Dr Ion Georgiou FGV-EAESP/IMQ 1

SODA - Basic Analyses of Complexity

1. Density2. Domain Analysis3. Heads-Tails (HT) Analysis4. Feedback analysis5. Pattern analysis

Dr Ion Georgiou FGV-EAESP/IMQ 2

Two erroneous assumptions

The more constructs in a map, the more complex it is This is NOT a valid statement because complexity is

not dependent on the size of one variable but on the interrelationship of variables.

Measurements provide answers Measurements are not answers. They are not a

substitute for thinking. They are to be used in conjunction with a more holistic understanding of the model and the situation it is describing, so that informed conclusions can be drawn.

Cognitive maps should be taken less as models of cognition and more as tools for investigating and reflecting upon problematic situations

Dr Ion Georgiou FGV-EAESP/IMQ 3

Overview of possibilities The identification and exploration of prime causes (the tails of the

map) The identification and exploration of objectives (the heads of the map) The identification and exploration of the highly affected constructs

(these are constructs with high indegree, or implosion grade, based upon a certain criterion)

The identification and exploration of the highly affecting constructs (these are constructs with high outdegree, or explosion grade, based upon a certain criterion)

The identification and exploration of the most cited constructs The identification of constructs with high degree, or domain grade,

and a critical examination of how the degree/domain grade of a construct can best be interpreted

The identification and exploration of the strategic options The identification and exploration of the feedback loops inherent in

the model This is not an exhaustive list!

Dr Ion Georgiou FGV-EAESP/IMQ 4

First analysis: Density

This analysis regards the whole map

Inexperienced mappers tend to generate a map with a smaller number of constructs than those identified by an experienced mapper

Inexperienced mappers generate more links that are probably redundant

Dr Ion Georgiou FGV-EAESP/IMQ 5

Density

Connective Density (CD) = Links / constructs Measures how densely the constructs are

connected Higher CD indicates a densely connected map High CD can indicate

High level of cognitive complexity Redundant links

In the example, each of the redundant links are true as summaries of more detailed paths, but

They do not represent a different causality to that given by the indirect linkage

The CD has increased from 0.75 to 1.5

Published research claims that typical CDs of professional maps range from 1.15 to 1.20

Dr Ion Georgiou FGV-EAESP/IMQ 6

Second analysis: Domain Analysis The domain of a

particular construct is constituted by the constructs which immediately lead into it emerge from it

Dr Ion Georgiou FGV-EAESP/IMQ 7

Domain Grade Domain analysis is about focusing on a particular construct to

uncover its degree of structural significance or influence on the map (dynamic

complexity in relation to other constructs) cognitive centrality

The degree is measurable by the construct’s domain grade Domain grade (DG) = total number of arrows in and out of a

construct Min = 0; Max = g – 1 (where g = no. of constructs in map)

If DG = g - 1, the construct is adjacent to all other constructs in the map Note: Domain analysis is a comparative analysis; domain grades between

constructs must be compared in order to draw conclusions about significance, influence, or centrality for any one of them

Dr Ion Georgiou FGV-EAESP/IMQ 8

Domain analysis highlights core constructs which may be used to produce a summary or overview of a map.

In merged maps, such constructs may be interpreted as being intersubjectively significant.

Domain grade (DG) = total number of arrows in and out of a concept

DG = 5

DG = 5

DG = 5DG = 4

Dr Ion Georgiou FGV-EAESP/IMQ 9

Domain Analysis – Explosion and Implosion grades

Domain analysis can be extended in various ways, depending on what information is required

One possible extension is to analyze the domain grade in terms of its outward and inward links

Two basic measures Explosion grade (EG) = total number of arrows out of

a construct Implosion grade (IG) = total number of arrows into a

construct

Dr Ion Georgiou FGV-EAESP/IMQ 10

DG = 5EG = 2IG = 3

DG = 5EG = 1IG = 4

DG = 5EG = 1IG = 4

DG = 4EG = 0IG = 4

DG = 2EG = 2IG = 0

If a construct has a relatively larger explosion grade than other constructs, then it is a significant

cause in the map If a construct has a

relatively larger implosion grade than other constructs, then it is a significant

consequence in the map

Explosion and Implosion grades

Dr Ion Georgiou FGV-EAESP/IMQ 11

Spatial Extension of Domain Analysis

Domain analysis begins by focusing on the immediate domain of a construct (as in the earlier example)

This is known as first-order domain analysis But this ignores the wider context of the construct It is possible to extend the analysis by considering successive layers of domain

(known as second-order domain analysis, third-order domain analysis etc)

Each successive layer is given a diminishing weight (known as a distance decay function)

For example, each construct directly linked to the central construct may be given a weight of 1

constructs in the next layer (second-order domain) are given a weight of ½, the next layer (third-order domain) 1/3 and so on

Weights need not follow this pattern but can vary depending on importance of any particular x-order domain to the analysis

Results from layered domain analyses may be added together to produce second-order grades, third-order grades etc.

Dr Ion Georgiou FGV-EAESP/IMQ 12

DG = 5EG = 2IG = 3

DG = 5EG = 1IG = 4

DG = 5EG = 1IG = 4

DG = 4EG = 0IG = 4

DG = 2EG = 2IG = 0

42DG2: 5(1) + 2(0.5) = 6EG2: 2(1) + 1(0.5) = 2.5IG2 = 3(1) + 1(0.5) = 3.541DG2: 5(1) + 6(0.5) = 8EG2: 1(1) + 1(0.5) = 1.5IG2 = 4(1) + 5(0.5) = 6.537DG2: 5(1) + 1(0.5) = 5.5EG2: 1(1) + 0(0.5) = 1IG2 = 4(1) + 1(0.5) = 4.5

52DG2: 4(1) + 5(0.5) = 6.5EG2: 0(1) + 0(0.5) = 0IG2 = 4(1) + 5(0.5) = 6.5

53DG2: 2(1) + 2(0.5) = 3EG2: 2(1) + 2(0.5) = 3IG2 = 0(1) + 0(0.5) = 0

Second-order domain analysis

Dr Ion Georgiou FGV-EAESP/IMQ 13

Questions relevant to Domain Analysis

Third order etc

What happens to constructs in the outer domains when things are going well (not going well) in the central construct?

What happens to the central construct when things are going well (not going well) in constructs in the outer domains?

Can you see ways in which changes in the central construct cause changes in outer domain constructs that then come back to affect the central construct?

Dr Ion Georgiou FGV-EAESP/IMQ 14

Domain Analysis and Clusters

Domain analysis can be used to compare issues (remember, clusters help define issues)

The heads of clusters can be compared with domain analysis measurements in order to uncover the degree of influence and structural importance of each cluster

Dr Ion Georgiou FGV-EAESP/IMQ 15

Third analysis: Heads-Tails (HT) Analysis A single head (outcome) on a map (pyramid) may indicate that

the problem owners are agreed on the objective are idealists are cognitively simple

Multiple heads on a map indicates A recognition of, and concern for, meeting multiple, and

possibly conflicting objectives Realism Complex cognition Holistic thinking

The content of constructs cannot be ignored in this analysis A head (outcome/objective) for one person appears as a tail

(constraint) for another

Dr Ion Georgiou FGV-EAESP/IMQ 16

Fourth analysis: Feedback analysis Analyzing feedback loops in maps is important because they

can indicate any of the following: possible errors by mapper in modeling cognition ambiguous cognition by client about what is cause and what

is effect systemic cognition by client that appreciates growth, decline,

or feedback control in issues counter-intuitive situational aspects that were not

understood prior to modeling deeper problems inherent to the situation under

consideration Whatever might be the case, feedback loops greatly influence

decision making because they can indicate dangers as well as benefits

They also test the consultant’s skills in effective modeling, facilitation, and contextual appreciation

Dr Ion Georgiou FGV-EAESP/IMQ 17

Possible feedback errors and ambiguity

Three different people discussed the same issue differently Three different mappers modeled the views of one person differently

The goals change between the first two maps A HT analysis between the first two maps would be useful A domain analysis would yield different understandings of the

constructs in all three cases Notice that in the third map all constructs are of the same status

Dr Ion Georgiou FGV-EAESP/IMQ 18

The nature of feedback

A loop constituted completely by positive (+ve) links, or by an even number of negative (-ve) links, suggests either Regenerative dynamics

(exponential growth) Degenerative dynamics

(exponential decline) It is up to the mapper and the client to

decide which of these two dynamics are actually impacting on the situation, based upon analyzing the content and relationship of constructs against the situational context

A feedback loop constituted completely by +ve links

Dr Ion Georgiou FGV-EAESP/IMQ 19

A feedback loop constituted by an even number of –ve links

Dr Ion Georgiou FGV-EAESP/IMQ 20

Stabilizing feedback

When the loop contains an odd number of -ve links then the loop is depicting self-control

Any perturbation in the state of the variables will result in stabilizing dynamics to bring activity under control

Two stabilizing feedback loops, each constituted by an odd number of –ve links, and both involving construct 8

Dr Ion Georgiou FGV-EAESP/IMQ 21

Feedback in merged maps Feedback loops are common in merged maps. They arise either

passively through the merging process, or actively, whereby the consultant has uncovered dynamics in the analysis and

chooses to insert them into a map

Dr Ion Georgiou FGV-EAESP/IMQ 22

Fifth analysis: Pattern analysis

Dr Ion Georgiou FGV-EAESP/IMQ 23

References

Ackermann A, Eden C, Brown I (2005) The Practice of Making Strategy: A Step-By-Step Guide. Sage: London

Bryson JM, Ackermann F, Eden C, Finn CB (2004) Visible Thinking: Unlocking Causal Mapping for Practical Business Results. Wiley: Chichester

Eden C & Ackermann F (1992) The analysis of cause maps. Journal of Management Studies 29(3): 309-324

Eden C (2004) Analyzing cognitive maps to help structure issues or problems. European Journal of Operational Research 159(3): 673-686

Wasserman S and Faust K (1994) Social Network Analysis: Methods and Applications. Cambridge University Press: Cambridge (especially chapter 4)