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correspond to nice mathematical properties, abstractly considered. Thus convexity is not posited and its implications explored; rather a change of search space is posited and the problem statement that admits it sought.
A single ancestral lineage should not be expected. Just as theorems can have many proofs, so methods can have many decompositions of their information. In fact, in one respect at least the line represented by M2 and M3 does violence to SM. It never recognizes the shift of problem into a set of equality constraints with the consequent change in dimensionality. Thus, the g's and the x's are handled separately, whereas it is a very distinct feature of the simplex procedure that it handles them uniformly. One could easily construct another line starting from SM, which would preserve this feature. (It would face a problem of making the transition to M1.)
The examples selected—linear programming and matrix inversionare certainly ones that seem most amenable to the kind of analysis we have proposed. If we considered methods, say, for determining inventory levels, the story might be different. Nevertheless, perhaps the case for continuity between weak and strong methods has been made plausible.
5. HUMAN BEHAVIOR IN ILL-STRUCTURED PROBLEMS
In the two issues discussed so far—the existence of weak methods, and the continuity between weak and strong methods—we have not seemed to be dealing directly with ill-structured problems. To re-evoke the concern of Reitman, the problem statements that we have exhibited seem quite precise. (Indeed, we took pains to make them so and in a more technical exposition would have completely formalized them.) According to our hypotheses the world is always formalized, seen from the viewpoint of the methods available, which require quite definite properties to operate. A human problem solver, however, would not feel that a problem was well structured just because he was using a method on it. Our second hypothesis identifies this feeling with the low power of the applicable methods.
The concern just expressed is still well taken. If we examine some problem solvers who are working on “really ill-structured” problems, what will we find? They will necessarily be human, since as noted earlier, men are the gatekeepers of this residual class of problems. Thus we cannot observe their problem-solving processes directly but must infer them from their behavior.
To have something definite in mind consider the following problem solvers and tasks:
A financial adviser: what investments should be made in a new account?
given market to which his firm is considering entry? None of these problems is as ill structured as the proverbial injunctions to “know thyself” (asked of every man) and to "publish or perish" (asked of the academician). Still they are perhaps more typical of management problems than these two almost completely open-ended problems. They do have the feature of most concern to Reitman; namely, neither the criteria for whether a solution is acceptable nor the data base upon which to feed are particularly well defined.
The framework we have been using says that below the surface we should discover a set of methods operating. Our two hypotheses assert, first, that we should find general but weak methods; and, second, that we should not find methods that deal with the unstructured aspects (however they come to be defined) through any mechanism other than being general enough to apply to a situation with little definite information.
Our first implication would seem to be upset if we discover that the human being has available very strong methods that are applicable to these ill-structured problems. This is a rather difficult proposition to test, since, without the methods themselves to scrutinize, we have very little basis for judging the nature of problem solving. Powerful methods imply good solutions, but if only men solve the problem, comparative quality is hard to judge.
The three tasks in our list have the virture that comparisons have been made between the solutions obtained by human effort and those obtained by some mechanical procedure. For the second two the actual tasks are close nonmanagement analogs of the tasks listed. However, they all have the property (implicit in our list) that the problem solver is a man who by profession is concerned with solving the stated type of problem. This condition is important in discussing real management problems, since the capabilities of a novice (e.g., a college student used as a subject in an experiment) may differ considerably from those of the professional. In particular, the novice may differ in the direction of using only very general reasoning abilities (since he is inexperienced), whereas the professional may have special methods.
In all of the cases the result is the same. Rather simple mechanical procedures seem to do as well as the professional problem solver or even better; certainly they do not do worse.
The first task was investigated by Clarkson (1) in one of the early simulation studies. He actually constructed a program to simulate a trust investment officer in a bank. Thus the program and the human being attain the same level of solution. The program itself consists of a series of elementary evaluations as a data base, plus a recognition structure (called a discrimination net) to make contact between the specific situation and the evaluation; there are also several generate-andtests. Thus the program does not have any special mechanisms for dealing with ill-structuredness. Indeed it deals with the task in a highly structured way, though with a rather large data base of information. The key point is that the human being, who can still be hypothesized to have special methods for ill-structured situations (since his internal structure is unknown), does not show evidence of this capability through superior performance.
The second task in its nonmanagement form is that of clinical judgment. It has been an active, substantial-and somewhat heated-concern in clinical psychology ever since the forties. In its original form, as reviewed by Meehl (12), it concerned the use of statistical techniques versus the judgments of clinicians. With the development of the computer it has broadened to any programmed procedure. Many studies have been done to confront the two types of judgment in an environment sufficiently controlled and understood to reveal whether one or the other was better. The results are almost uniformly that the programmed procedures perform no worse (and often better) than the human judgment of the professional clinician, even when the clinician is allowed access to a larger "data base" in the form of his direct impressions of the patient. Needless to say, specific objections, both methodological and substantive, have been raised about various studies, so the conclusion is not quite as clear-cut as stated. Nevertheless, it is a fair assertion that no positive evidence of the existence of strong methods of unknown nature has emerged.?
The third task is really an analog of an analog. Harris (7), in order to investigate the clinical versus statistical prediction problem just discussed, made use of an analog situation, which is an equally good analog to the marketing problem in our list. He tested whether formulas for predicting the outcome of college football games are better than human judgment. To get the best human judgments (i.e., professional) he made use of coaches of rival teams. Although there is a problem of bias, these coaches clearly have a wealth of information of as professional a nature
A recent volume (10) contains some recent papers in this area, which provide access to the literature.
as the marketing manager has about the market for his goods. On the program side, Harris used some formulas whose predictions are published each weck in the newspapers during the football season. An unfortunate aspect of the study is that these formulas are proprietary, although enough information is given about them to make the study meaningful. The result is the same: the coaches do slightly worse than the formulas.
Having found no evidence for strong methods that deal with unstructured problems, we might feel that our two hypotheses, are somewhat more strongly confirmed. However, unless the weak methods used by human beings bear some relationship to the ones we have enumerated, we should take little comfort. For our hypotheses take on substantial meaning only when the weak methods become explicit. There is less solid evidence on what methods people use than on the general absence of strong methods. Most studies simply compare performance, and do not attempt to characterize the methods used by the human problem solver. Likewise, many of the psychological studies on problems solving, although positive to our argument , employ artificial tasks that are not sufficiently ill structured to aid us here. The study by Clarkson just reviewed is an exception, since he did investigate closely the behavior of his investment officer. The evidence that this study provides is positive.
Numerous studies in the management science literature might be winnowed either to support or refute assertions about the methods used. Work in the behavioral theory of the firm , for instance, provides a picture of the processes used in organizational decision making that is highly compatible with our list of weak methods-searching for alternatives, changing levels of aspiration, etc. However, the characterizations are sufficiently abstract that a substantial issue remains whether they can be converted into methods that really do the decision making. Such descriptions abstract from task content. Now the methods that we have described also abstract from task content. But we know that these can be specialized to solve the problems they claim to solve. In empirical studies we do not know what other methods might have to be added to handle the actual detail of the management decision.
Only rarely are studies performed, such as Clarkson's, in which the problem is ill structured, but the analysis is carried out in detail. Reitman has studied the composition of a fugue by a professional composer (18), which is certainly ill structured enough. Some of the methods we have described, such as means-ends analysis, do show up there. Reitman's characterization is still sufficiently incomplete, however, that no real evidence is provided on our question.
We have explored three areas in which some positive evidence can be adduced for the two hypotheses. We have an explicit set of weak methods; there is some chance that continuity can be established between the weak and the strong methods; and there is some evidence that human beings do not have strong methods of unknown nature for dealing with ill-structured problems. Now it is time to consider some difficulties with our hypotheses. There are several.
6.1. The Many Parts of Problem Solving
At the beginning of this essay we noted that methods were only a part of problem solving, but nevertheless persisted in ignoring all the other parts. Let us now list some of them:
A single concern applies to all of these items. Do the aspects of problem solving that permit a problem solver to deal with ill-structured problems reside in one (or more) of these parts, rather than in the methods? If so, the discussions of this essay are largely beside the point.
This shift could be due simply to the power (or generality) of a problem solver not being localized in the methods rather than to anything specific to ill-structuredness. The first two items on the list illustrate this possibility. Some problems are solved directly by recognition; for example, who is it that has just appeared before my eyes? In many problems we seem to get nowhere until we suddenly "just recognize" the essential connection or form of the solution. Gestalt psychology has made this phenomenon of sudden restructuring central to its theory of problem solving. If it were true, our two hypotheses would certainly not be valid. Likewise for the second item, our methods say more about the organization of tests than about the tests themselves. Perhaps most of the power resides in sophisticated evaluations. This would work strongly against our hypotheses. In both examples it is possible, of course, that hypotheses of similar nature to ours apply. In the case of evaluations, for example, it might be that ill-structured problems could be handled only because the problem solver always had available some dis