Front Page Titles (by Subject) Section 3.: The greatest happiness of the greatest number requires, that those reasons be such, throughout, as shall show the conduciveness of the several arrangements to the all-comprehensive and only defensible end thus expressed. Rationale, indicat - The Works of Jeremy Bentham, vol. 4
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Section 3.: The greatest happiness of the greatest number requires, that those reasons be such, throughout, as shall show the conduciveness of the several arrangements to the all-comprehensive and only defensible end thus expressed. Rationale, indicat - Jeremy Bentham, The Works of Jeremy Bentham, vol. 4 
The Works of Jeremy Bentham, published under the Superintendence of his Executor, John Bowring (Edinburgh: William Tait, 1838-1843). 11 vols. Vol. 4.
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The greatest happiness of the greatest number requires, that those reasons be such, throughout, as shall show the conduciveness of the several arrangements to the all-comprehensive and only defensible end thus expressed. Rationale, indicates conduciveness to happiness.
Except in so far as they do this, whatsoever portions of discourse are given under the name of reasons, do what is nothing to the purpose: the name of reasons is not with any use or propriety applicable to them. Anything that has no influence on happiness, on what ground can it be said to have any claim to man’s regard? And, on what ground, in the eyes of a common guardian, can any one man’s happiness be shown to have any stronger or less strong claim to regard than any others? If, on the ground of delinquency, in the name of punishment, it be right that any man should be rendered unhappy, it is not that his happiness has less claim to regard than another man’s, but that it is necessary to the greatest happiness of the greatest number, that a portion of the happiness of that one be sacrificed.
Reasons, indicative of this conduciveness, are reasons derived from the principle known by the name of the principle of utility: more expressively say, the greatest-happiness principle. To exhibit these reasons, is to draw up the account between law and happiness: to apply arithmetical calculations to the elements of happiness. Political arithmetic—a name that has by some been given to political economy—is an application, though but a particular and far short of an all-comprehensive one, of arithmetic and its calculations, to happiness and its elements.
To convey a sufficiently clear, correct, and comprehensive conception of what is meant by reason, or a reason, when derived from the principle of utility, and applied to law, a few words of explanation seem indispensable.
The elements of happiness are pleasures and exemptions from pains: individual pleasures, and exemptions from individual pains.
The magnitude—the greatness—of a pleasure, is composed of its intensity and its duration: to obtain it, supposing its intensity represented by a certain number of degrees, you multiply that number by the number expressive of the moments or atoms of time contained in its duration. Suppose two pleasures at the same degree of intensity,—give to the second twice the duration of the first, the second is twice as great as the first.
Just so is it with pains: and thence with exemptions from pains.*
The magnitude of a pleasure, supposing it present, being given,—the value of it, if not present, is diminished by whatever it falls short of being present, even though its certainty be supposed entire. Pleasure itself not being ponderable or measurable, to form an estimate of this diminution, take the general source, and thence representative, of pleasure, viz. money. Take accordingly two sums of the same magnitude, say twenty pounds, the one sum receivable immediately, the other not till at the end of  years from the present time, interest of money being (suppose) at 5 per cent.—the value of the second sum will be but half that of the first; namely, ten pounds: in the same case, therefore, will be the value of two equal pleasures receivable at those several times. Just so is it with pains: and thence with exemptions from pains.
The magnitude of the pleasure derived from the source in question, supposing it present, being given—as also the value to which it is reduced by distance as above—the value of it is subjected to a further reduction by whatever it is deficient in, in respect of certainty: suppose, then, that at the time for its being received, as above, the probability, instead of being as infinity to one, i. e. at a certainty, is but as 1 to 2. On this supposition, the value of it is subjected to such further reduction, as leaves it no more than the half of that which it would have been, had the receipt of it at that remote period been regarded as certain: instead of twenty pounds, as by the first supposition, and ten pounds, as by the second supposition, it will now be no more than five pounds. Just so is it with pains, and with exemption from pains.
So much as to diminution of value by remoteness and uncertainty: now as to increase by extent.
Take any two sources of pleasure: the one productive of pleasure to one person and no more: the other productive of pleasure, the same in magnitude and value, to two other persons and no more. In the eyes of a common trustee, intrusted with the interests of all three, and acting according to his trust, the value of the second source of pleasure will be just twice as great as that of the first. As a pleasure comes to be experienced by a greater and greater number of persons in a community, it extends over a larger portion of that same community: in a political community, the extent of a pleasure is as the number of the persons by whom it is experienced.
Just so it is with pains and exemptions from pains.
Instead of pleasure itself, to show how an estimate might be formed, of the diminution its value is subjected to by diminution of propinquity and certainty, it became necessary to substitute to pleasure itself some external object known by experience to be of the number of its sources or say its causes: for example, money. But, how indubitable soever the title may be, of any object to be considered as belonging to the list of these same causes, the magnitude of the pleasure produced by it does not increase in so great a ratio as that in which the magnitude of the cause increases. Take, for instance, the same cause as before: namely money. Take thereupon any individual: give him a certain quantity of money, you will produce in his mind a certain quantity of pleasure. Give him again the same quantity, you will make an addition to the quantity of his pleasure. But the magnitude of the pleasure produced by the second sum will not be twice the magnitude of the pleasure produced by the first. While the sums are small, the truth of this position may not be perceivable. But let the sums have risen to a certain magnitude, it will be altogether out of doubt; and it will then be matter of mathematical certainty that the diminution cannot have been made to take place in the case of the greatest quantity without having been made to take place, to a proportionable amount, in the case of the several lesser quantities.
Take, for example, on the one hand, a labouring man, who, for the whole of his life, has a bare but sure subsistence: call his income £20 a-year. Take, on the other hand, the richest man in the country; who, of course, will be the monarch, if there is one: call his income £1,000,000. The net quantities of happiness, produced by the two incomes respectively—what will be their ratio to each other? The quantity of money received annually by the monarch is, on this supposition, 50,000 times as great as that received, in the same time, by the labourer. This supposed, the quantity of pleasure in the breast of the monarch will naturally be greater than the quantity in the breast of the labourer: Be it so. But by how much—by how many times greater? Fifty thousand times? This is assuredly more than any man would take upon himself to say. A thousand times, then?—a hundred?—ten times?—five times?—twice?—which of all these shall be the number? Weight, extent, heat, light—for quantities of all these articles, we have perceptible and expressible measures: unhappily or happily, for quantities of pleasure or pain, we have no such measures. Ask a man to name the ratio,—if he knows what the purpose is, his answer will vary according to the purpose: if he be a poet or an orator, and the purpose of the moment requires it, with as little scruple will he make the labourer’s happiness superior to the monarch’s, as inferior to it. For the monarch’s, taking all purposes together, five times the labourer’s seems a very large, not to say an excessive allowance: even twice, a liberal one.
After it has thus been applied to the case of the richest individual in the country, apply the estimate to the case of the next richest, suppose the man with £200,000 a year, and so downwards. If the monarch’s pleasure is not in any greater ratio to the labourer’ than that of 5 to 1, the excess of this next richest man’s pleasure, as compared with the labourer’s, cannot be so great. Carry the comparison down through the several intermediate quantities of income,—in the account of pleasure, the balance in favour of the non-labourer as against the labourer will thus be less and less.
As it is with money, so is it with all other sources or causes of pleasure: factitious dignity, for example. Give a man a ribbon, you will produce in his mind a certain quantity of pleasure. To this ribbon add another, you may add more or less to the former quantity of his pleasure. You may add to it: but you will not double it. Cover him with ribbons, as, at the expense of his starving subjects, some of the King of England’s servants are covered with gold lace, till the colour of the coat is scarcely visible—add even money in proportion—still will it be matter of doubt whether the quantity of pleasure in his mind will be double the quantity existing in the mind of the labouring man above mentioned.*
The footing, upon which the process of reasoning is thus placed by the principle of utility, is not only the only true and defensible footing, but the only one (it will be seen) on which any tolerable degree of precision can have place: and, even in so slight a sketch as the present, already it may have been observed, how near to mathematical the degree of precision is, in this case, capable of being made. Considered with reference to an individual, in every element of human happiness, in every element of its opposite unhappiness, the elements, or say dimensions of value (it has been seen,) are four: intensity, duration, propinquity, certainty; add, if in a political community, extent. Of these five, the first, it is true, is not susceptible of precise expression: it not being susceptible of measurement. But the four others are.
By this mode of reasoning, the doctrine of proportions is naturally introduced, and, on every occasion, held up to view. In so far as, is the formulary by which the case thus taken is announced, and the requisite effect produced. Without thus adverting to proportions, say absolutely and simply, of the thing, whatever it be—it is so and so, or it is not so and so—in either case, if, in your bucket, as it comes out of the well, you have more or less of truth, no one can say, for no one has inquired, in how large a proportion falsehood may not have come mixed with it.
To return to the application thus made of arithmetic to questions of utility. How far short soever this degree of precision may be, of the conceivable point of perfection—of that which is actually attained in some branches of art and science,—how far short soever of absolute perfection,—at any rate, in every rational and candid eye, unspeakable will be the advantage it will have, over every form of argumentation, in which every idea is afloat, no degree of precision being ever attained, because none is ever so much as aimed at.
Till the principle of utility, as explained by the phrase the greatest happiness of the greatest number, is, on each occasion, if not explicitly, implicitly referred to, as the source of all reasoning,—and arithmetic, as above, employed in making application of it, everything that, in the field of legislation, calls itself reasoning or argument will—say who can in what large proportion—be a compound of nonsense and falsehood; both ingredients having misrule for their effect, after having, in no small proportion, had it for their object. In words, opposite to one another in character, but all of them indeterminate in quantity, may be seen the ordinary instruments of debate:—the weapons with which the warfare of tongues and pens is, in a vast proportion, carried on. In penal law, justice and humanity—in finance, economy and liberality—in judicial procedure, strictness and liberality of construction—in constitutional law, liberty and licentiousness. It is with trash such as this, that corruptionists feed their dupes, teaching them, at the same time, to feed one another with it, as well as themselves. It is with one part of it in their mouths that the holders of power pass for wise, and the hunters after it for eloquent. Thus cheap is the rate, at which, in any quantity, each combatant finds matter of laud for those of his own side of the question (not forgetting himself,) and matter of vituperation for his antagonists. It is by nonsense in this shape that the war, made upon the principle of utility by ipsedixitism and sentimentalism, with or without rhyme, is carried on.
In the titles, with which the several sections of this paper are headed, it may be observed as a singularity, that the words, The greatest happiness of the greatest number, occupy the first place. The use of them is—to serve as a memento, that, whatever be the subject of consideration,—in so far as it belongs to the field of government, matters be so ordered, as that the only defensible end of government shall never be out of sight.
To this instructive phrase, substitute any of those unmeaning terms, to which, under the lash of perpetually-accusing conscience, the enemies of good government are, at every turn, constrained to have recourse. Substitute, for example, the word legitimacy, or the word order, and say—maintenance of legitimacy requires, or maintenance of order requires, that the state be provided with an all-comprehensive—with a rationalized code of law—that, in the rationale, the several reasons, or sets of reasons, be contiguously attached to the several arrangements to which they apply, and so forth. The substitution made, see then, ask yourself, what guide, what check, is furnished by the nonsense thus substituted to useful sense? Why then is legitimacy anywhere the word? Because, owing to intellectual blindness and weakness, absolute monarchy is still established by law in so many more countries than any better form of government is. Why is order the word? Because, while the best government can no more exist without order in some shape or other than the worst, the worst order is as much order as the best. In the worst government, order of some sort is established. Does it follow that it must be good, because it is established? Must everything be good that is established? What is thus said of the body politic, apply it thus to the body natural. Take a man in whose head or stomach the gout is established: take a man in whose bladder a stone is established. Established as it is, does the gout, does the stone, contribute anything to his happiness?
Good is pleasure or exemption from pain: or a cause or instrument of either, considered in so far as it is a cause or instrument of either.
Evil is pain or loss of pleasure; or a cause or instrument of either; considered in so far as it is a cause or instrument of either.
Happiness is the sum of pleasures, deduction made or not made of the sum of pains.
Government is in each community the aggregate of the acts of power exercised therein, by persons in whom the existence of a right to exercise political power is generally recognized. Every act of power, in the exercise of which evil as above is employed, is itself an evil: and, with small exceptions, no otherwise than by such acts can the business of government be carried on. No otherwise than through the instrumentality of punishment can even such parcels of the matter of good as are employed in the way of reward, be in any comparatively considerable proportion, got into the hands by which they are applied.
To warrant the employment of evil, whether in the character of punishment or in any other character, two points require to be made out: 1. That, by means of it, good to a preponderant amount will be produced; 2. That, at any less expense of evil, good in so great a proportion can not be produced.
In every rationale, both these points ought to be constantly kept in view: in the rationale hereby offered, they will be constantly kept in view.
No otherwise than by reference to the greatest-happiness principle, can epithets such as good and evil, or good and bad, be expressive of any quality in the act or other object to which they are applied: say an act of an individual: say an act of government: a law, a measure of government, a system of government, a form of government. But for this reference, all they designate is—the state of mind on the part of him in whose discourse they are employed.
When, and in proportion as, this standard is employed as the standard of reference,—then for the first time, and thenceforward for ever, will the import of those same perpetually employed and primarily important adjuncts, considered as indicative of qualities belonging to the objects they are applied to, be determinate.
[* ]A medicine, in so far as it produces the desired effect, is an instrument of exemption from certain pains. An instrument of political security in any shape, is an instrument of exemption from certain pains. Of the one as of the other, the value, at any point of time, is as the sum of the pains it has exempted men from, deduction made of the pains it has produced, and the pleasures it has excluded.
[* ]On the ground of these considerations, in the author’s work on legislation, on the field of the civil, or say the distributive branch of law, in settling the particular ends or objects of pursuit proper to be on that occasion kept in view, in the distribution made of benefits and burthens—on the ground of these considerations it is, that, to the objects expressed by the words subsistence, abundance, and security, was added that which is expressed by the word equality. For, on the occasion of the arrangements by which this distribution is effected, it is no less material that this object should be added to the list, than it is necessary that those others should be provided for and take the lead. Absolute equality, is that sort of equality which would have place, if, of the several benefits, as also of the several burthens, each man had exactly the same quantity as every other man: by practical equality, understand whatsoever approach to absolute equality can be made, when provision as effectual as can be made has been made for those three other particular ends of superior necessity. In regard to security, understand likewise, that, amongst the adversaries, against whose maleficent designs and enterprises security requires to be provided,—are not only foreign enemies and internal malefactors commonly so called, but moreover those members of the community, whose power affords them such facilities for producing, with impunity, and on the largest scale, those evils, for the production of which, upon the smallest scale, those who are without power are punished by them with so little reserve. As to absolute equality, it would be no less plainly inconsistent with practical equality than with subsistence, abundance, and security. Suppose but a commencement made, by the power of a government of any kind, in the design of establishing it, the effect would be—that, instead of every one’s having an equal share in the sum of the objects of general desire—and in particular in the means of subsistence, and the matter of abundance, no one would have any share in it at all. Before any division of it could be made, the whole would be destroyed: and, destroyed, along with it, those by whom, as well as those for the sake of whom, the division had been ordained.