# Hierarchical Information Integration: a New Method For the Design and Analysis of Complex Multlattribute Judgment Problems

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Jordan J. Louviere (1984) ,"Hierarchical Information Integration: a New Method For the Design and Analysis of Complex Multlattribute Judgment Problems", in NA - Advances in Consumer Research Volume 11, eds. Thomas C. Kinnear, Provo, UT : Association for Consumer Research, Pages: 148-155.

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http://acrwebsite.org/volumes/6233/volumes/v11/NA-11

The author would like to thank Joel Huber, John Lynch and David Curry for their helpful comments on a previous version of the manuscript. Additional input from seminar participants at Duke University and The University of Florida is also acknowledged. Les Johnson of Marquarie University worked on several commercial applications which will be discussed in future papers.

A method is proposed for handling multiattribute judgment problems with a large number of attributes. Attributes are grouped a priori into logical, functional or other subsets. Subjects evaluate profiles of attributes in each subset. Responses to profiles in separate sets are linked by means of an overall experimental design which treats each subset as a factor whose levels are values of the response scale(s) used in each subset experiment. By concatenating the judgment equations from each subset with the equation for the overall design a single, closed-form judgment equation can be derived. An experimental test is provided.

INTRODUCTION

The purpose of this paper is to propose, describe, and discuss a new approach for the design and analysis of complex descriptive (as opposed to normative) multiattribute judgment and decision making (JDM) research projects. Many problems of academic and applied interest potentially involve a large number of influential attributes. Current approaches to this problem generally fall into one of the following categories: (1) reducing the number of attributes by policy fiat, by negotiations with the client, or by using some other ad hoc method; (2) reducing the number of attributes by recourse to some analytic procedure such as content analysis, ranking by importance scores, Kelly's (1972) grid sorting method, factor analysis, or the like; (3) extending the Johnson (1974) tradeoff method to a fairly large number of attributes presented in pairs; (4) adapting the full profile methods of Conjoint and/or Functional Measurement to fairly large problems via various combinations of fractional factorial designs and blocking procedures (e.g., Green, 1974; Green and Srinivasan, 1978, Louviere, 1979; Louviere, et al., 1981; Louviere, 1983); or (5) normative approaches such as the Analytic Hierarchy Process of Saaty (1980).

The foregoing approaches have obvious limitations for complex multiattribute problems, which we shall define as those problems involving at least 10 or more attributes at various numbers of levels. Although one may argue that such problems are unrealistically large, it is nonetheless the case that many problems of managerial interest involve such complexity. Two examples of such problems which motivated the development of a new approach are as follows:

(1) A major public utility company receives many varied complaints about its services and can take a large number of different actions to ameliorate the complaints - management wishes to prioritize a long list of candidate actions; each action may be thought of as a different variable or attribute or each action will impact a variable or attribute.

(2) A major computer hardware or office equipment manufacturer produces a very complex product which involves much more than the actual hardware. The company seeks information on configuring or positioning product(s) which will be used to coordinate the activities of several divisions of the company such as a) Product Production, concerned with configuring hardware, b) Repairs/Maintenance, concerned with keeping the equipment operating properly, c) Billing and charges, concerned with accurate, fair and/or competitive accounting, d) Finance, concerned with arranging terms for the equipment or the lease, and e) Installation, concerned with delivery and installation schedules and procedures. Changes in the product or service which result from actions taken in each of these areas will be traded off against one another by potential customers when viewing the whole system. The number of attributes which are potentially relevant to this issue is very large and logically suggest a wholistic approach which would integrate the consequences of actions taken in any one area into an overall perspective.

It is sufficient to note that there are many research problems which could benefit from an approach which permits a researcher to examine the simultaneous effects of a large number of attributes.

The remainder of the paper, therefore, is organized as follows: In the next section we develop the conceptual background for the approach and the necessary experimental conditions to implement it; we then discuss the results of a laboratory experiment designed to test the basic ideas; and finally, we discuss questions related to limitations, future research, and implications of the approach.

CONCEPTUAL BACKGROUND

In much applied research employing factor analysis, multidimensional scaling, or related techniques it is frequently assumed (at least implicitly) that a number of related attributes can be collapsed mathematically into a reduced number of more basic or at least composite dimensions. While we do not necessarily endorse this methodological approach, it is at least conceptually similar to our proposed approach. We suggest that for many JDM problems individuals might organize the attributes of alternatives into clusters or sets and then evaluate some property of each of the sets to reach some overall judgment about each alternative. Such grouping into sets represents a cognitive simplification strategy and would enable individuals to consider a larger set of attributes than might be possible if he/she had to deal with all of them simultaneously. In order to study this process and to take advantage of the experimental economies that are possible if it is approximately true, we propose a hierarchical experimental method outlined in this paper.

Frequently the attributes of interest in a commercial research problem will be amenable to logical grouping a priori. Let us consider this case in detail to outline the approach. Suppose the attributes can be categorized into logical groups on the basis of an organization's areas of operation. Let there be G groups, each corresponding to a single area of management responsibility. Within each of the G groups let there be ai(i=l,., g,...,I) attributes. Let each of the G groups be defined by the attributes and their levels/range. Let each of these G groups of attributes map into a judgment dimension such as, "how good/bad is this combination of levels of these attributes?" Let each of the G groups therefore have levels defined by the judgments about 'how good/bad is this combination of these attributes?" Let each of the levels of the G groups map into an overall judgment dimension such as, "how likely are you to choose this alternative?" Figure 1 outlines these ideas more explicitly.

FLOWCHART OF PROPOSED HIERARCHIACAL JUDGMENT PROCESS

The idea therefore is to group the attributes into logical or at least useful subgroups which are either meaningful to the individual or actionable by management or both. For example, one could use factor analysis or multi-dimensional scaling procedures to determine sets of attributes, and then use these sets as the basis for the hierarchical task. As Figure 1 indicates, each subgroup contains a number of attributes which the individual must integrate into some judgment dimension relevant to the overall judgment task. After judging the attribute profiles in each subgroup, the individual is presented with treatment combinations of judgment scores on each subgroup dimension. That is, the individual integrates levels of judgments or scores on the G separate subgroup response dimensions into a single, overall dimension of primary research interest (e.g., "How likely are you to choose this alternative?")

Functional Measurement (Anderson 1974, 1981, 1982) or Judgment Policy Capturing (Hammond, et al., 1975) are multiattribute judgment methods which are compatible with this task structure. Both Functional Measurement and Judgment Policy Capturing are judgment paradigms which rely on combinatorial experiments and numerical ratings scales as response modes. Both rely upon general linear models assumptions to develop and test various algebraic specifications of the cognitive processes involved in judgment. The hierarchical task structure requires that the algebraic judgment models for each subgroup of attributes must map into the numerical levels or scores of the subgroup response dimension (e.g., a 0-10 category scale). Hence, a fixed numerical scale is required, which can be approximated by Functional Measurement or Judgment Policy Capturing methods.

Algebraically, we require the following to hold:

R = g(X_{1}, X_{2}, ..., X_{G}), (1)

X_{1} = f_{1}(A_{1}, A_{2}, ...A_{a1}),

X_{2} = f_{2}(A'_{1}, A'_{2}, ..., A'_{a2}), (2)

...

X_{G>} = f_{G}(A"_{1}, A"_{2}, ..., A"_{aG}),

where

R is the evaluative dimension of primary research interest. It is defined over the subgroup response dimensions (X1, X2,...,XG)

X1, X2, . . ., XG are the G subgroups response dimensions. These variables are measured in units of a predefined response scale (e.g., a 1-10 scale) used in each of the subgroup experiments as appropriate.

X1, X2, ..., XG are fixed levels of the G subgroups' response dimensions varied experimentally in the overall design. Although on the same scale as X1,X,... ,XG they are not taken from the subject's responses; they are fixed in advance by the researcher.

A1,A2,...,AZ are the various sets of different attributes which define each of the G subgroups. The unprimed, primed, and double primed A 's represent different attributes but the same attribute could appear in several of the G subgroups.

g,f1,f2,...,fG are different mappings appropriate to approximate the relevant overall and subgroup JDM processes.

There are a number of possible structures which are represented by the mappings g,f1,f2,...,fG, a next section we consider the consequences of a few reasonable combinations for the case of two subgroups of attributes and two attributes per subgroup.

SOME ALGEBRAIC CONSEQUENCES OF HIERARCHICAL JDM PROCESSES

A. All Functions Additive and Linear

We consider the simplest assumption first because it might be expected to be a reasonable first approximation (Dawes and Corrigan, 1974; Wainer, 1976; Anderson and Shanteau, 1977), and because it can be easily implemented via orthogonal, fractional factorial, main-effects plans if "true". That is, we require:

EQUATION (3) , (4) , (5) , (6)

where all terms are as previously defined. Equation 6 states that if all processes are additive and linear, the attributes combine by means of a simple linear and additive process.

B. The Overall JDM Process Non-Additive and Linear, and the Subgroup JDM Processes Additive and Linear

The overall process may be non-additive while each of the sub-group processes may be compensatory (see, e.g., Anderson, 1972, 1974, 1981; Einhorn, 1970, Green and Srinivasan, 1978). This process may be expressed as:

where all terms are as previously defined.

We assume that errors across each task are uncorrelated with mean zero; we also assume that the errors in (8) and (9) are independent of the levels in (7). Because the tasks are completed separately from one another these assumptions should be satisfied. This permits us to concatenate (7), (8), and (9) to derive the reduced form in (10) by elementary substitution and collection of terms:

where all terms represent combinations of previously defined terms. Adding this simple bit of complexity in the overall judgment process leads to considerable complexity in the combined, reduced form equation (10). In particular, substitution of equations (8) and (9) into equation (7) predicts that the attributes within each subgroup will interact with those of the other subgroups, but will not interact with those attributes within subgroups.

By logical extension and with similar assumptions about the various error terms, we can treat the case of (C) the overall equation additive and linear and the subgroups non-additive and linear: interactions occur only within and not between subgroup attributes. Case (D) is the overall equation and the subgroup equations all nonadditive and linear: interactions exist between all attributes in this case. It is important to note that the particular pattern of effects uniquely diagnoses the reduced form equation just as in normal applications of Functional Measurement (see, e.g., Anderson, 1981).

Hence, it is possible to test whether one obtains the same results from a full profile compared with a hierarchical processing experiment by running a full profile experiment concurrently with a hierarchical experiment: the diagnostic results and parameters should agree, although as we suggest in the discussion section, it is unclear whether lack of agreement would constitute a rejection of hierarchical processing because the cognitive processes may be different. We illustrate such a test in the next section.

TEST OF COMPARABILITY OF FULL PROFILE AND HIERARCHICAL PROCESSING

Experimental Details

In order to test whether empirically equivalent results could be obtained from a hierarchically structured judgment task compared with a traditionally structured 'full-profile' conjoint judgment task an experiment was devised in the following manner: (1) The object of interest was a new long-distance telephone service which competes with the Bell System. These systems have several cost and service components; three aspects of service and three cost components were selected as attributes. These six attributes and their levels were: a) installation charge ($10, $30), b) monthly rental or service fee ($2, $4), c) cost per call (discount of 15% or 45%), d) security and ease of use (the system is directly wired, or you require an access phone number with a personal code), e) billing and charges, accuracy and error correction (wrong numbers and errors corrected after billing, or corrected by operator and after billing), and f) can the system be used away from the installation (yes, no).

104 upperclass undergraduates in four different sections of a marketing research class at the University of Iowa were randomly assigned into the following three task conditions:

(1) Hierarchial Condition: The cost attributes and service attributes were separated into two subgroups, and an overall cost by service design was used to link the responses to the two subgroup designs with the desired overall response, i.e., 'likelihood of acquiring the service.' The three designs were structured as follows: i) the costs design involved the complete factorial of all three cost attributes at two levels. Subjects were requested to Judge 'how good a long distance telephone service would be with these cost levels' on a 0-10 category scale. The first two profiles were end anchors with either all higher or all lower costs than the combinations in the 2 ; their purpose is to avoid floor and ceiling effects in the use of the category scale. ii) the service design was identical in all respects to the cost design, except that subjects judged 'how good a long distance telephone service would be with these service levels' on a zero to ten category scale. iii) the overall design was a 3x3 factorial, consisting of levels (2,5,8) of 'how good' the cost and service levels were of a long distance telephone service described by the attributes used in the costs and services subdesigns. Hence, the category response scale used in the subdesigns determines the levels in the overall design. In the overall design, subjects responded on a zero to twenty category 'likelihood of purchase' scale. The ends of this scale (zero and twenty) were defined respectively as 'I am absolutely certain I would not acquire' and 'I am absolutely certain I would acquire;' the midpoint (10) was defined as 'there is a fifty-fifty chance that I would or would not acquire.' This response scale was identical to the response scale used in the full profile experiments.

(2) Two Full Profile Conditions. The complete 26 was divided into two 1/2 fractions of 32 treatments each (Hahn and Shapiro, 1966, Experimental Plan 5c, Master Plan 9) in which all main effects and two-way interactions are independent of each other and of three-way interactions, but are confounded with four-and five-way interactions. Subjects in these two conditions judged 34 profiles of all six cost and service variables - the first two profiles were end anchors consisting of all costs at high (low) and all services at less (more) preferred levels. The more and less preferred levels were identified from class discussions. Subjects judged each profile of the cost and service levels on the zero to twenty category 'likelihood of acquiring the service' scale described at the end of condition (1) above.

Although six attributes may not seem to be a complex multiattribute problem, it would be difficult to run complete full profile task with more than six attributes. In particular, eight or ten attributes each at only two levels would require 256 or 1024 treatments for a complete test. If one were willing to sacrifice information (ant make assumptions) about high order interactions, it would be possible to design tests in 64 or 128 treatments (see, e.g., Hahn and Shapiro, 1966). However, these are still large tasks, demanding of respondents. Hence, for a preliminary comparison of full-profile and hierarchical tasks we felt six attributes were sufficient. We have conducted applied work with the hierarchical approach using up to 30+ attributes; it is obviously difficult (if not practically impossible) to compare such tasks with full-profile tasks. So, for the present, compromise tasks appear to be necessary to study the comparative strengths and weaknesses of hierarchical and full-profile approaches.

ANALYTICAL DETAILS

There are two main concerns in analysis of the judgment data from the three conditions: (1) Developing a reasonable approximation to the "appropriate" functional form of the group judgment equation, and (2) Using the approximation to scale the levels of the attributes in the overall response metric. A general hypothesis is that a reasonable approximation would be a multilinear model (Anderson, 1981; Louviere, 1979; Lerman and Louviere, 1978). The additive motel, of course, is a subset of the general multilinear form, and hence, can be rejected if incorrect. As demonstrated in Louviere (1979), so long as any subset of the general multilinear form holds, the marginal response means of the levels of the attributes are the "appropriate" scale values to be estimated. So, in actual practice, it may make little real difference in prediction if the functional form is misdiagnosed, so long as the scale values are accurately recovered (see, e.g., Dawes and Corrigan, 1974).

In order to develop a reasonable algebraic model to approximate judgment data we use a multiple linear regression analog to repeated measures analysis of variance as the principal analytic device. As demonstrated by Anderson (1974, 1976, 1981) and Lerman and Louviere (1978), analysis of variance or its regression analogs serve as an error theory to diagnose/test various forms of multilinear judgment models. We employ this procedure to develop the aggregate judgment models for the full profile and hierarchical tasks. The specifics of the analyses are as follows:

(1) Regression equations were estimated for each subject in both full profile experiments. Because main effects and two way interactions are independent of each other and of three way interactions, we estimated all main and two way interaction effects for each subject. The largest and most meaningful interactions are usually the two way interactions; hence, estimation of the two-way terms provides a strong, although inconclusive test for non-additivities. The experiments are repeated measures designs; hence, the appropriate tests are the t-tests (or F equivalents) derived by computing the ratio of the mean of each coefficient relative to its standard error across the subjects.

(2) Regression equations were estimated for each subject for each of the three hierarchical tasks. These regression results permit calculation of exact tests for each main and interaction effect in each of the three factorial designs in the hierarchical condition. Hence, inferences about the significance of effects can be made for each factorial design in this condition by computing the ratio of each mean coefficient relative to the estimated standard deviation of the sampling distribution (cr// n) across the subjects. This ratio is distributed as t (or F = t2) and may be tested in the usual manner

Analytical Results

(1) Single Subject Regressions for Full-Profile Experiments

In the first analysis we pooled the regression results over all subjects in both full-profile conditions because the designs are mirror images. Results contained in Table 1 indicate that the only significant two-way interactions involve cost per call (discount) and how errors in billing or wrong numbers are handled. These interactions were graphed and the graphical results indicated that the departures from additivity were generally quite small. It is not possible to tell whether the departures are real, or reflect precision of the estimate, or are the result of experimental flaws. We conclude from these results that there are apparently reliable interactions in the group data for both sets of full-profile judgments.

Each of the two sets of full-profile judgments were analyzed separately to see if we could eliminate differences in the designs as a factor in the interactions. We were surprised to find that the interactions were not reliable: There were several significant interactions in each 1/2 fraction but the interactions were not the same in the two fractions. We then conducted a post-hoc analysis on other available measures to see if the two groups of subjects were different

Subjects answered a standard set of socio-demographic questions plus questions about their use of long distance telephone service. No differences were found between the subjects in the three conditions on any of the measures observed: a multiple discriminant analysis indicated that the three groups could not be reliably discriminated among on the basis of any of the survey measures. This result suggests that the differences may be due to statistical differences between the two fractions; those differences should not exist, however, because the fractions are mirror images.

We next analyzed a set of eight full-profiles which are a 1/8 fraction of the 2 in which main effects are estimable assuming negligible interactions. All three conditions responded to this fraction as a warm-up task to acquaint them with the attributes and their range. This fraction was administered in lieu of practice trials. Univariate statistical results indicated no reliable differences between the two full profile groups, but a reliable difference for four of the eight treatments between the hierarchical subjects and the full-profile subjects. discriminant analysis further confirmed the significant differences due to the responses of the hierarchical subjects.

These tests suggest that the interaction results are not reliable in the two full-profile groups and are related to between-condition effects which cannot be determined from these experiments. Hence, we tentatively conclude that despite the presence of significant interactions in the pooled data from both full-profile conditions, we cannot reject a simple additive hypothesis.

(2) Single Subject Regressions for Hierarchical Experiments

There are three sets of results - one for each subtask; they are contained in Table 2. Let us consider each in turn: (a) Costs Subtask: results indicate only one significant (at .05 level) interaction in addition to significant main effects (monthly rental fee by cost per call). (b) Services Subtask: results indicate no significant interactions, although all main effects are significant. (c) Overall Costs by Service Task: results indicate two of the four interaction components are significant (at the .05 level) and all main effects are significant.

These results suggest that costs and services interact, but the interaction is not large, a result confirmed by graphing the data. The costs by services interaction appeared to be localized in the costs = 5, services = 5 point. This combination was the first to appear after the two end anchors (0,0,0;10,10,10) and is probably an ordering effect. Future work should examine this by using end anchors, fillers and practice trials to see if the effect disappears. Similarly, the discount by monthly fee interaction in the costs subtask appears to be very small. We suggest that these interactions are likely to be due to failure to use practice trials and fillers. Future work should examine these hypotheses.

RESULTS OF SINGLE SUBJECT REGRESSIONS FOR HIERARCHICAL TASKS (N = 33).

A tentative conclusion, therefore, is that the process appears predominantly linear and additive over the ranges examined. Although the quadratic components of the main effects are significant it was clear from the interaction graphs that the non-linearity was very slight, however reliable. A tentative conclusion, therefore, is that we cannot reject the additive hypothesis for these judgment data, a conclusion similar to that reached in the full-profile condition.

(3) Estimates of Scale Values and Their Cross-Task Comparison

Both the full-profile and the hierarchical judgment tasks are variations of Functional Measurement tasks (Anderson, 1981; Louviere, 1982). A great many judgment processes can be approximated by some subset of the general multilinear model form; the statistical results from both the full-profile and hierarchical conditions are consistent with one of the subset models regardless of whether the interactions are real or not. Hence, the marginal means from the various conditions are the objects of scaling interest, as demonstrated by Lerman and Louviere (1978) and Louviere (1979).

The hierarchical condition does not directly yield marginal means which are comparable to the full-profile results. They must be predicted from the composite hierarchical model derived by concatenating the subtask and overall task models. The regression results for the hierarchical tasks are as follows:

Overall Judgment

= -1.83 + .99 Services Score + 1.15 Costs Score (11)

Costs Score

= 4.91 - .09 Installation Cost -.35 Monthly fee + .12 Cost Per Call (12)

Services Score

= 3.80 + 1.41 Security/Ease of Use -.83 Billing Errors + 2.85 Use Away (13)

By elementary substitution, expansion, and collection of terms we have:

Overall Judgment

= 7.58 - .10 Installation Cost -.40 Monthly Fee + .14 Cost Per Call + 1.40 Security/Ease of Use - .82 Billing Errors + 2.82 Use Away. (14)

The marginal means predicted from the composite model are contained in Table 3. Results indicate that the marginal means from the hierarchical task are significantly linearly related to the marginal means of the full-profile conditions. Indeed, the slope is approximately unity for the condition two, full-profile task; for the pooled full-profile tasks; and for the 1/8 fraction used as practice. The non-zero intercept indicates that the hierarchical scales tend to be separated from the full profile condition scales by an additive constant. Except for the means for use away from home, all other predicted means generally lie below the corresponding pairs of full-profile means. It is clear that the hierarchical equation could recover the full-profile data well, except for the intercept.

We tentatively conclude that the hierarchical condition yields scale values related to those of the full-profile condition by a linear transformation, a permissible transformation with interval scales. It is also possible that the scales are equivalent up to addition of a constant; future research should examine this question.

DISCUSSION AND CONCLUSIONS

This paper has proposed, described and tested a new method for dealing with complex multiattribute problems. The approach requires an analyst to develop a priori groupings of sets of attributes. These sets may be derived from theoretical considerations, empirical findings, or the ad hoc needs of a research project. Empirical work to date has relied upon ad hoc groupings of attributes into sets on the basis of either functional areas of operation of a firm (e.g., customer services, billing and charges, etc.) or common sense/logical divisions such as costs and services" used in the empirical example reported in this paper. We are uncertain how sensitive the results are to choice of grouping scheme. Hence, research is needed to determine whether the method used to select the groups or whether changing the sets of attributes within the groups will significantly affect the final results.

COMPARISON OF ESTIMATED SCALE VALUES

The paper considered several different types of possible functional specifications which may arise in applications of the method: (1) additive and linear (2) nonadditive and linear. These specifications can apply to the subgroup relationships or the overall relationship or both. Non-linearities can also be accommodated in a manner analogous to current practice in Functional Measurement (Anderson, 1981; 1982) or Judgment Policy Capturing (Hammond, et al., 1975). That is, if attributes with more than two levels are used, the possibility of non-linearities arise; such non-linearities can be specified in the usual way as a multiple regression or analysis of variance effect and included in the derived specifications, if appropriate.

Currently, the efficiency properties of the overall estimates are not known, although consistency should hold because each subgroup results and the overall result are assumed to obey classical general linear models assumptions regarding error distributions. There is no reason to believe that errors associated with subgroup judgments are related to overall judgments because of the structure of the experimental tasks. Hence, a zero error expectation and uncorrelated errors across tasks insure consistent estimates for the concatenated overall model.

Empirical support for these assumptions was provided by a comparison of parameter estimates from a 2 full-profile ratings task with estimates from a parallel hierarchically structured task. Parameter estimates from the hierarchical task were linearly related to those from the full profile task - the requirement that both sets of interval scales must meet to be considered equivalent. Because a rigorous comparison of both methods requires the use of a full factorial design (or at least a high order fraction) for the full profile task, comparisons must be limited to small numbers of attributes, probably each at two levels.

Moreover, we are uncertain whether such comparisons are empirically meaningful because the cognitive processes involved in a hierarchical task may be different from those involved in a full-profile task. If this is true, it then becomes an empirical question as to which is a better approximation to the "true' but unknown process of interest. So, comparisons with full-profile tasks may actually be counterproductive because the comparison assumes that results from full-profile tasks are 'right," and therefore the hierarchical task should be able to reproduce the same results. The resolution of this issue awaits further research beyond the scope of this paper.

This paper mate the tentative suggestion that hierarchically structured tasks offer a potential solution for complex multiattribute tasks. Additional research will be needed to determine all of the limitations as well as the advantages of the approach. Of particular importance are questions about parameter efficiency for the overall model(s), and of the effects of various ways of grouping attributes into sets for respondent evaluation. Despite these caveats we believe the approach to have sufficient promise to warrant further investigation and we offer it as a viable alternative to current methods for complex multiattribute problems. We have applied the method to several commercial problems of considerable size and have found it easy to apply in the field either using personal interviews or mail surveys. The results thus far give no indication of systematic bias or related problems. However, to date external validity has not be examined, although this is planned for the future. Thus, this paper should be viewed as a tentative suggestion that the approach is a logical decomposition of complex decision problems which has yet to be fully tested.

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