Political arithmetic

“ We may allow those who make Political Economy simply a piece of arithmetic to ignore these retrospective studies and their importance; for mathematics has little to do with history. But it is otherwise with the life of nations. ”

“ There is a notion that political economy is entirely mathematical; and its negative quantity is strongly recommended for study: it contains "the whole of the Funds, Credit, 32 parts out of 33 of the value of Land...." The mathematics are described as consisting of—first, number, or Arithmetic; secondly, the theory of dependent quantities, subdivided into dependence by cause and effect, and dependence by simultaneous variations; thirdly, "independent quantities or unconnected events, which is the theory of probabilities." ”

“ First, this scheme detects their error, who in the calculation they frame contemplate nothing but the wealth and plenty they see in rich cities and great towns, and from thence make a judgment of the kingdom’s remaining part, and from this view conclude that taxes and payments to the public do mostly arise from the gentry and better sort, by which measures they neither contrive their imposition aright, nor are they able to give a true estimate what it shall produce ”

“ The foregoing may serve to clear up the difficulty in the minds of many people, who have thought of the construction of a governmental machine as of a problem in mathematics, where only numbers are to be considered. As Mills the logician points out, the doctrine of pure numerical majority rule is not logical, and other considerations besides mere numbers must be given value in weighing the national verdict in political questions. ”

“ The comparison between the numerical results obtained at one time and place and another, and between those presented in different countries, is becoming a political method increasing in prevalence and repute. In many quarters, indeed, the value of purely numerical estimates has been much exaggerated, and its peculiar liability to error, when made a basis of political reasoning, has been too much ignored. ”

“ Is it in contemplation with the House of Representatives to extend a like improvement to our measures and weights, and to arrange them also in a decimal ratio? The facility which this would introduce into the vulgar arithmetic would, unquestionably, be soon and sensibly felt by the whole mass of the people, who would thereby be enabled to compute for themselves whatever they should have occasion to buy, to sell, or to measure, which the present complicated and difficult ratios place beyond their computation for the most part. ”

“ Conversely, the larger the political unit, the more opportunity for the abuse of political power. If there were any point in working it out, this fact of political science could be reduced to a mathematical formula. ”

“ As diverging lines in mathematics can never approximate, but must continue to widen as they are extended, so a false departure from a political "standpoint" can never be rectified unless by a return to correct first principles. This is what is meant by the democratic maxim, "that a frequent return to first principles is necessary to secure the ends of public liberty." ”

“ But in politics we must not trouble ourselves with exceedingly exceptional accidents; it is quite difficult enough to count on and provide for the regular and plain probabilities. To speak mathematically, we may easily miss the permanent course of the political curve if we engross our minds with its cusps and conjugate points. ”

“ And, if, when the factors are few and simple, the results may be so absolutely opposed to seeming probability, much more will they be often thus opposed when the factors are many and involved. The saying of the French respecting political events, that “it is always the unexpected which happens”—a saying which they have been abundantly re-illustrating of late—is one which legislators, and those who urge on schemes of legislation, should have ever in mind. ”

“ We pass on, therefore, to consider a second advantage which we derive from it, namely, the existence of a certain number of statesmen trained to political life from their youth. There have been recently scoffs at the idea that we could hope to obtain a body of hereditary statesmen any more than a body of hereditary mathematicians; but, if the question is looked into a little more narrowly, the scoffs will be found to be out of place. If politics could be exactly compared to mathematics, it is the members of the House of Commons, and not the Peers, who would be condemned by the comparison. ”

“ Legislative inaction and state constitutional provisions rejecting the principle of equal numbers have both contributed to the generally prevailing numerical inequality of representation in this country. ”

“ What I have said of editors I repeat of them. The preservation of a very marked instance, the association of political recklessness with cyclometrical and Apocalyptic absurdity, may have a tendency to warn, not indeed any hardened public-man and sinner, but some young minds which have yearnings towards politics, and are in formation of habits.
In the debate on decimal coinage of July 12, 1855, Mr. Lowe, [298] then member for Kidderminster, an effective speaker and a smart man, exhibited himself in a speech on which I wrote a comment for the Decimal Association. ”

“ But what is the state of the political administration, which has only attained to a stock-taking of the living people, of the healthy and the weakly, on whom the power and the prosperity of the country depend, which is only attempted every ten years, and is only completed in three years, leaving the numbers meanwhile to be got at by estimates, necessarily erroneous, often widely erroneous? ”

“ It should be added that the growing importance of political science, as well as its recent origin, is exhibited in the fact that nearly every modern nation has established within the last half century a bureau of general statistics for the uses of statesmanship and science. In the thirty states of Europe they are now assiduously cultivating the science. Not one of their central bureaus was fully organized before the year 1800.
“The chief instrument of American statistics is the census, which should accomplish a two-fold object. ”

“ We do not question, either, that a moderate per centage of members of Parliament are fair mathematicians; and that mathematical discipline is valuable. As, however, political problems are not susceptible of mathematical analysis, their studies in this direction cannot much aid them in legislation. To the large body of military officers who sit as rep­re­sen­ta­tives, we would not for a moment deny a competent knowledge of fortification, of strategy, of regimental discipline; but we do not see that these throw much light on the causes and cure of national evils. ”

“ II. But if it be thought that, either now, or at any future time, the citizens of the United States may be induced to undertake a thorough reformation of their whole system of measures, weights and coins, reducing every branch to the same decimal ratio already established in their coins, and thus bringing the calculation of the principal affairs of life within the arithmetic of every man who can multiply and divide plain numbers, greater changes will be necessary. ”

“ We believe that an example may be thus afforded, which will illustrate the great importance of enunciating almost all the principles of political economy, as exerting tendencies, rather than as producing immediate results. This has not been sufficiently recognised, and consequently the progress of political economy has been greatly retarded, and much prejudice and incredulity have been raised in the minds of practical men towards the conclusions of this science. In mathematics a force is measured by the effects which it has a tendency to produce, i.e. ”

“ Indeed, the numerical majority often fails to accomplish that at which it professes to aim — to take truly the sense of the majority. It assumes, that by assigning to every part of the State a representative in every department of its government, in proportion to its population, it secures to each a weight in the government, in exact proportion to its population, under all circumstances. But such is not the fact. The relative weight of population depends as much on circumstances, as on numbers. ”

“ He thought, also, that the ratio of representation proposed could not be safely fixed, since in a century and a half our computed increase of population would carry the number of representatives to an enormous excess; that the number of inhabitants was not the proper index of ability and wealth; that property was the primary object of society; and that, in fixing a ratio, this ought not to be excluded from the estimate. With regard to new states, he observed, that there was something peculiar in the business, which had not been noticed. ”

“ The utmost that we can expect (and perhaps that is too much) is, that the present number shall be continued to us;—"the number of representatives shall not exceed one for every thirty thousand." Now, will not this be complied with, although the present number should never be increased—nay, although it should be decreased? Suppose Congress should say that we should have one for every forty thousand; will not the Constitution be complied with?—for one for every forty thousand does not exceed one for every thirty thousand. There is a want of proportion that ought to be strictly guarded against. ”

“ But beside the objection of the “double emploi,” it is very certain that the method of reduction to unity presents, in their true light and in a complete and simple manner, all the questions of ratio which are the bases of arithmetical solutions; so that the subsequent introduction of proportions teaches nothing new to the pupils, and only presents the same thing in a more complicated manner. We therefore exclude from our programme of examination the solution of questions of arithmetic, presented under the special form which constitutes the theory of proportions. ”

“ There may be more Paretian points, such as B > A and C > A, with the Status Quo as A. When there is no Paretian order between B and C, then it suffices to decide on these points by simple majority. Of course, with more than two points, majority voting can result into cycling, but that again means indifference, which could be settled by dice, by the chairperson, or by other creative ways.
See my home page and The Economics Pack for implementation of these rules in the program Mathematica. Little helps so much as a trying it out for yourself. ”

“ The American people, too, have their limitations and peculiarities, one of which is that they do a great many things without any particular system. It is the French rather than the Anglo-Saxons that want mathematically perfect constitutions and who are disappointed when they don't work to perfection. ”

“ In addition to this, it is to be observed that there is a probability of an increase in the number of States, and no provision for a proportional augmentation of the ratio of votes.
But this is not all: what at first sight may seem a remedy, is, in reality, a poison. To give a minority a negative upon the majority, (which is always the case where more than a majority is requisite to a decision,) is, in its tendency, to subject the sense of the greater number to that of the lesser. ”

“ It was then judged that the number of people, as therein provided, was the best criterion for fixing the proportion of each state, and that proportion in each state to be raised in the most easy manner for the people. ”

“ Among the subjects which should be curtailed or omitted are compound proportion, cube root, abstract mensuration and the greater part of commercial arithmetic. Percentage should be reduced, and the needs of practical life—profit and loss, bank discount, compound interest, with such complications as result from fractional periods of time—are useless and undesirable. The metric system should be taught in application to actual measurements, and the weights and measures handled. ”

“ This, sir, is, I believe, about the true number. There is no occasion to exaggerate, where plain truth is of so much weight and importance. But whether I put the present numbers too high or too low, is a matter of little moment. Such is the strength with which population shoots in that part of the world, that, state the numbers as high as we will, while the dispute continues, the exaggeration ends. While we are discussing any given magnitude, they are grown to it. While we spend our time in deliberating on the mode of governing two millions, we shall find we have two millions more to manage. ”

“ No responsible advocate of proportional representation has contended that proportional systems, save when the country is treated as one constituency, will result in a mathematically accurate representation of opinion. ”

“ If, ridiculing this system, any one were to say that, in order to find the mean proportional and give form to the body of the government, it is only necessary, according to me, to find the square root of the number of the people, I should answer that I am here taking this number only as an instance; that the relations of which I am speaking are not measured by the number of men alone, but generally by the amount of action, which is a combination of a multitude of causes ”

“ Those resources, as I have shown, are political economy and statistics; political economy supplying the means of connecting the laws of physical agents with the laws of the inequality of wealth, and, therefore, with a great variety of social disturbances; while statistics enable us to verify those laws in their widest extent, and to prove how completely the volition of individual men is controlled by their antecedents, and by the circumstances in which they are placed. ”

“ They are lower than they were at the top of the wave all the world over. This fact, the explanation of which would furnish a very complicated task for trained statisticians and economists, is made a topic of easy interpretation and solution in political conventions and popular harangues, and it is proposed to adopt violent and portentous measures upon the basis of the flippant notions which are current about it. ”