Summary and Conclusion

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The results of both studies lend support for the hypothesis that the aggregate method

would produce the most complex collective maps, whereas the congregate method would

produce collective maps lower in complexity. The workshop method tended to produce

collective maps with an intermediate degree of complexity. This result is particularly

evident for the L/N ratio, but is also reflected in several map density comparisons. In terms

of distance ratios between individual maps and the collective maps, the congregate and

workshop methods were less distant than the aggregate method in both cases.

In terms of subjective ratings of the methods, Study 1 suggested that the aggregate

method was rated better than the congregate method for all criteria. Moreover, the

aggregate and the workshop mapping methods were equally good in terms of problem

representation and stakeholder implication. However, the aggregate method outperformed

the workshop mapping method in terms of solution implication. In Study 2 a

different pattern of results emerged. Workshop mapping was generally superior to

aggregate and congregate approaches across all four criteria. Further, congregate maps

generally received somewhat better ratings than aggregate maps. Together the two

studies lend mixed support to Hypothesis 2.

It is useful to consider the relationships between the objective and subjective results.

The objective results were for the most part consistent across the two studies, but there

were differences in the subjective results. Aggregate mapping fared better in Study 1 than

in Study 2, whereas congregate mapping fared better in Study 2 than in Study 1.

Workshop mapping was rated well for the most part in both studies. In Study 1 its ratings

were equivalent to those of aggregate mapping (except for solution implication), whereas

in Study 2 it was rated much higher than aggregate or congregate mapping. This suggests

that map complexity and the degree to which the map corresponds to individual

representations had different meanings for the two samples. In Study 1 map complexity

did not seem to correlate with lower ratings, whereas in Study 2 it did. In Study 1, degree

of difference between collective and individual maps did not correlate with ratings,

whereas in Study 2 it was positively correlated.

At least three explanations for this difference can be advanced. First, and most plausible

to us, the average number of links and nodes was much higher in the individual maps in

Study 2 than in Study 1 (an average of 10 nodes and 15 links in the individual maps in

Study 1 versus an average of 29 nodes and 83 links in the individual maps in Study 2).

Hence, the aggregate maps in Study 2 were likely to be much more complicated and

difficult to interpret than those in Study 1. This may have resulted in lower ratings by the

subjects. In addition subjects in Study 1 may have been able to see their own concepts

and ideas in the aggregate maps more easily than subjects in Study 2, and thus they might

be disposed to rate it higher than in Study 2. Both groups rated the workshop method

high, which suggests that higher levels of participation increase perceived value of the

collective map.

A second explanation is that the use of groups to build maps in all three conditions in

Study 1, but only for the workshop method in study 2, influenced ratings. Participation

in Study 1 may have mediated subject ratings of the maps, particularly those of the

subjects who built the maps. In Study 2, however, subjects only participated in finalizing

the maps for the workshop map and may have seen the aggregate and congregate maps

as “alien.” If this explanation is accurate, then one implication is that the aggregate

method used in a workshop is superior to the other methods although it performs less

well when the facilitator builds the maps. A third possible explanation for the results is

that they stem from cultural differences between the subjects in the two studies.

However, it is not apparent what cultural differences could account for the differences

in results.

Lessons Learned

We can advance several lessons learned about the three methods. The advantage of the

aggregate method is that it is simple and easy to implement. It is also very good at pooling

information from group members’ individual maps. As the comparative study suggested,

the aggregate method works best when individual maps are not very complex and/or when

the group is relatively homogeneous (as in Study 1). The disadvantage of the aggregate

method is that group maps derived from this method tend to be complex and dense. In

larger and more heterogeneous groups, the aggregate method may not be effective as it

is in small and homogeneous groups (as in the setting of this experiment).

It seems likely that the congregate method would be more effective in larger and

heterogeneous groups. The advantages of the congregate method are two-fold. First, it

is less complex (than the aggregate method). An increase in the number of causal loops

does not necessarily increase group map complexity. Second, it is better in representing

the interactions of multiple perspectives via causal loops. In organizational problem

formulation, the congregate method is proposed to apply at the organizational level,

where the number of groups is many and groups have more distinct perspectives. At the

organizational level, the congregate method will help identify different perspectives to

be included in the organizational model.

The workshop method fared best in terms of least complexity and highest subjective

ratings across the two studies. This is likely due, in part, to the higher level of involvement

subjects have in the map-building process. The workshop method can be used alone or

in combination with other methods to improve the shared effect of collective maps. Other

researchers (Ackermann et al., 1997; Diffenbach, 1982; Eden, 1989) have suggested that

such combinations improve the group mapping outcome. The workshop method can

replace the aggregate method at the group level when individual maps cannot be obtained

for some reason. This substitution may not seriously affect the effectiveness of group

maps. In combination with the workshop approach, the congregate method has potential

in handling multiple perspectives in complex systems.

One final point to bear in mind is that Study 1 showed that, in terms of objective measures,

the congregate and workshop methods had more variation in results than the aggregate

method. This is probably due to the fact that these require more judgment on the part of

the modeler and group than the aggregate method, which is for the most part based on

clear-cut rules. Subjective judgment may well be perceived as bias by some participants,

which may create a sense that both the congregate and workshop methods are not

representative of some user perspectives.

Based on the results of the two studies, we can also advance some suggestions

concerning the relationship between group size and effectiveness of mapping methods.

We propose that when group size increases, the effectiveness of the aggregate method

will decrease significantly, while the effectiveness of the workshop method may increase

slightly, and that of the congregate method will increase.

Table 16 summarizes our hypothesized relationship. This relationship may suggest the

best fit method for a given group size. Further study is, however, needed to fully test this

relationship because we are going beyond the four-person groups used in the first study

and the seven-person group in the second.

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Table 16. Dependency of method effectiveness on group size

Effectiveness Group size

Rank < 5 5 to 7 > 7 (hypothesized)

Best Aggregate method Workshop method Congregate method

Intermediate Workshop method Workshop method

Worst Congregate

Aggregate method =

Congregate method Aggregate method

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Endnotes

1 In the analysis, we use their distance ratio (DR) formula to measure the distance

between collective maps and individual maps.

2 This framework and a prototype of sustainable decision support systems were

developed to improve policy planning and decision making regarding urban

infrastructure investments such as investments in roads and bridges, fresh water

supply systems, waste water treatment, drainage and so forth.

3 These interviews were conducted by the participants and other researchers with

people who are involved with the city’s infrastructure management.

4 It was our intention to limit the number of nodes to 15 (maximum).

5 The power-related implications of a map can be surfaced if it can be used to show

how one group of stakeholders is advantaged in the current situation and how this

contributes to the problems or how one group can manipulate the organization to

serve their interests.

6 The map, which had more links, thus, higher degree of map density ratio, received

a higher rating.