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The results of Study 1 suggest that aggregate maps are more complex than congregate

and workshop maps. They also suggest that aggregate maps are perceived to be more

effective in suggesting solutions than both congregate and workshop maps and more

effective in representing stakeholders’ views than congregate maps. However, the

results also showed that groups using the congregate and workshop methods could vary

widely in the objective properties of the maps they created. Moreover, ratings of maps

varied between groups using the same method for all three mapping approaches.

Differences between groups using the aggregate and congregate methods may be due

to the skill of members involved. In the aggregate and congregate methods, facilitators

were not directly involved in the process of building group maps. Groups followed the

instructions for each method in their own way. It may be the case that the skill of members

in carrying out the mapping process had an impact on the outcome. If facilitators had been

more involved, there may have been more consistent results. It is well documented in the

literature that facilitation plays an important role in group process outcomes (Hackman,

1990; Phillips and Phillips, 1993; Vennix, 1996).

Differences between the two groups using the workshop mapping method, which was

aided by a facilitator, may be due to the nature of the facilitation. One of the facilitators

in the study had a good deal more experience than the other. Eden and Ackermann (1992)

observed that: “[I]nexperienced mappers [facilitators] tend to generate a map with a

smaller number of constructs than those identified by an experienced mapper and in

addition they generate more links.” As indicated in Table 5, the less experienced

facilitator for group F created a map with 11 factors and 21 links, whereas the more

experienced facilitator for group E created a map with 15 factors and 19 links. Thus, group

facilitation may account for the variance in the links/nodes ratios for the collective

mapping method.

The congregate method fared worst in terms of subjective ratings and also yielded models

with quite different objective properties for the two groups. This may be because

subjects were not familiar with thinking in terms of feedback loops (Hall, 1984; Weick and

Bougon, 1994; Richardson, 1991; Steinbruner, 1974; Levi and Tetlock, 1980). Without

special training it is difficult to identify important feedback loops, which in some cases

may require time to think through. Some feedback loops may be associated with long

delays that may take a long time to be effective. For many people, it is much easier to think

about a problem in terms of a “shopping list” in which only one-way impacts are


The HALONG raters consistently rated the two maps derived from the workshop method

as equally good, but the non-HALONG raters tended to rate one map of each pair as

significantly better than the other. This difference between the two groups of raters is

not difficult to explain. The HALONG raters are likely to have relied more on content when

making their judgments (e.g., whether the maps reflected the problem situation), while

the non-HALONG raters are likely to have relied more on the structural characteristics6

of the map (e.g., the amount of information in the maps).

In an attempt to illuminate the relationships between the subjective and objective

measures, we ran correlations between some objective measures (number of nodes,

number of links, L/N ratios, map density ratios, out-degree and in-degree of problem

variable – sales) and the subjective measures (problem representation, solution implication,

stakeholder implication). Some of the interesting correlations are reported in Table 10.

Problem representation (C1) and stakeholder implication (C3) are negatively correlated

with map complexity and L/N ratio, yet positively correlated with number of links.

Correlations are weaker for stakeholder implication (C3) than for problem representation,

and weaker still for solution implication (C2). Subjective measures have higher correlations

to map complexity than to the L/N indicator. No significant correlations were found

between subjective measures and the number of nodes, out-degree and in-degree of the

problem variable (sales).

The relationships between objective and subjective measures are interesting and may

suggest some implications for the conditions when the methods may be best applied. The

negative correlations between the subjective measures and complexity suggest that

maps with higher levels of complexity are not perceived to be as useful or as representative

as simpler maps. One implication of this, for example, is that the aggregate method

may not work well in larger and heterogeneous groups, as it tends to increase group map

complexity as the number of group members or the distinct perspectives increases. On

the contrary, the congregate method may be more suited to larger and heterogeneous

groups as it is able to handle heterogeneous perspectives via causal loops. An increase

in the number of causal loops does not necessarily increase group map complexity. The

positive correlation between the number of links in group maps and the effectiveness of

group maps is reasonable. Relationships in a map indicate the content or information in

a map, and thus a greater number of relationships may imply more information-content

in the map. However, too many relationships may increase map complexity, and this may

reduce the effectiveness of the group map for observers.

Results of Study 2

Seven individual maps were elicited from members of the research team following

procedures described above. These were used to build collective maps with the

Table 10. Correlations between objective and subjective measures

Note: C1 stands for problem representation criterion, C2 for solution implication criterion, and

C3 for stakeholder implication criterion.

Correlations C1 C2 C3

L/N ratio -0.60 -0.13 -0.39

Density ratio -0.82 -0.36 -0.67

Links 0.66 0.50 0.68

aggregate and congregate methods. Summary information about individual maps is

presented in Table 11. On average, an individual map had 19 factors (with a standard

deviation of 5.4), 43 links or relationships (with a standard deviation of 8), an L/N ratio

of 2.36 (with a standard deviation of .44), and a density ratio of 0.15 (with a standard

deviation of .07).

The aggregate model was built by the researcher without the assistance of the group. In

the aggregate method, all the factors and links from each individual map were included

in the collective map. The result was that the aggregate map had 39 factors and 193 unique

links. Its L/N ratio was 4.95 and density ratio was 0.13. Because the aggregate map was

quite complicated, we split it into two parts: a unique map and a common map. The unique

map (referred to as the aggregate map henceforth) contained unique relationships

extracted from individual maps. Relationships that appear in at least two individual maps

were entered into the common map (referred to as the common aggregate map henceforth).

The congregate model was built by the researcher, who identified the common causal

loops in the individual causal maps of Houston’s infrastructure and folded them into a

common model. The process of building the congregate model consisted of four steps:

(1) identification of key actors and their goals and behaviors in the infrastructure system,

(2) formulation of reference knowledge based on the interview transcripts, (3) identification

of causal loops in individual maps matching reference knowledge and formulation

of hypothetical causal loops to match the unexplained reference knowledge, and (4)

construction of a map incorporating a theory of the problem based on a model that

congregates causal loops identified in (3) with a consideration of temporal dynamics. The

Table 11. Descriptive statistics on individual causal maps

Individual Researchers

P1 P2 P3 P4 P5 P6 P7

Number of Factors (Nodes) 20 23 10 27 17 18 16

Number of Relationships (Links) 45 44 25 47 49 43 46

L/N ratio 2.25 1.91 2.50 1.74 2.88 2.39 2.88

Density ratio 0.12 0.09 0.28 0.07 0.18 0.14 0.19

Table 12. Descriptive statistics on common causal maps

Nodes Links L/N Density

Aggregate 39 193 4.95 0.13

Common Aggregate(*) 21 51 2.43 0.12

Congregate 16 32 2.00 0.13

Workshop 38 57 1.50 0.04

Average of Individual Map Statistics 29 83 2.72 0.11

Note: (*) The common aggregate map contains those beliefs (or relationships) that appear in at

least two individual maps.

resulting congregate model had 16 factors and 32 links. Its L/N ratio was 2.00 and density

ratio was 0.13.

The workshop model was built by five out of the seven researchers in a mapping

workshop. The workshop was initiated by a problem description that was based on the

interview transcripts of interviews previously conducted by the researchers. Each

participant received a ten-step instruction sheet to guide discussion. The subjects took

turns in describing the problem situation by identifying problem variables, consequent

factors, causal factors that affected the problem variables, and causal relationships

between them. The facilitator (the first author) recorded these factors/variables and their

relationships on a whiteboard and asked other members whether they agreed to include

these elements and agreed with the story being told in the group map. The process was

repeated until element entries were exhausted. The workshop took about an hour. The

resulting workshop model had 38 factors and 57 links. Its L/N ratio was 1.50 and its density

ration was 0.04.

In terms of map density ratio, shown in Table 12, we found that the aggregate method

produced the most complex collective map of the three methods, followed by the

congregate and workshop methods. The common aggregate map is simpler than the

whole aggregate map but it is still more complex than the workshop and the congregate

maps (in terms of L/N ratio). Although the workshop map has a great number of factors,

it is the simplest map in terms of L/N and map density ratio.

When compared to the individual maps within each group, only the congregate map has

fewer factors, while the workshop and aggregate maps have more factors than the

average individual map. In terms of the number of links, both congregate and workshop

maps have fewer links, while the aggregate map has more links than the individual maps.

In terms of L/N ratio, both congregate and workshop maps are less complex but the

aggregate map is more complex than the individual maps. In terms of map density ratio,

the workshop map is less dense while both congregate and aggregate maps are denser

than the individual maps.

Distance ratios (DRs) between the collective maps and the individual maps are shown

in Table 13. On average, the DR between group maps and individual maps is 0.07 with

a standard deviation of 0.02. The maximum DR is 0.12 and the minimum 0.05.

We observe from Table 13 that the method used to construct group maps might have some

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

observation, we used one-way ANOVA with one factor (method) and one dependent

variable (DR). For each method, we had seven cases. The results of the ANOVA revealed

Table 13. Distance ratios between collective maps and individual maps

P1 P2 P3 P4 P5 P6 P7

Aggregate 0.08 0.12 0.08 0.07 0.08 0.09 0.12



0.07 0.11 0.06 0.05 0.08 0.06 0.09

Congregate 0.07 0.10 0.05 0.06 0.06 0.07 0.09

Workshop 0.05 0.06 0.06 0.06 0.07 0.06 0.07

a significant main effect for the method factor that had an impact on DR (F = 3.941, df =

3/27, p = .02). Post-hoc tests (LSD) revealed that the aggregate map had higher DRs than

both the workshop (p < .002), and the congregate methods (p < .05).

Subjects were asked to evaluate the maps in terms of problem representation, solution

implication and stakeholder implication, as described in Study 1. Figure 5 shows the

means on problem representation for the three methods: the congregate method had the

lowest rating, followed by the aggregate method, with the workshop method receiving

the highest rating. There was no consensus on what model was best in terms of problem

representation among the raters. Three raters believed that the model based on the

workshop method was best, while two raters chose the model based on the aggregate as

the best and one rater preferred the model based on the congregate method.

A preparatory step in the rating for solution implication asked the rater to identify critical

paths that indicated where the problem was and what he/she agreed could be useful in

developing some resolution directions for the problem. Based on this activity, the rater

was asked to rate the degree to which the model could help in developing policies to

resolve the problem on a scale from 0 (strongly disagree) to 10 (strongly agree). The

workshop model received higher ratings than did the congregate model, which received

higher ratings than the aggregate model. However, none of these differences was

statistically significant.

Stakeholder implications were rated with reference to six groups of stakeholders: elected

officials, the city public works department, citizens, businesses, contractors, and media.

Figure 5. Comparison of group maps in terms of Problem Representation












Aggregate Congregate Workshop


Mean of Problem Representation

Table 14. Comparison of the three methods on stakeholder implications

Stakeholders Workshop Congregate Aggregate

Elected Officials 7 4.8 4.7

City Departments 6.2 5 4.2

Citizens 6.5 5.5 5

Businesses 6.8 6.2 5.8

Contractors 5.5 5 4.3

Media 5 4.5 3.5

Raters were also allowed to identify additional stakeholder groups that were not listed

in the questionnaire. As a result, two stakeholder groups were added to the set:

environmentalists and engineers. For each group of stakeholders, the rater was asked to

circle a number on a scale from 0 (strongly disagree) to 10 (strongly agree) indicating how

well the needs and interests of that stakeholder group were incorporated into the model.

Results are displayed in Table 14. On average, the workshop method received the highest

ratings for all stakeholders while the aggregate model received the lowest ratings. The

congregate model received intermediate values. However, these differences were not

statistically significant.

The three methods were compared on one additional criterion, multiple perspectives

implication, the degree to which the collective causal map is able to capture various

perspectives on the problem situation. In this study, multiple perspectives implication

indicated how adequately a group map represents six perspectives on infrastructure:

economic, political, technical, environmental, social, and ethical. Although raters were

asked to identify additional perspectives that were not listed in the questionnaire, they

did not suggest any. For each perspective, the rater was asked to circle a number on a

scale from 0 (strongly disagree) to 10 (strongly agree) to indicate how well the perspective

was represented in the model. Results are reported in Table 15. On average, the model

derived from the workshop method received the highest ratings for all perspectives, while

the aggregate model received the lowest ratings with the exception of the environmental

perspective. The congregate model was intermediate. ANOVA tests revealed that the

workshop model was able to better capture the political and technical perspectives of the

problems. Other differences were not statistically significant. Of interest is the fact that

none of the methods was judged able to capture the ethical perspective on the situation

as perceived by the raters.


In this study, we also found that the aggregate method produced the most complex

collective map. In terms of distance ratios between collective maps and individual maps,

we found that workshop maps had the lowest DRs, aggregate next lowest, and congregate

the highest DRs. An implication of this pattern is that the workshop method may enhance

Table 15. Comparison of the three methods on multiple perspectives implication

Note: Means in the same row labeled with (a) are significantly different at p < .05; means in the

same row labeled with (b) are significantly different at p < .10.

Perspectives Workshop Congregate Aggregate

Economic 8 7.2 7

Political 7.8 (a) 5 (a) 4.2 (a)

Technical 7.3 (b) 4.5 (b) 4.3 (b)

Environment 6.2 4.7 6

Social 6.2 5 4.8

Ethical 2.3 1.8 1.8

the effects of knowledge sharing among group members, while the congregate mapping

method may have difficulties in gaining acceptance from group members. In terms of

problem implication and solution implication, workshop maps were perceived to be

superior to aggregate or congregate maps, with congregate maps faring worse than

aggregate maps. The workshop model was also rated better in terms of stakeholder

implications and multiple perspective implications, with congregate maps next and

aggregate maps receiving the lowest ratings. Many of these results were not, however,

statistically significant due to the low power of the tests.

It is interesting to note the differences between subjective judgments of complexity and

the objective measures of complexity. Our observation during this study was that human

subjects tend to make judgments that are similar to the simplest objective measure (the

number of nodes) while placing less emphasis on objective measures based on both

nodes and links (L/N ratio or density). Most raters believed that the congregate map was

the simplest. One rater commented that “we don’t like it [the congregate map] because

it is too simple” compared to the other maps. However as indicated in Table 11, the

congregate map is actually more complex than the workshop map in terms of L/N ratio

and map density.