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SODA - Basic Analyses of Complexity

SODA - Basic Analyses of Complexity. Density Domain Analysis Heads-Tails (HT) Analysis Feedback analysis Pattern analysis. Two erroneous assumptions. The more constructs in a map, the more complex it is

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SODA - Basic Analyses of Complexity

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  1. SODA - Basic Analyses of Complexity Density Domain Analysis Heads-Tails (HT) Analysis Feedback analysis 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. DG = 5 DG = 4 DG = 5 DG = 5 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. Explosion and Implosion grades DG = 5 EG = 1 IG = 4 DG = 4 EG = 0 IG = 4 DG = 5 EG = 1 IG = 4 DG = 5 EG = 2 IG = 3 DG = 2 EG = 2 IG = 0 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. 52 DG2: 4(1) + 5(0.5) = 6.5 EG2: 0(1) + 0(0.5) = 0 IG2 = 4(1) + 5(0.5) = 6.5 42 DG2: 5(1) + 2(0.5) = 6 EG2: 2(1) + 1(0.5) = 2.5 IG2 = 3(1) + 1(0.5) = 3.5 41 DG2: 5(1) + 6(0.5) = 8 EG2: 1(1) + 1(0.5) = 1.5 IG2 = 4(1) + 5(0.5) = 6.5 37 DG2: 5(1) + 1(0.5) = 5.5 EG2: 1(1) + 0(0.5) = 1 IG2 = 4(1) + 1(0.5) = 4.5 DG = 5 EG = 1 IG = 4 DG = 4 EG = 0 IG = 4 DG = 5 EG = 1 IG = 4 DG = 2 EG = 2 IG = 0 DG = 5 EG = 2 IG = 3 53 DG2: 2(1) + 2(0.5) = 3 EG2: 2(1) + 2(0.5) = 3 IG2 = 0(1) + 0(0.5) = 0 Second-order domain analysis Dr Ion Georgiou FGV-EAESP/IMQ

  13. Questions relevant to Domain Analysis 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? Third order etc 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 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 Studies29(3): 309-324 • Eden C (2004) Analyzing cognitive maps to help structure issues or problems. European Journal of Operational Research159(3): 673-686 • Wasserman S and Faust K (1994) Social Network Analysis: Methods and Applications. Cambridge University Press: Cambridge (especially chapter 4) Dr Ion Georgiou FGV-EAESP/IMQ

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