When Jevons published his Theory of Political Economy in 1871, it was already widely felt that a simple imaginary man, or even a composite picture made up of a series of different simple imaginary men, although useful in answering examination questions, was of very little use in drafting a Factory Act or arbitrating on a sliding scale of wages. Jevons therefore based his economic method upon the variety and not the uniformity of individual instances. He arranged the hours of labour in a working day, or the units of satisfaction from spending money, on curves of increase and decrease, and employed mathematical methods to indicate the point where one curve, whether representing an imaginary estimate or a record of ascertained facts, would cut the others to the best advantage.

Here was something which corresponded, however roughly, to the process by which practical people arrive at practical and responsible results. A railway manager who wishes to discover the highest rate of charges which his traffic will bear is not interested if he is told that the rate when fixed will have been due to the law that all men seek to obtain wealth with as little effort as possible, modified in its working by men's unwillingness to break an established business habit. He wants a method which, instead of merely providing him with a verbal 'explanation' of what has happened, will enable him to form a quantitative estimate of what under given circumstances will happen. He can, however, and, I believe, now often does, use the Jevonian method to work out definite results in half-pennies and tons from the intersection of plotted curves recording actual statistics of rates and traffic.

Since Jevons's time the method which he initiated has been steadily extended; economic and statistical processes have become more nearly assimilated, and problems of fatigue or acquired skill, of family affection and personal thrift, of management by the entrepreneur or the paid official, have been stated and argued in quantitative form. As Professor Marshall said the other day, qualitative reasoning in economics is passing away and quantitative reasoning is beginning to take its place.[[43]]

How far is a similar change of method possible in the discussion not of industrial and financial processes but of the structure and working of political institutions?

It is of course easy to pick out political questions which can obviously be treated by quantitative methods. One may take, for instance, the problem of the best size for a debating hall, to be used, say, by the Federal Deliberative Assembly of the British Empire—assuming that the shape is already settled. The main elements of the problem are that the hall should be large enough to accommodate with dignity a number of members sufficient both for the representation of interests and the carrying out of committee work, and not too large for each member to listen without strain to a debate. The resultant size will represent a compromise among these elements, accommodating a number smaller than would be desirable if the need of representation and dignity alone were to be considered, and larger than it would be if the convenience of debate alone were considered.

A body of economists could agree to plot out or imagine a succession of 'curves' representing the advantage to be obtained from each additional unit of size in dignity, adequacy of representation, supply of members for committee work, healthiness, etc., and the disadvantage of each additional unit of size as affecting convenience of debate, etc. The curves of dignity and adequacy might be the result of direct estimation. The curve of marginal convenience in audibility would be founded upon actual 'polygons of variation' recording measurements of the distance at which a sufficient number of individuals of the classes and ages expected could hear and make themselves heard in a room of that shape. The economists might further, after discussion, agree on the relative importance of each element to the final decision, and might give effect to their agreement by the familiar statistical device of 'weighting.'

The answer would perhaps provide fourteen square feet on the floor in a room twenty-six feet high for each of three hundred and seventeen members. There would, when the answer was settled, be a 'marginal' man in point of hearing (representing, perhaps, an average healthy man of seventy-four), who would be unable or just able to hear the 'marginal' man in point of clearness of speech—who might represent (on a polygon specially drawn up by the Oxford Professor of Biology) the least audible but two of the tutors at Balliol. The marginal point on the curve of the decreasing utility of successive increments of members from the point of view of committee work might show, perhaps, that such work must either be reduced to a point far below that which is usual in national parliaments, or must be done very largely by persons not members of the assembly itself. The aesthetic curve of dignity might be cut at the point where the President of the Society of British Architects could just be induced not to write to the Times.

Any discussion which took place on such lines, even although the curves were mere forms of speech, would be real and practical. Instead of one man reiterating that the Parliament Hall of a great empire ought to represent the dignity of its task, and another man answering that a debating assembly which cannot debate is of no use, both would be forced to ask 'How much dignity'? and 'How much debating convenience'? As it is, this particular question seems often to be settled by the architect, who is deeply concerned with aesthetic effect, and not at all concerned with debating convenience. The reasons that he gives in his reports seem convincing, because the other considerations are not in the minds of the Building Committee, who think of one element only of the problem at a time and make no attempt to co-ordinate all the elements. Otherwise it would be impossible to explain the fact that the Debating Hall, for instance, of the House of Representatives at Washington is no more fitted for debates carried on by human beings than would a spoon ten feet broad be fitted for the eating of soup. The able leaders of the National Congress movement in India made the same mistake in 1907, when they arranged, with their minds set only on the need of an impressive display, that difficult and exciting questions of tactics should be discussed by about fifteen hundred delegates in a huge tent, and in the presence of a crowd of nearly ten thousand spectators. I am afraid that it is not unlikely that the London County Council may also despise the quantitative method of reasoning on such questions, and may find themselves in 1912 provided with a new hall admirably adapted to illustrate the dignity of London and the genius of their architect, but unfitted for any other purpose.

Nor is the essence of the quantitative method changed when the answer is to be found, not in one, but in several 'unknown quantities.' Take, for instance, the question as to the best types of elementary school to be provided in London. If it were assumed that only one type of school was to be provided, the problem would be stated in the same form as that of the size of the Debating Hall. But it is possible in most London districts to provide within easy walking distance of every child four or five schools of different types, and the problem becomes that of so choosing a limited number of types as to secure that the degree of 'misfit' between child and curriculum shall be as small as possible. If we treat the general aptitude (or 'cleverness') of the children as differing only by more or less, the problem becomes one of fitting the types of school to a fairly exactly ascertainable polygon of intellectual variation. It might appear then that the best results would come from the provision, say, of five types of schools providing respectively for the 2 per cent, of greatest natural cleverness, the succeeding 10 per cent., the intermediate 76 per cent., the comparatively sub-normal 10 per cent., and the 2 per cent, of 'mentally deficient.' That is to say the local authority would have to provide in that proportion Secondary, Higher Grade, Ordinary, Sub-Normal, and Mentally Deficient schools.

A general improvement in nutrition and other home circumstances might tend to 'steepen' the polygon of variation, i.e. to bring more children near the normal, or it might increase the number of children with exceptional inherited cleverness who were able to reveal that fact, and so 'flatten' it; and either case might make a change desirable in the best proportion between the types of schools or even in the number of the types.