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Incorporating Soft Variables Into System Dynamics Models:
A Suggested Method and Basis for Ongoing Research
Alan Charles McLUCAS
University College, University of New South Wales
School of Civil Engineering,
University College UNSW @ ADFA,
Australian Defence Force Academy,
Northcott Drive,
CAMPBELL ACT 2600
AUSTRALIA
+ 61 2 6268 8332 / +61 2 6268 8337
a.mclucas@adfa.edu.au
Abstract
How to determine the impact of soft variables, including intangibles or social variables, and
combining them as necessary with hard variables in system dynamics models is a significant
challenge. This paper identifies a weakness in system dynamics modelling practice, that is, in
reliably incorporating soft variables into system dynamics models. A method for
incorporating such variables and a basis for further research is offered. The method
combines systems thinking, research into causality analysis, multiple criteria decision
analysis (conjoint analysis) and system dynamics modelling, in an integrated approach.
“To omit such [soft] variables is equivalent to saying that they have zero effect —
probably the only value that is known to be wrong!” (Forrester, 1961: 57)
It is inescapable that from time-to-time we will need to build system dynamics models that
take soft ' variables into account. The challenge is to incorporate the influences of soft
variables in ways that produce meaningful, reliable and repeatable results. We need to
develop in-depth understanding of the roles and influences of soft variables. We must avoid
making guesses about the influences that soft variables might have. Rather, we must create
and repeatedly test dynamic hypotheses about soft variables. This will also demand that we
comprehensively document our hypotheses about influences and how those influences are
produced and combined, making the results available for peer review. Only when we do this
will we build a sound appreciation of the nature and significance of soft variables both in our
models and in the real world. Our track record in this area is not as good as it might be, as the
following example suggests.
Pseudo-algebraic Expressions in System Dynamics Models — An Example
It is disturbing to encounter system dynamics models reflecting guesses about soft variables
and as a result containing pseudo-algebraic expressions conveniently and artificially contrived
to make a model or simulation behave as the modeller intends. Evidence of this practice can
be found in models produced by students and experienced practitioners alike. Pseudo-
algebraic expressions are a corruption of mathematical logic used to conveniently and
artificially combine quantified soft variables. Such expressions may also involve mixes of
hard and quantified soft variables.
The assumptions underlying this practice seem to be that soft variables, including that class of
soft variables known as ‘intangibles’:
e conform to numerical scales;
e can be quantified in an absolute sense;
© quantification is both valid and universally acceptable; and
e once quantified, soft variables can be treated as dimensionless variables that can be
added or multiplied “ in exactly the same way as ordinary variables encountered
routinely in system dynamics modelling are.
In their totality, these assumptions are erroneous; when taken individually, caution is needed.
Further, any practice leading to the creation of pseudo-algebraic expressions, or their use,
must be closely scrutinised.
In one particular example seen recently, a management flight simulator was built to assist in
training managers to make decisions in the complex dynamic environment a particular firm
operates. The underlying model contained around 60 variables, of which some 20 could only
be described as being soft. Algebraic expressions made up of interesting mixes of hard and
soft variables were built into the model to replicate the modes of behaviour that the modeller
iii
had identified as important ".
One expression in the model contained the soft variables Organisational_Performance,
Qualifications_Held_By_ Individuals, and Individual’s_Motivation_Level.
Organisational_Performance was intended to describe how well the organisation performed
(in an average sense, rather than in relation to discrete events) in making decisions, where
decision makers were required to draw upon their own knowledge, skill and competence.
Qualifications_Held_By_ Individuals described how well equipped individuals, in terms of
formal qualifications held (including skills and competencies), were to make decisions and
Individual’s_Motivation_Level indicated motivation of individuals to take action, make the
necessary decisions, or to implement a particular strategy. The resulting algebraic expression
took the form:
Organisational _ Performance = [Qualifications _ Held _ By _ Individual x Individuals _ Motivation _ Level
The abuse of mathematical logic and system dynamics principles in this example should be
self-evident.
Despite obvious flaws in the model, the paper describing this model was peer reviewed and
ultimately accepted for a recent international system dynamics conference. This suggests that
as a group, we are prepared to accept these dubious modelling practices?
The intent of the modeller in producing this simulator was genuine although surprisingly
naive. The modeller apparently set out to do exactly what we teach, that is, to replicate
observed reference modes of behaviour. Our actions, both in terms of learning and system
dynamics modelling practice are both misguided and naive if we do not critically investigate
why and how reference modes of behaviour are produced. In this instance, it seems that the
modeller was actually mimicking what he saw as an important reference mode of behaviour
without having a clear understanding of how that particular reference mode was actually
created in the real world, or if he did he did not have the necessary tools (either physical or
intellectual) to build a faithful representation of the causal mechanisms.
In this instance, and probably of greater concern is that how the particular reference mode of
behaviour was actually created is unlikely ever to be questioned by anybody subsequently
flying the management flight simulator in a training session. This is because the underlying
structure of the model and its code, that making the simulator behave as it does, are masked
from the players. Players, like the layperson in many real-life systemic problem situations
will focus on the responses to their actions, rather than the (obscured) mechanisms producing
the responses. The absence of essential critical analysis in such instances is very likely to
lead to the unfortunate consequences that:
© poor practices become embedded in the design of simulations;
erroneous conclusions are drawn about systemic causality, where soft variables are
involved; and
« fallacious learning experiences occur.
This suggests we must look seriously at the treatment of soft variables in system dynamics
modelling.
Need to Take a Hard Look at Soft Variables in System Dynamics Models
Sterman (2002: 522-523) makes the following points regarding soft variables in system
dynamics models:
e Soft variables should be included in our models if they are important to the purpose.
e Omitting structures of variables known to be important because numerical data are
unavailable is actually less scientific and less accurate than using your best judgement to
estimate their values. Omitting concepts because they have no numerical data is a sure
route to narrow model boundaries, biased results and policy resistance.
e We must evaluate the sensitivity of our results to uncertainty in assumptions — whether we
estimated the parameters judgmentally '’ or by statistical means.
e It is important to use proper statistical methods to estimate parameters and assess the
ability of the model to replicate historical data when numerical data are available.
Rigorously defined constructs, attempting to measure them, and using the most
appropriate methods to estimate their magnitudes are important antidotes to causal
empiricism, muddled formulations and erroneous conclusions we often draw from our
mental models *.
e Most importantly, we should not accept the availability of data as given, as outside the
boundaries of our project or research. We must ask why concepts our modelling suggests
are important have not been measured. Frequently it is because no one thought these
concepts were important...[stemming] from the narrow boundaries of our understanding.
e Human creativity is great: once we recognise the importance of a concept, we can almost
always find ways to measure it. Today, many apparently soft variables such as customer
perceptions of quality, employee morale, investor optimism, and political values are
routinely quantified with tools such as content analysis, surveys, and conjoint analysis “’.
e Ofcourse all measurements are imperfect. Metrics for so-called soft variables continue to
be refined, just as metrics for so-called hard variables are. Quantification often yields
important insights into the structure and dynamics of a problem. Often, the greatest
benefit of a modelling project is to help the client see the importance of and begin to
measure and account for soft variables and concepts previously ignored.
Simply put, we need to take soft variables into account when they are likely to have an
impact; priority for incorporating such variables, as in the case of hard variables, must be
based on the likely extent of their impact. If these variables are likely to have an impact and
are, therefore, worthy of inclusion in our models, we should measure them if we can. If we
cannot measure them, we should estimate them as best we can by methods that give
consistent, repeatable and reliable results.
We cannot afford to take shortcuts and indulge in poor modelling practices regardless of how
tempting and convenient it might appear to be at the time; to do so could seriously damage
confidence in the system dynamics modelling discipline or, even worse, destroy our
credibility.
Purpose of This Paper
How to determine the impact of soft variables, including intangibles or social variables, and
combining them through the system dynamics modelling process with hard variables is
particularly vexing ““. This paper offers a method of incorporating soft variables into system
dynamics models. The method combines systems thinking, research into causality analysis,
multiple criteria decision analysis “" and system dynamics modelling, in an integrated
approach.
Concerns About Soft Variables Raised Previously
Prior to Sterman (2002), Nuthmann (1994) and Coyle (1999, 2000) raised concerns about the
meaning and impacts of soft variables in our system dynamics models, the way soft variables
are handled, the handling of mixes of soft and hard variables in system dynamics models and
validity of models *.
Improving Ways of Measuring Soft Variables
Clearly, investigating and implementing better ways of measuring soft variables will help our
quest. For example the system dynamics discipline could benefit greatly from having an
intangible assets register. By this I mean a compendium of information about the nature of
intangibles including a set of appropriate scales and measures by which we can gauge the
‘soft’ inputs to our models.
An intangible assets register might tell us how to measure or compare measurements made of,
for example, motivation, competence, or stress levels and a whole range of other intangibles
we know actually impact on performance of organisations and which we might wish to take
into account in system dynamics models. Sveiby, Linard and Dvorsky (2002) have addressed
the subject of an intangible assets register for system dynamics modelling where intangibles
need to be included. The creation of a robust, practical, meaningful and verifiable way of
measuring these intangibles would form an important foundation for development of system
dynamics models.
The creation of an intangible assets register and commitment to the progressive validation of
the methods of measurement, and eliminating the sources of variation in the values assigned
to intangibles in modelling, would be of enormous assistance. Work on an intangible assets
register is still in its infancy and considerable research is required. Results would have to be
validated, widely published and critically reviewed so that a valuable compendium of models
involving soft and intangible variables is built and made accessible for widespread use. The
system dynamics community should embrace this research, particularly because of the need to
shore up a significant weakness in current modelling practice.
We need both an intangible assets register, and robust methods for combining these
intangibles. Those methods exist * and are described briefly in this paper.
Estimating Values of Soft Variables
A method for estimating variables, in instances where data is not available but experienced or
expert personnel are, was enunciated by Ford and Sterman (1998). This method is equally
applicable to the task of estimating soft variables in the absence of comprehensive data sets.
The method involves polling and gaining consensus amongst those most experienced in a
problem situation. Similar techniques have existed for many years, albeit in different guises
* They are seen as essential rather than optional tools we need in our system dynamics
modelling toolbox.
Scales Applicable to Soft Variables
We must be very careful with assumptions about the scales, that is, nominal, ordinal and ratio
scales that might, or might not, be applicable to soft variables. Many soft variables are not
amenable to being ‘scaled’ in any absolute sense, in which case anything other than a
comparative measure might be misleading or inappropriate, and ratio scales can lead to
confusion when applied to different baselines.
In our opening example, the nominal scale used to measure Qualifications_Held_By_
Individuals and ratio scale would needed to measure /ndividual’s_Motivation_Level bring
attendant problems of incompatibility. They simply cannot be treated as the modeller did.
We might imagine Qualifications_Held_By_ Individuals to be measured in terms of numbers
of relevant subjects taken as part of a degree or diploma held in a relevant discipline,
applicable training courses completed or competencies the individual possesses measured
according to a set of predefined criteria. Estimating and quantifying
Individual’s_Motivation_Level is somewhat more problematic.
Dimensionless and Normalised Soft Variables
Further, for algebraic expressions involving soft variables to make sense in terms of
combining their influences, each of the variables would need to be dimensionless “". One
useful way of treating soft variables, once we have ascertained that it is practical and valid to
apply scales to them, is to treat them as having values in the range 0-1.0 “". This is applied
by pair-wise consideration of the relationships between linked variables. Any influencing
variable has an influence on the influenced variable also within normalised scales, that is,
from zero up to its expected maximum, to which a value of 100% (1.0) is assigned.
Integrated Methodology Briefly Described
Once the causal structure involving the most important and relevant soft variables has been
captured in the form of a causal loop diagram “ causal analysis and multiple criteria decision
analysis are used to determine aggregated soft variable inputs to calculation of parametric
values that, in turn, control flows through our system dynamics model.
Graphing Influences Between Pairs of Variables
For each pair of linked soft variables in our casual loop diagram we can develop causal
relationship depictions such that, for example, the level a(n) of an input variable ‘A’ produces
an influence ,,, (n) on the output variable ‘B’ “’. See Figure 1. Here n is the iteration
number, 6,,, is the influence of ‘A’ on ‘B’ in the corresponding iteration and the lower case
letters (e.g. a(n)) indicate the values taken on at each node in the iteration indicated.
output
B.(n) er eet
ant
# range
‘ of
/ inputs
0 a(n) A
Figure 1. Causal Relationship Between Node A and Node B
Similar relationships can be developed, that is, derived from information in our (future)
intangible assets register or estimated, as necessary, by employing a panel of expert or
experienced personnel, using the technique explained by Ford and Sterman (1998). In this
way, causal relationships can be developed for all relationships, A-B, B-C, C-N, and etc.,
shown in Figure 2. In the simplest case, the graph depicting the causal relationship will be a
straight line. However, the general case is taken to be non-linear. Because of the
computational effort that would be involved, no attempt is made to create a polynomial fit of
these curves. Rather, the curve is approximated by a series of straight-line segments. See
Figure 1. The mid point of each line segment is used to return the output for an input at any
point on a given segment. This technique is used to greatly simplify the calculations *’.
Causal Loop Diagrams Depicting Linkage Between Soft Variables
To develop our first approximation of the algebra needed to control the auxiliaries or
concentrators, and hence flows through our stock and flow model, we depict the influences
that we need to combine using a causal loop diagram, as is accepted system dynamics
modelling practice. However, at this stage we aim to treat soft variables separately from hard
variables, producing a single, aggregated influence which will then be applied to selected hard
variables in our stock and flow model. We draw a causal loop diagram ““" to depict the total
influence of a set of variables to be included in an auxiliary or concentrator “Y" we might
produce this in a generic form as shown at Figure 2 ““. Here the darker arrows indicate the
(incomplete) main loop identified to establish the correct sequence in the calculation of causal
influences.
Figure 2. Generic Causal Structure
To each causal link we assign the information depicted in Figure 3, taking into account the
nature of the causal relationship (influence) between linked pairs of variables as depicted
earlier. See Figure 1. At this stage, we assign an ‘importance’ or ‘preference’ weighting (e.g.
Wa,b) to each link in our causal loop diagram, having determined 6,,» for the relevant iteration.
Influence of node A on
node B, at iteration
number 'n'
Ou,o(n) B
Wa.» Preference
A weighting
Figure 3. Information Required for Calculation of Influences Across Each Causal Link
Once the initial values ““ have been estimated for each link, that is, in terms of both influence
and weighting, it is necessary to calculate the post-initialisation value, b(n+J) produced at
node B. The specific sequence of calculation intended to avoid double counting of influences
is shown in Figure 4, where the results of preceding iterations is shown at the bottom with the
iteration currently under consideration being at the top.
bint) = Sap(nt1) + Seb(n) + Snp(n) + Sup(n) + byp(n)
x A J
g(n-1) n(n-1) u(n-1)
\
Sent) Beult-L)—— Sx.u(n-L)
Ze N
c(n-1) v(n-1)
t ‘
Sy,e(n-1) Suy(n-2)
u(n-2)
Figure 4. Sequence of Calculation of Influences
This formulation assumes that the influences are added rather than being combined according
to some other scheme. To ensure the totality of influences at any node never exceeds 1.0, it is
necessary to set to unity the sum of weightings applied to links influencing each node. At ‘B’
this would be expressed as:
Wab + Web + Wnb + Wub+ Wyb = 1.0
These weightings are applied to the influences on each link having an impact at ‘B’ for that
iteration. For example, when the weightings are applied:
bantl) = Sap(1t)).wab + Sep(M). Web + Snp(1). Wap + Sup(t). Wu + Svb(n). Wr,b
It is important to note here that when establishing the weightings there is a need to ensure
consistency in application of the weightings simultaneously at nodes (where they sum to
unity), in connected links and loops, and across the more remote links and loops ““.
Challenges Confronted During Development of this Methodology
xxii
The challenges confronted in developing this methodology “" included:
e Finding ways of taking into account the causal influences for every link depicted in
the causal loop diagram.
e Determining the influences across each causal link:
o Taking the correct sequence of calculations into account.
o Avoiding double counting.
e After allocating weightings to the arrows influencing a node, assigning values to each
weighting to ensure:
o Total of preference weightings applied to each of the influences we require to
combine at each node sums to 1.0. This is a convenient device for which no
detailed justification is offered, other than to avoid computational
irregularities.
o That preference weightings reflect due consideration of the importance of each
causal link, for example, weighting applied to a particular link is not overly
weighted or given too little weight.
o Consistency in the pair-wise comparisons involving weightings applied to all
links.
Practical difficulties encountered include:
e Variations in estimating soft variables.
¢ Sensitivity, of the process of calculating the total influence at a node, to changes that
are made to the shape of influence relationships or to the weightings applied to
individual connecting links.
e Initialising the causal loop diagram, that is, choosing sets of nodal values, causal
influences across links and importance weightings that do not produce computational
inconsistencies “"".
e Selecting the number of straight-line segments to approximate curves in each of the
pair-wise causal relationship such as shown in Figure 1. Short segments are used
where we have confidence in the shape of the curve, longer segments are used where
confidence is low:
o When a large number of short line segments are used, calculations become
computationally demanding.
o When a small number of longer line segments are used, attempts to initialise a
causal loop diagram result in ‘hunting’ back and forth between values returned
from subsequent causal graphs encountered in the sequence of calculations.
A number of important issues require further research:
xxiv
e Are influences at a node additive “" as we have assumed? Research into heuristics in
decision making suggest that if influences are additive and we consider all influences
according to their importance, we apply Franklin’s Rule ““Y. However, Gigerenzer, et
al., 1999 and Klein 1998 suggest that we actually base choice and decision making on
a variety of heuristics. It follows that Franklin’s Rule may only be one of several
schemes we might consider when designing algorithms for combining influences at a
node *“,
e Can we actually assign meaningful values at each of the nodes — exactly what do these
nodal values mean?
The Way Ahead
The most obvious question here is... ‘why go to the amount of effort the application of this
methodology suggests?’ If sufficient justification cannot be found in the example cited at the
beginning of this paper, it surely must be found in the concerns raised over nearly a decade by
Nuthmann (1994), Coyle (1999; 2000) and most recently by Sterman (2002).
Further, system dynamics texts and teaching almost universally ignore the problems of
handling soft variables seemingly because it is simply too difficult. That avoidance must
ultimately translate to lack of skill and lack of consistency in the practice of our art; and
whilst this remains the case, system dynamics modelling will remain an art rather than being
recognised as science.
Concurrent and ongoing work by Sveiby, Linard and Dvorsky (2002) also needs to be
pursued and incorporated into system dynamics modelling practice to assure consistency in
the determination of values assigned to intangibles in system dynamics models.
A concerted research effort is needed to gauge the efficacy of the method offered here, or to
find alternatives. The products of research work of McLucas (2001; 2002) and practical work
by Schmidt and Gary (2002) suggests that such methods have both promise and applicability.
However, except in simple cases, considerable computation is needed, including the
employment of search techniques which are impractical to manually apply. So, these
methods need to be automated “" and the software tool must be designed to interface with
existing system dynamics modelling software applications.
References
Belton, V. and Stewart, T.J. 2002. Multiple Criteria Decision Analysis: An Integrated
Approach. Kluwer Academic Publishers, Boston.
Brown, B., Cochran, S. and Dalkey, N.C. 1969. The Delphi Method II: Structure of
Experiments. Rand Corporation RM-5957-PR, June 1969.
Coyle, R.G. 1999. Qualitative modelling in system dynamics or what are the wise limits to
quantification? Keynote address: Conference of the System Dynamics Society, Wellington,
New Zealand.
Coyle, R.G. 2000. Qualitative and quantitative modelling in system dynamics: some research
questions. System Dynamics Review, vol. 16, no. 3, (Fall) 2000, System Dynamics Society,
Wiley.
Ford D.N. and Sterman J.D. 1998. Expert knowledge elicitation to improve formal and mental
models. System Dynamics Review, Vol 14, No 4, pp 309-340.
Homer, J.B. 1996. Why we iterate: Scientific modeling in theory and practice. System
Dynamics Review, vol. 12, no.1, (Spring): 1-19.
Homer, J.B. 1997. Structure, data and compelling conclusions: notes from the field (1997 Jay
Wright Forrester Award Lecture). System Dynamics Review, vol. 13, no.4, (Winter): 293-
309.
McLucas, A.C. 2001. An Investigation Into The Integration Of Qualitative And Quantitative
Techniques For Addressing Systemic Complexity In The Context Of Organisational
Strategic Decision-Making. PhD Dissertation, University of New South Wales, Canberra,
Australia.
McLucas, A.C. 2002. Improving causal mapping practice using the System Dynamics ‘Front-
End’ Tool. Proceedings of the 20" International Conference of the System Dynamics
Society, July 28 — August 1, 2002, Palermo, Italy.
Nuthman, C. 1994. Using human judgement in system dynamics models of social systems.
System Dynamics Review, vol. 10, no. 1 (Spring 1994): 1-27.
Schmidt, M.J. and Gary, M.S. 2002. Combining system dynamics and conjoint analysis for
strategic decision making with an automotive high-tech SME. System Dynamics Review,
vol. 18, no. 3, (Fall 2002): 359-379.
Sterman, J.D. 2002. All models are wrong: reflections on becoming a systems scientist.
System Dynamics Review, vol. 18, no. 4, (Winter 2002): 501-531.
Sveiby, K., Linard K. and Dvorsky L. 2002. Building a knowledge-based strategy: A system
dynamics model for allocating value-adding capacity. Proceedings of the 20" International
Conference of the System Dynamics Society, July 28 - Aug 1, 2002, Palermo, Italy.
‘ ‘Soft’ means qualitative in nature. It does not mean unmeasured, estimated, uncertain or fuzzy. Soft
variables can be difficult to measure or estimate, and it may be difficult or impractical to apply
universally-applicable scales to them. Soft variables include a class of variables referred to as
‘intangibles’. For example, we might argue that ‘quality of leadership’ if used as a variable in a
system dynamics model could be measured according to the presence or absence of certain leadership
qualities; on this basis we could establish a measure of quality of leadership. However, the individual
leadership qualities such as personal integrity would be considered as intangibles. We might be able
sess that an individual has personal integrity, but applying a score to an individual leader on the
basis of some universal ‘integrity’ scale may prove problematic at best. This is the nature of
intangibles.
" Using conventional algebraic operators.
™ A strong criticism made by many system dynamics modellers of econometric modelling is that in
econometric modelling there is an implicit assumption that statistical correlation among a group of
variables is seen as causality. In effect this is what modellers are doing when they produce the type of
pseudo-algebraic expressions described in our opening example. With statistical correlation it is easy
to ignore demands for dimensional consistency. For example, in examination of the algebraic
expression ‘y = ax’+ bx +c’, found during statistical / correlation analysis, if ‘y’ and ‘x’ have the same
dimensions ‘q’, then ‘a’ must, by definition, have the dimensions ‘1/q’, and ‘b’ must be dimensionless
and ‘c’ must have dimension ‘q’.
'’ See Ford and Sterman (1998).
‘ See Homer (1996; 1997).
“ This paper takes the techniques described by Schmidt and Gary (2002) a step further by describing a
method for the general handling of soft variables as well as those which involve preferences, that is,
combining multiple criteria decision analysis (conjoint analysis) and systems thinking.
vii
Integrating hard and soft systems analysis, including the handling of soft variables were subjects of
the author’s PhD dissertation.
viii
For a comprehensive explanation of multiple criteria decision analysis, see Belton and Stewart
(2002).
“ The problem of how to treat mixes of hard and soft variables is not unique to system dynamics
modelling, it also arises in systems engineering where there is also ample evidence of the existence of
practices whereby soft variables are quantified using questionable methods.
* The technique has been demonstrated by McLucas (2001: 314-349).
“ These techniques are a variation of the Delphi Technique (Brown, et al. 1969).
“" Designers of new system dynamics software applications such as Powersim® Studio have gone to
considerable effort, and for very good reason, to make it difficult for modellers to build models that
ignore the units associated with either soft or hard variables. It has been conventional SD practice to
incorporate soft variables by use of the following causal logic: Level of Workforce Motivation (a soft
variable) leads to (or causes) a Measurable Effect of Motivation on Output (a hard variable), which, in
turn, contributes to Output (a hard variable). It has been a deliberate choice of Powersim® Studio
designers to inhibit calculations involving a mix of dimensionless and dimensioned variables, in effect
forcing the model builder to defining of units for all variables used in every model. The methodology
described in this paper might demand the creation of a ‘dimensionless modifier’ to be used in such
software applications. The ‘dimensionless modifier’ would input, to the model, the aggregated effect
ona hard variable created by soft or intangible variables.
“An example of normalisation might be explained with reference to an illicit drugs usage example.
The total number of drug users might be estimated on the basis of a proportion of the total of the
population. An estimate of expected growth, say 10%, over the period during which this study is to be
conducted would lead to the total numbers we might expect. In a city of 300,000, it might be
estimated that there is a maximum of 330 cocaine users (one in 1,000 plus 10%). It would then be
estimated that a maximum of 330 users would each consume x grams of cocaine per year on average;
the quantity being determined from Police and medical historical records. Note that we are not
interested in absolute numbers, per se, but the estimates are needed to enable normalisation of scales
on the axes of each graph. Maximum values on each axis are normalised to unity. Rationale behind
estimations made and normalisation calculations must be recorded for future reference, for consistency
and peer review.
“Y This method works equally for small numbers of soft variables not linked in a causal feedback
structure.
*Y Here we must be careful not to confuse correlation and causality. Each graph must depict our own
currently-existing dynamic hypotheses about causality. The starting point for the development of
these hypotheses may be found in the process of investigating the correlation between variables.
Whilst this may be necessary, it is unlikely to be sufficient. Causal relationships between linked pairs
of variables will have to be subjected to continued critical examination.
“' The exact details are not provided in this paper; however, a full explanation of the fuzzy algebra
calculation technique is contained in McLucas (2001: 314-349).
“" Output from multiple criteria decision analysis of causal loop diagrams is intended to be a single,
weighted and non-dimensional factor which is then used to modify the algebra of an auxiliary or
concentrator in which hard (rate controlling) variables appear.
*" We need a convention that identifies the output from this analysis with a label ‘Soft / Intangible
Variable (Dimensionless Modifier)’
““ Schmidt and Gary (2002) in their conjoint (multiple criteria preference / decision) analysis treated
causal influences as a hierarchy with each lower level being combined to produce the influence at the
top of the hierarchy. The validity of their approach is not questioned but the extent of its applicability
is. In this paper the aim is to demonstrate a generic approach applicable to systemic influences, that is,
where multiple feedbacks might exist and influences need to be considered iteratively because they
may change over time. Changes over time might stem from adjustments consumers, decision or
policy makers (actors in our problem formulation) make in their thinking. These may result from
advertising, market forces or shifts in perception by the actors involved.
* McLucas (2001) found that the process of initialising such a causal loop diagram (in the general
case the main loop shown in bold is complete), can be difficult to calculate without resorting to the
non-ideal fixing of values of selected nodes or by repeatedly adjusting the shapes of the curves that
define the causal relationships.
“' Tt is easy to invalidate the rule that the sum of weightings at a node is unity because this rule applies
simultaneously to all nodes whilst the pair-wise comparison of all weightings also is to be
concurrently satisfied. To resolve this can demand quite sophisticated mathematical search techniques
such as genetic algorithms.
““" Multiple criteria decision analysis techniques are used to support the combining of causal
influences appearing in our causal loop diagram.
“"" This suggests the need to support the process by use of computationally-intensive, but powerful,
mathematical techniques such as genetic algorithms.
*“" Tt is conceivable that influences might be multiplicative or combined in other ways. At this stage it
is assumed that influences are added. The veracity of that assumption requires examination.
*’ Franklin’s Rule, named after US President Benjamin Franklin, is a technique which involves
identifying all relevant factors then applying weightings to each on the basis of their considered
importance. The idea is that that the decision to be made must take into consideration all the
prevailing factors according to their importance or their perceived influence on the problem.
““' Tn contrast, we might only consider a single, important factor as we do when applying the ‘Take-
the-best’ heuristic. See Gigerenzer, et al., 1999.
““"" Such as is being done through the development of the SD ‘Front End Tool’ described by McLucas
(2001; 2002).
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