Contrary Schools of Thought Within Military Decision-making Groups

1. Contrary Schools of ThoughtWithin Military Decision-making Groups Fred Cameron Operational Research Advisor to the Commander, 1st Canadian Division

2. Agenda • Introduction • Methodology • An Application • A Second Example • Observations on Methodology • Conclusion

3. Introduction • ‘Squishy’ problems • No obvious quantitative analysis • Seeking problem investigation, not necessarily a solution • Rule by majority • Consideration of minority

4. The Methodology • Participants develop: • Alternatives, with descriptions • Individual rankings of alternatives • CDSP* derives the group ranking • Analyst calculates: • Kendall’s Coefficient of Concordance, W • Rank Correlations, Tau-b or tb • Distance Metrics • Multidimensional Scaling • Cluster Analysis *CDSP = Consensus Decision Support Program

5. Rank Correlation Coefficients • Kendall’s Tau-b and Spearman’s Rho • Examples for two judges, four objects: • A B C D and A B C D  Tau-b = 1 • A B C D and A B D C  Tau-b = 0.67 • A B C D and B D A C  Tau-b = 0.0 • A B C D and D C B A  Tau-b = -1 • Ties: • A B C D and A (B C) D  Tau-b = 0.914

6. Pairwise rank correlations between judges. Pairwise distances between judges. Ranking and Rank Correlations Ranks of ten objects by three judges. Note the use of Kendall’s convention where tied objects are given the average rank. Judge X has tied B and D after E (3rd place) so they are given rank 4½.

7. Past Applications • Workshops on Characteristics of the Future Environment • Workshops on Re-organization of the Army • Questionnaire on Future Reconnaissance Capabilities

8. Canada’s Future Army • Management and Objectives • Three Parallel Initiatives: • Future Environment • Future Force Capabilities • Future Force Concept Matrix • Workshops on Future Environment • 18 Participants in two workshops • Structured brainstorming • List of elements, with descriptors in shorthand • Consensus on critical elements

9. Workshops on Future Environment • Grouping of concepts from structured brainstorming: • ‘Advance of technology’ • ‘Emergence of the information age’ • ‘Importance of space’ • ‘Revolution in military affairs - Non-linear Battle Space’ • ‘Globalization - coalition operations’ • ‘Greater global instability’ • ‘Evolution of the social order’ • ‘Civil-military relationship - Interdependence of institutions’ • ‘Resource constraints’

10. CDSP Consensus Ranking Algorithm • Choose winner(s) in pairwise majority voting (the Condorcet winner) • Remove winner(s) and repeat until all objects have been ranked • Problems: • ties • intransitivity - the voting paradox

11. CDSP Results of Workshops on Future Environment 1. ‘Advance of technology’ 2. ‘Greater global instability’ 3.‘Emergence of the information age’ & ‘Resource constraints’ 5. ‘Globalization - coalition operations’ 6. ‘Revolution in military affairs - Non-linear Battle Space’ 7. ‘Civil-military relationship - Interdependence of institutions’ & ‘Evolution of the social order’ 9. ‘Importance of space’

12. Correlations between Individuals and CDSP • Note: • Same value of correlation coefficient does not imply same ranking • Each participant’s nom de guerre (A01 to A18) was assigned based on this ranking

13. Matrix of Pairwise tb

14. Configuration By Multidimensional Scaling A14 A16 A10 A05 A07 A01 A18 A11 A03 A02 GROUP A04 A08 A06 A09 A17 A12 A13 A15 Multidimensional Scaling

15. MDS Algorithm Derive distance matrix from correlations: dij = 1-tij For 2-D MDS: MinimizeSTRESS =(S(dij-d´ij)2/Sdij2))½ Over all (xi,yi), i=1,…,n (coordinates in 2-space) where n = number of participants dij = distance between i and j in multiple dimensions d´ij = distance between i and j in 2 dimensions, d´ij = ((xi-xj)2+(yi-yj)2)1/2

16. Cluster Tree By Single Linkage A14 A16 A18 A12 A13 A17 A08 A11 A05 A01 A03 A02 A04 A09 A06 A10 A07 A15 Cluster Analysis • Note: • Single linkage is also called ‘nearest neighbour’ • Start with the two individuals who are the closest pairwise • Distance to a new cluster is the distance to the nearest member

17. Cluster Analysis Algorithm ‘Nearest Neighbour’ • At each stage we may combine any pair of objects (individuals or clusters of individuals). At the first stage, all objects are individuals. • Then two steps: • 1. Combine the two objects that are closest • 2. Recalculate distances for the new cluster: If objects s and t were combined to form object j dij = min(dis,dit), for all remaining objects i • Stop when only one cluster remains

18. MDS Map with Clusters • The Problem of Stopping Criteria • Cluster of all 18 • Clusters of 16 and 2, outlined with light blue lines • Cluster of 7, outlined with darker blue line

19. A Second Example • Two captains on the Technical Staff Course • Future reconnaissance capabilities • Seven main areas of interest • Several concepts in each • Workshop ruled out -- cost and logistics • Results by questionnaire

20. Future Reconnaissance Doctrine Options as provided: • Formation of ISTAR Unit(s) • Integration of LOS with NLOS Capabilities • 360° Reconnaissance and Surveillance Capability • Maintenance of Reconnaissance Platoons and Troops • Light Reconnaissance and Dismounted Reconnaissance Functions • Interoperability with Allies • Joint Operations with Air Force Reconnaissance and Surveillance Assets • Centralize and Standardize Reconnaissance Training

21. Reconnaissance Results 1. Integration of LOS with NLOS Capabilities, 2. Interoperability with Allies, 3. (multi-way tie) • Maintenance of Reconnaissance Platoons and Troops, • Formation of ISTAR Unit(s), • Joint Operations with Air Force Reconnaissance and Surveillance Assets, • Centralize and Standardize Reconnaissance Training, • Light Reconnaissance and Dismounted Reconnaissance Functions, and • 360° Reconnaissance and Surveillance Capability

22. MDS Configuration Map Question 1: Doctrinal Concepts A07 A09 A12 A04 A10 A06 A14 A03 A19 A16 A05 GROUP A01 A20 A11 A08 A15 A13 A02 A18 A17 A21 Multidimensional Scaling

23. Cluster Analysis

24. MDS Configuration Map Question 1: Doctrinal Concepts MDS Map with Clusters Sub-group of 9 Sub-group of 12 A07 A09 A12 A04 A06 A10 A14 MINORITY A03 A19 A16 A05 GROUP A01 A20 MAJORITY A11 A08 A15 A13 A02 A18 A17 A21

25. Observations on Methodology • Ease of use (e.g., Excel, Systat, SPSS, SAS, Statistica) • Use of ranks • Number of clusters • Optimization in the MDS procedure • Clustering algorithms • Flexible interpretations

26. Observations on Methodology (cont’d) • Anonymity • Workshops or questionnaires • Dictatorships • Contamination between participants • A closure crutch • More ruthless decision making

27. Conclusion • Consensus Ranking Valuable • Include a Measure of Concordance • Include Other Diagnostics • Pairwise Rank Correlations • Multidimensional Scaling • Cluster Analysis

28. Further Information • Fred Cameron • Operational Research Advisor to Commander 1st Canadian Division • 1-613-992-4584 (Ottawa) or 1-613-541-5010 x 8719 (Kingston) • FCameron@ncs.dnd.ca • References: Maurice Kendall and Jean Dickinson Gibbons, Rank Correlation Methods, 5th ed., Oxford University Press, 1990 Joseph B Kruskal and Myron Wish, Multidimensional Scaling, Sage, 1977 John A Hartigan, Clustering Algorithms, Wiley, 1973 Charles Romesburg, Cluster Analysis for Researchers, 1990 Leland Wilkinson, SYSTAT 6.0 for Windows: Statistics, Systat Inc., 1996