ABSTRACT
Before going into this problem, however, there are certain preliminary steps we must take. In the first place, we must try and indicate the method of representation which we shall choose for our patterns; in the second place, we must elaborate some kind of formal model within which to incorporate our results. Let us take up these two points in that order.The most usual method of describing large numbers of heterogeneous objects in science is by means of some kind of dimensional system in which the dimensions are chosen in such a way that each of them corresponds to one of the principles of heterogeneity present. A homely example may illustrate the point. If we take a random selection of nylon stockings, we shall find that their texture differs considerably, but that all the variability observed can be reduced to two fundamental dimensions. These are, respectively, called denier, or the thickness of the thread, which may very from 15 to 4 5 ? and gauge, which refers to the closeness of the knit. It is measured in terms of the number of stitches across inches. This may vary from 45 to 66. Figure 15 will indicate the resulting two-dimensional system, and I have also included examples of four very commonly found combinations of denier and gauge, namely, the 15/51, 15/66, 30/45, and 30/54 stockings. It will be noted that this method of representation is very convenient because it is graphical; in other words, we can see at a glance where any particular stocking may lie with respect to these two dimensions. The two axes representing gauge and denier have been drawn at right angles, which is the customary way of indicating that these two are quite independent of each other; theoretically, at least, you could have any combination between denier and gauge, although in actual practice, of course, some of these are not used.Another point will be noted. By allocating a given stocking to a certain point on this diagram we have not described it completely. Colour, for instance, is another important variable which is used to characterize the stocking, and if we wanted to include that in our diagram we should have to have a third axis or dimension at right angles to both the other two, i.e. sticking out from the plane of the paper. Even that, of course, would not completely describe the stocking. We should need at least one other dimension, namely, that of size. This dimension again would be at right angles to the other three, but, as we have by now run out of dimensions in physical space, we could not illustrate this four-dimensional model
in any sort of graphical or representative way; it would remain a purely mathematical construction in multi-dimensional space. How can we apply this conception to politics? Let us start with a
Diagram Illustrating Two-Dimension Description of Nylons purely common-sense source of evaluation. It is often said that in the political spectrum Socialists are to the left of Liberals, Liberals to the left of Conservatives, with Communists and Fascists, respectively, constituting the extreme left and the extreme right. In109
terms of dimensions, therefore, we might represent the position somewhat as in Figure i 6a , with one dimension being thought sufficient to represent political parties.On the other hand, it is also sometimes said that there is a considerable similarity between Fascists and Communists; so much so, indeed, that there is very little to choose between them. Both, on this reckoning, are opposed to the democratic parties, i.e. the Socialist, Conservative, and Liberal parties, and some observers (usually Liberals) would add that both the Conservatives and Socialist parties have advanced some way towards the Communist-Fascist outlook, leaving the Liberals, as it were, at the other end of this continuum, which might therefore look something like that indicated in Figure i 6b .Much might be said in favour of both these hypotheses, but clearly they cannot both be true as long as we restrict ourselves to a one-dimensional system. They could easily be reconciled if we accepted a two-dimensional system, as illustrated in Figure 16c, where our abscissa represents our left-right continuum, and our ordinate represents our democratic versus autocratic continuum, as we may provisionally call it. It should be noted, of course, that we are presenting this two-dimensional pattern merely as an heuristic hypothesis, not as a definite fact; it is inserted to indicate the kind of descriptive result which we might obtain from a dimensional study of the structure of opinions and attitudes. So far it merely pictures in diagrammatic form commonly held opinions regarding the relationships between the attitudes characterizing members of these five parties.So far we have thus given a rough common-sense sort of answer to the question of how we shall describe the structuring of attitudes. We must do so in terms of dimensions which are preferably independent of each other, and which can be measured. Can we integrate this demand with the information we have already unearthed in previous chapters, and achieve some kind of model which will help us to translate this projected system into an empirical reality? We can do this by taking note of the fact that attitudes appear to be arranged in some kind of hierarchical system. This was already noted by McDougall, and some of the other writers we quoted in our first chapter, and this notion of hierarchical structure or arrangement will provide us with the necessary hypothesis regarding the model we wish to construct,
Roughly speaking, we can discriminate four different degrees of organization or structure. Right at the bottom we have opinions which are not related in any way to other opinions, which are not in any way characteristic of a person who makes them, and which are not reproducible in the sense that if the same or a similar question were asked again under different circumstances, the
Diagram Illustrating Three Hypotheses Regarding Relative Position of Five Main Political Groups answer might be different. Such purely ephemeral opinions are of no great interest or value; they do not go beyond themselves and they do not throw any light either on the personality or on the ideologies of the people holding them.A higher level is reached when we come to opinions which are reproducible and which form a relatively constant part of an individual’s make-up. In other words, these are opinions which are
voiced in the same or a similar manner on different occasions, and which are not subject to sudden arbitrary changes, such as are opinions at the lowest level. In terms of the statistical concepts we mentioned earlier, these opinions are reliable in the sense of being stable.At the third level, we have what we may call attitudes. Here we find not only that an individual holds a particular opinion with regard to a particular issue with a certain degree of stability; we
also find that he holds concurrently a large number of other opinions on the same issue which in combination define his attitude towards that issue. As an example of such an attitude, we might think of anti-Semitism and the large number of opinions which went to make up the questionnaire on anti-Semitism given in the previous chapter. Anti-Semitism as an attitude is demonstrated not so much by the fact that any given opinion out of the twenty-four is endorsed by a subject, but by the fact that the whole set of opinions is interrelated and gives rise to a uni-dimensional attitude of anti-Semitism, which can be measured. At this level, in other words, we have the first indication of structure. Opinions do
It will have been noticed that the definition of our levels, as well as proof for their existence, depends entirely on the empirical fact of correlation. When we find that a specific opinion as voiced on one occasion is also voiced on another, i.e. when the two correlate, then we speak of opinion measurement proper. When we find that certain opinions are inter-correlated in a certain way, we speak of attitudes, and when we find that certain attitudes are inter-correlated in a certain way, we speak of ideologies. Thus, the concept of correlation is quite fundamental for our system. It is equally fundamental that such correlations should be signs of empirical
Diagram Illustrating Geometrical Representation of Correlation Coefficients rather than logical implication. In other words, if one attitude logically implies another, then to find that the two are in fact related is of comparatively little interest. There is no logical relationship between, say, anti-Semitism, strict child-rearing practices, and religious attitudes; it is precisely because of this lack of logical implication that the factual, empirically observed correlations between these attitudes are of interest.However, one obvious difficulty appears to arise; correlations are arithmetical and algebraic in nature; the kind of dimensional pattern which we sketched out in Figure 16 is geometrical. How can we go from one to the other? The answer lies in the fact that a correlation can be translated into a geometrical relationship, as in-
dicated in Figure 18.* When two attitudes, A and B, are highly correlated as in (i) they will appear close together, separated by only a small angle. If they are quite uncorrelated, as in (II), they will be at right angles, as in the diagram. When the correlation is negative, A and B will be separated by an obtuse angle, as in (III). Quite generally, the convention is that the cosine of the angle between the two attitudes is exactly equal to the given correlation coefficient, as shown in (IV). This convention enables us to transform abstract concepts, like correlation coefficients, into observable features like angles and lines.
