the essentials of the analytic network process
TRANSCRIPT
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The Essentials of the Analytic Network Process with Seven Examples (1)
Decision Making with Dependence and Feedback
The Super Decisions Software
Thomas L. Saaty
A Theory for Measuring Intangibles by Deriving Scales
from Paired Comparisons•Lay out the world in structures of influences and priorities that lead to outcomes;
• Use expert knowledge to derive measurements of tangibles and intangibles from paired comparisons, or use the actual measurement of tangibles if it is desired to use them.
•The importance and influence of everything is measured according to its importance to our value system.
•When many individuals and groups are involved one combines their judgments to produce a representative outcome for the group; possibly weighted by the importance of the judges.
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Most Decision Problems are Multicriteria
• Maximize profits• Satisfy customer demands• Maximize employee satisfaction• Satisfy shareholders• Minimize costs of production• Satisfy government regulations• Minimize taxes• Maximize bonuses
WHAT KIND AND WHAT AMOUNT OFKNOWLEDGE TO MAKE DECISIONS
Some people say
• What is the use of learning about decision making? Life is so complicated that the factors which go into a decision are beyond our ability to identify and use them effectively.
I say that is not true.
•We have had considerable experience in the past thirty years to structure and prioritize thousands of decisions in all walks of life. We no longer think that there is a mystery to making good decisions.
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• Decision Making involves all kinds of tradeoffs among intangibles. To make careful tradeoffs we need to measure things because a bad may be much more intense than a good and the problem is not simply exchanging one for the other but they must be measured quantitatively and swapped.
• One of the major problems that we have had to solve has been how to evaluate a decision based on its benefits, costs, opportunities, and risks. We deal with each of these four merits separately and then combine them for the overall decision.
THE GOODS THE BADS AND THE INTANGIBLES
Linear Hierarchy
component,cluster(Level)
element
A loop indicates that eachelement depends only on itself.
Goal
Subcriteria
Criteria
Alternatives
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The Analytic Network Process (ANP)involves Dependence and Feedback
• Real life problems involve dependence and feedback. Such phenomena can not be dealt with in the framework of a hierarchy but we can by using a network with priorities.
• With feedback the alternatives can depend on the criteria as in a hierarchy but may also depend on each other.
• The criteria themselves can depend on the alternatives and on each other as well.
• Feedback improves the priorities derived from judgments and makes prediction more accurate.
Feedback Network with components having Inner and Outer Dependence among Their Elements
Loop in a component indicates inner dependence of the elements in that component with respect to a common property.
Arc from componentC4 to C2 indicates theouter dependence of the elements in C2 on theelements in C4 with respectto a common property.
C4
C1
C2
C3
Feedback
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Inner and Outer Dependence and the Control Hierarchy
In a network, the elements in a component • may be people (e.g., individuals in the White House) and those in
another component may also be people (e.g., individuals in Congress),• may influence other elements in the same component (inner
dependence) and those in other components (outer dependence) with respect to each of several properties.
We want to determine the overall influence of all the elements.
organize the properties or criteriaprioritize them in the framework of a control hierarchyperform comparisonssynthesize to obtain the priorities of these propertiesderive the influence of elements in the feedback systemweight the resulting influences obtain the overall influence of each element.
About Ratio Scales and Absolute NumbersBecause of feedback the ANP requires the use of numbers that canbe added and multiplied. The only such numbers can belong to an absolute or to the same ratio scale. Both scales are fundamental in the AHP/ANP.
There is an interesting relationship between the process of making paired comparisons to derive priorities in the form of ratio scalesand the absolute numbers we use in each paired comparison.
The ratio of two numbers from the same ratio scale is an absolute number. It is dimensionless. Dividing six pounds of bananas by three pounds of bananas yields the number 2. This number says that the six pounds are twice as heavy as the three pounds. Thisnumber cannot be changed to another number and say the same thing: twice as heavy.
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RELATION BETWEEN MULTICRITERA SYNTHESIS WITH ABSOLUTE NUMBERS AND WITH RELATIVE NUMBERS (CRITERIA WEIGHTS DEPEND ON THE THE MEASUREMENTS OF THE ALTERNATIVES)
Assume that we have two criteria and two alternatives measured in dollars. To synthesize with relative measurement, we see that the criteria inherit their importance from the relative total measurement of the alternatives under each to the total under both. If we normalize the values of the alternatives under each criterion, weight by the importance of that criterion and add, we obtain their normalized final values. The criteria weights depend on the weights of the alternatives and a feedback network structure is needed.
6/10642A2
4/10431A1
Normalized Sum
SumC2C1
6/104/72/3A2
4/103/71/3A1
Weighted Sum
C2
(7/10)C1
(3/10)
Absolute Synthesis Relative Synthesis
CRITERIA WEIGHTS INDEPENDENT FROM THE WEIGHTS OF THE ALTERNATIVES (THE IDEAL)
In a hierarchy, the weights of the criteria are derived independently from the measurements of the alternatives. In that case we can continue to use the measurements, but need to use the idealized form of the alternatives by dividing by the largest value in each column. The proportionality among the alternatives remains the same as before, even when the values are different.
25A2
31A1
C2C1Different measures
2/31A2
11/5A1
C2C1Idealized Values
Absolute Measurement Ideal Measurement
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Why ANP?• The ANP is a mathematical theory that makes it possible for one to
deal systematically with dependence and feedback, and includes the AHP as a special case. The reason for its success is the way it elicits judgments and uses measurement to derive ratio scales.
• Priorities as ratio scales are a fundamental kind of number amenable to performing the basic arithmetic operations of addition within the same scale, multiplication of different scales and combining the two operations by meaningfully weighting and adding different scales to obtain a unidimensional scale.
Why ANP? (Cont’d)
• In the AHP one asks:What is more preferred or more important? Both are more or less subjective and personal.
• In the ANP one asks:What has greater influence? This requires factual observation
and knowledge to yield valid answers and thus is more objective.
• Decisions with the ANP should be more stable because one can consider their effect on and survival in the face of other influences.
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Main Operations of the ANP
• Relative measurement: Reciprocal relation
• Judgments: Homogeneity
• Hierarchy or Network: Structure of problem; the control hierarchy
• Priorities, Dominance and Consistency: Eigenvector
• Weighting the components
• Composition, Additive to also handle dependence through the supermatrix
• Supermatrix: Interdependence; raising the supermatrix to powers
Weighting The ComponentsIn the ANP one often needs to prioritize the influence of the components themselves on each other component to which the elements belong. This influence is assessed through paired comparisons with respect to a control criterion.
The priority of each component is used to weight the priorities of all the elements in that component. The reason for doing this is to enable us to perform feedback multiplication of priorities by other priorities in a cycle, an infinite number of times. The process would not converge unless the resulting matrix of priorities is column stochastic (each of its columns adds to one).
To see that one must compare clusters in real life, we note that if a person is introduced as the president it makes much difference, for example, whether he or she is the President of the United States or the president of a local labor group.
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Comparison MatrixGiven: Three apples of different sizes.
SizeComparison Apple A Apple B Apple C
Apple A S1/S1 S1/S2 S1/S3
Apple B S2 / S1 S2 / S2 S2 / S3
Apple C S3 / S1 S3 / S2 S3 / S3
Apple A Apple B Apple C
We Assess Their Relative Sizes By Forming Ratios
Pairwise ComparisonsSize
Apple A Apple B Apple C
SizeComparison
Apple A Apple B Apple C
Apple A 1 2 6 6/10 0.6
Apple B 1/2 1 3 3/10 0.3
Apple C 1/6 1/3 1 1/10 0.1
When the judgments are consistent, as they are here, any normalized column gives the priorities.
Relative Size of Apples From Any ColumnNormalized
Priorities
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ConsistencyIn this example Apple B is 3 times larger than Apple C. We can obtain this value directly from the comparisons of Apple A with Apples B & C as 6/2 = 3. But if we were to use judgment we may have guessed it as 4. In that case we would have been inconsistent.
Now guessing it as 4 is not as bad as guessing it as 5 or more. The farther we are from the true value the more inconsistent we are. The AHP provides a theory for checking the inconsistency throughout the matrix and allowing a certain level of overall inconsistency but not more.
Verbal Expressions for Making Pairwise Comparison Judgments
Equal importance
Moderate importance of one over another
Strong or essential importance
Very strong or demonstrated importance
Extreme importance
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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
The fundamental scale has been derived mathematically from stimulus-response theory in psychology.
Fundamental Scale of Absolute NumbersCorresponding to Verbal Comparisons
Which Drink is Consumed More in the U.S.?An Example of Estimation Using Judgments
Coffee Wine Tea Beer Sodas Milk Water
DrinkConsumptionin the U.S.
Coffee
Wine
Tea
Beer
Sodas
Milk
Water
1
1/9
1/5
1/2
1
1
2
9
1
2
9
9
9
9
5
1/3
1
3
4
3
9
2
1/9
1/3
1
2
1
3
1
1/9
1/4
1/2
1
1/2
2
1
1/9
1/3
1
2
1
3
1/2
1/9
1/9
1/3
1/2
1/3
1The derived scale based on the judgments in the matrix is:Coffee Wine Tea Beer Sodas Milk Water.177 .019 .042 .116 .190 .129 .327with a consistency ratio of .022.The actual consumption (from statistical sources) is:.180 .010 .040 .120 .180 .140 .330
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Estimating which Food has more Protein
A B C D E F GFood Consumptionin the U.S.
A: Steak
B: Potatoes
C: Apples
D: Soybean
E: Whole Wheat Bread
F: Tasty Cake
G: Fish
1 9
1
9
1
1
6
1/2
1/3
1
4
1/4
1/3
1/2
1
5
1/3
1/5
1
3
1
1
1/4
1/9
1/6
1/3
1/5
1
The resulting derived scale and the actual values are shown below:Steak Potatoes Apples Soybean W. Bread T. Cake Fish
Derived .345 .031 .030 .065 .124 .078 .328Actual .370 .040 .000 .070 .110 .090 .320
(Derived scale has a consistency ratio of .028.)
(Reciprocals)
Extending the 1-9 Scale to 1- ∞
• The 1-9 AHP scale does not limit us if we know how to use clustering of similar objects in each group and use the largest element in a group as the smallest one in the next one. It serves as a pivot to connect the two.
• We then compare the elements in each group on the 1-9 scale get the priorities, then divide by the weight of the pivot in that group and multiply by its weight from the previous group. We can then combine all the groups measurements as in the following example comparing a very small cherry tomato with a very large watermelon.
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.07 .28 .65Cherry Tomato Small Green Tomato Lime
.08 .22 .70Lime
1=.08.08
.65 1=.65
Grapefruit
2.75=.08.22
.65 2.75=1.79
Honeydew
8.75=.08.70
.65 8.75=5.69
.10 .30 .60Honeydew
1=.10.10
5.69 1=5.69
Sugar Baby Watermelon
3=.10.30
5.69 3=17.07
Oblong Watermelon
6=.10.60
5.69 6=34.14This means that 34.14/.07 = 487.7 cherry tomatoes are equal to the oblong watermelon
Why Is the Eigenvector Necessary1
max
1
1) Consistent matrix: ; .2) Perturbed matrix: .
13) Transitivity lim / , (1,...,1). By Cesaro sumability
this converges to the same limit as / . 4) Necessi
k k
mk T k T
k kk T k
Aw nw A n AAw w
A e e A e w em
A e e A e
λ
−
→∞=
= ==
→ → =∑
ty : Priority must be invariant with respect to whatever process of synthesis one chooses. We start with an initial priority vector (1,...,1) and thenderive a first estimate of priorities from it. We then use this vector it to weight the alternatives or weight squares of differences and derive a new priority vector,and so on. For uniqueness we must have , where indicates the composition pri
A x cx=o o
nciple used and indicates proportionality of the new vector and the old vector . For additive composition we have . More generally,
x and because initially , , the principak k k k
c cxx Ax cx
A x c x e A e c e w=
= = = → l right eigenvectorof . Thus it is necessary to use the eigenvector to derive a priority vector.A
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... ...... ...
1 n
1 1 1 1 n 1 1
n n 1 n n n n
A Aw w w w w wA
Aw n nww w w w w wA
= = =
M M M M M
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12 1
12 2
1 2
1 ...1/ 1 ...
1/ 1/ ... 1
n
n
n n
a aa a
A
a a
=
M M M M
ija jiai
Let A1, A2,…, An, be a set of stimuli. The quantified judgments on pairs of stimuli Ai, Aj, are represented by an n-by-n matrix A = (aij), ij = 1, 2, . . ., n. The entries aij are defined by the following entry rules. If aij = a, then aji = 1 /a, a 0. If Ai is judged to be of equal relative intensity to Aj then aij = 1, aji = 1, in particular, aii= 1 for all i.
Clearly in the first formula n is a simple eigenvalue and all other eigenvalues are equal to zero.
A forcing perurbation of eigenvalues theorem:
If λ is a simple eigenvalue of A, then for small ε > 0, there is an eigenvalue λ(ε) of A(ε) with power series expansion in ε:
λ(ε)= λ+ ε λ(1)+ ε2 λ(2)+…
and corresponding right and left eigenvectors w (ε) and v (ε) such that w(ε)= w+ ε w(1)+ ε2 w(2)+…
v(ε)= v+ ε v(1)+ ε2 v(2)+…
Aw=nw
Aw=cw
Aw=λmaxw
How to go from
to
and then to
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w = w a ijij
n
1 =j λmax∑
1 = wi
n
1=i∑
0256)4)(1(
4321
)(
00
,1001
,4321
2 =−λ−λ=−λ−λ−=λ−
λ−
λ−=λ−
λ
λ=λ
=
=
IA
IA
IIA
2335
2335
2
1
−=λ
+=λ
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max1 1
max1 1
max max1 1
max for max
min for min
Thus for a row stochastic matrix we have 1=min max 1, thus =1.
n nj
ij ij ij j i
n nj
ij ij ij j i
n n
ij ijj j
wa a w
w
wa a w
w
a a
λ
λ
λ λ
= =
= =
= =
≥ =
≤ =
≤ ≤ =
∑ ∑
∑ ∑
∑ ∑
w)wv )-/(w A v( = w jjTjj11
Tj
n
2j=1 λλ∆∆ ∑
Sensitivity of the Eigenvector
The eigenvector w1 is insensitive to perturbation in A, if 1) the number of terms is small (i.e. n is small), 2) if the principal eigenvalue λ1 is separated from the other eigenvalues , here assumed to be distinct (otherwise a slightly more complicated argument can also be made and is given below) and, 3) if none of the products vj
T wj of left and right eigenvectors is small and if one of them is small, they are all small. Howerver, v1
T w1, the product of the normalized left and right principal eigenvectors of a consistent matrix is equal to n which as an integer is never very small. If n is relatively small and the elements being compared are homogeneous, none of the components of w1 is arbitrarily small and correspondingly, none of the components of v1
T is arbitrarily small. Their product cannot be arbitrarily small, and thus w is insensitive to small perturbations of the consistent matrix A. The conclusion is that n must be small, and one must compare homogeneous elements.
When the eigenvalues have greater multiplicity than one, the corresponding left and right eigenvectors will not be unique. In that case the cosine of the angle between them which is given by corresponds to a particular choice of and . Even when and correspond to a simple they are arbitrary to within a multiplicative complex constant of unit modulus, but in that case | vi
T wi| is fully determined. Because both vectors are normalized, we always have | vi
T wi | <1.
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Fundamentals of the AHP/ANP
•How to structure complexity as a hierarchy or as a network;
•Why make comparisons to derive priorities;
•Why reciprocals and why homogeneous groups of elements;
•Why the fundamental scale 1-9, what does it mean to assign a number for a judgment;
•Why allow inconsistency;
•What is the minimum number of judgments needed and why use redundant judgments;
•Why the principal right eigenvector;
•Why ratios and ratio scales;
•Why weight and add for synthesis;
•Why the distributive and ideal modes;
•Why the supermatrix and what does raising it to powers do;
•Why stochastic supermatrix;
•Why weight the components;
•Why BOCR – why reciprocal vector for the smaller than instead of larger than;
•Why the ideal mode;
•How to allocate resources –the need for ratio scales;
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Some Answers(Only to be a little helpful)
• One structures a hierarchy from a goal download to criteria, subcriteria and goals, involving actors and stakeholders and terminating in alternatives at the bottom. The ideas to go gradually from the general to the particular. In a network, elements are put in clusters or components with their connections indicating influence.
•Comparisons are more scientific in deriving scales because they use a unit and estimate multiples of that unit rather than simply assigning numbers by guessing.
•Reciprocals are needed because if one element is five times more important than another then the other is a forteori one fifth as important as the first. One deals with homogeneous clusters to make the comparisons possible, closer and more accurate.
•The scale 1-9 helps us quantify our feelings and judgments in comparing elements.
•Human judgment expressed in the form of paired comparisons is naturally inconsistent. A modicum of inconsistency enables us to improve our understanding by focusing on the most inconsistent judgments.
• The minimum number of judgments needed to connect n elements is n-1. Redundant judgments improve the validity of the derived priority vector.
•Ratios and ratio scales give us information on both the rank order of the elements and on their relative values. It also makes possible proportionate resource allocation.
•Weighting and adding follows from simple operations we do all the time and is no different for priorities. Suppose the goal has two components of values 0.6 and 0.4, and assume that one has a 0.2 share in the first component and a 0.7 share in the second. The total share with respect to the goal is 0.6 x 0.2 + 0.4 x 0.7 = 0.4.
•The supermatrix is the framework for organizing the priorities derived from paired comparisons. Raising it to powers gives the overall influence of each element on all the other elements.
•The powers of the supermatrix do not converge unless it is stochastic, because then its largest eigenvalue is one. Other eigenvalues that are roots of one are also important. Certain functions of a matrix A, known as entire functions, for example in the simple case of all the eigenvalues of multiplicity one, can be written ( in the spirit of Lagrange’s formula for a polynomial of degree n-1 completely determined in terms of n values (shown below) because one can solve a linear system of n equations to determine its n coefficients,) as
•The components are weighted because we need to combine the priorities of the element s simultaneously in all of them, and not just in each one. Each component has a top element, the question is which element has the highest priority in all? We must compare the components to answer this question.
•Human values are expressed in terms of the merits: benefits (B), opportunities (O), costs (C) and risks (R). They are all made in response to the question:which of two elements dominates the other and how much. The principal left eigenvector gives the reciprocal priorities for costs and risks. To obtain their priorities, the BOCR are rated in terms of strategic criteria one at a time and then normalized. BO and CR are then combined by adding each pair and the pairs combined using inverses or subtraction, both possible.
•The ideal mode is used to combine the priorities of the alternatives from each of the influence networks under each of the “control” criteria that detail each of the BOCR.
•In the distributive mode the criteria derive their importance from the alternatives, whereas in the ideal mode, the alternatives are unitized under each criterion. The criteria are compared to determine the tradeoff between one unit of one against one unit of the other, by answering the question: How many units of the lesser criterion make up a unit of the greater one?
1
1
i
( ) / ( )
( ) ( ) ( ) / ( )
which converges as
if 1 or is a complex root of 1.
j j ij i j i
n
i j j ii j i j i
nk k
ii
I A
f A f x x I A x x
A kλ λ λλ
λ≠ ≠
= ≠ ≠
=
− −
= − −
= →∞
=
∏ ∏
∑ ∏ ∏
∑
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Networks and the Supermatrix
W =
C1 C2 CN
e11e12 e1n1e21e22 e2n2
eN1eN2 eNnN
W11 W12 W1N
W21 W22 W2N
WN1 WN2 WNN
C1
C2
CN
e11e12
e1n1e21e22
e2n2eN1eN2
eNnN
c1.
C3
c4c2.Feedback
where
Wi1 Wi1 Wi1
Wij =
(j1) (j2) (jnj)
(j1) (j2) (jnj)Wi2 Wi2 Wi2
WiniWini
Wini
(j1) (j2) (jnj)
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Three Supermatrices in ANP1. The original supermatrix of column eigenvectors
obtained from pairwise comparison matrices of elements
2. Weighted supermatrix in which each block of column eigenvectors belonging to a component is weighted by the priority of influence of that component. This renders the weighted supermatrix column stochastic.
3. The limit supermatrix obtained by raising the weighted supermatrix to large powers. There are two kinds of limit supermatrices: one that does not cycle and one that does. In the second case one uses the Cesaro sum for the limit.
Supermatrix of a Hierarchy
0 0 0 0 0
W21 0 0 0 0W =
Wn-1, n-2 0 00 0 0 Wn, n-1 I
0 W32 0 0 0
0 0
C1
C2
CN
e11
e1n1
e21
e2n2
eN1
eNnN
C1 C2 CN-2 CN-1 CN
e11 e1n1e21 e2n2
eN1 eNnNe(N-2)1 e(N-2) nN-2
e(N-1)1 e(N-1) nN-1
22
Wk=
Wn,n-1 Wn-1,n-2 W32 W21 Wn,n-1 Wn-1,n-2 W32
for k>n-1
Wn,n-1 Wn-1,n-2 Wn,n-1 I
00
0
00
0
00
0
00
0
00
0
… ...
GoalSatisfaction with School
Learning Friends School Vocational College MusicLife Training Prep. Classes
SchoolA
SchoolC
SchoolB
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Goal Learning Friends School life Vocational trainingCollege preparation Music classes A B CGoal 0 0 0 0 0 0 0 0 0 0
Learning 0 0 0 0 0 0 0 0 0 0Friends 0 0 0 0 0 0 0 0 0 0
School life 0 0 0 0 0 0 0 0 0 0Vocational training 0 0 0 0 0 0 0 0 0 0
College preparation 0 0 0 0 0 0 0 0 0 0Music classes 0 0 0 0 0 0 0 0 0 0Alternative A 0.3676 0.16 0.33 0.45 0.77 0.25 0.69 1 0 0Alternative B 0.3781 0.59 0.33 0.09 0.06 0.5 0.09 0 1 0Alternative C 0.2543 0.25 0.34 0.46 0.17 0.25 0.22 0 0 1
Goal Learning Friends School life Vocational trainingCollege preparation Music classes A B CGoal 0 0 0 0 0 0 0 0 0 0
Learning 0.32 0 0 0 0 0 0 0 0 0Friends 0.14 0 0 0 0 0 0 0 0 0
School life 0.03 0 0 0 0 0 0 0 0 0Vocational training 0.13 0 0 0 0 0 0 0 0 0
College preparation 0.24 0 0 0 0 0 0 0 0 0Music classes 0.14 0 0 0 0 0 0 0 0 0Alternative A 0 0.16 0.33 0.45 0.77 0.25 0.69 1 0 0Alternative B 0 0.59 0.33 0.09 0.06 0.5 0.09 0 1 0Alternative C 0 0.25 0.34 0.46 0.17 0.25 0.22 0 0 1
The School Hierarchy as Supermatrix
Limiting Supermatrix & Hierarchic Composition
SOURCES AND SINKS
The goal of a hierarchy is a source component consisting of one node that feeds into the nodes of the component in the second level but nothing feeds back into it. The alternatives of a hierarchy are sink nodes in the bottom level component and do not feed back into any nodes in a higher level component. The columns corresponding to sink nodes of a network in the supermatrix must have a unit entry on the diagonal corresponding to that node. Otherwise all these columns’ entries would be zero and the weighted matrix cannot be stochastic. A loop is implicitly attached to such nodes with zero columns.
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The Questions to Answer About the Dominance of InfluenceFour kinds of questions to answer in the ANP:
1. Given a criterion, which of two elements has greater influence (is more dominant) with respect to that criterion?
2. Given an alternative, which of two criteria or properties is more dominant in that alternative?
3. Given a criterion and given an element X in any cluster, which of two elements in the same cluster or in a different cluster hasgreater influence on X with respect to that criterion?
The entire decision must use the idea of something “influencing”another. Otherwise it must use the idea of “influenced by” throughout the analysis as follows:
4. Given a criterion and given an element X in any cluster, which of two elements in the same or in a different cluster is influenced moreby X with respect to that criterion.
A Feedback System with Two Components
Flood Recreation Hydro-Control Electric
Power
Low Intermediate HighLevel Level Level
25
1) Which level is best for flood control?
3) Which level is best for power generation?2) Which level is best for recreation?
Flood Control
Low Med HighLowMediumHigh
Eigenvector
Consistency Ratio = .107
1 5 7 .7221/5 1 4 .2051/7 1/4 1 .073
Low Med HighLowMediumHigh
Eigenvector
Consistency Ratio = .056
1 1/7 1/5 .0727 1 3 .6495 1/3 1 .279
Recreation
Low Med HighLowMediumHigh
Eigenvector
Consistency Ratio = .101
1 1/5 1/9 .0585 1 1/5 .2079 5 1 .735
Power Generation
Real Life Problems Exhibit:
Strong Pressures and Weakened Resources
Complex Issues - Sometimes There are No “Right” Answers
Vested Interests
Conflicting Values