Study 2

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In Study 2, the objective was to construct a systems model of infrastructure for the city

of Houston that represented the perspectives of a multidisciplinary research team. The

research team, composed of engineers, environmental scientists, and social scientists,

had been trying to build a decision support system for infrastructure decision making as

part of a larger project. The team desired to build a systems model of infrastructure that

reflected commonalities among their perspectives, a “best science” model of factors that

influenced infrastructure growth and the positive and negative impacts that infrastructure

growth had on the urban area .The basic approach taken was similar to Study 1: first

build individual causal maps for the researchers, derive collective causal maps using

different methods, and compare the methods in terms of which the researchers felt yielded

best fit. The first step was to define a problem/issue. After consultation with members

of the group, we framed the issue as: “The impact of infrastructure growth on quality of

life of Houstonians.” The second step was to select participants. We had seven members,

who were involved in developing a conceptual framework2 for the city’s infrastructure

decision making system, participate in the experiment. The experiment consisted of two

stages: individual causal mapping and building group maps.

We followed the same procedure as in Study 1 to capture individual causal maps.

Individual maps provided the basis for building collective maps and also provided a

standard of comparison for the final group maps. Participating in the individual stage

provided the subjects with an opportunity to learn and become accustomed to the

mapping method. Based on the interview transcripts3 and related literature (Forrester,

1969; Lee, 1995), we developed a list of 16 factors or constructs. The subjects were asked

to select factors that are relevant to the problem of study and assess possible causal

relationships between pair-wise selected factors. The purpose was to gather information

that would enable us to draw a causal diagram that shows how the subjects believed

infrastructure resource allocation affects the city. The process was assisted using a

questionnaire (available from the authors).

After the individual maps were constructed, we applied the aggregate and congregate

methods to build the aggregate and congregate maps based on the individual maps.

Unlike Study 1, the subjects did not build the aggregate or congregate maps in groups.

The experimenters constructed the maps. The subjects were then gathered in a workshop

under the researcher’s facilitation to build the workshop map using a procedure similar

to that described in Study 1. Following the completion of the workshop maps, subjects

filled out a questionnaire similar to that utilized in Study 1.

Results of Study 1

In the actual implementation of the experiment, only 24 out of 30 planned subjects were

able to participate in the experiment throughout the entire period of the study. (One

participant was absent. Two persons left after the individual cognitive mapping because

they developed “headaches.” Three other people left due to urgent duties). The

outcomes of this experiment were six derived group maps (A, B, C, D, E, and F), which

are provided in the Appendix. Each method of developing group maps was utilized for

two groups. Information about treatments for these groups is provided in Table 4.

Objective Measures

A straightforward measure of map complexity is the number of links and nodes in the

maps. Table 5 compares the total nodes (links) of group maps to the average number of

nodes (links) in individual maps. An average individual map has ten nodes with a

standard deviation of 2.6 nodes. The minimum number of nodes is four and the maximum

number 15. Generally, the group maps have more nodes than the average individual maps,

as indicated by the group/individual node ratio shown in Table 5. This observation is

consistent across all groups. The use of the congregate method (groups C and D) tends

to produce group maps that have relatively more nodes than average individual maps.

On average the individual maps have 15 links (minimum 8, maximum 22). The group maps

have more links than the average individual maps, with the exception of group C, as

indicated by the group/individual link ratios in Table 5. The use of the aggregate method

Table 4. Grouping and treatments

Table 5. Total number of nodes in individual and group maps

Treatments Aggregate method


Congregate method


Workshop method


Group A (4 subjects) Group C (4 subjects) Group E (4



Group B (4 subjects) Group D (4 subjects) Group F (4




Group 11 11 11 11 15 11

Individual Average 9.25 9.25 9.00 8.25 12.75 10.75

Individual Std. Dev. 4.03 1.50 1.63 3.50 2.36 0.50


Group/Individual Ratio 1.19 1.19 1.22 1.33 1.18 1.02

Group 22 22 17 16 19 21

Individual Average 11.5 12.75 17.75 11 18.5 16.25

Individual Std. Dev. 2.08 2.22 5.32 4.08 4.73 2.50


Group/Individual Ratio 1.91 1.73 0.96 1.45 1.03 1.29

Note : A and B use the aggregate method; C and D use the congregate method; E and F use the

workshop method.

 (groups A and B) tends to produce the group maps with more links than the average

individual maps.

From the link and node data another measure of map complexity, the links to nodes ratio

(L/N) was calculated. The links to nodes ratio indicates how dense the maps are in terms

of linkages among the concepts (nodes) in the maps. These ratios are shown in Table 6.

The individual maps in our experiment have an average links to nodes (L/N) ratio of 1.54

with a standard deviation of 0.3 (maximum L/N ratio for individuals was 2.4; minimum L/

N ratio for individuals was 1.0). Generally, the group maps have an average ratio of 1.7

with a standard deviation of 0.3 (maximum 2.0, minimum 1.27).

As shown in Table 6, only for the aggregate method did the collective maps consistently

have higher L/N ratios than the individual maps. For both congregate and workshop

methods, the collective maps have about the same ratios as the individual maps with large

variances. The aggregate models consistently have higher ratios than either the congregate

or the workshop models, even though the individual maps for the aggregate method

had lower L/N ratios on the average than did the other groups’ individual maps. One other

interesting result was for congregate group C: this group had by far the highest individual

L/N ratio, yet the resulting collective map was simpler than both aggregate maps and one

of the workshop maps. This suggests that congregate mapping may simplify the

collective map more than aggregate mapping.

Although Eden and Ackermann (1992) report typical ratios of 1.15 – 1.20 for maps elicited

from interviews, several studies reported higher ratios. For example, Hart’s (1977) maps

have ratios ranging from 1 to 1.4. The causal maps of subjects in Klein and Cooper (1982)

have ratios ranging from 1.2 to 1.7. The causal maps in Laukkanen (1994) have ratios of

1.96 and 1.67. Thus our average individual ratio of 1.5 is consistent with other studies.

Table 6. Links/nodes ratios

L/N ratios A B Avg

(A & B) C D Avg

(C & D) E F Avg

(E & F)

Group 2.00 2.00 2.00 1.70 1.45 1.58 1.27 1.91 1.59

Individuals 1.38 1.39 1.38 1.95 1.50 1.72 1.47 1.52 1.49

STD (ind.) 0.28 0.10 0.20 0.43 0.44 0.47 0.27 0.25 0.24

Map density A B C D E F

Group map 0.20 0.20 0.19 0.15 0.09 0.19

Average individual maps 0.21 0.18 0.25 0.30 0.13 0.16

STD (individuals) 0.10 0.06 0.05 0.25 0.03 0.03

Table 7. Map density as a measure of map complexity

Note: A and B use the aggregate method; C and D use the congregate method; E and F use the

workshop method

Note: A and B use the aggregate method; C and D use the congregate method; E and F use the

workshop method.

The reason for smaller ratios reported by Eden and Ackermann is that their maps contain

a large number of nodes and their method of eliciting maps results in less links than the

cross-impact method that was used in this research. In the cross-impact method, the map

builder considers many possible impacts of every factor on all other factors, while in the

interviewing method the map builder only considers direct impacts.

As shown in Table 7, the individual maps have an average density of 0.20 (with a standard

deviation of 0.12). In terms of map density as an indicator of map complexity, there were

no statistically significant differences between the group maps and average individual

maps. This result is not consistent with the results obtained using the L/N ratios, in which

the aggregate models have higher ratios than average individual maps. However,

inspection of Table 6 indicates that for both the congregate and workshop methods, one

of the two groups had lower density than the two groups employing the aggregate

method. There seemed to be more variation in density for the congregate and workshop

methods than for the aggregate method.

Our maps are denser than those reported in previous studies. For example, maps in Hart

(1977) have an average density of 0.03 (ranging from 0.024 to 0.042). The causal maps of

subjects in Klein and Cooper (1982) have density ratios ranging from 0.06 to 0.21. The

causal maps of subjects in Laukkanen (1994) have ratios of 0.09 and 0.10. The maps in

this study are denser than those reported in the literature because these maps have

smaller numbers of nodes4 and the method we used to elicit maps was “cross-impact”

rather than “interviewing” or coding from documents or transcripts. Our result is

consistent with the observation that Klein and Cooper (1982) drew from their studies: the

smaller the maps, the larger density. They explain that in smaller maps the concepts tend

to be of central importance to the situation, and thus the decision makers identify many

relationships between them, making the maps dense.

Finally, we used the distance ratio (DR) proposed by Markoczy and Goldberg (1995) and

the program provided by the authors to calculate DRs between the group maps and the

individual maps. A summary of distance ratios between collective maps and individual

maps is given in Table 8. On average, the DR between group maps and individual maps

is 0.13 with a standard deviation of 0.03. The maximum DR is 0.19 and the minimum 0.08.

The results shown in Table 8 suggest that the method used to construct group maps has

an impact on the average DR from the collective map to the individual maps. To test this

Table 8. Distance ratios between collective maps and individual maps

Note: A and B use the aggregate method; C and D use the congregate method; E and F use the

workshop method.

Groups A B C D E F

0.19 0.15 0.19 0.13 0.1 0.15

0.17 0.14 0.19 0.11 0.08 0.1

0.15 0.14 0.16 0.13 0.09 0.11

Group- individual

distance ratios

0.12 0.17 0.12 0.12 0.08 0.12

Average 0.16 0.15 0.17 0.12 0.09 0.12

observation, we conducted a one-way ANOVA with method as the factor and distance

ratios between the collective maps and the respective individual maps as the dependent

variable. For each method, we had eight cases. We found that the workshop mapping

method had the lowest DR as compared to the congregate method (p < .006) and the

aggregate method (p < .001). However, there was no difference between the aggregate

and the congregate methods.

In summary, the results obtained for the links-to-nodes ratio and the distance ratio

measures are supportive of the expectation that the aggregate method would produce

more complex collective maps than the congregate method and the workshop method.

And while the map density results were not significantly different, the pattern was also

consistent with this expectation.