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Causality and diagrams for system dynamics
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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. Introduction: polarity and causality
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For the last two years, Ive 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 Ill 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.



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Im grateful to Erling Moxnes and the students of the Bergen University for their critical questions and
comments
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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:

time
v
a
l
u
e
s
time
v
a
l
u
e
s
Independent variable
Dependent variable
+
-
?

Figure 1: example of an impossible case of polarity
After all, the independent variable went up and the dependent one went down, didnt 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
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. 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

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knowledge is used here in the sense of best available belief.
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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
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).
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