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# Decision Making and Pairwise Comparisons

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• 1. Decision Making, Hierarchical Structures and Pairwise Comparisons February 2010Proprietary & confidential. © Decision Lens 2010
• 2. Concepts Decision Making and Hierarchical Thinking Criteria Pairwise Comparisons Priorities 2
• 3. Analytical Hierarchy Process (AHP) The Analytic Hierarchy Process enables decision makers to structure decisions hierarchically: the goal of the decision at the top, strategic objectives in the higher levels, evaluation criteria in the middle, and alternative choices at the bottom. 3
• 4. Criteria Definition At the most basic, a criterion is a driving factor that is used in making a decision. In Decision Lens, we use a criteria hierarchy At the highest level, objectives are • Don’t confuse criteria with strategies, actions, stated as actions or goals to be or methods of execution accomplished • The criteria should be the end state, not the − i.e., Increase Impact to Mission path to get there. At the lowest level, drivers or – i.e. “Increase Growth” is a good indicators used to evaluate criterion. “International Expansion” is alternatives at a detailed level not a criterion, it is a strategy to achieve the objectives. − i.e., Mission Area 1 – “Expand Brand” is a good criterion. “Acquire New Products” is not a criterion, it is a strategy to achieve the objectives. Module 1: Building the Model 4
• 5. Criteria Modeling Example – Selecting WhichNew Products to Bring to Market Module 1: Building the Model 5
• 6. Best Practice Criteria Concepts While dependencies may exist, criteria should be as mutually exclusive, collectively exhaustive (MECE) as possible We normally see at least 2 levels of criteria where a criterion is too broad of a “bucket” but not more than 3 levels is recommended The ideal number of criteria at the highest level is 7 Human Cognitive Capacity Magic number of seven plus or minus two 6
• 7. Purpose of Comparing Criteria Perform Pairwise Comparisons to develop relative weights on criteria hierarchy Facilitating discussion during voting to reveal stakeholder viewpoints and positions Defining consensus and how to use it in support of prioritization Consistency and Alignment among decision-makers is measured as a result of their comparisons Module 2: Compare Criteria 7
• 8. Do Numbers Have an Objective Meaning? Butter: 1, 2,…, 10 lbs.; 1,2,…, 100 tons Sheep: 2 sheep (1 big, 1 little) Temperature: 30 degrees Fahrenheit to New Yorker, Kenyan, Eskimo Since we deal with Non-Unique Scales such as [lbs., kgs], [yds, meters], [Fahr., Celsius] and such scales cannot be combined, we need the idea of PRIORITY. PRIORITY becomes an abstract unit valid across all scales. A priority scale based on preference is the AHP way to standardize non-unique scales in order to combine multiple criteria. Module 2: Compare Criteria 8
• 9. This is Today’s Reality: Liter and KilogramThe Basis of Any Scale is Arbitrary In 1889, the first Conference Generale des Poids et Mesures (CGPM) sanctioned the international prototype of the kilogram, made of platinum-iridium, and declared: This prototype shall henceforth be considered to be the unit of mass. The third CGPM (1901), in a declaration intended to end the ambiguity in popular usage concerning the word weight, confirmed that: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. The International Prototype Kilogram (IPK) kept in Sèvres, near Paris, is the standard of mass. National prototype kilograms are maintained in several countries and periodically checked against the International Prototype. Module 2: Compare Criteria 9
• 10. Pairwise Comparison Participants perform multiple sets of comparisons for each level of hierarchy For each judgment, participants determine which criterion is more important AND by how much Judgments are used to form ratios in a matrix; The matrix is used to calculate priorities for the judgment set (eigenvector) Module 2: Compare Criteria 10
• 11. Scale for Pairwise Comparison 1 Equal importance 3 Moderate importance of one over another 5 Strong or essential importance 7 Very strong or demonstrated importance 9 Extreme importance 2,4,6,8 Intermediate values Use Reciprocals for Inverse Comparisons Module 2: Compare Criteria 11
• 12. Pairwise Comparison Steps The facilitator will Click the click Next Vote Compare to move to the Criteria tab next comparison until all criteria have been compared to 2 1 5 each other Select the Pairwise Comparison 3 step 4 The facilitator will askUse the tree view the group, “With respect Each person makes judgmentsin the left to the goal of buying a using keypads. First, evaluate whichnavigation as an car, what is more criteria is more important. Second,alternative way to important, safety or evaluate by how much using theselect which performance?” Equal to Extreme scalecriteria are beingselected Module 2: Compare Criteria 12
• 13. Best Practice Pairwise Criteria Concepts Keep in mind: The facilitator should promote group discussion to inform and provide rationale for voting discrepancies To make a comparison one holds the smaller one in the pair in mind as the unit and estimates how many times larger the other is Module 2: Compare Criteria 13
• 14. Viewing Priority Graph Once all comparisons are made you can view results in 3 ways: CA B A) Clicking the second sub step Priority Graph B) Clicking Next Vote at the last comparison there are no more votes so it will take you to the next step) C) Or by clicking Next (see previous slides) Module 2: Compare Criteria 14
• 15. Priority Graph Options Click Sort Descending to get a highest to lowest graph of the weighted priorities. Note that you will see the weights for what is selected on the criteria tree view on Click the Current Properties drop the left navigation panel. down to pick which data set is shown. You can choose to see results of a specific individual’s judgments or the group.Click eitherGlobal orLocal radio 1 2button tochange how theweights areshown in thetree view.Global shows You can select either the Graphoverall weights or the Tree view. Graph viewof sub factors. provides a bar chart like whatLocal shows you see here. Tree view is ahow sub factors blown up version of the treeare distributed view that you see on the leftwithin that node navigation pane.only See next slide 3 The Alignment is an index shown in percentage to 5 indicate how much consensus 4 the re were around judgments. Module 2: Compare Criteria 15
• 16. Inconsistency and Alignment Feature Definition Use Helpful Hint Individual’s inconsistency will always be higher than If the group’s (not an the groups. Groups are The consistency of the known to be more accurate individual’s) inconsistency is judgments is tracked using and consistent. more than .10 or 10%, certainInconsistency the rigorous math analytics pairwise comparisions should behind the AHP to validate be revisited to ensure that Having good consistency the decision process. logical integrity is kept does not mean you are closer to the “right answer” in the decision The final priorities in the The largest score in the The smaller the Alignment Priority Graph, tells you the Alignment Index is 100, telling Index score drops from mix of values for the group, you that the final weighted 100, the farther away are and the Alignment Index priorities for each individual the individuals’ priorities Alignment score then tells you how came out exactly the same as from those of the group, close that Priority Graph the final weighted priorities for and the less alignment was for all of the individuals the group. there is. as compared to the group There is no action regardless average. of the Alignment number. Module 2: Compare Criteria 16
• 17. Inconsistency Diagram A B C A is bigger than B B is bigger than C C is bigger than A!? This is not logical – the inconsistency tracker tracks individual and group logic when judgments are made in pairwise comparisons Group consistency is best to be within 10% Module 2: Compare Criteria 17
• 18. Evaluating Inconsistency Click the Compare Criteria tab and the Inconsistency Analysis sub step. 1 Alternatively, if you are using the Next button at the right of the screen to navigate through tab 2, you will see Inconsistency at the end of each comparison set following the Priority Graph for that comparison set.2 3 In this case, Inconsistency is fairly close to zero therefore, no action is necessary. You can click the Go To Comparison button next to those Ensure the comparisons that are high. You want to decrease goal level of overall consistency to 10%. This may require the tree is changing one or more judgments. selected Module 2: Compare Criteria 18
• 19. Critical Facilitation Technique – 3 Part Test Using facilitation techniques, ensure that participants pass….. The 3 Part Test: 1.Can I live with the decision made here today? 2.Can I refrain from behaving or speaking negatively to others about the decision? 3.Can I readily support the decision and devote the resources necessary to make the decision successful? Module 2: Compare Criteria 19
• 20. SummaryPrioritize decision-making criteriaInputs Any previously developed decision criteria; Decision makers are identified; Any assumptions are understood.Actions Complete head-to-head (pairwise) comparisons of criteria. Ensure that the group’s logic is not too inconsistent.Helpful Hints Encourage participants to discuss the rationale behind their voting as a way to get information and insights out in the open. Ensure consistency is less than 10%.Things to Avoid Do not let any one individual dominate the discussion. Make sure your criteria are defined very specifically and that all participants understand and agree with their meaning. When making judgments, participants are encouraged to explain their position but should not be forced to agree with everyone else.Outputs Weighted decision criteria model. Module 2: Compare Criteria 20