale
The minimum value of Rioter Enthusiasm occurs when all individuals have no en-
thusiasm, as expressed by them not recruiting anyone from a sympathetic popu-
lation, and leaving the riot in the shortest possible time. A maximum value follows
from the limited capacity of a person to engage in any activity. If a person reaches
that capacity then there would be no reason to envisage more enthusiasm as that
extra enthusiasm would have no effect on any dynamical element.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
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Units
Once a maximum has been set then a percentage of the maximum would be a
natural unit. However other units could be constructed, such as the fraction of
rioters involved in skirmishes with the authorities.
Nature
Enthusiasm for a cause can be generated internally as well as from external
stimuli. As the cause in this case is a serious breach of the peace by a group, it will
be assumed that unless there is an external cause then that enthusiasm to partici-
pate in a riot will fade. Thus a stock is the most natural element, with any internal
reinforcement mechanisms being covered by the memory effect of a stock
Thus Rioter Enthusiasm is constructed in a similar fashion to Media Interest, using the
soft variable on a limited scale model, figure 8.
effect ofrioters on enthusiasm.effect
of cause and riot on enthusiasm
effect of enthusiasm
eftacton enthusiasm) 3)
\\ | inerease {| \. maximum rioter enthusiasm
\ enthusiasm B2e
pat BI Ld Rioibe lose
a SJ _/ Enthusiasm enthusiasm.
reaction time of floter| available rioter, fale ofosindg}\ _hatural oss rate of enthusiasm
/ “enthusiasm enthusiasm) \
effect of arrests on enthusiasm.effect
of
maximum rloter enthusiasm] f arrests on loss of enthusiasm
Figure 8: Rioter Enthusiasm Sub-Model
Inputs
Rioter Enthusiasm has two inputs: the positive effect of the number of rioters; the
negative effect of the number of arrests. The former is connected to the inflow,
and the latter to the outflow affecting the proportional rate of loss from the stock
(indicated in bold). An additional parameter to represent a natural loss of enthu-
siasm in the absence of any arrests is required. The effect of arrests on enthusi-
asm is over and above this natural rate.
Outputs
The output is related to the stock Rioter Enthusiasm. Like Media Interest division
by the maximum value achieves the privacy of the units and scale of enthusiasm,
constraining the scale to 0 to 1.
Thus a case has been made for both soft variables to have dimensionless outputs on a
scale 0 to 1. Coyle (2000) described such a scale as tempting but questioned the mean-
ing of a value of 0.5. In the models above such a value would mean that the variables
have 50% of the effect that they would have had at their maximum value. However it
does not require that any measure of the variable would be at 50% of its scale as the
measure is related to the internal stock value, which may not have a linear relationship,
nor even be a ratio scale (Levine, 2000). For example if the output of media interest is
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 17
50% then it means that the effect of the media is half what it could potentially be. It
does not mean that half the newspaper is filled with news of the riot.
As the model is constructed the input also places an interpretation on the meaning of
the value 50%. Because of the loop B1m it would be harder to raise the value from 50%,
than to reduce the value. Put another way, it takes less effort to raise the soft variable
value to the halfway point than to take it from halfway to saturation. It has been as-
sumed that as the media gets close to saturation there is a greater reluctance to increase
coverage. Alternative models could be constructed if a linear relationship were pre-
ferred.
These approaches to the interpretation of the soft variable value raise important issues
for model calibration. The parameters connected with the soft variable should be de-
termined by its response to the causes, and the effect of the variable in the model, not
necessarily by any potential measures. In this sense the soft variable is referentially
transparent, that is, in the model it is understood in terms of its inputs and outputs
alone. For example in the case of Rioter Enthusiasm then in two different runs, with
identical inputs, the output should be the same for the same values of its two internal
parameters, reaction time to Rioter hostility and the initial value of the variable. The lat-
ter is scaled in a similar way to the output to preserve privacy. The sub-model can then
be used without any knowledge of its internal workings, apart from the parameter
values.
4.4 Use of Soft Variables
Having established that the effect of a soft variable can be distinguished from its meas-
ures, then modules to control the effect of each soft variable on the population module
are introduced.
Effect of Soft Variables on Population
Media interest has an effect on the potential sympathetic population; rioter enthusiasm
affects rioter retention (figure 5). There is a third effect of both soft variables combined
on recruitment to the riot. The output of both soft variables is on a 0 to 1 scale, thus
converting the output into an effect is relatively straightforward and the effects can be
combined using the algebra of table 1.
The media effect on the sympathy of the potential rioters is by parameter multiplica-
tion, a converter to convert media on its normalised scale to sympathy, figure 9. This in
turn links to the fraction of the population influenced per day, which is handled by a
graphical converter to allow for potential non-linearities in the effect, and to deal with
the change of units from [unitless] to [day]*(-1).
For the effect of the enthusiasm, E, on the average time a rioter spends in the riot, f,,,,,a
maximum, f,,,,, and minimum time, ¢,,,,, is used, ,,,. = twin + (1 JE, figure 10. The
0 to 1 scale of E ensures the bounds are not exceeded. The dimensions balance, as the
effect of the soft variable is unitless.
min? max bin
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 18
QqMaximum Time in Riot
Enthusiasm of Rioters.effect
Media tect
cn srmpathy Of enthusiasm 7
Media interestEffect ofmedia oO +O BO time in rot
leffect of enthusiasm ail
eect of media on sympaty ‘racion oF poputaton
iluenced pet cay O'itinirnan Time in Riot
Figure 9: Media Effect on Sympathy Figure 10: iasm Effect on Riot
The effect of both soft variables on the probability of a successful influence by a rioter
P.,,-requires some thought as to how the two variables combine. The riots in question
took place in the 1960s before the advent of social media, and occurred over a very
short period of time, thus direct recruitment through media exposure has been ruled
out of this model. Instead media exposure enhances the likelihood of successful re-
cruitment. It is assumed that media exposure would make a sympathiser more likely to
accept, and rioter enthusiasm would enhance a rioter’s ability to persuade.
Thus it is conceivable that the media interest M would have been sufficient to cause
rioters to recruit people to the riot, even if their enthusiasm was zero. This would be the
situation where a rioter merely informs the sympathisers of the fact that the riot is tak-
ing place. That is, there is a demand from people to join the riot, provided someone tells
them the place. Likewise a riot is possible without any media exposure to enhance the
likelihood of acceptance, as the persuasion of the rioter would be sufficient. Thus OR
logic, the lenient combination, is deemed the most suitable.
Let the effect of the media be scaled by a parameter, media effect on recruitment e,, <1.
Likewise scale the effect of the enthusiasm, enthusiasm effect on recruitment e, <1.
Then the probability of successful influence is P.,.. =e,M+e,E —e,,Me,E, figure 11.
The limited scale of the two soft variables, and the two associated parameters, ensures
the scale of the probability lies on 0 to 1. The two parameters allow the relative effects
of the two soft variables on recruitment to be adjusted.
Media effect
on Recruitment,
effect of media
—
on recruitment
probability of
‘Media interestEffect of media succesful influence
effect of enthusiasm
on recruitme — combined effect
a of enthusiasm and
media on recruitment
Enthusiasm of Rioters.effect
of enthusiasm y
C¥emoeninusiasm
effect on Recruitment
Figure 11: Effect of Media and Enthusiasm on Rioter Recruitment
There are other potential models of how these two variables could be combined.
Effect of Population on Soft Variables
The population has two effects on rioter enthusiasm; positively through the numbers in
the riot, and negatively through the arrests. Enthusiasm has two inputs to accommodate
this. The positive effect on enthusiasm is also affected by the exogenous strength of the
rioters’ cause. The population also has an effect on the media interest. There are three
separate outputs from the population module for these three effects.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 19
Three separate modules provide the linkage between the population module and the
three effects. Unlike the soft variables the population variables are not hidden, nor are
they on a limited scale. Thus each of the effect modules will need to translate the popu-
lation outputs into suitable scales. This is achieved using a Holling function of type II,
f =xI(X,,y +X) (Holling, 1959; Freedman, 1980). The parameter x,,,-is the value of the
input x that produces an output of 0.5, unity being the maximum output. The curve is
monotonic of decreasing positive gradient. It corresponds to the logit term (Sterman,
2000). x, governs the strength of the effect of the input on the output.
The effect of arrests on rioter enthusiasm follows the Holling construct, figure 12. In-
creasing arrests gives an increasing output, whose effect on Enthusiasm is to subtract,
figure 8.
The effect of the riot size on Media interest is via events per day, which is a flow leading
to the cumulative reported events, figure 13. A parameter, events per rioter per day, con-
trols the impact of the rioters on such events. Events per day is passed through a Holling
type II function to achieve a normalised scale output.
Poputation with RiotRioters Events per Rioter per day,
Cummulative
NS coe
8 events ;
Qharrests for hatfimpact
Population with effect of arrests on per day 4D) [Events size for
RiotArrested Rioters. loss of enthusiasm "half impact
> effect of i
events on media
effect of arrests on enthusiasm effect on media
Figure 12: Effect of Arrests on Enthusiasm Figure 13: Effect of Rioters on Events
The final module contains the combined effects of the size of the riot e, and the strength
of the cause that underlies the riot C. C and e, do not have a symmetric effect on rioter
enthusiasm. If there is no riot e, =0, a cause worth fighting for C >0 is sufficient to
produce enthusiasm: ég¢(C,€g) = €c(C,0) > 0. However if there is no cause C =0, thena
riot will not of itself produce enthusiasm in the rioters e,.(0,e,) =0. It might encourage
some to join in with looting, but to engage with the authorities there would need to be
some grievance, or cause to fight for. The combination needs a cause, and an occurring
riot enhanced by the cause.
The strength of the cause, and the effect of riot size are placed on a scale 0 to 1, the lat-
ter again achieved with a Holling function. The riot enhanced by the cause is given by
OR logic, table 1, e€p,,¢ =p +C —egC. The final output is achieved with AND logic be-
tween this and the strength of cause: go = €p,,c X C = (eg +C -e,C)C, given by effect of
cause and riot on enthusiasm in figure 14. This satisfies e,.(C,0) >0 andeég(0,e,) =0.
However large the riot, even if e, =1, its maximum value, then eg.cannot be unity, un-
less the strength of the cause is unity. Thus however large a riot, it cannot have the
maximum effect on rioter enthusiasm unless the strength of the cause is total.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 20
___ effect of cause and
~~ riot on enthusiasm
*
Riot Size for
half impact
_-* Sffect of riot size
_-—~ enhanced by cause.
Population with RiotRioters| effect of riot size
‘on enthusiasm
Figure 14: Effect of Rioters and Strength of Cause on Enthusiasm
The full model code is given in the appendix, with Stella 10 files in the additional ma-
terial.
5 Model Testing
5.1 Soft Variable on a Limited Scale Sub-Model
A generic single stock model was used for both media interest and the enthusiasm of
rioters, referred to as a soft variable on a limited scale model (SVLS). The model has a
goal seek balancing loop to control the growth and a draining process on the outflow to
allow for decline in the absence of any input. An alternative model for soft variables is
the standard stock adjustment (SA) process, where the input is through the goal of the
process. Of course this latter process cannot handle a limited scale, unless the limits are
achieved within the calibration window of the model.
To test the SVLS sub-model, its response to standard inputs is compared with the stock
adjustment process, figure 15. Two such results are shown in figure 16. For a low input
value, that keeps output significantly less than unity, the SVLS can follow stock adjust-
ment for a suitable choice of parameters (left hand graph). However when the input
value is increased, the output of the SVLS is compressed to keep it under unity, the in-
tended result (right hand graph). By contrast the stock adjustment output has exceeded
unity. Thus the SVLS is an improved version of stock adjustment if the scale is to be lim-
ited, producing similar responses and delays.
sa
justement time
Aajustement time aig Stock Adjustment SA,
fo SA gap
input Cy ——a-4 input scale
shape GY”
\ SA goal
\ svLs Soft Variable ore
\ in Limited Scale SVLS ay
SVL
growth rate SVLS drain rate
‘SVLS max
Figure 15: Stock Adjustment Process & Soft Variable on Limited Scale Model
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 21
1: Stock Adjustment SA Soft Varab.ted Scale SVLS. 3: input sha "Sac armen 3A
1
lan A ae We /
olf \ olf a
0.00 62 i299 18.75, err) 0.00 6.28 12.50 18.75 25.00
Figure16: Comparison of Stock Adjustment with Soft Variable on Limited Scale Model
5.2 Calibration & Historical Fit
The starting point for calibration is the historical fit to the reported events of the Los
Angeles 1965 riot for the original model, as given in Burbeck et. al. (1978). This fit was
reproduced with the loops through Media Interest and Enthusiasm of Rioters switched
off, figure 17. Additionally the attempt was made to ensure around 30,000 people par-
ticipated in the riot (Burbeck et. al., 1978). The effects due to the new hypotheses were
introduced gradually until the desired effect of the soft variables was reproduced. At
each stage the historical fit of reported events per day!, figure 17, was the benchmark
for re-calibration.
1. The arrest rate was calibrated to give the total arrests after 5 days of about 4000
people (Martin Luther King Jr., 2014).
2. A realistic graph for media interest was obtained; starting at zero it rises rapidly,
but delayed following the onset of the riot (figure 18). It peaks after the peak of the
riot, and does not return to zero when the riot has ceased, as there was still signifi-
cant media coverage.
3, A realistic graph for rioter enthusiasm was produced. This was assumed to start
high, rise and peak before the peak of the riot due to the freshness of the original
enthusiastic rioters, and then fall slowly due to the effect of the arrests, and the
dwindling riot numbers (figure 18). Care was taken to ensure the strength of the
cause and the riot numbers both contributed to the rise in enthusiasm. The fixed
strength of cause has the effect of reproducing the contour of the effect of the rise in
rioters, but squashing the combined response into a narrower range, thus making
the change of enthusiasm respond to riot size in a less than linear fashion (figure
19). This follows from the combination e,.. = (eg +C -—egC)C discussed earlier.
4. The effect of the media on producing sympathisers was slowly calibrated so that
Potential Sympathisers initially matched the sympathisers, figure 20. Sympathisers
starts by rising before the effects of riot recruitment deplete its numbers. This left
about 20,000 people who did not participate in the riots, a much larger figure than
1 The reported events per hour were compiled by Burbeck et. al., (1978), and appear in that paper. For
this paper the units have been changed to events per day, figure 17.
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 22
that obtained by Burbeck et el (1978) who had criticised their own data fitting for
depleting too much of the sympathetic population. Thus the introduction of the Me-
dia Interest soft variable, and the concept of sympathy, has improved the Bur-
becks’s original model.
The effect of enthusiasm on the time in the riot was calibrated to give a small vari-
ation, where the average of the minimum and maximum values was similar to the
time in riot obtained by Burbeck et. al. (1978), figure 21. This enabled a moderate
effect of falling enthusiasm on rioter retention. There would be scope at this point
for alternative calibrations in order to produce the asymmetry seen in other doc-
umented rioter numbers (Burbeck et. al., 1978).
Finally the effect of enthusiasm and media on rioter recruitment was introduced.
The effect of the media was adjusted to exceed the effect of enthusiasm by around
the end of the second day when the media exposure had become established, figure
22. The final historical fit for events per day, figure 17 was reproduced again. Pa-
rameter values are given in table 2.
Module Parameter Values
Global strength of cause 0.5
effect of rioters on entk Riot Size for half impact 400
effect of arrests on enthusiasm. Arrests for half impact 600
effect of rioters on media. Events Size for half impact 30
Events per Rioter per day 0.01
effect of enthusiasm on riot retention | Minimum Time in Riot 0.1
Maximum Time in Riot 0.42
effect of enthusiasm and media on Media effect on Recruitment 1.0
riot recruitment
Enthusiasm effect on Recruitment 0.82
effect of media on sympathy for riot Media effect on Sympathy 1.0
Media Interest reaction time of Media to Events 0.2
rate of losing Interest 0.7
Initial Media effect 0.0
Enthusiasm of Rioters reaction time of Rioter 0.3
natural loss rate of enthusiasm 0.4
Initial effect of Entt 0.5
Population with Riot Potential Number of Contacts per day per 18.9
person
Arrest Rate 0.49
Total Population 50,000
Initial Sympathisers 25,000
Initial Rioters 90
Table 2: Parameter Values for Historical Data Fit, Los Angeles Riot 1965
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 23
X Reported Events per Day
Events per Day
20,000,
10,000
ost 57 ~ == strength of cause \
r — = effect of rot size on enthusiasm
effect of cause and riot on enthusiasm
° r °
° 1 2 oes 3 4 s
Figure 19: Effect of Riots on Enthusiasm
1 04 1
Rioters
= — Media Interest
=== Rioter Enthusiasm
Figure 18: Rioters, Media and Enthusiasm
Potential Sympathisers
~~ Sympathisers
== effect of media on sympathy
fraction of pop. influenced per day
pag 3 4 5
Figure 20: Effect of Media on Sympathy
= = Rioter Enthusiasm
time in riot
° 1 2 3
Days
Figure 21: Effect of Enthusiasm on Time in Riot
== effect of enthusiasm
4 = = effect of media
combined effect
Prob. of suce influence
pays? 4 5
Figure 22: Combined Effects on Recruitment
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 24
6 Discussion
6.1 Model Improvements
The inclusion of soft variables into the Burbeck et. al. (1978) model for the dynamics of
riot growth has improved the model in two ways. Firstly there are improved parameter
values. The initial number of rioters has increased from 10, which Burbeck et. al. admit-
ted was too low, to 90. This follows from the effects of rioter enthusiasm and media in-
terest on riot recruitment and retention. It is quite conceivable that the initial number
may improve even further with more refined data fitting. Additionally, the total number
of sympathisers has increased dramatically from the Burbeck et. al. value, which was
only just above the total number of rioters. With the inclusion of the soft variables a
realistic historical fit is obtained with about half the initial sympathisers never joining
the riot, closer to the recorded facts. This followed from the effects of media interest on
the potentially sympathetic population.
The second improvement in the model is that it now tells a better story. Burbeck et. al.
admitted that the probability of rioter recruitment and retention were unlikely to be
constant, and that their enthusiasm played a part in the dynamics. Likewise the sympa-
thy of the potential population was believed to increase with media exposure. Soft vari-
ables have allowed the model to reproduce that story.
6.2 Methodological Improvements
The methodology presented has made at least five potential improvements over exist-
ing ones. Firstly, the use of data hiding in the methodology has helped to separate out
the measurement of soft variables from their use. Hiding the soft variable units has en-
abled the effects of the variables to be handled without being confused by their meas-
urement schemes. This approach now encourages the modeller to think about the rela-
tionship of measures of the soft variable independently of its use.
Consider an analogy from physics. Solar physicists require measures of key variables of
the sun such as temperature, pressure etc. These variables interact with each other dy-
namically as the solar composition changes. The variables cannot be measured directly
but indirect measures can be obtained by the radiation that is produced. However the
measures of the radiation are not used in the dynamical computation of the sun, they
are only an indication of what the underlying variables are. Likewise measures of soft
variables are not directly used in the construction and calibration of a system dynamics
model, but are only an indication of how those variables behave.
As a specific example consider the case where a measure of Media Interest has been ob-
tained in terms of length of radio broadcasts. A general measure of the media can be
modelled as a separate output from the Media Interest module, figure 23a. The Media
Interest module is then connected to a module dedicated to the radio broadcast meas-
ure of the media, figure 23b. The radio broadcast module, receives the hidden value of
Media Interest as input and then models the relationship between it and the length of
radio broadcasts by whatever means, functional or look up table, possibly non-linear.
Finally length of radio broadcast is output, figure 23c. This preserves the privacy of the
Media Interest soft variable, whilst making the measure available. The calibration of the
model will not directly depend on the values of this measure, although indirectly, to-
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 25
gether with its own model of its relationship to the soft variable, it could tighten up a
calibration.
maximum media Effect
of media
Media
Interest
—— Media
Interest
Media Interest Measure Length of
of media Radio Broadcasts
effect of Media Interest on
‘ Radio
jeasure
py Broadcasts length of radio broadcasts
(@ () iG)
Figure 23: Measurement of a Soft Variable. (a) Media Module with Separate Outputs for Measure & Effect.
(b) Modular View of Media Interest & Radio Broadcast. (c) Model of Radio Broadcast Measure of Media
The second methodological improvement is that data hiding has enabled different soft
variables with a limited scale to be combined on a common scale, normalised to 0 to 1.
The normalisation of the output indicates the maximum effect the soft variable has on
other system elements, not influenced by its measure. Thus cognitive algebra and
probability laws can be employed to create a more systematic approach to variable
combination. Although in this current study soft variables have been restricted to a lim-
ited scale, the maximum of the scale is not limited as it is hidden.
Thirdly, the use of referential transparency has allowed the sub-modules encapsulating
the soft variables to be tested prior to their inclusion in the model. Likewise the mod-
ules for the causes and effects of the variables can be independently tested in their dif-
ferent combinations. The inner details of the models are not required to be seen for the
sub-modules to be used; a knowledge of their parameters is sufficient. Thus in the
model the soft variable is understood by its use and behaviour, not its internal construc-
tion.
Fourthly, following on from referential transparency, model calibration has been made
more systematic. The effects of the population on the soft variables can be introduced
gradually before their feedback on the population is introduced. With slow calibration
from the prior historical fit without soft variables, the model user only needs to concen-
trate on a small number of adjustable parameters at any one time.
Fifthly the staged procedure for the identification and construction of soft variables
brings clarity to the modelling process for both other modellers and clients involved in
the process. Undoubtedly the procedure presented here is not unique in its order or
number of stages. However such an agreed procedure would bring more confidence to
the model building and make it easier to deal with ambiguities and errors in the model-
ling process
7 Conclusion
A procedure for the identification, construction and use of soft variables has been pro-
posed. A modular structure was used to encapsulate the soft variables enabling their
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 26
values and units to be hidden, thus separating out the effect of the soft variable from its
measure. The modular system enforces referential transparency that each soft variable
is understood by the relationship between its inputs, and outputs alone, for given pa-
rameter values. The method was applied to an existing SIR type model of the progress
of a riot which employed only population, ie. non-soft, variables. The method also en-
abled the population to be encapsulated in a module with a state composed of a number
of stocks, i.e. multi-dimensional. It is felt the method shows promise as it produced an
improved model, with a sharper understanding of the identification, construction and
use of soft variables.
Although beyond the scope of the current paper, there is much that could be done with
sensitivity analysis to produce alterative historical fits and stories. In particular it would
be interesting to explore a greater variation on the probability of successful influence,
and the time in riot, which are quite conservative in the above results. Although a sys-
tematic approach to calibration was tried, there would be much scope for improvement
here. Additionally the model could be applied to other riots, especially those where
there is a degree of asymmetry in their rise and fall (Burbeck et. al., 1978). Nevertheless
it is felt the current analysis is sufficient to create an interest in this type of methodol-
ogy. As such it would be interesting to apply the method to other scenarios.
It is not claimed that this methodology is complete, explored fully, or better than exist-
ing attempts to include soft variables. Instead it is hoped that the paper will inspire fur-
ther research in the area.
Acknowledgements
Soft variables have been used extensively in student projects on the undergraduate sys-
tem dynamics course at the University of South Wales for a number of years. Particular
thanks go to former students Dr Alex Berriman, Dr John Mehers, Amira Irshad and Cath-
erine Evans for the helpful contributions they made to the methodology given in this
paper. Thanks are also due to Professor Paul Roach, of the same university, for inspiring
discussions on the use of cognitive algebra.
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Appendix — Model Code
Reported_events = GRAPH(time_in_hours)
(0.00, 0.00), (1.00, 1.00), (2.00, 1.00), (3.00, 0.00), (4.00, 0.00), (5.00, 1.00), (6.00, 1.00), (7.00, 1.00), (8.00, 0. 00), (9.00, 0.00), (10.0,
.0, 1.00), (14.0, 1.00), (15.0, 2.00), (16.0, 1.
‘0, 1.00), (24.0, 1.00), (25.0, 2.00), (26.0, 3.00), (27.0, 4.00), (28.0, inn. (29.0, 3.00), (30.0,
.0, 9.00), (34.0, 11.0), (35.0, 12.0), (36.0, 11.0), (37.0, 8.00), (38.0, 9.00), (39.0, 12.0), (40.0,
0), (44.0, 27.0), (45.0, 31.0), (46.0, 29.0), (47.0, 28.0), (48.0, 27.0), (49.0, 28.0), (50.0,
.0, 41.0), (58.0, 42.0), (59.0, 41.0), (60.0,
.0), (61.0, 45.0), (62.0, 45.0), (63. .0, 33.0), (68.0, 28.0), (69.0, 23.0), (70.0,
25.0), (71.0, 26.0), (72.0, 30.0), (73: .0, 12.0), (78.0, 13.0), (79.0, 10.0), (80.0,
8.00), (81.0, 7.00), (82.0, 8.00), (83. , (87.0, 4.00), (88.0, 4.00), (89.0, 5.00), (90.0,
4.00), (91.0, 5.00), (92.0, 4.00), (93.0, 4.00), (94.0, 5.00), (95.0, 4.00), (96.0, 4.00), (97.0, 3.00), (98.0, 3.00), (99.0, 2.00), (100,
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 28
3.00), (101, 2.00), (102, 2.00), (103, 2.00), (104, 1.00), (105, 1.00), (106, 1.00), (107, 1.00), (108, 2.00), (109, 1.00), (110, 3.00),
(111, 5.00), (112, 5.00), (113, 4.00), (114, 2.00), (115, 2.00), (116, 1.00), (117, 1.00), (118, 1.00), (119, 1.00), (120, 1.00)
{events per hour as given in Burbeck et al, 1978}
strength_of_cause = 0.5
time_in_hours = time*24
effect of enthusiasm on riot retention:
effect_of enthusiasm = Enthusiasm _of Rioters.effect_of enthusiasm
Maximum_Time_in_Riot = 0.42
Minimum_Time_in_Riot = 0.1
time_in_riot = Minimum_Time_in_Riot+(Maximum_Time_in_Riot-Minimum_Time_in_Riot)*effect_of enthusiasm
effect of enthusiasm and media on riot recruitment:
combined _effect_of_enthusiasm_and_media_on_recruitment = ef-
fect of enthusiasm_on_recruitment+effect_of_media_on_recruitment-
effect_of_enthusiasm_on_recruitment*effect_of_media_on_recruitment
effect_of enthusiasm_on_recruitment = _effect_on_Recruitment \_ of Rioters.effect_of |
effect_of_media_on_recruitment = Media_effect_on_Recruitment*Media_Interest.Effect_of_media
Enthusiasm_effect_on_Recruitment = 0.8
Media_effect_on Recruitment = 1
probability_of succesful influence = GRAPH(combined_effect_of_enthusiasm_and_media_on_recruitment) (0.00, 0.005), (0.1, 0.13),
(0.2, 0.19), (0.3, 0.24), (0.4, 0.3), (0.5, 0.415), (0.6, 0.545), (0.7, 0.605), (0.8, 0.65), (0.9, 0.7), (1, 0.8)
effect of media on sympathy for rio
effect_of_media_on_sympathy = Media_effect_on_Sympathy*Media_ Interest Effect_of_ media
fraction_of_population_influenced_per_day = GRAPH(effect_of_media_on_sympathy) (0.00, 0.0597), (0.1, 0.0903), (0.2, 0.116), (0.3,
0.144), (0.4, 0.171), (0.5, 0.197), (0.6, 0.227), (0.7, 0.274), (0.8, 0.306), (0.9, 0.334), (1.00, 0.369)
Media_effect_on_Sympathy = 1
effect of rioters on enthusiasm:
effect_of_riot_size_enhanced_by_cause = effect_of_riot_size_on_enthusiasm+strength_of_cause-
effect_of_riot_size_on_enthusiasm*.strength_of_cause
effect_of_riot_size_on_ with Riot Rioters /(Riot_Size_for_half_impact+Population_with_Riot.Rioters)
(Holling type 2 function - impact is absolute not relative total population)
effect_of_cause_and_riot_on_enthusiasm = effect_of_riot_size_enhanced_by_cause*strength_of_cause {either the cause, or the pro
test size enhanced by the cause - thus cause is sufficient to provide enthusiasm, but size with no cause is not}
Riot_Size_for_half_impact = 400
effect of rioters on media:
Cummulative_Events(t) = Cummulative_Events(t - dt) + (events_per_day) * dt
INIT Cummulative_Events = 0
INFLOWS:
events_per_day = Events_per Rioter_per_day*Population_with Riot Rioters
Events_per_Rioter_per_day = ees
Events Size_for_half.i
effect of arrests on enthusiasm:
Arrests_for_half_impact = 600
effect_of_arrests_on_enthusiasm = total_arrests /(total_arrests+Arrests_for_half_impact)
effect_of_arrests_on_loss_of enthusiasm = effect_of arrests_on_enthusiasm
Enthusiasm of Rioters:
Rioter_Enthusiasm(t) = Rioter_Enthusiasm(t - dt) + (increase_enthusiasm - lose_enthusiasm) * dt
INIT Rioter_Enthusiasm = Initial_effect_of_Enthusiasm*maximum_rioter_enthusiasm
INFLOWS:
increase_ = effect_on_ ‘available_rioter_« i ‘reaction_time_of_Rioter
OUTFLOWS:
lose_ = Rioter_| jasm*rate_of _losing_.
available_rioter__ = _rioter_ R a, ), _rioter_¢
effect_of _rioter
effect_on_enthusiasm = effect_of rioters_on_enthusiasm.effect_of_cause_and_riot_on_enthusiasm
Initial_effect_of_Enthusiasm = 0.5
maximum_rioter_enthusiasm = 1
natural_loss_rate_of_enthusiasm = 0.4
rate_of_losing_enthusiasm = effect_of_arrests_on_enthusiasm.effect_of_arrests_on_loss_of_enthusiasm + natu-
ral_loss_rate_of_enthusiasm
reaction_time_of Rioter = 0.3
Media Interest:
Media_Interest(t) = Media_Interest(t- dt) + (increase_interest -lose_interest) * dt
INIT Media_Interest = Initial_Media_effect * maximum_media interest
INFLOWS:
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
Page 29
increase_interest = effect_on_Media*available_media_interest/reaction_time_of_ Media_to_Events
OUTFLOWS:
lose_interest = Media_Interest*rate_of_losing_Interest
available_media_interest = (maximum_media_interest-Media_Interest)/maximum_media_interest
Effect_of_ media = Media_Interest/maximum_media_interest
effect_on_Media = effect_of_rioters_on_media.effect_on_media
Initial_Media_effect = 0
maximum_media_interest = 1
rate_of_losing Interest = 0.7
reaction_time_of_Media_to_Events = 0.2
Population with Riot:
Arrested _Rioters(t) = Arrested Rioters(t - dt) + (arrests_per_day) * dt
INIT Arrested_Rioters = 0
INFLOWS:
arrests_per_day = Rioters*Arrest_Rate
Ex Rioter(t) = Ex_Rioter(t - dt) + (Ieave_riot) * dt
INIT Ex_Rioter = 0
INFLOWS:
leave_riot = Rioters/time_in_riot
Potential_! ) = Potential_: t- dt) + (-become_sympathetic) * dt
INIT Potential_s = Total_Pop Initial
OUTFLOWS:
become_s ic = Potential_! fraction_of_ ion_influenced_per_day
Rioters(t) = Rioters(t- dt) + (join_riot -leave_riot - arrests_per_day) * dt
INIT Rioters = Initial_Rioters
INFLOWS:
join_riot = Rioters*number_influenced_to_join_per_rioter
OUTFLOWS:
leave_riot = Rioters/time_in_riot
arrests_per_day = Rioters*Arrest_Rate
Sympathisers(t) = Sympathisers(t - dt) + (become_sympathetic - join_riot) * dt
INIT Sympathisers = Initial_Sympathisers-Initial_Rioters
INFLOWS:
become_symp: = Potential_; fraction_of_ \_influenced_per_day
OUTFLOWS:
join_riot = Rioters*number_influenced_to_join_per_rioter
actual_number_of_contacts_per_day_per_person = frac-
tion_of_population_sympathisers*Potential_Number_of_Contacts_per_day_per_person
Arrest_Rate = 0.49
fraction_of_population_sympathisers = Sympathisers/Free Population
fraction_of_population__influenced_per_day = effect_of_media_on_sympathy_for_riot.fraction_of_population_influenced_per_day
Initial_Rioters = 90
Initial_Sympathisers = 25000
number_influenced_to_join_per_rioter = actual_number_of_contacts_per_day_per_person*probability_of succesful_influence
Potential_Number_of_Contacts_per_day_per_person = 18.9
probability_of succesful_influence = effect_of_enthusiasm__and_media_on_riot_recruitment probability_of_succesful_influence
Riot_Participants = Ex_Rioter+Arrested_Rioters+Rioters
time_in_riot ffect_of_enthusiasm_on_riot_retention.time_in_riot
Total_Population = 50000
Free_Population = Sympathisers + Rioters + Potential_Sympathisers + Ex_Rioter
Model Building with Soft Variables - Hayward, Jeffs, Howells & Evans - ISDC 2014
