This document discusses concepts related to hierarchical decision making and pairwise comparisons. It describes how the Analytic Hierarchy Process (AHP) enables structuring complex decisions into a hierarchy, defining criteria, and performing pairwise comparisons to derive criteria weights. Criteria should be mutually exclusive and collectively exhaustive. Pairwise comparisons involve determining which criterion is more important and by how much to calculate priority ratios and weights. Consistency is measured to ensure logical judgments.

1. Decision Making, Hierarchical
Structures and Pairwise
Comparisons
February 2010
Proprietary & 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 Which
New 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 Kilogram
The 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 ask
Use the tree view the group, “With respect Each person makes judgments
in the left to the goal of buying a using keypads. First, evaluate which
navigation as an car, what is more criteria is more important. Second,
alternative way to important, safety or evaluate by how much using the
select which performance?” Equal to Extreme scale
criteria are being
selected
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:
C
A 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 either
Global or
Local radio
1 2
button to
change how the
weights are
shown in the
tree view.
Global shows You can select either the Graph
overall weights or the Tree view. Graph view
of sub factors. provides a bar chart like what
Local shows you see here. Tree view is a
how sub factors blown up version of the tree
are distributed view that you see on the left
within 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%, certain
Inconsistency 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. Summary
Prioritize decision-making criteria
Inputs 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