ON THE APPLICATION OF THE CALCULUS OF PROBABILITIES TO LEGAL AND JUDICIAL

SUBJECTS.

BY JAMES JERWOOD, M.A., F.G.S., F.C.P.8., ETC.

it was the opinion of the illustrious Turgot, that the truths of the moral and political sciences are susceptible of being established upon the same mathematical certainty as astronomy, and the other physical sciences. With the view of carrying Turgot's notions into actual effect, his disciple, the Marquis Condorcet, composed his celebrated treatise, entitled Essai sur l'Application de l'Analyse à la Probabilité des Decisions. The work will always claim admiration for the gifted author's talents, and occasion regret for his ill-starred fate.

Laplace has written de l'espérance morale et de la probabilité des jugemens in his celebrated Theorie Analytique des Probabilités; he has also interestingly treated on the application of probabilities to the moral sciences-to testimony-to the choice of decisions of assemblies, and the judgments of tribunals in his Essai Philosophique sur les Probabilities.

L'Acroix, in his Traité du Calcul Probabilités, has also applied the calculus to testimony and decisions; Les Recherches sur la Probabilité des Jugemens en matière Criminelle et en matière Civile: Par Poisson, contain the application of the theory to legal matters. Perhaps this is the most complete treatise that has been written on the subject. English authors have not hitherto turned their attention with much effect to this part of the theory of probabilities. Except the tract in Mr. Galloway's treatise, taken from the Encyclopædia Britannica; another in Professor De Mogan's more elaborate work in the Encyclopædia Metropolitana, and the article by Sir John Lubbock, in the Uuseful Knowledge Society's publications, it is not known where the English student can find even a compilation on the subject. Mr. Tozer's interesting memoir in the Cambridge Transactions must not be omitted; and Dr. Young's tract on

the force of testimony should be mentioned. Cournot's masterly work, entitled Exposition de la Theorie des Chances et des Probabilités, should have been referred to above.

The late Professor Starkie, in his valuable treatise on Evidence, has slightly touched upon the subject; and Mr. Wills, in his interesting essay on Circumstantial Evidence, has merely adverted to the subject. W. M. Best, Esq., barrister-at-law, has published a treatise on Presnmptions of Law and Fact, with the theory and rules of presumption or circumstantial proof in criminal cases-a work for which the whole profession ought to feel indebted to the learned author. The performance does him great credit, both as a scholar and a lawyer, notwithstanding the disparaging opinions of some of his very conceited critics. If legal critics, instead of bestowing their objurgations on Mathematicians for their presumption in attempting to apply the calculus of probabilities to legal topics, were to advise scientific men in the first place to provide themselves with the requisite materials for such application, they would be acting judiciously towards their own profession, and friendly towards abstract science. When, however, the master minds of the age have applied all the vigour of their understandings to the subject, it cannot with justice be considered altogether without interest. Critics may throw their dark light on it by verbose dissertations; philosophic word-stringers may sneer at what they cannot comprehend, and deny that the calculus can ever be applied to testimony or to judgments with any effect. But Laplace, on the same topic, says: Je vais essayer d'appliquer le calcul à cet objet: pursuadé que les applications de ce genre lorsqu'elles sont bien conduites et fondées sur des données que le bon sens nous suggère sont toujours préférables aux raisonnemens les plus specieux."*

Lock says: "In every day affairs, the sole foundation of our judgments and rules of action is probability. We act upon propositions or facts, according to their conformity or their repugnance to our general knowledge, observation, and experience. Our judgment also frequently rests on the testimony of others, who vouch their knowledge, observation, or experience for the truth or falsehood of such proposition or facts as form the matter in question. In this and similar cases, our judgments rely on the credit of the relators, generated by past experience of their veracity, or from the intrinsic probability of their story."†

Theorie Analytique des Profs supp. 1re. p. 28 me. + Lock's Essay, lib. iv. c. 15, sect. 4.

Since, then, probability is the mainspring of all our actions. If the calculus of probability be only good sense put into analytical language, and if such calculus be preferable to the most specious reasoning, the mere attempt to extend its application, one might suppose, would deserve commendation, and not censure. The calculus is an instrument ready to adapt itself to all the business of life. If we are not prepared to use it; if we have not stored away facts for it to rest upon; if our stock of experience be too slender to support it, we ought to set about qualifying ourselves by supplying the deficiency: at all events, we ought not, in consequence of our own wants or imperfections to throw discredit on the calculus. We may not be in a position to apply it satisfactorily to many subjects; but the calculus is not to blame; it might be no imperfection in a musical instrument, if a man without fingers could not fetch out its tones.

No one pretends to measure motives with mathematical exactness. Is there any inducement upon which we act that we can so measure? If we cannot submit testimony which is, or ought to be, the foundation of legal decisions to actual calculation, what circumstances prevent us? The plain answer is, the want of proper data derived from observation and experience.

With regard to the application of the theory of probabilities to such matters, we are now in nearly the same position as our predecessors were with respect to its application to somewhat similar subjects a century or two ago. Take, for instance, the insurance of lives. At first, the uncertainty of life would appear to render every application of the calculus entirely nugatory, as no one can determine the exact length of time that any individual will live; that his life will end at sometime seems very probable, but the length of time that may elapse before he will cease to exist is a problem that cannot be solved. When insurance on lives began to be established in the beginning of the last century, their true principles were so little understood or acted upon, that every insurer, of whatever age he might be, paid the same premium; the only restriction being that his life should be between five and forty years.*

Life is proverbially uncertain; since casting of nativities, &c., became obsolete, no sane person has attempted to apply calculation to determine the exact time that any individual will exist the attempt would be just as absurd, as it would be to measure the probity or duplicity of any witness in a court

Sir John Lubbock on Chances.

of law; or to try to prove by any calculus, that a decision of such court is right or wrong. But notwithstanding the uncertainty of human life in individual cases, the calculus of probability has been successfully applied to the subject, and the insurance of lives founded upon such application, is become a matter of national importance. Companies safely invest their capital on it; individuals contribute their annual payments with entire confidence; and all parties, when their transactions rest on the principles which the calculus really indicates, find their interests mutually safe, and their whole proceedings grounded on moral certainty. There are upwards of eighty insurance offices of different kinds in London: whatever may be said of some of them, the whole together are become a matter of national consideration. Immense sums of capital are invested in them, and the welfare of millions depends, and very generally safely depends, upon the soundness of their principles. What then formed the germ of these vast establishments? Perhaps the tables constructed by Halley from the Registers of Brislaw: these tables, and others similarly though more carefully formed, have become data upon which companies rest all their calculations; these data are the result of experience and observation, but the calculus of probabilities renders them practically useful. How then is a subject, appearing as intricate and as far beyond the powers of calculation as human testimony can possibly be, to which, nevertheless, the calculus of probabilities has been applied with marked success. This point has been discussed at some length, because the calculus of probabilities has been applied with admitted success to the insurance of lives; and although such insurance and the subjects which form the groundwork of legal proceedings are not exactly analogous, it is thought they are not so totally unlike as to admit of no comparison.

It has been remarked that the practical accuracy of insurance matters depends upon recorded experience and observation; these have furnished materials for the calculus of probabilities to work with. The calculus could be applied to legal subjects with the same facility, and probably with like success, if we were prepared with similar data in legal proceedings. The calculus is an instrument fully comprehensive, and sufficiently accommodating to adapt itself to the general outline of such matters, if we had had the precaution to store up the results of experience necessary for its foundation: the calculus is not deficient, though we may not at present possess sufficient power to apply it effectively.

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The registers of births, marriages, and deaths, shew the number of boys and girls born in a year, &c. They have supplied the calculus with many interesting topics for its application. Registers of this kind, carefully kept, shew what has happened. The calculus using the data thus supplied, teaches us what will most likely happen again at given periods.

By way of showing the futility of attempting to apply the theory of probability to legal testimony, it has been said that the value of an Englishman's testimony is different from that of an inhabitant of Hindostan; the value of a partizan's testimony is different from that of an indifferent person's testimony; the evidence of a friend, of an enemy, of a relation, of a stranger, is to be weighed in different scales, and tried by a different standard. Nay, the evidence of the same man will be entitled to far more consideration in some circumstances than in others. Now, admitting all this to be true, before the calculus can be pronounced to be altogether inapplicable, the question must be answered, "Is an Englishman more likely to speak the truth in a given number of relations than an inhabitant of Hindostan is, and if so, how much more likely?" Do the different distinctions pointed out admit of the terms more or less? If they do, the calculus is applicable. The exact quantity constituting the difference, whether more or less, is matter of observation; but, undoubtedly, if that quantity be not accurately determined, the error must not be attributed to the calculus. Were those values assumed, and the assumptions wrong, and were those assumptions employed in the calculus, and the consequent results be fallacious or absurd, no blame could fairly be attached to the calculus. The calculus is an instrument quite free from all liability to error, if we only prepare ourselves for its operations. If we supply it with substantial facts, it will furnish results that may be depended upon. That a machine may form a silk thread, we must supply it with the silk; it cannot make the silk. In like manner the calculus of probabilities cannot make the material for producing correct results. Give it well-grounded data, and its working may be relied upon. But in the ease of the machine, you would hardly find fault with it if, without your furnishing the silk, it produced no thread; and in such failure, it would be ridiculous to blame those who work the machine, and it would be quite as absurd to find fault with the instrument or its managers, if it were supplied with cotton and did not produce silk. Just so with respect to the calculus; you inust supply well