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Measuring the intangibles in social decisions: Assessing benefits and costs of energy policy options
Mathematics North-Holland
and Computers
in Simulation
XXV (1983) 135- 145
MEASURING THE INTANGIBLES IN SOCIAL COSTS OF ENERGY POLICY OPTIONS Kenneth
H. MITCHELL
Woods Gordon Management
135
DECISIONS:
ASSESSING
BENEFITS
AND
and Mary P. SOYE Consultants,
P.O. Box 251, Toronto- Dominion Centre, Toronto, Canada
This article describes the use of the Analytic Hierarchy Process (AHP) of Saaty for measuring intangibles in social decision-making. The traditional cost-benefit analysis approach is discussed and some key problems pointed out. Use of AHP to avoid some of these problems is discussed. An example is given of applying AHP to assess social, political, economic and environmental benefits and costs of energy policy options.
1. Introduction
Cost-benefit analysis is a traditional method for determining whether or not a public project is worth undertaking on the basis of the benefits and costs associated with the project. The conventional cost-benefit analysis measured only the economic costs and benefits ignoring and social or environmental impacts of the project. As societal concerns and damage to the environment become more important, it becomes necessary to incorporate these benefits and costs into the analysis as well. This complicates the conventional cost-benefit analysis to the extent that: (1) it is impossible to value all of the related information; and (2) the time required is often a prohibiting factor. The Analytic Hierarchy Process (AHP) is a decision-making tool which structures all of the factors, objectives and options hierarchically in order to evaluate the options in terms of the relevant factors and objectives. AHP is an approach which offers some solutions to the age-old problems of cost-benefit analysis.
2. Cost-benefit
analysis
Cost-benefit various means
analysis is a tool used to examine to a particular end in light of all of
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0 1983 Elsevier Science Publishers
the costs and all of the benefits of each of the means. This includes all benefits and costs, both direct and indirect, over the economic life of the project. Cost-benefit studies can be very effective decision-making tools provided that all costs and all benefits are taken into account. There are both direct and indirect costs and benefits associated with any major undertaking. Direct costs and benefits are those affecting the decision-makers and the user of the options being analyzed. Direct costs and benefits are usually readily quantifiable and constitute such things as the operating, maintenance and capital costs and the revenue and the pleasure extracted from the end-product. However, even with these costs and benefits it is often difficult and time-consuming to place an exact value on them. Indirect costs and benefits, or the externalities involved in implementing the options, are more difficult to evaluate than the direct costs. They are those costs not borne by the decision-maker or the user and those benefits not directly accruing to either of these parties. Using the classic case of the neighbours, one a beekeeper, and one a farmer, the concept of externalities can be illustrated. The bees take the nectar from the flowers increasing honey production and as a side-effect pollinate the flowers thereby increasing the production of fruit. Here are two examples of indirect benefits-they are benefits which do not accrue directly to the beekeeper or the fruit farmer, but indirectly they benefit each other. The bees stinging the orchard
B.V. (North-Holland)
136
K. H. Mitchell, M. P. Soye / Measuring
keeper is an example of an indirect cost. The work involved in measuring these costs and benefits is substantial. There are, indeed, inherent difficulties with cost-benefit analysis. Imagine the problems involved with measuring all costs and benefits, direct and indirect, with a mega-project such as the Canadian James Bay Hydro Electric Power project. Not only would the costs of construction, the maintenance costs and the operating costs have to be measured, but so too would the social costs of disrupting the life of native peoples and the costs to the environment such as the effect on the water-life of damming the rivers and the destruction of the natural life in the construction process. The return on investment would have to be estimated as well as the benefits derived by the consumers of this additional source of power. Finally, alternatives to this power supply and alternate sites should be considered to determine whether this is the best course of action to take. Krutilla and Fisher in The Economics of Natural Environments bring up several other important concerns with regard to cost-benefit analysis, concentrating largely on projects affecting the natural environment. The authors seem to classify the projects into three categories. First, there are those projects which do not require a valuation of the environmental impact as the measurement of non-environmental costs and benefits are sufficient to reject the project as uneconomical. They advocate that the conventional cost-benefit analysis in which environmental impacts are ignored is sufficient for this category of projects. However there is still the question of the time-consuming nature of the full-scale cost-benefit analysis. The second category is those projects in which it is necessary to measure the environmental impact and it is possible, albeit difficult, to quantify much of the information. In such cases Krutilla and Fisher use the conventional cost-benefit analysis together with estimating some of the environmental impacts. Even this may not be enough, as some environmental costs and benefits are not considered. The authors assert that the “option value”, the value “that arises from retaining an option to a good or service for which future demand is uncertain” [ 1, p. 701, cannot be measured
the intangibles in social derisions
either because there are no techniques or there is not the time to do so.
capable
of it
we find that there are a number of aspects of benefits that we do not know how to estimate quantitatively. These are the value of natural environments that have remarkable qualities for scientific research; the value that individuals place on retaining an option when faced with actions having irreversible consequences, and the value that some individuals place on the knowledge of the mere existence of gifts of nature, even when they feel certain they will never have or choose an opportunity to experience them VI situ. In addition, although methods for estimating the demand for outdoor recreation are known, neither time nor available research resources.. encouraged a serious professional effort directed toward the application of such methods.
One can see the difficulties in quantifying such benefits. However, these benefits may be important enough that they should be accounted for. In such cases, a conventional cost-benefit analysis, even with estimates of the values of the more important environmental impacts, will not suffice. The final category of Krutilla and Fisher contains those projects in which it is necessary, but impossible, to measure the environmental impacts. In such cases, a conventional cost-benefit analysis is definitely not sufficient in deciding what course of action should be taken. It is quite obvious that the conventional costbenefit analysis, even with an estimation of some of the indirect benefits and costs, is not, by any means, a perfect method of evaluating a proposed project. To recapitulate, there are at least two key reasons for this. First, it is not always possible to evaluate certain costs and benefits and secondly. to place a value on all the costs and benefits of a given project is a time-consuming procedure. For these reasons, a full-scale cost-benefit analysis is often not commissioned even though everyone involved agrees it would be desirable to have a comprehensive study of the matter. Because the conventional cost-benefit analysis does not always suffice, another means of evaluating the costs and benefits of a proposed project is necessary. D.W. Pearce in his book Cost-Benefit Ana!vsis [2] aptly sums up the dilemma associated with affixing a value to items which are difficult to quantify.
K. H. Mitchell, M.P. Soye / Measuring
If a measure is suggested, the analyst is accused of attempting to ‘measure the immeasurable’. If no measure is suggested, the critic argues that cost-benefit has failed to produce answers which are any better than those which would have been achieved by a simple political or planning decision.
Best Science Project
FOCUS
CRITERIA
The Analytic Hierarchy Process offers an effective alternative to cost-benefit analysis, making use of decision-makers’ judgements to take into account all the quantitative and the qualitative information which is relevant, while going beyond simple ‘gut-reaction’ as a basis for the decision.
3. The Analytic
Hierarchy
Process
The Analytic Hierarchy Process is a method which can incorporate all significant factors in a decision situation. It does so by structuring the problem into a hierarchical framework containing criteria and options. The AHP concept is simple. It is based on helping decision-makers (and their advisors) to measure their own judgemental insights and preferences in a structured, analytical way. The nucleus of AHP is a way of prioritizing a group of factors using a ratio scale to consider them two at a time, measuring their importance to some objective or criterion. This is combined with a hierarchical way of laying out the objectives, criteria, and options which are relevant. The resulting AHP method is straight-forward to use and yet capable of handling complex situations. The AHP methodology has been well documented elsewhere. For our purposes, it will suffice to present a simple illustration by way of introduction, before plunging into an example of a complex social planning application. The example comes from personal experience of one of the authors, helping an eight year old select a school science project. Three projects were being considered: how magnets work; how clouds are formed; types and origins of sea shells. There was some indecision as to which project to do, and the deadline was fast approaching. Upon questioning as to why each one of the options-magnets, clouds or shells-might be desirable, three criteria were identified: how much
137
the intangibles in social decisions
I. Fun
III. Prize Winning
II. Easy
OPTIONS
Fig. 1. Hierarchical
problem
structure.
fun there would be in doing the project, how easy the project would be and how much chance the project would have of winning a prize. Now we had the elements of a structure to assess the child’s preferences. Using AHP, the structure is presented as in Fig. 1. The other part of the AHP method is measurement of preferences. First, the criteria are compared as to their relative importance. This was done by the analyst asking the decision-maker to give verbal pair-wise comparisons, and using Saaty’s ratio scale from 1 (two elements equally important) to 9 (one element absolutely dominant over the other) as shown in Table 1. (Diagonally opposite elements are reciprocals.) The principal eigenvector of the resulting reciprocal matrix is a measure of the relative weight given to each of the three criteria. Next, we ask the decision-maker to compare the options against each criterion as shown in Table 2. (We only need to show the upper triangle of judgements.) This allows us to calculate a com-
Table
1
How much more does element (row) than element (column) contribute to Best science project?
I
I Fun II Easy III Prize winning
14 ‘1 4
Consistency
ratio: 0.12
II
III
Weights
;
0.16 0.06 0.78
9’ 9
1
138
K. H. Mitchell,
M. P. Soye / Measuring
Table 2
A Magnets B Clouds C Shells
A
B
C
Weights
1
3 1
2
0.53 0.14 0.33
3’ 1
ratio: 0.05
A Magnets B Clouds C Shells
B
C
Weights
1
3’ 1
3 5
0.20 0.70
1
0.10
ratio: 0.12
How much more does element (row) than element (column) contribute to Prize winning? A Magnets B Clouds C Shells Consistency
A
A
B
C
Weights
1
3 1
3 2 1
0.59 0.25 0.16
ratio: 0.05
posite score for the options. This composite score measures “how well the options perform against the more important criteria”. The result is shown in Table 3. It was interesting to notice that the preferred decision became known to the child just at the
Table 3
A Magnets B Clouds C Shells Total
Fun
Easy
Prize winning
Composite total
0.09 0.02 0.06 0.16
0.01 0.04 0.01 0.06
0.46 0.20 0.12 0.78
0.56 0.26 0.18 1 .oo
without
How much more does element (row) than element (column) contribute to Best science project? A Magnets B Clouds C Shells Consistency
How much more does element (row) than element (column) contribute to Easy?
Consistency
in social decisions
-Table 4 Direct preference
How much more does element (row) than element (column) contribute to Fun?
Consistency
the rntangibles
criteria
A
B
C
Weights
1
5
3
1
:
0.64 0.10 0.26
I ratio: 0.03
point when the analyst was computing the composite results. However, when questioned directly (Table 4) as to preferences for options, even though the result was the same in terms of the winning choice, the second choice was opposite. In fact, the child’s direct consideration seemed to be the same as the comparison against the criterion of ‘Fun’. Although hardly a full scientific empirical investigation, this is an interesting illustration of how difficult multi-criteria choices are, and how without good analysis they may be dominated by one factor, which may not even be the factor which the decision-maker feels is most important. (Prize Winning in this case.) The Analytic Hierarchy Process was developed by Saaty in the early 70’s. The development came out of practical problem solving, and only in the past five years has the theory been published. Now several books and many papers describe the theory and application of AHP.
4. AHP and cost-benefit analysis As was stressed in the brief description of costbenefit analysis, there are at least two major drawbacks to cost-benefit analysis as it is presently practiced. The first is the difficulty of evaluating those costs and benefits which do not lend themselves to valuation. The second is the time required to carry out a traditional cost-benefit analysis. In addition to these two internal problems of cost-benefit analysis, there is a third major problem area which is perhaps not as well recognized
K. H. Mitchell, M. P. Soye / Measuring
by analysts as it is by decision-makers. This is the problem of deciding and taking action. Too often, extensive costly analysis is done which does not influence or support decision-making. Often, this is a result of the problems of measurement and valuation and of analysis timeliness. But also it is a result of a failure to integrate the analysis work with the decision-making process. Decision-making in complex social situations involves people with all of their biases and individual concerns. Therefore, deciding and acting on a socially significant project is a political process with a variety of interests involved. The planning and decision-making process involves people and if the analytical work is done as an isolated theoretical exercise as is often the case, then one should not be surprised that the results of the analysis have little influence on the decision. AHP. because it is a decision-making process which incorporates structured analysis, provides a means of integrating the analysis with the decision-making. Because AHP can incorporate any factors which the decision-makers feel are significant to the decision, it gets around the valuation problem. And an AHP assessment can be done in whatever time is available before a decision must be made. The number of factors to be considered may have to be reduced; and one may wish for more time to do basic research on impacts. But one can weigh the alternatives in a structured way in the time available, using the information at hand and judgements of experts who can be consulted. In Section 6, we illustrate the use of AHP for a fairly complex assessment of the costs and benefits of alternative energy policies.
5. Steps in using AHP for a cost-benefit ment
assess-
There are a number of broad activities to be carried out in a typical AHP assessment project. Although no two situations are identical, each assessment includes some requirements to structure the analysis, assemble information, identify criteria, conduct the actual analysis of preferences and report on the outcome.
the intungibles in social decisions
139
The most outstanding feature of the approach is that it can ensure, given a group which has a problem it wants to resolve, that an answer is arrived at within a reasonable period of time. The period might vary from a few days, if the situation is well defined, to several weeks for a situation which is more complex. For a very complex problem with a large impact, it might be worthwhile to carry out several months of analytical and research work, if such time is available. To ensure that the process runs smoothly, the right preparatory steps must be carried out. The following is a sequence of typical steps for a problem which is quite complex and yet is to be resolved within a few weeks: (1) Purpose, Data and Participant Group: Define the purpose of the assessment. Identify the relevant sources of information which can be assessed within the available time and budget. Select Participant Group, including a suitably senior decision-making level and covering appropriate interest and expertise. Time: f - 1 week. (2) Preparation and General Research: Create a common information base. Participants review information. Prepare detailed procedures for Group Assessment Meetings. Schedule Meetings and provide briefing material to Participants. Time: 1-2 weeks. (3) Group Assessment Meeting I: Structure and Criteria : Conduct the first Group Assessment Meeting to develop and agree on a structure for analyzing the problem, and to identify and prioritize the criteria. The outcome is first an agreed structure including finalized definitions of overall focus, alternatives and criteria. Secondly. at the end of the Meeting the criteria are reduced by eliminating those which have been found from the analytical prioritization to be inconsequential to the outcome. Time: l-2 days, in a retreat environment. (4) Specific Research and impact Analysis: Using the information available, individuals or sub-groups study the relative impact (or performance) of the options on each of the relevant criteria. Evidence is marshalled. Time: 1 day to 1 week. (5) Group Assessment Meeting II: Assessment of Options: Participant Group debates the relative
K. H. Mitchell, M. P. Soye / Measuring
140
impact or performance of options on the criteria, and submits resulting judgements as a Group consensus or by individual ballot. Evidence presented is carefully recorded. Time: 1-2 days, in a retreat environment. (6) Group Assessment Meeting III: Findings, Conclusions and Recommendations: The results of the analysis are discussed. Appropriate sensitivity analyses are performed. The Participant Group agrees on the Conclusions and Recommendations. Time: f-1 day. (7) Report: A report is prepared documenting the Group’s deliberations and Conclusions and Recommendations. The report provides a record of the evidence which was presented and shows in considerable analytic detail how the Group’s judgements as to the weight of evidence were synthesized to produce the Conclusions. Time: 2-3 weeks.
6. Assessing options
benefits
the intangibles VI social decisions
The group agreed on four energy options which were the most viable. It was these four energy policies which were examined in light of a variety of costs and benefits. The next step was to structure the hierarchy in a cost-benefit design. The structure was set up as two separate hierarchiesthe one incorporating all of the benefits and the other, all of the costs. The options, already established, formed the bottom line of each hierarchy. The group developed a number of benefits criteria and sub-criteria relating the four options to the overall benefits and also developed a number of cost criteria and subcriteria relating these options to the overall costs (Figs. 2 and 3). The contributions to the benefits and costs were considered separately for each of three periods-short-term (1982-85) mediumterm (1985-2000) and long-term (2000-on)-in order to recognize the time-dependent impacts in the system. This completed the hierarchical structuring of the issue.
and costs of energy policy
6. I. Background A national government had to decide upon an energy option which would best fulfill its objectives. Because of the time constraints, the inavailability of ‘hard’ economic data and the difficulty of quantifying many of the important factors in the complex situation, the Analytic Hierarchy Process was chosen as a more appropriate methodology to provide an initial assessment than would be a classical economic cost-benefit analysis. (This example, is based on a project which was carried out by K. Mitchell, T. Saaty, H. Schumann and L. Vargas.) 6.2. Overall process and structure A very important aspect of the AHP process is the selection of the participant group. In this case, the group was composed of middle-level civil servants. It is generally preferred, however, that those directly responsible for the outcome, with the power to make the final decision, be involved in the process.
6.3. Measurement
of judgemen ts
In order to explain this part of the process, the benefits hierarchy will be used as an example. Working from the top of the hierarchy downward, the criteria were prioritized with respect to the focus. Using pairwise comparisons, the importance of each criterion to the focus was compared to that of each of the other criteria. An example of the questions asked to elicit the responses from the group is: In the short-term, how much more important is the criterion Energy Benefit than the criterion Socio-Political Benefits, to Overall Benefits to the Country? This question was asked of each pair of criteria, resulting in the matrix of Table 5. To interpret the table, Energy Benefits are mildly more important than Socio-Political Benefits in the short-term (a 3 on the scale). Overall, Energy Benefits, in the short-term, receives 0.303 of the weight of the Overall Benefits to the Country. This was then repeated for the medium-term and the long-term. The next step was to prioritize the time periods with respect to each criterion. The question was
K.H. Mltcheli, M. P. Soye / Measuring
OVERALL
ENERGY BENEFITS
BENEFITS
I
aspects
-AL--
A
Fig. 2. Hierarchy
OPTION
of energy policy benefit
I3
i
spin-offs national prestige preservation of technology base regional aspects
--ALOPTION
COSTS TO COUNTRY
ENVIRONMENTAL COSTS
COSTS TO GOVERNMENT
‘S
-jiiiy
national (public acceptability) international (safeguards) regional (jurisdiction)
E
support health problems
-AL----LL Fig. 3. Hierarchy
A
OPTION
-LL-OPTION
D
This was asked for each pair of time periods, and for each criterion. (This large volume of judgemental data is not presented here.) Logically there are twelve criteria at the second level of the benefits hierarchy: short-, mediumand long-term Energy Benefits, short-, mediumand long-term Socio-Political Benefits and the
Are Macro-Economic Benefits in the short-term or in the medium-term going to contribute more to Overall Benefits from the implementation of any of these power generation options, and how strongly? (Table 6)
OVERALL
C
factors.
asked:
OPTION
141
TO COUNTRY
aspects
OPTION
the mrangibles in social decisions
B
of energy policy cost factors.
OPTION
C
OPTION
D
142
K.H. Mitchell, M.P. Soye / Measuring
Table 5 Prioritization
of benefit criteria
for the short term
How much more does element (row) than element (column) contribute to Overall benefits to country? E S-P I M-E
Energy Socio-Political Industry Macro-Economic
Consistency
E
S-P
I
M-E
Weights
1
3 1
I I
1 1 3 1
0.303 0.130 0.389 0.178
;
ratio: 0.057
same categories for the other two benefits criteria, Industry and Macro-Economic. Instead of making all the judgements involved in a twelve-by-twelve matrix we combine the judgements of the first two steps described above in an incomplete twelve-bytwelve matrix (Table 7). The outcome, using the Saaty algorithm to calculate weights, is that longterm energy benefits is the most important benefit (i.e. contributes most to the Overall Benefits) with a weight of 0.351. Long-term industry benefits is next with 0.149 followed by medium-term energy benefits with 0.142. Where the criteria were broken down into subcriteria it was necessary tc distribute the weight of the criteria among the various sub-criteria. An example of the prioritization of the sub-criteria
Table 6 Prioritization
of time periods
How much more does the energy benefits in the time period (row) than in the time period (column) contribute to Overall benefits to country? S Short-term M Medium-term L
Long-term
Consistency 0.06 1
the intangibles in social decisions
ratio:
can be seen in Table 8. The Energy criterion was broken out into three sub-criteria: Savings; Security and Reliability; and Regional Aspects. Each was compared to the others in a pairwise fashion and those weights in Table 8 resulted; this was repeated for each time period. To measure the importance of these sub-criteria to the Overall Benefit to the Country, these weights were multiplied by the weights of the criteria to which they contributed. The sub-criteria, Medium-term Savings Benefit, was multiplied by the weight of the criteria, Medium-term Energy Benefit to obtain the contribution of the sub-criteria to the focus. Table 9 shows the weights of the benefit subcriteria with respect to the focus, overall Benefits to the Country. The next step is to prioritize the options with respect to the benefit sub-criteria. This was achieved by asking the following type of question:
for a benefit criterion
In the medium-term, contribute more to strongly? (Table 10).
L
Weights
i’
$
1
1 ;
0.063 0.194 0.743
S
M
1
will Option A or Option B Energy Savings, and how
The question was repeated for all combinations of time periods, benefit sub-criteria and all pairs of options. Table 10 is an example of the prioritization of the options with respect to the sub-criterion Energy Savings. Finally, all of the information is synthesized using matrix mathematics. The contribution an option makes to each of the sub-criteria is added together allowing the option to accumulate weight. The more impact an option has on important sub-criteria, the more weight that option will accu-
K. H. Mitchell, M. P. Soye / Measuring
Table I Prioritization
of benefit
How much more does element (row) than element (column) contribute to Overall benefits to country? ES EM EL SPS SPM SPL IS IM IL MES MEM MEL
Energy Short Energy Medium Energy long Socio-Pol Short So&-Pol Medium Socio-Pol Long Industry Short Industry Medium Industry Long Economic-Short Economic-Medium Economic-Long
criterion
in each time period
ES
EM
1
with respect
of benefit
How much more does sub-criterion (row) than sub-criterion (column) contribute to Medium-term energy benefits? SA SR ER
Savings Security Reliability Regional Aspects
Consistency
ratio: 0.03
to the focus (incomplete
EL
SPS
SPM
SPL
ii’
9I
I
f 1
3 0 0 1
0 I 0 3 1
0 0 7 5 4 1
mulate. The resulting composite benefit priority weights of each of the options are as follows: Option A : 0.195 Option B: 0.250 Option C: 0.160 Option D: 0.384 The same procedure which was carried out for the benefits hierarchy is followed for the costs hierarchy. First, the cost criteria were prioritized in each time period. Then, the time periods were prioritized for each cost criterion. These judge-
Table 8 Prioritization
the intangibles in social decisions
143
matrix)
IS
IM
IL
MES
MEM
MEL
Weights
0 5 0 0
0 0 5 0 0
0.042 0.142 0.35 1 0.033 0.020 0.016 0.055 0.071 0.149 0.02 1 0.049 0.053
1
0
0
0 0
3 0
0 4
’
0
0
1 0 0 1
i’oo’ 4 1
:
’
0
;
0 1
: : 1
’ t!l 0 1
0 3 0 1 1”
ments were used in an incomplete matrix prioritizing the three cost criteria in each time period with respect to the focus (this is in place of making the full number of judgements required for a nine-bynine matrix). The next step was to prioritize the cost subcriteria and then the options with respect to the cost sub-criteria. Finally, the composite cost weights of each of the options with respect to all of the sub-criteria combined are calculated.
sub-criteria
SA
SR
1
L ;
I
; 0 3 1 3 1 1
ER
Weights
Times benefit weight (x0.142)
3 5 1
0.258 0.637 0.105
0.037 0.090 0.015
144
K.H. Mitchell, M.P. Soye / Measuring
Table 9 Sub-criteria
benefit weights (with respect
the intnngrbles in social decisions
to Focus)
Sub-criteria
Short-term
Medium-term
Long-term
Energy - Savings - Security and Reliability - Regional Aspects
0.014 0.014 0.014
0.037 0.090 0.015
0.073 0.258 0.020
Socio-Political
0.033
0.020
0.016
Industrial - Engineer and Professional - Unskilled Trades - Skilled Trades - Regional Employment - Spinoffs - National Prestige - Preservation of Technology _ Regional Technology Aspects
0.008 0.001 0.004 0.000 0.011 0.002 0.023 0.005
0.003 0.001 0.00 1 0.000 0.015 0.003 0.037 0.005
0.012 0.002 0.006 0.00 1 0.032 0.006 0.080 0.010
Macro-Economic - Balance of Payments - GNP
0.002 0.019
0.007 0.043
0.007 0.043
Table 10 Prioritization
of options
with respect
In the medium-term, will option (row) or option (column) contribute more to Energy savings? Option Option
A B
Option Option
C D
Consistency
A B C D
A 1
B
C
D
Weights
Times subcriterion weight ( x 0.037)
1
1 1 1
9I 9I I
0.083 0.083 0.083 0.750
0.007 0.007 0.007 0.068
1
; ratio: 0.000
Table 11 Benefit to cost preference
Option Option Option Option
to the benefit sub-criteria
6.4. Benefit to cost preferences ratios Benefits/
Relative benefits priority
Relative costs priority
costs
0.195 0.250 0.160 0.384
0.196 0.262 0.224 0.308
0.995 0.954 0.714 I.247
When the overall benefits priority weight for each of the options is divided by the costs weight, a benefit to cost preference ratio for each of the four options results (Table 10). The option with the highest rating, Option D, is the best option for the Country, in that it provides the greatest benefit to cost preference. As long as one must act to implement some option, and the four options
K. H. Mitchell, M. P. Soye / Measuring
studied represent the best options known, then this preference ratio can provide a useful basis of understanding about the choice and a reasonable basis for action. Using the Analytic Hierarchy Process, a value was established for the overall relative costs and the overall relative benefits of each of the options. This value was afixed through using judgement to make pairwise comparisons. This is a much less time consuming and less costly way to assess the relative merits of the options than the analysis which is customarily done in an economic cost-benefit analysis. This study was carried out in eight weeks whereas the client had estimated that a traditional economic cost-benefit analysis for this problem would have taken at least twelve months.
Appendix.
Calculation
A. 1. Calculating
of priorities
and consistency
the priorities
Let us suppose that we have n objects A,, . . . , A, whose vector of corresponding weights w = it,,. . . , w,) is known. Let us form the matrix of pairwise comparisons of weights ’ A, WI/U’, . . . (‘3-Y . A,, / “;,/“,
A=
A,
...
A,
. .
WI/Yl
...
%/%
We note that we can recover the scale of weights M’,. . . “;, by multiplying A on the right by w, obtaining nw, and then solving the eigenvalue problem AH. = nw which has a nontrivial solution since II is the largest eigenvalue of A. (The matrix A has unit rank, hence all but one of its eigenvalues x ,... h,,arezero. SinceCy=&Xn=trace(A)=n, II is the maximum eigenvalue.) In our AHP method, we do not exactly know the w’s or the ratios w/w,, but we have estimates of the ratios from experienced judges. We elicit a judgement and automatically enter its reciprocal in the transpose position. In that case, we have perturbations of A which lead to perturbations in the eigenvalue of A. We can show that now we must
ihe intangibles in social decisions
145
solve the problem of Aw = Xmaxw to obtain an estimate of the weights w. An approximation of the weights of each matrix can be made by calculating the geometric mean of each row, then normalizing to 1.0. The geometric mean is the nth root of the product of all of the numbers in the row (n being equal to the number of elements in the row). A.2. Calculating
the consistency
It has been shown that X,,, > n always and inthat h,,, - n/(n - 1) serves as a consistency dex which gives the departure from consistency in estimating the ratios w,/w,, with consistency obtaining if, and only if, X,,, = n. Consistency is defined by the relation between entries of A: a,,ajk = ark. The consistency index is compared with what it would be if our numerical judgments were taken at random from the scale 4, 4, f,. . . , i, 1, 2,. . . ,9 (using a reciprocal matrix). An average consistency index which ranges from 0 for 1 or 2 element matrices through 0.9 for 4 element matrices to 1.49 for 10 element matrices has been established by generation of random entry reciprocal matrices. A consistency ratio (consistency index as a percentage of the appropriate random average consistency) of about 10% or less is considered good. When the consistency is poor, one needs to get more information on the activities being compared with respect to the criterion of and typically such information comparison, gathering is then followed by another round of judgements.
References
111J.V. Krutilla,
A.C. Fisher, The Economics of Natural Environments (Resources for the Future, Washington, 1975). 121D.W. Pearce, Cost-Benefit Analysis (Macmillan, London, 1971). 131 T.L. Saaty, A scaling method for priorities in hierarchical structures, J. Mafh. Psychology I5 (3) (1977) 234-28 1. [41T.L. Saaty, Decision Makingfor Leaders (Lifetime Learning, Belmont, CA, 1982). [51T.L. Saaty, The Analytic Hierarchy Process (McGraw-Hill, New York, 1980). The Logic of Priorities 161T.L. Saaty and L.G. Vargas, (Kluwer-Nijhoff, Boston, 1982).
and Computers
in Simulation
XXV (1983) 135- 145
MEASURING THE INTANGIBLES IN SOCIAL COSTS OF ENERGY POLICY OPTIONS Kenneth
H. MITCHELL
Woods Gordon Management
135
DECISIONS:
ASSESSING
BENEFITS
AND
and Mary P. SOYE Consultants,
P.O. Box 251, Toronto- Dominion Centre, Toronto, Canada
This article describes the use of the Analytic Hierarchy Process (AHP) of Saaty for measuring intangibles in social decision-making. The traditional cost-benefit analysis approach is discussed and some key problems pointed out. Use of AHP to avoid some of these problems is discussed. An example is given of applying AHP to assess social, political, economic and environmental benefits and costs of energy policy options.
1. Introduction
Cost-benefit analysis is a traditional method for determining whether or not a public project is worth undertaking on the basis of the benefits and costs associated with the project. The conventional cost-benefit analysis measured only the economic costs and benefits ignoring and social or environmental impacts of the project. As societal concerns and damage to the environment become more important, it becomes necessary to incorporate these benefits and costs into the analysis as well. This complicates the conventional cost-benefit analysis to the extent that: (1) it is impossible to value all of the related information; and (2) the time required is often a prohibiting factor. The Analytic Hierarchy Process (AHP) is a decision-making tool which structures all of the factors, objectives and options hierarchically in order to evaluate the options in terms of the relevant factors and objectives. AHP is an approach which offers some solutions to the age-old problems of cost-benefit analysis.
2. Cost-benefit
analysis
Cost-benefit various means
analysis is a tool used to examine to a particular end in light of all of
0378-4754/83/$03.00
0 1983 Elsevier Science Publishers
the costs and all of the benefits of each of the means. This includes all benefits and costs, both direct and indirect, over the economic life of the project. Cost-benefit studies can be very effective decision-making tools provided that all costs and all benefits are taken into account. There are both direct and indirect costs and benefits associated with any major undertaking. Direct costs and benefits are those affecting the decision-makers and the user of the options being analyzed. Direct costs and benefits are usually readily quantifiable and constitute such things as the operating, maintenance and capital costs and the revenue and the pleasure extracted from the end-product. However, even with these costs and benefits it is often difficult and time-consuming to place an exact value on them. Indirect costs and benefits, or the externalities involved in implementing the options, are more difficult to evaluate than the direct costs. They are those costs not borne by the decision-maker or the user and those benefits not directly accruing to either of these parties. Using the classic case of the neighbours, one a beekeeper, and one a farmer, the concept of externalities can be illustrated. The bees take the nectar from the flowers increasing honey production and as a side-effect pollinate the flowers thereby increasing the production of fruit. Here are two examples of indirect benefits-they are benefits which do not accrue directly to the beekeeper or the fruit farmer, but indirectly they benefit each other. The bees stinging the orchard
B.V. (North-Holland)
136
K. H. Mitchell, M. P. Soye / Measuring
keeper is an example of an indirect cost. The work involved in measuring these costs and benefits is substantial. There are, indeed, inherent difficulties with cost-benefit analysis. Imagine the problems involved with measuring all costs and benefits, direct and indirect, with a mega-project such as the Canadian James Bay Hydro Electric Power project. Not only would the costs of construction, the maintenance costs and the operating costs have to be measured, but so too would the social costs of disrupting the life of native peoples and the costs to the environment such as the effect on the water-life of damming the rivers and the destruction of the natural life in the construction process. The return on investment would have to be estimated as well as the benefits derived by the consumers of this additional source of power. Finally, alternatives to this power supply and alternate sites should be considered to determine whether this is the best course of action to take. Krutilla and Fisher in The Economics of Natural Environments bring up several other important concerns with regard to cost-benefit analysis, concentrating largely on projects affecting the natural environment. The authors seem to classify the projects into three categories. First, there are those projects which do not require a valuation of the environmental impact as the measurement of non-environmental costs and benefits are sufficient to reject the project as uneconomical. They advocate that the conventional cost-benefit analysis in which environmental impacts are ignored is sufficient for this category of projects. However there is still the question of the time-consuming nature of the full-scale cost-benefit analysis. The second category is those projects in which it is necessary to measure the environmental impact and it is possible, albeit difficult, to quantify much of the information. In such cases Krutilla and Fisher use the conventional cost-benefit analysis together with estimating some of the environmental impacts. Even this may not be enough, as some environmental costs and benefits are not considered. The authors assert that the “option value”, the value “that arises from retaining an option to a good or service for which future demand is uncertain” [ 1, p. 701, cannot be measured
the intangibles in social derisions
either because there are no techniques or there is not the time to do so.
capable
of it
we find that there are a number of aspects of benefits that we do not know how to estimate quantitatively. These are the value of natural environments that have remarkable qualities for scientific research; the value that individuals place on retaining an option when faced with actions having irreversible consequences, and the value that some individuals place on the knowledge of the mere existence of gifts of nature, even when they feel certain they will never have or choose an opportunity to experience them VI situ. In addition, although methods for estimating the demand for outdoor recreation are known, neither time nor available research resources.. encouraged a serious professional effort directed toward the application of such methods.
One can see the difficulties in quantifying such benefits. However, these benefits may be important enough that they should be accounted for. In such cases, a conventional cost-benefit analysis, even with estimates of the values of the more important environmental impacts, will not suffice. The final category of Krutilla and Fisher contains those projects in which it is necessary, but impossible, to measure the environmental impacts. In such cases, a conventional cost-benefit analysis is definitely not sufficient in deciding what course of action should be taken. It is quite obvious that the conventional costbenefit analysis, even with an estimation of some of the indirect benefits and costs, is not, by any means, a perfect method of evaluating a proposed project. To recapitulate, there are at least two key reasons for this. First, it is not always possible to evaluate certain costs and benefits and secondly. to place a value on all the costs and benefits of a given project is a time-consuming procedure. For these reasons, a full-scale cost-benefit analysis is often not commissioned even though everyone involved agrees it would be desirable to have a comprehensive study of the matter. Because the conventional cost-benefit analysis does not always suffice, another means of evaluating the costs and benefits of a proposed project is necessary. D.W. Pearce in his book Cost-Benefit Ana!vsis [2] aptly sums up the dilemma associated with affixing a value to items which are difficult to quantify.
K. H. Mitchell, M.P. Soye / Measuring
If a measure is suggested, the analyst is accused of attempting to ‘measure the immeasurable’. If no measure is suggested, the critic argues that cost-benefit has failed to produce answers which are any better than those which would have been achieved by a simple political or planning decision.
Best Science Project
FOCUS
CRITERIA
The Analytic Hierarchy Process offers an effective alternative to cost-benefit analysis, making use of decision-makers’ judgements to take into account all the quantitative and the qualitative information which is relevant, while going beyond simple ‘gut-reaction’ as a basis for the decision.
3. The Analytic
Hierarchy
Process
The Analytic Hierarchy Process is a method which can incorporate all significant factors in a decision situation. It does so by structuring the problem into a hierarchical framework containing criteria and options. The AHP concept is simple. It is based on helping decision-makers (and their advisors) to measure their own judgemental insights and preferences in a structured, analytical way. The nucleus of AHP is a way of prioritizing a group of factors using a ratio scale to consider them two at a time, measuring their importance to some objective or criterion. This is combined with a hierarchical way of laying out the objectives, criteria, and options which are relevant. The resulting AHP method is straight-forward to use and yet capable of handling complex situations. The AHP methodology has been well documented elsewhere. For our purposes, it will suffice to present a simple illustration by way of introduction, before plunging into an example of a complex social planning application. The example comes from personal experience of one of the authors, helping an eight year old select a school science project. Three projects were being considered: how magnets work; how clouds are formed; types and origins of sea shells. There was some indecision as to which project to do, and the deadline was fast approaching. Upon questioning as to why each one of the options-magnets, clouds or shells-might be desirable, three criteria were identified: how much
137
the intangibles in social decisions
I. Fun
III. Prize Winning
II. Easy
OPTIONS
Fig. 1. Hierarchical
problem
structure.
fun there would be in doing the project, how easy the project would be and how much chance the project would have of winning a prize. Now we had the elements of a structure to assess the child’s preferences. Using AHP, the structure is presented as in Fig. 1. The other part of the AHP method is measurement of preferences. First, the criteria are compared as to their relative importance. This was done by the analyst asking the decision-maker to give verbal pair-wise comparisons, and using Saaty’s ratio scale from 1 (two elements equally important) to 9 (one element absolutely dominant over the other) as shown in Table 1. (Diagonally opposite elements are reciprocals.) The principal eigenvector of the resulting reciprocal matrix is a measure of the relative weight given to each of the three criteria. Next, we ask the decision-maker to compare the options against each criterion as shown in Table 2. (We only need to show the upper triangle of judgements.) This allows us to calculate a com-
Table
1
How much more does element (row) than element (column) contribute to Best science project?
I
I Fun II Easy III Prize winning
14 ‘1 4
Consistency
ratio: 0.12
II
III
Weights
;
0.16 0.06 0.78
9’ 9
1
138
K. H. Mitchell,
M. P. Soye / Measuring
Table 2
A Magnets B Clouds C Shells
A
B
C
Weights
1
3 1
2
0.53 0.14 0.33
3’ 1
ratio: 0.05
A Magnets B Clouds C Shells
B
C
Weights
1
3’ 1
3 5
0.20 0.70
1
0.10
ratio: 0.12
How much more does element (row) than element (column) contribute to Prize winning? A Magnets B Clouds C Shells Consistency
A
A
B
C
Weights
1
3 1
3 2 1
0.59 0.25 0.16
ratio: 0.05
posite score for the options. This composite score measures “how well the options perform against the more important criteria”. The result is shown in Table 3. It was interesting to notice that the preferred decision became known to the child just at the
Table 3
A Magnets B Clouds C Shells Total
Fun
Easy
Prize winning
Composite total
0.09 0.02 0.06 0.16
0.01 0.04 0.01 0.06
0.46 0.20 0.12 0.78
0.56 0.26 0.18 1 .oo
without
How much more does element (row) than element (column) contribute to Best science project? A Magnets B Clouds C Shells Consistency
How much more does element (row) than element (column) contribute to Easy?
Consistency
in social decisions
-Table 4 Direct preference
How much more does element (row) than element (column) contribute to Fun?
Consistency
the rntangibles
criteria
A
B
C
Weights
1
5
3
1
:
0.64 0.10 0.26
I ratio: 0.03
point when the analyst was computing the composite results. However, when questioned directly (Table 4) as to preferences for options, even though the result was the same in terms of the winning choice, the second choice was opposite. In fact, the child’s direct consideration seemed to be the same as the comparison against the criterion of ‘Fun’. Although hardly a full scientific empirical investigation, this is an interesting illustration of how difficult multi-criteria choices are, and how without good analysis they may be dominated by one factor, which may not even be the factor which the decision-maker feels is most important. (Prize Winning in this case.) The Analytic Hierarchy Process was developed by Saaty in the early 70’s. The development came out of practical problem solving, and only in the past five years has the theory been published. Now several books and many papers describe the theory and application of AHP.
4. AHP and cost-benefit analysis As was stressed in the brief description of costbenefit analysis, there are at least two major drawbacks to cost-benefit analysis as it is presently practiced. The first is the difficulty of evaluating those costs and benefits which do not lend themselves to valuation. The second is the time required to carry out a traditional cost-benefit analysis. In addition to these two internal problems of cost-benefit analysis, there is a third major problem area which is perhaps not as well recognized
K. H. Mitchell, M. P. Soye / Measuring
by analysts as it is by decision-makers. This is the problem of deciding and taking action. Too often, extensive costly analysis is done which does not influence or support decision-making. Often, this is a result of the problems of measurement and valuation and of analysis timeliness. But also it is a result of a failure to integrate the analysis work with the decision-making process. Decision-making in complex social situations involves people with all of their biases and individual concerns. Therefore, deciding and acting on a socially significant project is a political process with a variety of interests involved. The planning and decision-making process involves people and if the analytical work is done as an isolated theoretical exercise as is often the case, then one should not be surprised that the results of the analysis have little influence on the decision. AHP. because it is a decision-making process which incorporates structured analysis, provides a means of integrating the analysis with the decision-making. Because AHP can incorporate any factors which the decision-makers feel are significant to the decision, it gets around the valuation problem. And an AHP assessment can be done in whatever time is available before a decision must be made. The number of factors to be considered may have to be reduced; and one may wish for more time to do basic research on impacts. But one can weigh the alternatives in a structured way in the time available, using the information at hand and judgements of experts who can be consulted. In Section 6, we illustrate the use of AHP for a fairly complex assessment of the costs and benefits of alternative energy policies.
5. Steps in using AHP for a cost-benefit ment
assess-
There are a number of broad activities to be carried out in a typical AHP assessment project. Although no two situations are identical, each assessment includes some requirements to structure the analysis, assemble information, identify criteria, conduct the actual analysis of preferences and report on the outcome.
the intungibles in social decisions
139
The most outstanding feature of the approach is that it can ensure, given a group which has a problem it wants to resolve, that an answer is arrived at within a reasonable period of time. The period might vary from a few days, if the situation is well defined, to several weeks for a situation which is more complex. For a very complex problem with a large impact, it might be worthwhile to carry out several months of analytical and research work, if such time is available. To ensure that the process runs smoothly, the right preparatory steps must be carried out. The following is a sequence of typical steps for a problem which is quite complex and yet is to be resolved within a few weeks: (1) Purpose, Data and Participant Group: Define the purpose of the assessment. Identify the relevant sources of information which can be assessed within the available time and budget. Select Participant Group, including a suitably senior decision-making level and covering appropriate interest and expertise. Time: f - 1 week. (2) Preparation and General Research: Create a common information base. Participants review information. Prepare detailed procedures for Group Assessment Meetings. Schedule Meetings and provide briefing material to Participants. Time: 1-2 weeks. (3) Group Assessment Meeting I: Structure and Criteria : Conduct the first Group Assessment Meeting to develop and agree on a structure for analyzing the problem, and to identify and prioritize the criteria. The outcome is first an agreed structure including finalized definitions of overall focus, alternatives and criteria. Secondly. at the end of the Meeting the criteria are reduced by eliminating those which have been found from the analytical prioritization to be inconsequential to the outcome. Time: l-2 days, in a retreat environment. (4) Specific Research and impact Analysis: Using the information available, individuals or sub-groups study the relative impact (or performance) of the options on each of the relevant criteria. Evidence is marshalled. Time: 1 day to 1 week. (5) Group Assessment Meeting II: Assessment of Options: Participant Group debates the relative
K. H. Mitchell, M. P. Soye / Measuring
140
impact or performance of options on the criteria, and submits resulting judgements as a Group consensus or by individual ballot. Evidence presented is carefully recorded. Time: 1-2 days, in a retreat environment. (6) Group Assessment Meeting III: Findings, Conclusions and Recommendations: The results of the analysis are discussed. Appropriate sensitivity analyses are performed. The Participant Group agrees on the Conclusions and Recommendations. Time: f-1 day. (7) Report: A report is prepared documenting the Group’s deliberations and Conclusions and Recommendations. The report provides a record of the evidence which was presented and shows in considerable analytic detail how the Group’s judgements as to the weight of evidence were synthesized to produce the Conclusions. Time: 2-3 weeks.
6. Assessing options
benefits
the intangibles VI social decisions
The group agreed on four energy options which were the most viable. It was these four energy policies which were examined in light of a variety of costs and benefits. The next step was to structure the hierarchy in a cost-benefit design. The structure was set up as two separate hierarchiesthe one incorporating all of the benefits and the other, all of the costs. The options, already established, formed the bottom line of each hierarchy. The group developed a number of benefits criteria and sub-criteria relating the four options to the overall benefits and also developed a number of cost criteria and subcriteria relating these options to the overall costs (Figs. 2 and 3). The contributions to the benefits and costs were considered separately for each of three periods-short-term (1982-85) mediumterm (1985-2000) and long-term (2000-on)-in order to recognize the time-dependent impacts in the system. This completed the hierarchical structuring of the issue.
and costs of energy policy
6. I. Background A national government had to decide upon an energy option which would best fulfill its objectives. Because of the time constraints, the inavailability of ‘hard’ economic data and the difficulty of quantifying many of the important factors in the complex situation, the Analytic Hierarchy Process was chosen as a more appropriate methodology to provide an initial assessment than would be a classical economic cost-benefit analysis. (This example, is based on a project which was carried out by K. Mitchell, T. Saaty, H. Schumann and L. Vargas.) 6.2. Overall process and structure A very important aspect of the AHP process is the selection of the participant group. In this case, the group was composed of middle-level civil servants. It is generally preferred, however, that those directly responsible for the outcome, with the power to make the final decision, be involved in the process.
6.3. Measurement
of judgemen ts
In order to explain this part of the process, the benefits hierarchy will be used as an example. Working from the top of the hierarchy downward, the criteria were prioritized with respect to the focus. Using pairwise comparisons, the importance of each criterion to the focus was compared to that of each of the other criteria. An example of the questions asked to elicit the responses from the group is: In the short-term, how much more important is the criterion Energy Benefit than the criterion Socio-Political Benefits, to Overall Benefits to the Country? This question was asked of each pair of criteria, resulting in the matrix of Table 5. To interpret the table, Energy Benefits are mildly more important than Socio-Political Benefits in the short-term (a 3 on the scale). Overall, Energy Benefits, in the short-term, receives 0.303 of the weight of the Overall Benefits to the Country. This was then repeated for the medium-term and the long-term. The next step was to prioritize the time periods with respect to each criterion. The question was
K.H. Mltcheli, M. P. Soye / Measuring
OVERALL
ENERGY BENEFITS
BENEFITS
I
aspects
-AL--
A
Fig. 2. Hierarchy
OPTION
of energy policy benefit
I3
i
spin-offs national prestige preservation of technology base regional aspects
--ALOPTION
COSTS TO COUNTRY
ENVIRONMENTAL COSTS
COSTS TO GOVERNMENT
‘S
-jiiiy
national (public acceptability) international (safeguards) regional (jurisdiction)
E
support health problems
-AL----LL Fig. 3. Hierarchy
A
OPTION
-LL-OPTION
D
This was asked for each pair of time periods, and for each criterion. (This large volume of judgemental data is not presented here.) Logically there are twelve criteria at the second level of the benefits hierarchy: short-, mediumand long-term Energy Benefits, short-, mediumand long-term Socio-Political Benefits and the
Are Macro-Economic Benefits in the short-term or in the medium-term going to contribute more to Overall Benefits from the implementation of any of these power generation options, and how strongly? (Table 6)
OVERALL
C
factors.
asked:
OPTION
141
TO COUNTRY
aspects
OPTION
the mrangibles in social decisions
B
of energy policy cost factors.
OPTION
C
OPTION
D
142
K.H. Mitchell, M.P. Soye / Measuring
Table 5 Prioritization
of benefit criteria
for the short term
How much more does element (row) than element (column) contribute to Overall benefits to country? E S-P I M-E
Energy Socio-Political Industry Macro-Economic
Consistency
E
S-P
I
M-E
Weights
1
3 1
I I
1 1 3 1
0.303 0.130 0.389 0.178
;
ratio: 0.057
same categories for the other two benefits criteria, Industry and Macro-Economic. Instead of making all the judgements involved in a twelve-by-twelve matrix we combine the judgements of the first two steps described above in an incomplete twelve-bytwelve matrix (Table 7). The outcome, using the Saaty algorithm to calculate weights, is that longterm energy benefits is the most important benefit (i.e. contributes most to the Overall Benefits) with a weight of 0.351. Long-term industry benefits is next with 0.149 followed by medium-term energy benefits with 0.142. Where the criteria were broken down into subcriteria it was necessary tc distribute the weight of the criteria among the various sub-criteria. An example of the prioritization of the sub-criteria
Table 6 Prioritization
of time periods
How much more does the energy benefits in the time period (row) than in the time period (column) contribute to Overall benefits to country? S Short-term M Medium-term L
Long-term
Consistency 0.06 1
the intangibles in social decisions
ratio:
can be seen in Table 8. The Energy criterion was broken out into three sub-criteria: Savings; Security and Reliability; and Regional Aspects. Each was compared to the others in a pairwise fashion and those weights in Table 8 resulted; this was repeated for each time period. To measure the importance of these sub-criteria to the Overall Benefit to the Country, these weights were multiplied by the weights of the criteria to which they contributed. The sub-criteria, Medium-term Savings Benefit, was multiplied by the weight of the criteria, Medium-term Energy Benefit to obtain the contribution of the sub-criteria to the focus. Table 9 shows the weights of the benefit subcriteria with respect to the focus, overall Benefits to the Country. The next step is to prioritize the options with respect to the benefit sub-criteria. This was achieved by asking the following type of question:
for a benefit criterion
In the medium-term, contribute more to strongly? (Table 10).
L
Weights
i’
$
1
1 ;
0.063 0.194 0.743
S
M
1
will Option A or Option B Energy Savings, and how
The question was repeated for all combinations of time periods, benefit sub-criteria and all pairs of options. Table 10 is an example of the prioritization of the options with respect to the sub-criterion Energy Savings. Finally, all of the information is synthesized using matrix mathematics. The contribution an option makes to each of the sub-criteria is added together allowing the option to accumulate weight. The more impact an option has on important sub-criteria, the more weight that option will accu-
K. H. Mitchell, M. P. Soye / Measuring
Table I Prioritization
of benefit
How much more does element (row) than element (column) contribute to Overall benefits to country? ES EM EL SPS SPM SPL IS IM IL MES MEM MEL
Energy Short Energy Medium Energy long Socio-Pol Short So&-Pol Medium Socio-Pol Long Industry Short Industry Medium Industry Long Economic-Short Economic-Medium Economic-Long
criterion
in each time period
ES
EM
1
with respect
of benefit
How much more does sub-criterion (row) than sub-criterion (column) contribute to Medium-term energy benefits? SA SR ER
Savings Security Reliability Regional Aspects
Consistency
ratio: 0.03
to the focus (incomplete
EL
SPS
SPM
SPL
ii’
9I
I
f 1
3 0 0 1
0 I 0 3 1
0 0 7 5 4 1
mulate. The resulting composite benefit priority weights of each of the options are as follows: Option A : 0.195 Option B: 0.250 Option C: 0.160 Option D: 0.384 The same procedure which was carried out for the benefits hierarchy is followed for the costs hierarchy. First, the cost criteria were prioritized in each time period. Then, the time periods were prioritized for each cost criterion. These judge-
Table 8 Prioritization
the intangibles in social decisions
143
matrix)
IS
IM
IL
MES
MEM
MEL
Weights
0 5 0 0
0 0 5 0 0
0.042 0.142 0.35 1 0.033 0.020 0.016 0.055 0.071 0.149 0.02 1 0.049 0.053
1
0
0
0 0
3 0
0 4
’
0
0
1 0 0 1
i’oo’ 4 1
:
’
0
;
0 1
: : 1
’ t!l 0 1
0 3 0 1 1”
ments were used in an incomplete matrix prioritizing the three cost criteria in each time period with respect to the focus (this is in place of making the full number of judgements required for a nine-bynine matrix). The next step was to prioritize the cost subcriteria and then the options with respect to the cost sub-criteria. Finally, the composite cost weights of each of the options with respect to all of the sub-criteria combined are calculated.
sub-criteria
SA
SR
1
L ;
I
; 0 3 1 3 1 1
ER
Weights
Times benefit weight (x0.142)
3 5 1
0.258 0.637 0.105
0.037 0.090 0.015
144
K.H. Mitchell, M.P. Soye / Measuring
Table 9 Sub-criteria
benefit weights (with respect
the intnngrbles in social decisions
to Focus)
Sub-criteria
Short-term
Medium-term
Long-term
Energy - Savings - Security and Reliability - Regional Aspects
0.014 0.014 0.014
0.037 0.090 0.015
0.073 0.258 0.020
Socio-Political
0.033
0.020
0.016
Industrial - Engineer and Professional - Unskilled Trades - Skilled Trades - Regional Employment - Spinoffs - National Prestige - Preservation of Technology _ Regional Technology Aspects
0.008 0.001 0.004 0.000 0.011 0.002 0.023 0.005
0.003 0.001 0.00 1 0.000 0.015 0.003 0.037 0.005
0.012 0.002 0.006 0.00 1 0.032 0.006 0.080 0.010
Macro-Economic - Balance of Payments - GNP
0.002 0.019
0.007 0.043
0.007 0.043
Table 10 Prioritization
of options
with respect
In the medium-term, will option (row) or option (column) contribute more to Energy savings? Option Option
A B
Option Option
C D
Consistency
A B C D
A 1
B
C
D
Weights
Times subcriterion weight ( x 0.037)
1
1 1 1
9I 9I I
0.083 0.083 0.083 0.750
0.007 0.007 0.007 0.068
1
; ratio: 0.000
Table 11 Benefit to cost preference
Option Option Option Option
to the benefit sub-criteria
6.4. Benefit to cost preferences ratios Benefits/
Relative benefits priority
Relative costs priority
costs
0.195 0.250 0.160 0.384
0.196 0.262 0.224 0.308
0.995 0.954 0.714 I.247
When the overall benefits priority weight for each of the options is divided by the costs weight, a benefit to cost preference ratio for each of the four options results (Table 10). The option with the highest rating, Option D, is the best option for the Country, in that it provides the greatest benefit to cost preference. As long as one must act to implement some option, and the four options
K. H. Mitchell, M. P. Soye / Measuring
studied represent the best options known, then this preference ratio can provide a useful basis of understanding about the choice and a reasonable basis for action. Using the Analytic Hierarchy Process, a value was established for the overall relative costs and the overall relative benefits of each of the options. This value was afixed through using judgement to make pairwise comparisons. This is a much less time consuming and less costly way to assess the relative merits of the options than the analysis which is customarily done in an economic cost-benefit analysis. This study was carried out in eight weeks whereas the client had estimated that a traditional economic cost-benefit analysis for this problem would have taken at least twelve months.
Appendix.
Calculation
A. 1. Calculating
of priorities
and consistency
the priorities
Let us suppose that we have n objects A,, . . . , A, whose vector of corresponding weights w = it,,. . . , w,) is known. Let us form the matrix of pairwise comparisons of weights ’ A, WI/U’, . . . (‘3-Y . A,, / “;,/“,
A=
A,
...
A,
. .
WI/Yl
...
%/%
We note that we can recover the scale of weights M’,. . . “;, by multiplying A on the right by w, obtaining nw, and then solving the eigenvalue problem AH. = nw which has a nontrivial solution since II is the largest eigenvalue of A. (The matrix A has unit rank, hence all but one of its eigenvalues x ,... h,,arezero. SinceCy=&Xn=trace(A)=n, II is the maximum eigenvalue.) In our AHP method, we do not exactly know the w’s or the ratios w/w,, but we have estimates of the ratios from experienced judges. We elicit a judgement and automatically enter its reciprocal in the transpose position. In that case, we have perturbations of A which lead to perturbations in the eigenvalue of A. We can show that now we must
ihe intangibles in social decisions
145
solve the problem of Aw = Xmaxw to obtain an estimate of the weights w. An approximation of the weights of each matrix can be made by calculating the geometric mean of each row, then normalizing to 1.0. The geometric mean is the nth root of the product of all of the numbers in the row (n being equal to the number of elements in the row). A.2. Calculating
the consistency
It has been shown that X,,, > n always and inthat h,,, - n/(n - 1) serves as a consistency dex which gives the departure from consistency in estimating the ratios w,/w,, with consistency obtaining if, and only if, X,,, = n. Consistency is defined by the relation between entries of A: a,,ajk = ark. The consistency index is compared with what it would be if our numerical judgments were taken at random from the scale 4, 4, f,. . . , i, 1, 2,. . . ,9 (using a reciprocal matrix). An average consistency index which ranges from 0 for 1 or 2 element matrices through 0.9 for 4 element matrices to 1.49 for 10 element matrices has been established by generation of random entry reciprocal matrices. A consistency ratio (consistency index as a percentage of the appropriate random average consistency) of about 10% or less is considered good. When the consistency is poor, one needs to get more information on the activities being compared with respect to the criterion of and typically such information comparison, gathering is then followed by another round of judgements.
References
111J.V. Krutilla,
A.C. Fisher, The Economics of Natural Environments (Resources for the Future, Washington, 1975). 121D.W. Pearce, Cost-Benefit Analysis (Macmillan, London, 1971). 131 T.L. Saaty, A scaling method for priorities in hierarchical structures, J. Mafh. Psychology I5 (3) (1977) 234-28 1. [41T.L. Saaty, Decision Makingfor Leaders (Lifetime Learning, Belmont, CA, 1982). [51T.L. Saaty, The Analytic Hierarchy Process (McGraw-Hill, New York, 1980). The Logic of Priorities 161T.L. Saaty and L.G. Vargas, (Kluwer-Nijhoff, Boston, 1982).