Computer Simulation

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As reported in Axelrod (1976), Bonham and Shapiro used a computer simulation approach

to analyze the cognitive map of a Middle East expert and to predict three years later his

explanation of the Syrian Intervention in Jordan in 1970. The authors found a striking

resemblance between the predicted explanation and the explanation the expert gave when

asked about the actual crisis three years later.

Nozcika et al. (1976) detailed the computer simulation approach Bonham and Shapiro

used to generate the predictions. Representing the causal map in matrix form, they

derived the reachability matrix (see Chapter II), before generating the predictions. The

The six steps employed by Nozcika et al. (1976) were:

1. Search for antecedent paths: Involves the identification of the various linear sequences of concepts leading

to the concepts highlighted. From the full set of antecedent paths identified, a set of plausible set is derived

based on the degree to which relationships on the path are historically supported.

2. Search for consequent paths: This step is similar to the previous one but the focus is on the value concepts.

3. Formulation of alternative explanations: Explanation selection is based on a path balance matrix, under the

axiom that the explanation that will be preferred by the decision maker will be the one with the highest

cognitive centrality.

4. Selection of preferred explanation: The cognitive centrality of each path is computed and using the

preferred explanation search algorithm, explanations are identified.

5. Search for relevant policy options: This involves the examination of reachability matrix to determine if for

each policy concept, one or more concepts that are part of the explanation are reachable.

6. Evaluation and ranking of relevant policy options. Here again a policy impact index is calculated to

evaluate and rank policy options.

The authors constructed a simulation model in FORTRAN IVH for the IBM 370/135 system available at the

American University Computer Center.

Box 1. Nozchika, Bonham and Shapiro's six step process

authors chose some concepts for their policy relevance, and once the concepts were

established, they employed a six-step process of deriving the predictions (See Box 1).

Bonham and Shapiro argued that this mode of analysis of behavior is very useful in

inductive efforts to build a theoretical model of decision making in specific domains. We

may add that this approach may also have great value in predicting behavior (e.g.,

competitors) as well.

Influence Diagrams

In the Roos and Hall (1980) example cited in Chapter I, the authors analyzed the causal

map they derived qualitatively to discover the cycles of cause-effect links that explained

the behavior of the director of the emergency care unit they studied. The authors

acknowledged the limitations of their approach:

It ignores the more complex dynamic properties of feedback, such as dampened or

sustained oscillations arising from multi-order negative feedback loops.

To identify the critical feedback loops, Roos and Hall redrew the complex causal map they

obtained, by identifying as a starting point variables characterized by a large number of

inflows and outflows and by tracing paths through the original causal map that were

recursive, i.e., led back to the starting point. This was repeated until every possible path

through the system was accounted for. The loops thus identified were analyzed by

summing the signs of correlation around each loop in the direction of causality. Roos and

Hall noted that they could infer the polarity of a loop since an odd number of negative

signs results in a negative feedback loop while no negative signs or an even number of

negative signs generates a positive feedback loop. Of course, a negative feedback loop

will tend to restore the system to some equilibrium by constraining changes, whereas a

positive feedback loop will amplify the changes in the variables in that loop.

Roos and Hall thus illustrated that a complex causal map may not only incorporate direct

linkages between variables, but also a set of indirect linkages to both virtuous and

vicious cycles as represented by the feedback loops. According to them, each loop

presented policy choices to accelerate or dampen changes in the emergency care unit

under study, and the director of the unit could enact some, but not all of these policy


Roos and Hall (1980) noted that the use of influence diagrams derived from larger causal

maps may be a particularly valuable tool for consultants in conflict-laden situations.

Stated in our terms, this approach may be useful primarily for intervention contexts.

Fuzzy Causal Map

The connection between Axelrod’s causal mapping and fuzzy logic was originally made

by Bart Kosko. Kosko’s Ph.D. advisor, Lofti Zadeh, then a professor at the University

of California Berkeley, had introduced the term “Fuzzy Set,” to a set or groups of objects

whose elements belonged to the set to different degrees. A technical treatment of fuzzy

logic and its application is beyond the scope of this chapter. The interested reader is

urged to consult the references given in this chapter as a starting point.

When introduced, fuzzy logic was a controversial idea, but Kosko applied it to the study

of causal maps, calling them fuzzy cognitive maps. In his words, “A fuzzy cognitive map

or FCM draws a causal picture. It ties facts and things and processes to values and

policies and objectives. And it lets you predict how complex events interact and play


The connection of the causal maps to fuzzy logic occurs in two ways. First, causal arrows

in the maps can be weighted with any number between 0 and 1, and with a s + or – sign

specified. Second, each node can be fuzzy also by “firing” to some degree from 0% to


In Fuzzy Thinking, Kosko illustrated his ideas with three examples:

1. An example of the first kind was based on an article by Henry Kissinger, “Starting

Out in the Direction of Middle East Peace,” that appeared in Los Angeles Times in

1982. Kosko represented Kissinger’s reasoning by means of an FCM, and showed

that this FCM had no feedback loops.

2. A second example was an FCM that showed how bad weather could affect the speed

with which someone drives on a Los Angeles highway. This had two feedback

loops built into them, which made the FCM more complex than the earlier one.

3. A third example was the economic logic behind Walter Williams’ article, “South

Africa is Changing,” that appeared in the San Diego Union, which detailed the

relationship between foreign investment and apartheid in South Africa.

Kosko made the intriguing connection between the behavior of fuzzy causal maps and

dynamic systems, thus opening up the possibility of empirically examining the behavior

of causal maps, with predictions grounded in complexity theory. Thus when simulated,

FCMs may settle down on one of the three attractors: a fixed-point attractor, a limit-cycle

attractor, or chaotic attractor. Kosko argued that FCMs can be simulated by neural nets

to discover the behavior of the dynamical system represented by the FCM.

Kosko emphasized that his approach dealt with the intrinsic logic of the causal map, i.e.,

it can not establish if the predictions are correct but can give insight into the dynamics

if the map were accurate. Nonetheless, in all the above examples, he argued that FCMs

yielded predictions that on a common sense basis were acceptable.

In recent years, many have advocated the use of fuzzy causal logic for the analysis of

causal maps. An illustrative set of papers is listed in Table 1. Yet empirical works using

FCMs are still rare, both in organization sciences and in IT. This may partly be due to the

lack of awareness of the technique by the empirically minded research community. Given

the increasing interest in complexity theory on the part of organizational science

scholars, this technique may provide a valuable avenue to move the empirical research

onto a solid theoretical foundation.