Schaffernicht, Martin, "Causality and diagrams for system dynamics", 2007 July 29-2007 August 2

Causality and diagrams for system dynamics

Martin Schaffernicht
Facultad de Ciencias Empresariales
Universidad de Talca
Talca - Chile
martin@utalca.cl

Abstract

Polarity and causality are important concepts but have not received much attention in the system
dynamics literature. The great effort it takes students to properly understand them has motivated this
inquiry. In the framework of a conceptual model of interacting with complex systems, several cognitive
tasks are proposed. This paper concentrates on one of them that deals with causal links’ polarity. An
examination of other approaches that deal with causality and use more or less similar diagram languages
shows that usually causality is only very broadly defined, and where it is operationally defined, this is
done with respect to events rather than behavior. In contrast to these approaches, system dynamics is
about behavior rather than events. We then revisit the traditional criticism of causal loop diagrams and
show a way out, but add two new criticisms related to the inability of causal loop diagrams to address
behavior: in fact it seems that they are closer to the event-related definition of causality. Also, the
impossibility to execute them in simulations means that executable concept-models are to be preferred:
they express important information a causal loop diagram cannot represent and on top of it they render the
behavioral consequences visible (as opposed to the events). In conclusion, causal loop diagrams should
only be used by experienced modelers, and be banned from educational use.

Keywords: causal link, polarity, dynamic complexity

1

1. Introduction: polarity and causality

For the last two years, I’ve had the opportunity to teach system dynamics as an elective for

undergraduate business students at my university. This course spends a substantial span of time

dealing with the very basic aspects like polarity and stock-and-flow thinking. For my students,
it has been very challenging to understand and get used to the “correct” definition of polarity:

— positive (+): when the independent variable changes with a particular sign (+ or -), then the
following values of the dependent variable will be above (or less) than what they would
have been.

— negative (-): when the independent variable changes with a particular sign (+ or -), then the
following values of the dependent variable will be less(or above) than what they would have
been.

They strongly prefer what I'll call here the “popular” definition:

— positive (+): when the independent variable changes, then the dependent variable changes in
the same direction;

— negative (-): when the independent variable changes, then the dependent variable changes in
the opposite direction.

‘lm grateful to Erling Moxnes and the students of the Bergen University for their critical questions and
comments
As a means of persuading them, I use a series of examples where the behavior-over-time graph
of two variables is used to decide which type of polarity is involved.

When confronted with a task like the one shown in the following figure, most of my students
intuitively believe this is a case of negative polarity:

Independent variable Dependent variable

8
8 | ~~
g S
3 g
. @
time

time

?

Figure 1: example of an “impossible” case of polarity
After all, the independent variable went up and the dependent one went down, didn’t it?
However, if one applies the “complete” definition (see Sterman, 2000), the dependent variable
takes on values higher than what would have been the case; since the independent variable
experienced a rise, this is a case of positive polarity. Why, then, do beginners prefer the
simplified (or “popular’”) definition?
I was troubled by this difficulty and decided to inquire into how many different configurations
of causal influence I could produce to confront my students with such deceptive tasks. If we
limit ourselves to “step” changes in the variables, and admit that the dependent variable may
have a base behavior — a slope that is positive, null or negative, then the usual 4 combinations
for two polarities become 12. If we admit “step” and “ramp” changes in the dependent variable,
there are already 24 combinations. It became evident that there is a “mystery” about causal loop
diagrams and polarity. How could it be that a tool meant to help you is so tricky to use?
The subsequent inquiry into the relationship between causal loop diagrams, polarity and
behavior made it necessary to reflect upon the notion of causality for system dynamics. As
described by (Pedercini, 2006), leading and publishing dynamicists assume the world to be such
that one can specify stable causal relationships between variables in order to explain phenomena
or design decision policies; causality is understood as the polarity of each link and there is
widespread use of “causal loop diagrams”.
The notion of causality and causal diagrams are also used by researchers in other disciplines
interested in mental models and/or causality — for different purposes ranging from studying to
influencing causal reasoning (Eden, 1990; Halper and Pearl, 2005a and 2005b; Johnson-Laird,
1999). However, beyond the similarities, there are differences. In usual causal diagrams,
feedback loops may be identified, but they are not separately conceptualized and signaled.
Also, system dynamics puts emphasis on the polarity of causal relationships (Richardson, 1991),
which is one necessary condition for converting knowledge about structure into knowledge
about behavior’. The nodes do not always refer to variables, but also to conceptual constructs,
actions and events. How do these acceptions of causality and the different types of causal
diagrams relate to each other? And what can this mean for system dynamics? It is the purpose
of this paper to contribute some elements to the answer of these questions. I believe this is
worthwhile for the following reasons.
System dynamics has a well defined normative apparatus with rules that tell us how to decide
which factors shall be part of a model, how to define the type of variable and how to quantify

“knowledge” is used here in the sense of “best available belief”.
and validate. In a way, system dynamics is a method to enhance causal thinking. On the other
side, there has been growing concern about how people fail to perceive causal relationships (the
so-called misperception of feedback; see Sterman, 1989; Moxnes, 2000; 2004) and fail to think
adequately about them (stock-and-flow thinking; see Booth-Sweeny and Sterman, 2000 *).

The system dynamics literature has been the stage for a brief dispute concerning causal loop
diagrams, in which the simple (and most popular) definition of polarity was shown to be flawed
and only one of the commonly used notations for “positive” and “negative” did not fail the test
(Richardson, 1997). However, the dispute seems not to have been settled, since there are still
articles using the popular definition (Warren, 2004). There must be some reason for this
popularity.

Also, the mental models thread seems not to have aroused investigations into the way how we
think with causal relationships. System dynamics has its own definition of mental models
(Doyle and Ford, 1998; 1999:114):

“A mental model of a dynamic system is a relatively enduring and accessible, but
limited, internal conceptual representation of an external system (historical,
existing or projected) whose structure is analogous to the perceived structure of that
system.”

This definition does not mention “causality” nor “polarity”; neither did their paper deal with
ways to represent mental models. However, mental models are used to study causal reasoning
and frequently use “causal maps” (Johnson-Laird, 1999). So may it be that causality is a
concept that system dynamics just takes as granted, like Pedercini (2006) suggests? May it be
that dynamicists simply take it for granted that “causal loop diagrams” represent articulated
mental models? In the face of the reported failures to perceive and correctly think with
feedback loops, there may be good reasons to study how we actually perceive causal
relationships and how we fail to, and how we actually think with causal (mental) models. And
in a context where the debate over the use and usefulness of “causal loop diagrams” still goes on
(Homer and Oliva, 2001; Richardson, 1997; Warren, 2004), it may be worthwhile to ask what
this type of diagram expresses and should or should not be used for.

This paper inquires into the meaning of causality for system dynamics by relating it to what it
means for other fields and leads to a renewed critique of causal loop diagrams. The second
section introduces a conceptual model of a perceiving, thinking and acting person interacting
with a complex dynamic system. It introduces a sequence of cognitive operations that must be
accomplished in order to appreciate the probable behavior of a multi-loop model.

The following section reviews the concepts of causality and the tools used to represent it for
those who use concept mapping, cognitive mapping, causal mapping and causal diagrams. We
find that they are concerned with events rather that behavior and that most do not search
quantification/simulation.

Then the fourth section treats the case of system dynamics. We find that its interest for
behavior distinguishes it from the other approaches. We revisit the previous criticisms of causal
loop diagrams and extend the list of shortcomings: they have no notational means to distinguish
between behavior (first derivative) and event (second derivative), which is not good for an
approach where this difference is important. Also, they cannot represent the fact that the effects
of a cause show up in a smoothed way. Even though causal loop diagrams have the
comparative advantage of explicitly representing feedback loops, they allow too many
misunderstandings.

So the conclusion of this inquiry is that system dynamics has a very detailed and rich notion of
causality, since it goes beyond events. However, causal loop diagrams are a poor tool for
modeling with this notion, and its use should be reserved to experienced dynamicists.

> the “Bathtub” line of work has been readily uptaken and there have been many presentations about the
subject in the international system dynamics conference since the original paper.
2. Interacting with complex dynamics systems

Each person can be thought to be a constantly interacting with external systems. System
dynamics conceives these systems to consist of structures that generate behaviors.

a Structure
“System” frames slowly
frames
\ Behavior
| shows as triggers
Change Change
(Event) Conversation Simulating (Event)

Thinking aloud — Diagramming

~ &
3
8 <
2 Cognition
A
System 1
(intuitive judgem
ent)
unconscious System 2
mental model (conscious,deduct
ion,
~~ | decision)
¥ 5 conscious
‘Person’ mantal model

Figure 2: interaction with complex dynamic systems

As has been indicated (Reichel, 2004), other schools of thinking also recognize that behavior
slowly transforms structure. The person appears as a system consisting of perception, cognition
and action. According to (Kahnemann, 2002), perception is more sensitive to change (events)
than to states: “a difference that makes a difference”. It is thought that cognition can be
decomposed into two different systems: system 1 represents unconscious, intuitive thinking,
which brings into play unconscious mental models. System 2 realizes the conscious thinking,
part of which can be articulated as mental models. Intuitive action (and the judgment it reveals)
is based on system1, while deliberate decisions are produced by system 2. The internal activity
of thinking also has an effect back on perceiving; this is something we all know as “you see
what you know”, but it has also been experimentally found (for example, Payne and Baguley,
2006).

This perception often triggers cognitive processes that remain in system | and finish with some
action. At other times, system 2 may become activated and conscious thinking intervenes.

Let us assume that we find ourselves in a classroom situation where we expose students to a
causal loop diagram and want to see to which degree they will be able to make an adequate
statement about the probable behavior of a feedback loop’s behavior. Students are beginners
and as such, they will use system 2.

Consider what has to happen by chaining from the final stage of thinking backward: in order to
think well the feedback loop, one has to detect its polarity, which cannot be done without
detecting previously the loop and each individual causal link’s polarity; this in turn has to be
preceded by detecting the causal link between the two variables and the variables themselves in
the first place. Figure 3 illustrates this process:

5: conjecture loop behavior

t

4: detect loop polarity

-—+—,

3a: detect link polarity 3b: detect loop

+______+

2: detect causal link

I

1: distinguish variables

Figure 3: steps towards conjecturing loop behavior. Arrows represent precedence, not causality.

The phases drawn in higher places (with higher numbers) are closer to usual system dynamics
questions, and this is where we have rules and tools. However, the lower numbered phases
arouse relevant questions:

1) how do we come to consider something as a relevant variable?

2) how do we come to believe in the existence of a causal link between two variables?

3a) how do we come to see the polarity of a causal link?

3b) how do we come to detect a feedback loop?

Even though to the trained system dynamicist this may seem ridiculously obvious, it is usually
not so for other people. We can wonder if the failure comes more from perception or from
cognition (and which of the two possible systems), and if the subjects fail to perceive a causal
link between two variables they do perceive or if they fail to realize that there is a feedback loop
(even though all participating variables and causal links have been identified).

However, for the remainder of this paper, we assume that step | “distinguish variables” and step
2 “detect causal link” have already been absolved, because we wish to focus on the thinking
about and with the causal relationships between the variables *. Let us define “variable” as “an
attribute of some entity that is stable in time but takes on different values over time”. We will
now examine the ways causality can be understood and the different diagram languages we can
use to reflect upon it.

* It should be recognized that distinguishing variables is not a trivial activity; it is out of the scope of this
paper, but the interested reader may start consulting Argyris (1993) — in an appendix concerning design
causality, writes how the fact to consider one or another flow of events as one variable affects the
following steps of perceiving and thinking. As for recognizing variables and links between them, there
are different competing explanations for how we do it; see Gopnik et al., 2004, Allan and Tangen, 2005
and L6pez et al., 2005. The most prominent one is associative learning, where the occurrences of events
or “cues” is used to form causal attributions.
3. Causality and polarity

Some historical facets of the concept “causality”

Causality has been a subject for philosophers and scientists for a very long time (in human
standards); Aristotle elaborated ideas concerning four kinds of causes:

— material: what A is [made] out of

— formal: what it is to be A

— efficient: what produces A

— final: what A is for

When we talk about causal links between variables, we are mainly interested in the efficient
cause:

— what is it that caused a variable to perform a specific behavior?

— what is it that produces a certain effect in a variable we want to govern?

David Hume (1984) got to the conviction that — be there causality in the world or not — the
human individual can only develop thoughts about his impressions and experiences and by
consequence, humans can only attribute causes. We perceive one object A doing something
and then some other object B near to A does another thing. If this repeats a sufficient number of
times, we’ ll believe that A (somehow) causes B to do something.

Since the middle of the 20" century, psychologists have developed attribution theory, which
deals with how people come to their causal beliefs in everyday situations (Heider, 1958; Kelley,
1973). System dynamics is pragmatic from its outset and has always been interested in causal
beliefs that people articulate from their mental database (as observed by Pedercini, 2006).

4. Different meanings and diagram languages outside the system
dynamics realm

In several fields, people explicitly use a concept of causality and rely on some form of causal
diagram to reflect upon it. Since there are differences between them, it seems important to
present each of them in turn and then focus on the one proper to system dynamics.

Causal links are currently used in (at least) four different ways: concept mapping, cognitive
mapping, causal maps causal diagrams as used in psychology and A.I.

Concept mapping.

In concept mapping, concepts are “things usually referred to by nouns or noun phrases” that can
be “linked to form propositions” (Rebich and Gautier, 2005, p. 358). In this case, the nodes in
the diagram are concept phrases, for example “aerosol emissions [are generated by] industrial
activities” or “longwave radiation trapping [is associated with] greenhouse effect”.
(longwave radiation trapping } (aerosol emissions )

is associated with are generated by

greenhouse effect
industrial activities

a) ‘b)
natural processes land use changes
include include

Ay

sun volcanic
variability aerosols urbanization || deforestation

°) d)

Figure 4: two examples of concept maps. Extracted from a cognitive map that is referred to in
Rebich and Gautier, 2005 *,

Note that the links have name labels that are usually verbs. In the examples shown in Figure 4,
we can see several aspects relevant from a SD point of view. In 4b), it shows that sometimes
the concept statements are similar to variables (“aerosol emissions”), and at other times they are
rather entities to which several attributes or variables could be attached (like “industrial
activities”). Sometimes the concept points to a process, like “sun variability” in 4c); this is
possible since — even though a process is something active, like a verb — one can substantiate
this verb. One might as well posit the causal link in active voice, such as to make the link’s
arrowhead point in the same direction as the causal influence; however, there is no rule that
would require this. Finally, 4d) “land use changes” is a case where the concept is a change
(which will many times be perceived as “event”).

Also, not all links refer to causality: in 4a) “is associated with” simply states that one concept
has something to do with another one, and in 4c) and 4d) we see that they can create a logical
order amongst the concepts. In 4b) the link “are generated by” is clearly of causal nature;
however, it appears in passive voice. This is possible when links have names. One might as
well have said “industrial activities [generate] aerosol emissions”.

We note that concept maps are very flexible, because they do not impose many restrictions on
the modeling process and the symbols: concepts may be variables, processes, entities or events.
Links may be anything that is relating two or more concepts. Clearly, one may elaborate a
concept map that contains only variables (as concepts) and causal links (as links and in active
voice), but this would only be a special sub-class of all possible concept maps.

According to this, we conclude that concept maps are not meant to focus on causal effects; so it
is not surprising that there is no particular definition of what causality is: it is just some
influence.

This kind of modeling is easy to learn because it is intuitive; in particular, it does not separate
structure from behavior. It is used to express and organize knowledge and also assess learning
about complex situations like climate change (like in Rebich and Gautier, 2005).

° The diagrams have been elaborated with “CMapTools”, a specialized software for creating, managing
and analyzing concept maps. It can be obtained at http://cmap.ihme.us
Cognitive mapping

As mentioned by Doyle and Ford (1999), “cognitive maps” mean different things to different
authors. Tolman (1948) referred to maps that are constructed in the cognitive system; Axelrod
(1976) was interested in mapping cognitive contents.

We discuss cognitive mapping as a “technique used to structure, analyze and make sense of
accounts of problems” (Ackermann et al., 1996, p. 1; good introductions can also be found in
Eden, 1990 and Bryson et al., 2004). This kind of modeling effort is concerned with uncovering
and relating between each other assumptions, action possibilities, strategies and goals, hence the
name of SODA (strategic options development and analysis). It is assumed that actions lead to
outcomes over a causal link. Cognitive mapping is based on the theory of personal constructs
(Kelley, 1973). Such a construct is like a chunk of discourse concerning some theme, for
example climate change or a business problem. A typical chunk is about 10 words long; in
addition to the positive statement (“centralize our services in Leeds”, see Ackermann et al.,
1996, pp. 6-8) may be complemented by its opposite (“centralize our services in Leeds ... open
local offices”, where “ stands for “rather than”. A typical map developed from the
mentioned construct might be the one shown in the following figure.

5 tisk of impaired
treatment of clients
»» ensure
uniformity of .
treatment 3 higher
N administration costs

is

4 too much ms
centralization 2 running costs
Be a
1 centralize
services at Leeds
.» open local
offices
St By
8 lack of
understanding about 6 lower purchase
risks costs of offices in
; at other cities
7 use experience of higher costs in
local offices Leeds

Figure 5: example of a cognitive map (adapted from Ackermann et al., 1996, p. 10).

In these diagrams, the nodes (constructs) are numbered. This is useful later on for analyzing the
map, in order to detect “heads” (no links coming in), “tails” (no links leaving), central nodes
(heavily linked) and loops (amongst others) °. Clearly, some nodes refer to actions (1 and 7),
while others mention what might be considered a variable, together with some information
about its state (“lack of” “lower”, “higher”, “too much”) and sometimes dynamics. In some
cases this qualification informs about an event going on in a variable, like in 3 “higher
administration costs”.

° This map has been elaborated using “Decision Explorer”, a specialized software tool used for cognitive
mapping, for example in SODA. It can be purchased at www.banxia.com.
The links mean “leads to” and are clearly about causation. “Higher administration costs” are the
consequence of decisions taken upstream. However, it is also possible to insert “time links”
denoting a “before/afterwards” relationship and “connotative links” that articulate a “has
something to do with” relationship. Sometimes an action leads to an effect related to the
negative pole of a construct; then the link is labeled with a “-“ sign.

Cognitive maps are elaborated to better understand a problem or an opportunity. This is why in
SODA, the nodes are grouped into categories like goals, strategies, options and assumptions.
The orientation is clearly causal, however it is not attempted to quantify or to simulate. This is
justified by the fact that decision takers often are involved in delicate political systems that push
not to disclose all the information and intentions; they are also under time pressure, and would
not be willing to use a complex tool that requires learning and long working sessions. Cognitive
mapping is intuitive and easy to learn, since it does not separate behavior from its underlying
structure, nor does it require to identify the variables. This may be worth some discussion (see
Homer and Oliva, 2001), and one may wonder if it is not possible to complement cognitive
mapping with system dynamics modeling; this has been done (Howick et al., 2006).

It has to be noted that in cognitive mapping, causality is assumed to link events (including
actions).

Causal mapping
A causal map is a representation of causal beliefs of an individual or a group of individuals
(Mark6vski and Goldberg, 1995). In consists of variables and links that may indicate a type of
relationship (“positive” or “negative”) and indication of strength (an integer number, often
between | and 3).

-1

3 Vision and strategic direction 5 Market share

20 Competition in market 30 = Leadership in organization
33 Knowledge of market needs 35 Brand recognition
43 Bank connections 47 Efficiency /productivity

Figure 6: example of a causal map (Source: Markévski and Goldberg, 1995, p. 307)

Just like in the case of cognitive mapping, the nodes in the diagram are numbered; however,
note that now they represent variables, not the “constructs” including particular values or
events.

In such diagrams, only structure is explicitly represented. Behavior has been abstracted away
(no verbs in the labels). It is noticeable that the notion of polarity appears as “strength” of the
links, understood according to what we will call the “popular” definition.
These diagrams can be represented as association matrix and analyzed for similarities and/or
differences (Mark6vski and Goldberg, 1995; Langan-Fox, et al., 2001; Langan-Fox, Code and
Langfield-Smith, 2000; Langfield-Smith and Wirth, 1992). Even though the possibility to find
feedback loops exists, these are not conceptualized. In these diagrams, causality is not
explicitly based on events; rather it means “leads to a target state” without specifying how the
effect is transmitted.

Causal diagrams

Researchers interested in automated reasoning and the possibilities of its tools to theorize about
cognition, also use causal diagrams (Gopnik et al., 2004; Halper and Perl, 2005a and 2005b;
Pearl, 1995). Such diagrams contain variables and causal links, like shown in the following
figure (taken from a case about judging the cause of a forest fire):

/™
4

F

ML

Figure 7: example of a causal diagram (Source: Halpern and Pearl, 2005a, p. 850).

The variables are meant to hold, at each moment, one of two or more discrete values. Let us
assume that the fire may have come from a lightning or a lit match dropped by somebody.

— Fmeans “Forest fire” (F=1 means “fire”, F=0 means “no fire”);

— Lmeans “Lightning” (L=1: “there is a lightning”, L=0: “no lightning”);
— ML means “Match Lit” (ML=1: “match lit”, ML=0:"no match lit”)

—  U stands for the set of context variables, like the degree of oxygen in the air, if it is
raining...
Causality means that two variables are linked by “a chain of events each directly depending on
its predecessor” (Halper and Perl, 2005a, p. 844; emphasis added). In this sense, an event is
what makes the value of a variable take on the specific value it has at a moment - for example,
the occurrence of a “lightning” or its absence “no lightning”.

Strict formal rules are imposed on the causal diagram, assuring that only variables that are in the
causal arc be part of the set of variables modeled as endogenous. A set of structural equations
represents the way an event in one variable is caused by events in its preceding variables.

The rules and the equations make automatic treatment possible. Thus if we are in the
possession of a causal diagram that satisfies the formal conditions, and we have the structural
equations, and we know the context variable’s values, then we can automatically determine the
cause of an event or the effect of an intervention.

However, like the example shows, the focus is on discrete events and the variables have discrete
sets of values. Causal diagrams represent only structure, the dynamics of events has been
abstracted away.
Summary

We may now outline the relevant findings about the different approaches, as shown in the
following table:

Type of | Mainuse Nodes Links Driving | Degree of
diagram force abstraction
behind
causality
Concept Structure Concepts in general | Links of any | Undefined | Low
maps knowledge in type
form of
propositions
Cognitive Uncover, structure | Constructs (phrases | Qualitative | Events, Low
maps and analyze | with entities, | causal links | actions
problem accounts | variables and | including
descriptions of their | negative and
values or changes _| positive type
Causal maps | Represent beliefs | Variables Qualitative Undefined | High
about the causal causal links,
structure. including
polarity
(popular
definition)
Causal Determine causes | Variables with | Quantified Events High
diagrams of events or | discrete values causal links
consequences of (structural
interventions equations)
(actions)

Table 1: comparation of non-SD diagrams related to causality.

The diagramming languages that allow nodes to be simply concepts or constructs do not impose
the task of defining the variables on the modeler. These diagrams are more intuitive to
construct and to read. However, concept maps are not meant to aid in decision problems, and
cognitive maps are developed to articulate and organize ideas such as to discover goals,
strategies and actions in a world of discrete events that are not quantified; these “models” are
not meant to inform about the evolution of the quantities of the variables - they don’t even force
to specify variables.

Causal maps and causal diagrams force to specify the variables. This makes them more abstract
to elaborate and to interpret. However, they are not intended to generate quantitative behavioral
information: causal maps represent what people believe the causal structure to be and search to
compare these beliefs. Causal diagrams are about what happens between events as cause and as
effect.
5. Causality and behavior - system dynamics

Causality for system dynamics

For system dynamics, the main concern is to understand how structure (variables and causal
links) generates behavior in a world of continuous processes, rather than discrete events. On its
way, system dynamics has created specific concepts as well as symbols to represent them: the
signed feedback loop, the type of variable (accumulation or flow), the delay and — where
quantification comes into play, the non-linearity.

Initially, the “stock-and-flow” diagrams were used as graphical language; they had a symbol for
each of the special concepts and allowed quantification, which is necessary for simulation.
There is wide agreement on that the presence of multiple feedback loops makes simulation
necessary in order to assess the continuous behavior.

System dynamics has a very specific definition of causality, which has to do with its conceptual
universe. The world is assumed to be in continuous development, and can be described by two
types of variables. If we define behavior as the different values a variable takes over time, then
stock variables are accumulators or stocks with a behavior determined by their own value “just
before” and the sum of all connected flows. The behavior of a flow variable is defined for a
period of time; it is inferred only by the currently visible value of stock variables and possibly
some converters (or auxiliary variables) and by implicit or explicit decision policies. Thus there
is a fundamental difference between the two types of variables, since accumulators depend on
their state and the connected flow rate’s quantity. Flow rates depend on the quantities in stocks
and decision policies.

Also, whereas in the philosophic discussion about causality (Halper and Pearl, 2005a), causality
has to do with how events cause events, system dynamics deals with how behavior causes
behavior (through a causal structure; in this, there is agreement between the communities). So
what is behavior and how does it relate to events?

In a continuous world, a stock variable has a specific value at each point in time. Flow
variables are defined for a period of time. Since perception occurs at points in time, only stock
variables can be directly perceived - even though the mind computes behavior from sequences
of perceptions and is more sensitive to changes that to states (Kahneman, 2002). Behavior is
then the change of values. An event should then be either a specific episode of the behavior or a
change of behavior.

This is something the other approaches presented above do not touch upon: concept maps,
cognitive maps and causal maps do not pretend to reason in continuous behavioral (quantitative)
terms. Accordingly they do not need an operational definition of causality. Causal diagrams
deal with events, and behavior does not appear in the same way. In the example of the forest
fire, there is fire or there is not — there is no need to ask for the forest fire behavior before or
afterwards; this may be represented by a step change in an integer number variable that varies
between 0 and 1. I argue that the event is the transition from 0 (no fire) to | (fire) — the change
of behavior.

There are several possible meanings to behavior, too. It may be the sequence of numbers that
describe the measured or inferred quantities. It may as well be a more qualitative description of
what this sequence is: growth (linear or nonlinear) or its contrary, stagnation, stabilization or
oscillation. In this list, some of the behaviors are not elementary, and can be decomposed into
successions of more elementary behaviors. For example, oscillation can be decomposed in
phases of positive/negative derivatives (first or second), and then an event may be the transition
from one of these modes to another one.

It is debatable if behavior can be thought of as first derivative and events a second derivative.
This might be considered for cases of linear behaviors; however, in more general cases one can
always argue that the second derivative also forms part of the behavior and so the notion of
event is pushed further. I did not find a discussion of the relationship between behavior and
event in the literature (beyond stating that system dynamics concerns itself with continuous
phenomena and not events). If it is fair to say that the human mind is sensitive to events, it
might be helpful to develop a clear definition of how system dynamics interprets this
relationship’.

The following figure illustrates some cases:

values
values

time time
a) 5)

values
values
4

time time

¢)

values
values
4 | ;

time time

Figure 8: a “step” and a “ramp” event as a change of behavior (change of values) above different
behaviors.

It seems that for system dynamics’ concerns, there are two types of fundamental events: one is a
vertical translation of the graph, represented as a “step” event (figures a, c and e). The second
one is a change of slope, represented by a “ramp” event (figures b, d and f). Other forms like a
“pulse” event are combinations of fundamental events, like two “step” (one upwards, the other
downwards) *.

While figures 8a and 8b do not look unusual, they refer to cases when the variable is static
during the whole considered period of time, except the change event. Clearly there are many
cases when this is not so: the employment of a country’s economy may be rising (slowly) but
the government wishes to push it up or rise faster (cases c and d). Or the sales of a company are
descending and management would like to give them a push or at least slow down the decrease

7 Pd like to thank the referees for their critical comments concerning this aspect.

* One may wonder if a “ramp” event could not be decomposed in a sequence of little “step” events; after
all, an instruction like “ramp(1,10)” is like a superposition of “step(1)” from time “10” on. However, this
would blur the difference between event and behavior, and since I’m interested in inquiring it I prefer not
to take this step.
(cases e and f). This is one characteristic that distinguishes system dynamics from the other
approaches presented above: here we care not only for events, but for behavior in general.

The very specific relationship between flow and stock variables means that between two
variables, there are rules as for what kind of event causes what kind of event:

— a“step” event in a flow variable causes a “ramp” event in the stock variable; if the flow is
an inflow, then the ramp has the same sign as the step; if the flow is an outflow, the ramp
has the inverse sign of the step.

— a “ramp” event in a flow variable causes a non-linear “ramp” event in the stock variable ’; if
the flow is an inflow, then the stock’s ramp has the same sign as the flow’s one; if the flow
is an outflow, the stock’s ramp has the inverse sign of the flow’s one.

We see that there is never a “step” event in a stock variable (unless we define “ramp = sequence

of steps”).

Flow variables are free to react to a stock’s “ramp” event in any manner, bound only by the

polarity of the link.

The relationship between behavior and event, as well as the rules derived from the relationship
between stock and flow variables, are inherent in the “stock-and-flow” diagram language. This
means that such a diagram, thanks to these incorporated regularities, can be simulated once
quantified. It then helps to understand the connection from structure to behavior.

Causal loop diagrams

Later on, the so-called “causal loop diagrams” (CLD) started to be used as a means to
communicate selected insights from a simulation study (Homer and Oliva, 2001). Once this
diagram language existed, it became tempting to use it also in other phases, especially for
articulating causal beliefs in the early phases of modeling projects. This diffusion of CLD has
lead to two debates: for once, there is argument on if simulation is always necessary or
recommendable (Coyle, 1998; Homer and Oliva, 2001). Also, there has been criticism of the
simplification of polarity (Richardson, 1997). Finally, one may wonder why CLD have become
so much more popular than “influence diagrams” (Wolstenholme, 1990), if the former do not
distinguish between accumulators and flows, but the latter do. Maybe this can be explained by
the simplicity that is won by forgetting about the difference.

In order to see the fundamentally limited character of CLD, we will now examine them from
scratch.

A causal link is given between two variables when a subject believes that what happens in one
of the variables will cause some consequence in the second variable. We may call the first
variable “independent variable”, since it does not depend on any variable that appears inside the
(mental) model; the second variable may be called “dependent variable” for the obvious reason
of being influenced by the first one '°. An articulated causal link is then the smallest possible
mental model.

In system dynamics, the arrow representing the causal link has the usual arrowhead to indicate
the direction of influence and also a “+” or “-“ indicating the link’s polarity. Polarity is what
determines an essential quality of the cause’s effect. Each of the two variables is a placeholder
for a series of quantities: the cause will be observable as a distinct behavior of the independent
variable, and the dependent variable will display a distinct behavior as effect. This behavior will
be an increase or a decrease; this may be in absolute terms or relative to what would have
happened otherwise, depending on which definition is used. During all this time, we should not
forget that both variables always “behave” in some way, so neither the cause nor the effect can

° If we define “ramp” like in the preceding footnote, then it becomes clear that he sequence of “steps” in
the flow variable will cause a sequence of superposing “ramp” events in the stock variable.

'° This is of cause only possible as long as there are no loops; however, polarity does not need a loop to
be explained and our reflection suffices with one link.
be something different from a modification of behavior. Since we are thinking in terms of a
continuous world, our variables have to have a behavior; the “events” that are perceived and
thought of as cause and effect must then be a change in the variables’ behavior.

We often use PULSE, STEP or RAMP functions to introduce such “events” and observe their
effects. This is testimony of the fact that humans perceive change more easily that state
(Kahnemann, 2002) and that habituation makes a constant behavior appear as state.

Also, we should recall that there will be other variables: no interesting system will consist of
only two variables: consequently, the variable we call “dependent” during this mental exercise
may be subject to other influences. As will be shown below, this has not always been the case
in the debate.

Let us assume that for one instant, there are no other variables. Now, when an increase event

(A) in the independent variable triggers an increase event (A) in the dependent variable, then
we have a case of what is intuitively classified as positive polarity:

values

Independent variable

Dependent variable

ve

time

time

is a case of

+

Independent

Dependent
variable

variable

Figure 9: an example of positive polarity

When we think in terms of a variable, then the variable is a shortcut for all the instances of
behavior we have seen before. In a way, Hume’s logic goes from the upper part of the figure,
where the behaviors are, to the lower part which corresponds to an abstraction of the variables
and a judgment of “causal link”. If we have two variables capable of two types of changes each,
it is clear that there are 4 basic configurations:

Dependent variable

AA
Vv

oY.
AV

Figure 10: 4 basic configurations for 2 polarities

2

Independent variable

According to this state of affairs, the simple or “popular” definition of polarity seems rather
convenient:

— positive (+): when the independent variable changes, then the dependent variable changes in
the same direction;

— negative (-): when the independent variable changes, then the dependent variable changes in
the opposite direction.

When both the independent and the dependent variables distinctively increase or decrease, we
speak of positive polarity. When one distinctively increases and the other decreases, we speak
of negative polarity.

However, this definition is easily shown to be flawed (Richardson, 1997): if we take the mini
model where the birth rate influences the population with a positive link, an increase in the birth
rate would cause an increase in the population. However, is it meaningful to assert that a
decrease of the birth rate would bring about a decrease of population?

birth rate POPULATION
—L, =
time time
is a caseof?

+
birthrate ———————>>_ POPULATION

Figure 11: can the birth rate lead to lower population?

As indicated by Richardson (1997), this apparent problem is due to the popular definition and is
overcome by using the full definition.

— positive (+): when the independent variable changes with a particular sign (+ or -), then the
following values of the dependent variable will be above (or less) than what they would
have been.

— negative (-): when the independent variable changes with a particular sign (+ or -), then the
following values of the dependent variable will be less(or above) than what they would have
been.

This is the “official” definition that students find in the textbooks (for instance, Sterman, 2000).
With this definition in mind, there is certainly no problem with thinking that a decrease of the
birth rate causes population to decrease below the level it would have had without the birth
rate’s decrease. Note that this des not require the population to decrease in absolute terms: we
compare what was to what would have been. Note also that the difference between what was
and what would have been appears from one specific moment on: it is tempting to think that a
specific event has caused this bifurcation (rather that a continuous behavior)

One can attribute this, for instance to the effects of other variables that cause changes in
population, like the death rate.

birth rate POPULATION death rate
Figure 12: the birth rate can lead to lower population

In Figure 12, there is a new variable that influences the population. It is intuitively understood
that the death of people reduces the population; so one can easily imagine that without births,
the usual behavior of population is downwards. So if there is a sudden “‘step” decrease in the
birth rate, the population will respond with a negative “ramp” and will be lower than it would
have been. (Of cause, if one wishes to understand why a “step” cause provokes a “ramp” effect,
one has to re-introduce the distinction between flow and accumulation.) There may be a rather
diverse set of possibilities for the basic behavior of population, in which the birth rate influences
in a different manner after the “event” constituted by its change of behavior:

w | birth rate o POPULATION w | birth rate o POPULATION

Sy 3 St 3

8 T 8 8 g rea
time time time time

are other cases of

+

birth ——— > POPULATION
rate

Figure 13: other cases of behavior of the same model

On the left hand of this figure, we see that a downwards step in the birth rate causes the decline
of population to accelerate. On the right hand, the same cause triggers population growth to
slow down. The precise shape will depend on the numerical values of the birth rate and the
death rate: as long as the former is larger than the latter, the net flow will be larger than zero and
the population will continue growing, only slower: a relative decline. Both cases (and more if
one wishes) are included in the set of behaviors that the model structure represented in the
causal loop diagram can generate.

Why, then, is the simple definition so popular? It continues to be used in so-called systems
thinking '' publications and scholarly publications (Warren, 2004). The suggested reason is that
it is simpler. After all, it is easier to think in terms of “events” and forget about the rest of
behavior, i.e. do as if it did not exist (constant values). This would bring us back to the model
without death rate, where the population is implicitly assumed to be constant when there are no
births. It is easier to focus on what happens between the birth rate and population without
bearing in mind the existence and effect of the death rate. We see now that this erroneous
judgment is attributable to the simple way we have to think about these variables, since causal
loop diagrams do not enforce the observation of the rules and regularities stated in the previous
section. They allow for these simplifications — at the price of implicitly assuming false
behavioral consequences. In particular, the causal arrows in causal loop diagrams appear to
symbolize only events, whereas system dynamics is interested in behavior in general.

However, there is more to be criticized about causal loop diagrams, which cannot be overcome
with the “complete” definition.

\" The choice to call system dynamics without stocks and flows and without simulation “systems thinking”
is a debatable one. For the sake of those who use the distinction and do simulate, are they not thinking?
And as far as the communication with people from outside the system dynamics community is concerned,
why are they supposed to understand then inside system dynamics “systems thinking” does mean
something very different from what it usually does?
Not only “events” (as a special episode or a change of behavior) possess causality; ordinary —
constant — behavior also does. As soon as we acknowledge the difference between flows and
accumulations (a distinction that cannot be expressed in causal loop diagrams, though), it
becomes inevitable to think that the absolute value of the birth rate (flow) causes behavioral
effects in the population (accumulation). This is well-known to those who master graphical
integration (see for example Sterman, 2000, chapter 7); however, for the sake of explicitness,
the following figure illustrates the case:

» birth rate a POPULATION
8 8

3 —=—<=> | —
Bq g
_

time time

birth rate ™ POPULATION
3 8
2 2

&: \o—— S| —— >

time time

Do you see both cases in the following diagram?

+

birth —_— POPULATION
rate

Figure 14: examples of causality without event

In this figure, two cases are shown: first, the birth rate has a positive value and appears to cause
population to grow. Then the birth rate equals zero and the population remains constant.
Clearly, both cases are compatible with the causal diagram displayed beneath them. (If we had
taken the net flow, we could even add the case where this flow is negative.)

As long as an individual bears in mind the fact that the birth rate is a flow and the population is
a stock, as well as the relationship between these types of variables, this individual may indeed
“see” all these possibilities in the diagram. However, if CLD are meant to be used with people
who do not master system dynamics, would this individual want to use this type of diagram?
Richardson (1997) as mentioned an alternative definition of polarity:

— positive (+):the independent variable adds to the dependent variable;

— negative (-):(+):the independent variable subtracts from the dependent variable.

If we think “the birth rate adds to population” then the usual behavior and the change event (say,
a “step”) are accurately reflected. However, even if we replace CLD by “influence diagrams”
(Wolstenholme, 1990) and population appears as stock and the birth rate as rate, it is impossible
to express the behavioral effect of the birth rate’s absolute value for population on a diagram
(unless we add a new symbol category like “>”, “0” and “<” to mean “positive”, “zero” and
“negative” respectively. Even though this may in principle be possible, it would deprive the
diagrams of their simplicity. Note also that a rate that can be positive or negative corresponds
to a “bi-flow”; inflows and outflows implicitly carry a restriction on the range of possible
values, which causal loop diagrams do not express.

The last limitation is that causal loop diagrams do not have a means to represent the “smoothing
in” of the caused effect over time. As observed by Moxnes (1998) and Moxnes & Saysel
(forthcoming), people appear think statically: they assume implicitly that the effect of an

18
intervention in a control variable will realize itself immediately. This is, of cause, an erroneous
assumption that leads them into faulty decisions. It can be attributed to not recognizing stock
variables as such (and not adequately taking into account the behavioral implications of this
fact). Again, one would have to be a accustomed dynamicist to bear in mind all this while
working with a causal loop diagram.

It has to be concluded that causal loop diagrams cannot capture what causality really means for
system dynamics, since they talk only about events and not behavior in general. For system
dynamics., causality includes behavior, the way the value of a variable is determined in each
period of time (not the way it changes is determined, which is only a special part of it).

What are causal loop diagrams good for?

After all, it turns out that causal loop diagrams are a qualitative tool that should be used only
when it is not demanded to process structure into behavior or to reason about behavior. If used
with the complete or the “adds/subtracts” definition after having understood the behavior via
simulation, it can help to make sense of the behavior found; still, if the specific notions of
system dynamics help to better think about behavior, the pedagogical value of causal loop
diagrams may be put into doubt (since they avoid confronting oneself with these things).

Maybe causal loop diagrams are a useful tool for exploring beliefs concerning the causal
structure of a situation. However, in situations where it is important to understand the
behavioral consequences of decisions (interventions), the “automated reasoning” of simulation
becomes necessary or at the very least desirable. One could probably figure out some plausible
guesses concerning the probable quality of behavior in cases without feedback loops or when all
the loops have the same polarity; but these are extreme cases and should not be used to design a
tule. This would require a notational change in causal loop diagrams (distinguish stocks and
flows and add the “>,0,<”); additionally, one would have to identify the “tails” (independent
variables) and trace their assumed behavior, and then trace the superposed influences through all
the causal links. A lot of work: probably causal loop diagrams would be just “stock-and-flow”
diagrams and they would not be so popular any longer

So it appears that causal loop diagrams are so popular because they are well adapted to intuitive
thinking. But if the situation at hand requires computations that intuitive thinking is bad at, one
would expect the tools to enhance this thinking (and not to have the same shortcomings). On
the other side, if the situation is politically delicate or time presses, an approach like SODA may
be more convenient: it does not force to separate structure from behavior and thus is easier to
use.

In which way can the use of causal loop diagrams help to discover or articulate (attributed)
causal links? How are they usually recognized? Let us return to the first two phases presented
in the conceptual model in Figure 3 (p. 5):

1) how do we come to consider something as a relevant variable?
2) how do we come to believe in the existence of a causal link between two variables?

We will try to explore this question using the different tools on the population example.

I an 1
birth rate + population_ death rate

Figure 15: the population case as a causal map or causal loop diagram
We start restating the typical CLD, where most people are tempted to use the “popular”
definition and thus project structural information into behavioral conclusions that can easily be
mislead.

subtracts

adds to ——_» 4e0rn

<<

Figure 16: the population case as a concept map

When the same case is expressed as a concept map, there seems to be exactly the same
structural information as in the CLD. Note that in this example, I have used the “adds to”
definition (however, one can also name the links according to the other definitions). The fact of
doing so may be seen as a /ittle help to think adequately about the causal relationships.

2 Population falls 3 death rate remains
1 birth rate falls— > below its previous constant
path

Figure 17: the population case as a cognitive map

When the story is told by a cognitive map, we see that behavioral aspects are now explicitly
stated in the “constructs” (and it is not necessary to compute them based on the polarity
indications). This is less general than a causal loop diagram (that offers the structure for all
cases of behavior without contaminating it with information about one of the possible behavior
contexts).

birth rate ———] POPULATION |<¢——— death rate

Figure 18: the population case as an influence diagram

The influence diagram recalls us that “population” is of a different type than the other variables.
This is not expressed in the CLD; however, the observer has to do the thinking in order to
understand what this difference means.

—— Pr POPULATION ———— Os

birth rate death rate

Figure 19: the population case as a stock-and-flow diagram

20
Seen as a stock-and-flow diagram, it is easier to see that the birth rate “adds” and the death rate
“subtracts”. But even so: what difference does this make?

birth rate death rate
2 >

Figure 20: the population case as stock-and-flow diagram with behavioral information

Everything changes with simulation. Each of the mayor modeling software packages has its
own way to visualize the variables’ behavior in the context of the stock-and-flow diagram.
Now one can readily see what the current structure, together with the parameter context, means
in behavioral terms.

If structure is inferred from behavior and then is used to generate behavior, using a tool that
represents only the structure forces the user to carry the behavioral part on his mind. While this
can be expected from an experienced user, a beginner is left with a problem. Due to the
apparent simplicity of the tool, he may rapidly gain a feeling of progress; however, his mental
model of what the diagram means may contain all kinds of errors concerning the model’s
behavior, and since this part does not become articulated, it is not open to critique and the
subsequent improvement.

It follows that causal loop diagrams should not be used without the guidance of an experienced
modeler who will point out the adequate behavioral aspects.

The population case is admittedly a very simple one. Since it does not involve feedback loops,
the causal loop diagram could not play out its notational advantage over concept maps or
cognitive maps. Neither did we gain much by using an influence diagram. The stock-and-flow
diagram was not more complex to draw, but it had the big advantage of allowing simulation,
enabling the tool to show the behavior. This real-time feedback of the meaning of the structure
is a huge help, also during the modeling, since it helps to discover inconsistencies and errors. It
cannot possibly be offered by CLD.

In more complex cases, where there are interacting feedback loops, causal loop diagrams have
one advantage over the other diagram languages: feedback loops exist as a concept and have a
symbol to be represented explicitly in the diagram. However, even the most expert of system
dynamicists will not be able to guide his clients through the behavioral interpretations without
simulating.

In conclusion: CLD should be banned from use as decision-finding tool and limited to exploring
causal (structural) beliefs - where they more expressive power than the other tools presented
here:

— concept maps and cognitive do not focus on variables and causal structure and will waste
mental energy; they may be even more intuitive, but their product has still to be translated in
terms of variables;

— causal diagrams strive to understand cases better described in terms of discrete events;

— causal maps lack the pos ity to express “feedback loop” and “delay”.

Another recommendable use might be for simplification purposes when explaining the
simulation model’s behavior. However, there remains a big doubt as for how neatly one can
mentally separate behavior from structure: after all, we cannot infer structure without behavior

21
and we cannot conjecture behavior without structure. In the end, the “concept model” approach
described by Richardson (2006) may be more fruitful for system dynamics.

One may treat “practitioner use” and “teaching use” in a different form. It has been argued that,
since practitioners do not use CLDs for what they are not meant for, the shortcomings of this
diagram language do not matter much '*. However, in “teaching use”, this may be different.
Let us consider the (probably) most used textbook, “Business dynamics” (Sterman, 2000),
which introduces “structure and behavior of dynamic systems” in chapter 4 using causal loop
diagrams. Then, these diagrams are the first of the “tools for systems thinking” to be
introduced. Later on, discussion moves to stock-and flow diagrams, and each of the generic
behaviors in analyzed in-depth. However, during these early chapters (and the “challenges”
proposed to students), discussion is based on CLDs; whenever there is doubt as for the
consequences of a specific causal link, students will have to set up an example and computed
themselves through on their own. The evident benefit is that when such doubts do not arise,
discussion is much faster and one can stay focused on the essential items.

There is probably a trade-off: CLD’s simplicity is an advantage for rapidly introducing intuitive
issues, but they are not of much help once discussion moves beyond what is intuitive. Maybe a
wise strategy would be to avoid an either-or position and combine both, CLDs and stock-and-
flow models in one learning tool; steps in this direction have been made, for example in the case
of the “MacroLab” learning environment (Wheat, 2007).

6. Conclusions

This article started remarking that despite its fundamental importance for system dynamics,
polarity and causal thinking have not received much attention in the specialized literature. The
apparent effort to learn the meaning of polarity was the starting point of this inquiry. An
examination of other approaches that deal with causality and use more or less similar diagram
languages has shown that usually causality is only very broadly defined, and where it is
operationally defined, this is done with respect to events rather than behavior.

In contrast to these approaches, system dynamics is about behavior rather than events. We have
proposed to understand an event as a change of behavior, the second derivative of a function.
Part of being attentive to behavior is that there are specific differences between accumulators
and flow variables which have implications for behavior. We have found that causal loop
diagrams could be used in a way that avoids the flaws shown in previous critiques: for doing so,
one has to use the full definition rather that the popular one. However, the popular definition
continues to be just this: popular.

We have then found that causal loop diagrams are not able to help taking into account behavior
in a way that keeps coherent with system dynamic’s conceptual world, especially the
relationship between flow and stock and the gradual realization of effects. It is as if causal loop
diagrams were better equipped to think about events than about behavior. This would help to
understand why they are so popular, just like the popular definition, and why my students find it
much harder to understand the “complete” definition, which appears to address behavior and
event at the same time..

Finally, if behavior is even harder to think with than events, tools for causal thinking should
help keeping coherence in our minds between structure and behavior. This is exactly what our
modeling software does: the diagram language of “stock-and-flow” is not only able to express
important aspects of a modeled system, it also allows the computer to enhance our mind.

This is certainly not the end of my inquiry. In closing these lines, it has become my conviction
that executable “concept models” have many advantages over causal loop diagrams, that should
be used only by experienced modelers. One personal consequence is that I’m now very busy
replacing all the causal loop diagrams of my educational materials by simple stock-and-flow
models.

'? T thank one of the reviewers for reminding me of that point.

22
In the future, it should be asked how we recognize variables and causal relationships — steps 1
and 2 in Figure 3 (p. 5). Many beginners find it hard to come up with variables at the outset of
the modeling process; “‘ask the client” only shifts the burden to other people. If we believe that
humans are sensitive to change (to events), then how do we articulate our mental contents as
variables? Further, if theories about causal learning are based on events, what is the status of
behavior (the slope of the curve or the first derivative of the function)?

System dynamics has its advantages, since it can help to improve understanding of situations
where the other approaches do not have a lot to offer. However, most adults nowadays not only
ignore system dynamics, they do know other approaches and it is well known that most adults
prefer avoiding changes. If we wish more people to become system dynamics thinkers — that is
to say when we think as educators — then it may be helpful to know the answers to these
questions.

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Pedercini, M. 2006. What’s behind the blue arrow? - The notion of causality in System
Dynamics; Proceedings of the 24th International Conference of the System Dynamics
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Rebich, S. and Gautier, C., 2005. Concept Mapping to Reveal Prior Knowledge and Conceptual

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Communications

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Vol. 13, No. 3, (Fall 1997): 247-252

Richardson, G. P. 2006 Concept Models. Proceedings of the 24th International Conference of
the System Dynamics Society, Nijmegen

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Dynamics Review Vol. 9, no. 2 (Summer 1993):113-133

Sterman, JD. 1989. Modeling managerial behavior: misperceptions of feedback in a dynamic
decision making experiment. Management Science 35(35): 321-339

Sterman, John, 2000. Busyness Dynamics — systems thinking and modeling for a complex
world, John Wiley

Tolman EC. 1948. Cognitive maps in rats and men. Psychological Review 55: 189+208.

24
Warren, Kim, 2004. Why has feedback systems thinking struggled to influence strategy and
policy? Systems Research and Behavioral Scienc; Jul/Aug 2004; 21, 4; pg. 331

Wheat, David. 2007. The Feedback Method - A System Dynamics Approach to Teaching
Macroeconomics, PhD thesis, University at Bergen, March 2007

Wolstenholme, E. 1990. Systems Enquiry. Wiley

25
| a Causality and diagrams for system dynamics hh

UNIVERSIDAD DE Martin Schaffernicht FACE-UTALCA
TALCA Facultad de Ciencias Empresariales
Universidad de Talca
Talca — Chile

martin@utalca.cl

Students have a hard time learning to correctly use polarity.

Most approaches use causality between events, not behavior. System dynamics focuses on behavior,
but intuitive thinking focuses on events; the relationship between them is not clearly defined.

System dynamics has several definitions of polarity

the “popular” one is simple but allows false statements;

the “complete” one avoids false statements, but is hard to learn and ambiguous with respect to the
relationship between behavior and event.

Causal loop diagrams (CLDs)

sallow to model “fast-and-dirty”

*can represent mental models that contradict basic system dynamics truths;
*cannot represent some of the basic system dynamics truths.

CLDs are easy and risky to use

*the expert dynamicist does not need external help to avoid errors and can use CLDs safely;

*the beginner needs external help but resists the effort of learning stock-and-flow modeling before
thinking about a problem.

Approach Main use Nodes Links Driving Degree of
force abstrac-
tion
Concept Structure knowledge in | Concepts in general Any type Undefined Low
mapping form of propositions
Cognitive Uncover, structure and | Constructs Qualitative Events, Low
mapping analyze problem causal links, | actions
accounts negative and
positive type
Causal Represent beliefs Variables Qualitative, Undefined High
mapping about the causal including
structure. “popular”
polarity
Causal Determine causes of Variables with | Quantified Events High
diagrams events or discrete values causal links
consequences of
actions
System Structure decision Variables with | Quantified Behavior | High
dynamics policies continuous values causal links

Quantitative Computer

Z\ ° y NX

the sequence of quantities CO) e @

the trend (quality of behavior) NN NOUS

“first descends”,
then grows”

Sw

the change of the trend “switches from
A decreasing to

“decreases”

Specialization

Levels of description

rowth”
ae : ¥
Qualitative Modeler

Behavi0reee,ccedee

when the independent variable changes, then the dependent variable changes

positive in the same direction
“ a when the independent variable changes, then the dependent variable changes
negative in the opposite direction
Change = dV Change = dV,- aV,
rh dt
dt dV,
dv av, 77 at
dt
at dv, ae
A dt
dt dt
av dv, av, .
V.
dv ; at 2
dt -
XN

Behavior as change of quantities Behavior as change of the quality of behavior (event)
soeantoneg

when the independent variable changes with a particular sign (+ or -), then the

positive following values of the dependent variable will be above (or less) than what
they would have been.
“negative” when the independent variable changes with a particular sign (+ or -), then the
9g following values of the dependent variable will be less(or above) than what
they would have been.
a
7
aN
NY XN
4
>
4 ‘4 .
Behavior as change of quantities Behavior as change of the quality of behavior (event)

PegoP0ogg
:

deaths

This part of the CLD is used to
critique the “causal loop
diagram” language as a tool for
“systems thinking” in

natality
rq

mortality
+

birth control public health
policy policy

~See the “population case.itm” model in the additional material.
+ .
population
“Popular” definition “Comolete” definition

Is the moment of
bifurcation an event?

births

Sy
> > >
If births decrease, /f births decrease,
then population will decrease. then population will be less than what it

would have been.

“Complete” definition seems to avoid contradiction.
However, “less than what would have been” does not
imply “no absolute decrease”.

+
population
Any definition
A A
births A -
>
10) inca aia Ri moana
> >
a
ie ” ii >
A >
> >

No “flow” variables that are “inflow” or No bounds on quantities (like
“outflow”, no quantities a negative inflow).

No “stock” variables that maintain values

» Aconstant independent variable can lead
to a growing dependent variable.

No flow-stock integration
Population depends on various
variables and also influences them.
births — population is too reduced.

natality
+

birth control

policy

population

What does “ceteris paribus” then
mean: “population has no other
influences” or “all other
influences on population remain
as they are”?

deaths
+
mortality
+
public health
policy

—Experiment with the
“population case.itm” model
in the additional material.

CLDs allow event-oriented
(intuitive) thinking.

CLDs have few

implied
concepts.
CLDs allow to go fast and do not
require much previous study.
Use of CLDs does not
educate proper
Thinking with systems thinking.
We generally cannot CLD is popular.
CLDs allow false avoid to make . a
behavioral Behavieral A beginner is likely to
. 1 think in terms of

interpretations constructs and events.

He is not aware of the

interpretations.
“hazard zones”.

An expert can think in terms
of variables and behavior; he
embodies the rules and will
not err: CLDs as shorthand.

Only disciplined use in teaching!

Use by experts OK.
A beginner is likely to System

We generally cannot think in terms of dynamics has
avoid to make constructs and events. several -
_ behavioral He is not aware of the “complicated)
interpretations “hazard zones”. concepts.

\

Learning “stock-and-flow’ thinking
and modeling takes time.

Adults have few —

time to learn. Improve definition
of relationships
with “event
thinking”
approaches.

Start teaching earlier.

__ expert can think in terms
of variables and behavior; he
embodies the rules and will
not err: CLDs as shorthand.
1. Booth-Sweeney, L. and Sterman, JD., 2000. Bathtub dynamics: initial results of a systems thinking inventory, System
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development, System Dynamics Review 16(4):325-348

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Review 20(2): 139-162

8. Pedercini, M. 2006. What's behind the blue arrow? - The notion of causality in System Dynamics; Proceedings of the 24th
International Conference of the System Dynamics Society, Nijmegen

9. Richardson, 1991 Feedback thought in social sciences and systems theory. Pegasus Communications

10. Richardson, G. P. 1997 Problems in causal loop diagrams revisited, System Dynamics Review Vol. 13, No. 3, (Fall 1997):
247-252

11. Richardson, G. P. 2006 Concept Models. Proceedings of the 24th International Conference of the System Dynamics
Society, Nijmegen

12. Richmond, B., 1993, Systems thinking: critical thinking skills for the 1990s and beyond, System Dynamics Review Vol. 9,
no. 2 (Summer 1993):113-133

13. Sterman, JD. 1989. Modeling managerial behavior: misperceptions of feedback in a dynamic decision making experiment.
Management Science 35(35): 321-339

14. Sterman, John, 2000. Busyness Dynamics — systems thinking and modeling for a complex world, John Wiley

15. Warren, Kim, 2004. Why has feedback systems thinking struggled to influence strategy and policy? Systems Research and
Behavioral Scienc; Jul/Aug 2004; 21, 4; pg. 331

16. Wheat, David. 2007. The Feedback Method - A System Dynamics Approach to Teaching Macroeconomics, PhD thesis,
University at Bergen, March 2007

17. Wolstenholme, E. 1990. Systems Enquiry. Wiley
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3.

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