It is of course very difficult to make any generalization here as to the comparative prevalence of various motives amongst mankind; but when one considers what is the difference which most quiet ordinary whist players feel between a game for ‘love’ and one in which there is a small stake, one cannot but assign a high value to the influence of a wish to emphasize the excitement of loss and gain.
I would not for a moment underrate the practical dangers which are found to attend the practice of gambling. It is remarked that the gambler, if he continues to play for a long time, is under an almost irresistible impulse to increase his stakes, and so re-introduce the element of uncertainty. It is in fact this tendency to be thus led on, which makes the principal danger and mischief of the practice. Risk and uncertainty are still such normal characteristics of even civilized life, that the mere extension of such tendencies into new fields does not in itself offer any very alarming prospect. It is only to be deprecated in so far as there is a danger, which experience shows to be no trifling one, that the fascination found in the pursuit should lead men into following it up into excessive lengths.[3]
§ 8. The above general treatment of Gambling and Insurance seems to me the only rational and sound principle of division;—namely, that on which the different practices which, under various names, are known as gambling or insurance, are arranged in accordance with the spirit of which they are the outcome, and therefore of the results which they are designed to secure. If we were to attempt to judge and arrange them according to the names which they currently bear, we should find ourselves led to no kind of systematic division whatever; the fact being that since they all alike involve, as their essential characteristic, payments and receipts, one or both of which are necessarily uncertain in their date or amount, the names may often be interchanged.
For instance, a lottery and an ordinary insurance society against accident, if we merely look to the processes performed in them, are to all intents and purposes identical. In each alike there is a small payment which is certain in amount, and a great receipt which is uncertain in amount. A great many persons pay the small premium, whereas a few only of their number obtain a prize, the rest getting no return whatever for their outlay. In each case alike, also, the aggregate receipts and losses are intended to balance each other, after allowing for the profits of those who carry on the undertaking. But of course when we take into account the occasions upon which the insurers get their prizes, we see that there is all the difference in the world between receiving them at haphazard, as in a lottery, and receiving them as a partial set-off to a broken limb or injured constitution, as in the insurance society.
Again, the language of betting may be easily made to cover almost every kind of insurance. Indeed De Morgan has described life insurance as a bet which the individual makes with the company, that he will not live beyond a certain age. If he dies young, he is pecuniarily a gainer, if he dies late he is a loser.[4] Here, too, though the expression is technically quite correct (since any such deliberate risk of money, upon an unproductive venture, may fall under the definition of a bet), there is the broadest distinction between betting with no other view whatever than that of risking money, and betting with the view of diminishing risk and loss as much as possible. In fact, if the language of sporting life is to be introduced into the matter, we ought, I presume, to speak of the insurer as ‘hedging’ against his death.
§ 9. Again, in Tontines we have a system of what is often called Insurance, and in certain points rightly so, but which is to all intents and purposes simply and absolutely a gambling transaction. They have been entirely abandoned, I believe, for some time, but were once rather popular, especially in France. On this plan the State, or whatever society manages the business, does not gain anything until the last member of the Tontine is dead. As the number of the survivors diminishes, the same sum-total of annuities still continues to be paid amongst them, as long as any are left alive, so that each receives a gradually increasing sum. Hence those who die early, instead of receiving the most, as on the ordinary plan, receive the least; for at the death of each member the annuity ceases absolutely, so far as he and his relations are concerned. The whole affair therefore is to all intents and purposes a gigantic system of betting, to see which can live the longest; the State being the common stake-holder, and receiving a heavy commission for its superintendence, this commission being naturally its sole motive for encouraging such a transaction. It is recorded of one of the French Tontines[5] that a widow of 97 was left, as the last survivor, to receive an annuity of 73,500 livres during the rest of the life which she could manage to drag on after that age;—she having originally subscribed a single sum of 300 livres only. It is obvious that such a system as this, though it may sometimes go by the name of insurance, is utterly opposed to the spirit of true insurance, since it tends to aggravate existing inequalities of fortune instead of to mitigate them. The insurer here bets that he will die old; in ordinary insurance he bets that he will die young.
Again, to take one final instance, common opinion often regards the bank or company which keeps a rouge et noir table, and the individuals who risk their money at it, as being both alike engaged in gambling. So they may be, technically, but for all practical purposes such a bank is as sure and safe a business as that of any ordinary insurance society, and probably far steadier in its receipts than the majority of ordinary trades in a manufacturing or commercial city. The bank goes in for many and small transactions, in proportion to its capital; their customers, very often, in proportion to their incomes go in for very heavy transactions. That the former comes out a gainer year after year depends, of course, upon the fact that the tables are notoriously slightly in their favour. But the steadiness of these gains when compared with the unsteadiness of the individual losses depends simply upon,—in fact, is merely an illustration of,—the one great permanent contrast which lies at the basis of all reasoning in Probability.
§ 10. We have so far regarded Insurance and Gambling as being each the product of a natural impulse, and as having each, if we look merely to experience, a great mass of human judgment in its favour. The popular moral judgment, however, which applauds the one and condemns the other rests in great part upon an assumption, which has doubtless much truth in it, but which is often interpreted with an absoluteness which leads to error in each direction;—the duty of insurance being too peremptorily urged upon every one, and the practice of gambling too universally regarded as involving a sacrifice of real self-interest, as being in fact little better than a persistent blunder. The assumption in question seems to be extracted from the acknowledged advantages of insurance, and then invoked to condemn the practice of gambling. But in so doing the fact does not seem to be sufficiently recognized that the latter practice, if we merely look to the extent and antiquity of the tacit vote of mankind in its favour, might surely claim to carry the day.
It is of course obvious that in all cases with which we are concerned, the aggregate wealth is unaltered; money being merely transferred from one person to another. The loss of one is precisely equivalent to the gain of another. At least this is the approximation to the truth with which we find it convenient to start.[6] Now if the happiness which is yielded by wealth were always in direct proportion to its amount, it is not easy to see why insurance should be advocated or gambling condemned. In the case of the latter this is obvious enough. I have lost £50, say, but others (one or more as the case may be) have gained it, and the increase of their happiness would exactly balance the diminution of mine. In the case of Insurance there is a slight complication, arising from the fact that the falling in of the policy does not happen at random (otherwise, as already pointed out, it would be simply a lottery), but is made contingent upon some kind of loss, which it is intended as far as possible to balance. I insure myself on a railway journey, break my leg in an accident, and, having paid threepence for my ticket, receive say £200 compensation from the insurance company. The same remarks, however, apply here; the happiness I acquire by this £200 would only just balance the aggregate loss of the 16,000 who have paid their threepences and received no return for them, were happiness always directly proportional to wealth.
§ 11. The practice of Insurance does not, I think, give rise to many questions of theoretic interest, and need not therefore detain us longer. The fact is that it has hardly yet been applied sufficiently long and widely, or to matters which admit of sufficiently accurate statistical treatment, except in one department. This, of course, is Life Insurance; but the subject is one which requires constant attention to details of statistics, and is (rightly) mainly carried out in strict accordance with routine. As an illustration of this we need merely refer to the works of De Morgan,—a professional actuary as well as a writer on the theory of Probability,—who has found but little opportunity to aid his speculative treatment of Probability by examples drawn from this class of considerations.