Scenario Construction Via Cross Impact

Scenario Construction Via Cross Impact

Prof. Victor A. Bañuls

Management Department

Pablo de Olavide University

Seville, Spain

Email: [email protected]

Web: http://webdee.upo.es/vabansil

The Network Nation and BeyondA Festschrift in Honor of Starr Roxanne Hiltz and Murray Turoff

Distinguished Prof. Murray Turoff

Information Systems Department

New Jersey Institute of Technology

Newark NJ, USA


Web: http://web.njit.edu/~turoff/

NJIT – October 2007

mailto:[email protected]


Index

• Research motivations• Methodological background• Basics of the CIM-ISM• Generating scenarios• Conclusions

Research motivations

• Why do we need scenarios?– Strategic decision making (policy, business, etc.)

compromise resources in the long term.– We need to think about what will happen tomorrow

before acting today.– A scenario is a tool for managing the uncertainty of

the future.– Our proposal is aimed at contributing to this goal.

Research motivations

• What is the aim of our proposal?– Helping decision makers to manage the uncertainty.

• How?– Structuring and sharing the beliefs and the knowledge

of the people involved in decision making.

• But… how can we do that?– By the structural analysis of the impacts between the

atomic events that are relevant to the decision-making problem.

Methodological background

• Cross-Impact Method– Events cannot be analyzed in a isolated way.– Alternative cross-impact approach (Turoff, 1972):

Inferring impacts between events based on experts’ hypothesis about their occurrence (or not).


1 2 3 4 5 6 7 8 .. n

1

2

3

4

5

6

7

8

..

n

Gi 1 2 3 4 5 6 7 8 .. n

C43

+/-Impacts between events in

the model

Impacts of the events not included in the model

Cross-Impact Matrix


• Interpretive structural modeling– Taking as an input the impacts obtained with the CIM,

this methodology will help us to:• Making hypotheses about the occurrence or not of

the set of events and analyzed them (to generate scenarios).

• Detecting and analyzing the key drivers (critical events).


3

1

5

2

8 10

6

4

7

9Occurring events Non-Occurring events

Key drivers

Scenario


Pi Sij Rij

Cij Gi

CIM

EiEvents

Set of probabilities (isolated and conditional)

Cross-Impact Matrix

Input

Output

Cross-Impact Method


Pi Sij Rij

Cij Gi

CIM

ISM

Scenarios

EiEvents

Set of probabilities (isolated and conditional)

Cross-Impact Matrix

Cross-Impact Method

Interpretive Structural modeling

Input

Output

Basics of the CIM-ISM

• Starting point– Cross-Impact Matrix (Turoff 1972 paper example).


1 2 3 4 5 6 7 8 9 10

1 OVP -0.29 0.00 -0.81 -0.33 1.57 0.00 -0.25 -0.22 0.00

2 -0.50 OVP -0.23 0.46 0.00 -0.77 0.90 0.29 0.25 0.42

3 -0.41 0.31 OVP 0.43 0.74 -0.58 0.00 0.27 0.24 0.68

4 -0.81 0.58 0.07 OVP 0.33 -1.21 0.33 0.25 0.22 0.33

5 -0.88 0.58 -0.14 0.81 OVP -0.31 0.74 0.00 0.00 0.36

6 0.88 -0.36 0.00 -2.70 -0.42 OVP -0.38 -0.31 -0.28 -0.38

7 -0.41 0.99 0.00 0.88 1.16 -0.29 OVP 0.00 0.00 0.68

8 -1.62 -0.50 0.00 0.58 0.48 -1.16 0.00 OVP 0.60 0.58

9 -1.49 0.00 0.00 0.93 0.00 -1.07 1.25 1.01 OVP 1.25

10 -0.41 0.99 -0.14 0.88 1.16 -0.58 0.68 0.00 0.00 OVP

Gi 0.23 -1.33 -0.30 -0.05 -1.02 0.88 -0.91 -0.97 -3.29 -0.74

Cross-Impact Matrix



• Transforming the Cross-Impact matrix – Transition Matrix (square and positive matrix).


Occurring events Non occurring events

Occurring events

+ cij - cij

Non occurring

events- cij + cij

Transforming the Cross-Impact Matrix




• Transforming the Transition Matrix– Adjacency Matrix (taking an arbitrary Cij value (0.85)).





– Connection Matrix (adding the Identity Matrix).





– Connection Matrix (adding the Identity Matrix).– Reachability Matrix (powering until it is stable).


• Scenario Generation– Determining antecedent and succedent sets– Obtaining the graphical scenario (using graph theory)


• Scenario Generation– Determining antecedent and succedent sets.– Obtaining the graphical scenario (using graph theory).

• Interpretation of the scenario– Analyzing key drivers.– Analyzing the set of probabilities.


LEVEL 1

LEVEL 5

LEVEL 4

LEVEL 2

LEVEL 3

1

5

2

8

10

9

6 4

7

ScenarioOccurring events Non-Occurring events

P9=0.1 Key drivers

Why 0.85?

And event 3?

Generating scenarios

• Sensitivity Analysis– Studying the Cij distribution.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

Percentile 90 1.1581










Normal distribution with a reliability of 99% (using K-S test)

LEVEL 2

LEVEL 1

LEVEL 3

1

98

6 4 10











LEVEL 2

LEVEL 1

LEVEL 3

LEVEL 4

1

5

8

10

9

7

6 4 2











LEVEL 1

LEVEL 5

LEVEL 4

LEVEL 2

LEVEL 3

1

5

2

8

10

9

6 4

7











LEVEL 2

LEVEL 1

LEVEL 3

58 10

3

7

6 4 1

2

9












• Sensitivity Analysis– Studying the Cij distribution

• Solving the forecasted scenario– Determining the limit of the forecasted scenario

LEVEL 2

LEVEL 1

5

8

10

3

76 4 1 2

9

Limit = |0.4975|

Forecasted Scenario


-1,-6,2,4,5,7,10 3 8,9

-1,-6,2,4,5,7,10 OPV 0 0

3 1,99 OPV 0

8,9 11,53 0 OPV

G' -9,78 -0,70 -9,56

Cross-Impact Matrix for the Forecasted Scenario




• Solving the forecasted scenario– Determining the limit of the forecasted scenario.

• Solving the alternative scenarios– Determining the limit of the alternative scenarios.



• Solving the forecasted scenario– Determining the limit of the forecasted scenario.

• Solving the alternative scenarios– Determining the limit of the alternative scenarios.

• Interpretation of results– Analyzing the information included in each scenario.

Forecasted Scenario

Alternative Scenario I

Alternative Scenario II

Alternative Scenario III

Limits (||, |0.4975|) (|0.4975|, |0.3804|) (|0.3804|, |0.2318|) (|0.2318|, 0)

Interval of reliability

0.5253 0.1019 0.1400 0.2327

cij sum 35.2527 3.9272 6.1414 1.0224

Event Pi Clusters of Events

1 0.5 A A A A

2 0.3 B B B A

3 0.6 B B B B

4 0.5 B B B B

5 0.4 B A B A

6 0.3 A B A

7 0.6 B B B

8 0.2 B A B

9 0.1 B B B

10 0.6 B B B A


Forecasted Scenario




Limits (||, |0.4975|) (|0.4975|, |0.3804|) (|0.3804|, |0.2318|) (|0.2318|, 0)


0.5253 0.1019 0.1400 0.2327

cij sum 35.2527 3.9272 6.1414 1.0224


1 0.5 A A A A

2 0.3 B B B A

3 0.6 B B B B

4 0.5 B B B B

5 0.4 B A B A

6 0.3 A B A

7 0.6 B B B

8 0.2 B A B

9 0.1 B B B

10 0.6 B B B A


Forecasted Scenario




Limits (||, |0.4975|) (|0.4975|, |0.3804|) (|0.3804|, |0.2318|) (|0.2318|, 0)


0.5253 0.1019 0.1400 0.2327

cij sum 35.2527 3.9272 6.1414 1.0224


1 0.5 A A A A

2 0.3 B B B A

3 0.6 B B B B

4 0.5 B B B B

5 0.4 B A B A

6 0.3 A B A

7 0.6 B B B

8 0.2 B A B

? 0.1 B B B

10 0.6 B B B A


Forecasted Scenario




Limits (||, |0.4975|) (|0.4975|, |0.3804|) (|0.3804|, |0.2318|) (|0.2318|, 0)


0.5253 0.1019 0.1400 0.2327

cij sum 35.2527 3.9272 6.1414 1.0224


1 0.5 A A A A

2 0.3 B B B A

3 0.6 B B B B

4 0.5 B B B B

5 0.4 B A B A

? 0.3 A B A

? 0.6 B B B

? 0.2 B A B

9 0.1 B B B

10 0.6 B B B A


Conclusions

• Aims of the model– Handle complex systems.– Obtain a set of plausible snapshots of the future.– Analyze interaction between events.– Detect critical events.

• Application areas– Technology Foresight.– Strategic Management.– Policy Analysis.– Emergency Response.– Etc…

Conclusions

• Strong points– A strong theoretical background of the techniques on which

the authors proposal in based.

– The possibility of working with large sets of events.

– Tools for analyzing the key drivers of the scenarios.

– Specific software is not needed for making the calculations.

– A graphic output that gives a clear representation about the forecast.

– It is strongly compatible with other techniques such as the Delphi or multicriteria methods.

Conclusions

• Limitations– We cannot kwon the probability of occurrence of a

specific scenario if it is not an output of the model. – The estimation of the occurrence or non-occurrence

estimation of the scenarios needs the interpretation of the key drivers and sometimes it would be difficult if there is a probability of occurrence close to 0.5.

Scenario Construction Via Cross Impact

Prof. Victor A. Bañuls

Management Department

Pablo de Olavide University

Seville, Spain


Web: http://webdee.upo.es/vabansil

Distinguished Prof. Murray Turoff

Information Systems Department

New Jersey Institute of Technology

Newark NJ, USA


Web: http://web.njit.edu/~turoff/

Thank you for your attention!



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Scenario Construction Via Cross Impact