that the common way of stating the conclusion is rather misleading; and that, on the assumption in question as to the law of dependence of happiness on wealth, it really is the case that the effective element in rendering gambling disadvantageous is its tendency to the increase of the inequality in the distribution of wealth.
§ 20. This raises two questions, one of some speculative interest in connection with our subject, and the other of supreme importance in the conduct of life. The first is this: quite apart from any particular assumption which we make about moral fortunes or laws of variation of happiness, is it the fact that gambling tends to increase the existing inequalities of wealth? Theoretically there is no doubt that this is so. Take the simplest case and suppose two people tossing for a pound. If their fortunes were equal to begin with there must be resultant inequality. If they were unequal there is an even chance of the inequality being increased or diminished; but since the increase is proportionally greater than the decrease, the final result remains of the same kind as when the fortunes were equal.[11] Taking a more general view the same conclusion underlies all our reasoning as to the averages of large numbers, viz.[** TN: space] that the resultant divergencies increase absolutely (however they diminish relatively) as the numbers become greater. And of course we refer to these absolute divergencies when we are talking of the distribution of wealth.
§ 21. This is the theoretic conclusion. How far the actual practice of gambling introduces counteracting agencies must be left to the determination of those who are competent to pronounce. So far as outsiders are authorised to judge from what they read in the newspapers and other public sources of information, it would appear that these counteracting agencies are very considerable, and that in consequence it is a rather insecure argument to advance against gambling. Many a large fortune has notoriously been squandered on the race-course or in gambling saloons, and most certainly a large portion, if not the major part, has gone to swell the incomes of many who were by comparison poor. But the solution of this question must clearly be left to those who have better opportunities of knowing the facts than is to be expected on the part of writers on Probability.
§ 22. The general conclusion to be drawn is that those who invoked this principle of moral fortune as an argument against gambling were really raising a much more intricate and far-reaching problem than they were aware of. What they were at work upon was the question, What is the distribution of wealth which tends to secure the maximum of happiness? Is this best secured by equality or inequality? Had they really followed out the doctrine on which their denunciation of gambling was founded they ought to have adopted the Socialist's ideal as being distinctly that which tends to increase happiness. And they ought to have brought under the same disapprobation which they expressed against gambling all those tendencies of modern civilized life which work in the same direction. For instance; keen competition, speculative operations, extended facilities of credit, mechanical inventions, enlargement of business operations into vast firms:—all these, and other
similar tendencies too numerous to mention here, have had some influence in the way of adding to existing inequalities. They are, or have been, in consequence denounced by socialists: are we honestly to bring them to this test in order to ascertain whether or not they are to be condemned? The reader who wishes to see what sort of problems this assumption of ‘moral fortune’ ought to introduce may be recommended to read Mr F. Y. Edgeworth's Mathematical Psychics, the only work with which I am acquainted which treats of these questions.
1 The question of the advisability of inoculation against the small-pox, which gave rise to much discussion amongst the writers on Probability during the last century, is a case in point of the same principles applied to