Management consultancy: The right approach — Ian Angell's billion dollar question

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    Management Consultancy: The Right Approach - Ian Angells Billion Dollar Question Benedict Seifert Senior Lecturer, Computing and Management Information Systems EAP European School of Management, Oxford

    B en Seifert believes that Ian Angells objections to the use of mathematical logic as a strategy in solving business problems are misconceived. Modelling, which can cope with many business situations, and embraces degrees of complexity, uses mathematical logic. Alternative logics may be a chimera.

    The last decade has seen a truly monumental financial investment in operations research, decision-support systems, management information systems, applied artificial intelligence systems, etc., with literally billions of pounds invested and armies of specialized executives, management consultants, and information engineers making lucrative careers based on the idea that the mathematical-analytical approach to business and management problems has a crucial role to play in making management more efficient and cost- effective. The logical-analytical approach to business is increasingly being applied not only to routine data- processing tasks, but to such sophisticated problems as airline scheduling or predicting the prices of bonds. Why, even the London School of Economics has created a chair in Information Systems, and not, I believe, in medieval witch-craft, presumably in the belief that that purest of products of the mathematical mind-set, the computer, is more useful to economic decision-makers than black magic. It is precisely in vielv of this that the question posed by Professor Angells bold challenge to this approach is so interesting: is the mind-set of mathematical logic which is pervading management techniques appropriate in the area of business decision making?

    By means of his analysis of the prison wardens IQ

    test. Ian Angell contends that simplistic logical view of the world, the rigid type of thinking are inadequate for management, and indeed can be harmful. He advocates the existence of alternative logics, for instance the logic of the lawyer, of the gambler, and the observer of human nature, whose use will be more advantageous to the prisoner than the application of logical analysis. Of course, this view raises many questions. One might ask, for instance, what criterion should be used to select one of these competing logics when faced with a particular problem. Under what circumstances, for instance, should a firm call in management consultants, and when might it be more advisable to consult President Reagans astrologer or Professor Angells disbarred lawyer? I do not wish to discuss this dilemma, for I believe the assumption from which this dilemma arises, namely the existence of a menagerie of competing logics to be profoundly mistaken.

    So what is the role of the mathematical-analytical approach in business? I would argue that in business, as in every-day life, there are many situations in which the remarkable ability of the trained human mind to discern patterns, to invent and to perceive are far superior to the capacities of even the most powerful computer to digest information and make a decision. Artificial intelligence research has come up against very severe limitations of present-day computing technology in this regard. Much of what is known as entrepreneurial ability consists in that kind of non- deductive intelligence, which, at the moment, cannot be taught to a computer. It is true in this sense that the manager who relies exclusively on formal, rigorous models which can be implemented on a computer would not operate successfully in the world of business. However, in these situations, what is called for is not the application of some alternative logics, but the workings of an imaginative mind which are at present not captured by any academic description or category like those which Professor Angel1 proposes. The decision to diversify into a new line of business, for instance, is often of this kind, and indeed all decisions in which the essential unpredictability of the external world are more important than the known and predictable environment of a firm which is trying to carry out a particular, complex task more efficiently, or operating in a largely familiar market.

    However, in any reasonably large organizations, there are situations which can in fact be modelled, and in which the unaided intelligence of even the most brilliant human mind are hopelessly inadequate, but where logical and mathematical modelling, as implemented on a digital computer are immensely useful. Apart from the rather routine aspects, of such applications familiar to all managers (for instance, data bases), there is now a growing body of techniques

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    which would be immensely useful to management if only they were aware of them. Unfortunately, many traditional, accountancy based management consultancy firms are slow in discovering and adapting this technology. But the point I wish to stress here is that, in those situations which are susceptible of modelling, such as the one Professor Angel1 proposes, there is only one valid system of logic, which allows to arrive at conclusions which are precisely as good as the hypotheses from which they are derived (I am of course aware of intuitionistic and other restrictive systems of logic, but for the purposes at hand these distinctions are of no importance). I do believe, however, that most situations arising in the real world which managers have to deal with, can only be modelled approximately. For this reason the conclusions drawn from the model must be treated with great care, lest the simplification involved in making the model might lead one seriously astray. The great interest of Professor Angells article consists in having chosen what appears to be a very straight- forward idealized example of decision-making, far more susceptible to rigorous solution than the great majority of business problems arising in the real world, but which none-the-less provides pretty traps for the naive practitioner of model-making. As I shall spell out in an appendix, Professor Angells alternative logics are only different models of the prisoners dilemma, which he then analyses by using precisely the same rigid mathematical reasoning as the one he criticizes. (The only exception to this is his disbarred lawyer - a disbarment which is hardly a great loss to his profession, for no jury would accept the idea that the listing of all possible answers to a question constitutes an answer.) Thus the only legitimate lesson, and a most important one which can be drawn from Professor Angells analysis, is that a real-world situation may not be adequately described by the most simple-minded axiomatization that may spring to mind at first. The correct model may be too cumbersome to state or too difficult to analyze to be of any use. The simplification one can deal with may or may not be adequate to give the right solution. While this is a point one finds systematically ignored in text books on DSS, etc., it is a very important one. However, this same point applies to physics and biology, two areas in which the mathematical mind-set has none the less been spectacularly successful.

    Clearly there is a hierarchy of complexity, from physics, dealing with comparatively simple systems, such as atoms, gases, or solids with well defined and fairly homogeneous interactions, to biology with its macro-molecules and physiological systems of enormous complexity, to human beings interacting in an economic system, such as a firm interacting with other firms, which is the theatre in which the manager needs to operate. There is a corresponding hierarchy

    of difficulty in understanding these systems. However, there is no reason to believe that mathematics can not play an equally important role in the analysis of decision making and other economic processes as has been the case in physics. Indeed, the successful application of mathematics to such well known problems as combinatorial optimization, scheduling problems, etc., and the computerization of business in general give some idea of the power of rigorous mathematical thinking in business. I believe it is right to be extremely rigorous and critical in the manner in which models are made in this area, but extremely dangerous to confuse this point with the ill-conceived invention of alternative logics when the tried and tested logic which has proved itself in other areas of human thought is the only road to success, even though it is not always easy to apply it competently.

    This point has been amply demonstrated by the successful application to such problems as scheduling and production problems of computing and mathematical techniques such as linear programming and combinatorial optimization. With some of my collaborators at Oxford University and the European School of Management. I have myself been extending some known techniques in this area to new and exciting business problems. We often find that there are beautiful and surprising analogies between problems arising in engineering, and indeed physics, and problems with which we are confronted in our contacts with businessmen dealing with problems arising in their day to day management problems.

    Appendix. Modelling the Prisoners Dilemma

    I refer the reader to Ian Angells preceding article for a statement of the brain-teaser about the prison warden.

    (i) The expected 1 t so u ion. The idea behind this solution is the following simple consideration. Suppose it is known that the prison warden has pinned white disks on two of the prisoners. Then, in view of the fact that there are only two white disks in all, the third prisoner must have a black disk on his back. The argument then goes that any one of the three prisoners, say prisoner 1, with their black disks envisages the partial information known to his fellow prisoners under the assumption that he himself has a white disk: white-?- black. This yields the two possibilities, say for prisoner 2: white-white-black and white-black-black. Prisoner 2 now infers the information available to prisoner 3 on both hypotheses: white-white-? and white-black-?. The first of these possibilities completely determines the disk on 3s back, namely black. Hence, and this is the crux of the matter, 2 is supposed to assume that 3 will


    correctly infer that this is so, and give black as his own colour, winning release.

    Professor Angel1 now goes on to argue that this mathematical-logical approach is in general less suitable than alternative logics which he then goes on to describe.

    My first observation, and my purpose in spelling out the solution above in detail, is that the conclusion above is not just based on the simple combinatorial enumeration above, but on implicit assumptions about the psychology of the fellow prisoners. Hence it is simply wrong, as a matter of logic, to deduce from the hypotheses given, that 1 is bound to have a black disk on his back. Indeed a moments thought would convince anyone that the fact that 3 does not give the answer black in no way implies the colour on ls back. As Ian Angel1 fully realizes, no logical conclusion can be drawn from the silence of 2 and 3 without additional hypotheses about their psychology, speed of reflection, etc. As the answer is thus in no way a conclusion logically arrived at, the defect of this solution in no way invalidates the logical- mathematical mind-set, but only serves as a welcome reminder that logic, like other tools, must be handled competently to be of use.

    On the other hand, the alternative logics advocated by Professor Angel1 turn out to be nothing of the sort. For instance, the student of human nature actually engages in the following perfectly logical consideration:

    Assuming that the prison warden wishes to confront each of us with identical situations, in order to get an unbiassed opinion of our intellect, then, given that there are three of us, and that black is the only colour of w,hich there are three disks in his possession, he is forced to pin black on each of our backs.

    If the prisoner is as shrewd about human nature as Ian Angel1 makes him out to be, he will of course realize that the assumption about the prison wardens psychology is actually rather risky. Far more likely, one might think, that the prison warden, like many a vice- president for personnel at one of our companies, has actually made up the I.Q. test only as a pretext for

    freeing his favourite prisoner in order to impress the Home Office with his fair play. So, if there is anything shrewd at all about his example, it surely is the logical deducation from the assumption about the prison warden, But that deduction is a (very trivial) mathematical and not a psychological one.

    The same point can be made about Professor Angells gambler. Again, it is not the decision to gamble that is clever, it is the method, logical deduction, in which he attempts to deduce the best course of action from the ones available to him.

    As mentioned above, the hapless debarred lawyer lives up to his disreputable past, without the slightest chance of being the one who will go free.

    The real lesson from Ian Angells example is really this: Anyone wishing to act rationally, by following the one and universal logic which has ever been shown to apply to the real world, in whatever domain, must first take great care in correctly modelling the situation at hand. He may find, for instance, that he needs to model the uncertainty of the external world - his competitors, his creditors, taste, interest rates, etc. He needs to be sure that the simplifications of the model, which are necessary if the model is to be more enlightening than the messy real-world situation in the first place, do not significantly alter the optimal solution selected. He must be sure that time, when ignored in the model, is indeed immaterial, etc. While the process of dealing with the model is a science, in which applied mathematics and computer science play the chief role, the construction of the model itself is a delicate art, in which the mathematician, unaided by common sense and experience, is likely to go astray. But, as one sees very often in business, insufficient skills in dealing with it are quite as likely to lead astray as inadequate care in building a formal model. Most frequently of all one meets managers who prefer to muddle along without giving any systematic thought about how one might improve efficiency. They often flatter themselves that, as practical men and women, they intuitively find the best possible solution without going through the rigmarole of logical thought. More often than not, their companies and share-holders pay the bill for this attitude.