Ignoratio Elenchi II

It turns out that Maurice Dobb was not the first to invoke ignoratio elenchi in connection with the fixed work-fund fallacy. In his Unemployment (1913), Arthur Cecil Pigou reviewed at length "certain popular explanations" of unemployment that start from the theory that "there is not enough work to go round." Unlike Dobb, Pigou seems to accept the premise that the fallacy is common and explicates the fixed work-fund idea as a fallacy of composition.

So far so good. But where Pigou's discussion departs from the usual routine is, first, in his disclaimer that not all the diagnoses and prescriptions "involve an equal measure of folly" and, second, in his criticism of "the reasoning process, which seeks to rebut a conclusion merely by disproving the cogency of a particular argument used in its support, itself involves a fallacy to which logicians have given a name — the fallacy ignoratio elenchi."

Dobb goes a step further in disputing the assumption -- made here by Pigou -- that maximizing aggregate output is necessarily in the workers' best interest.

SOME POPULAR EXPLANATIONS OF UNEMPLOYMENT

As a prelude to the positive part of our inquiry into the causes by which the average volume of unemployment is determined, it is convenient to pass in review certain popular explanations by which, in this matter, counsel is frequently darkened. These explanations all start from the theory that, as things are at present, "there is not enough work to go round," and they all end in the practical conclusion that, in some way or another, more work ought to be made. Here meet on common ground the enemies of foreign imports, the denouncers of prison-made goods, and those who would cure unemployment by reducing the hours of labour. It is not suggested that all their various diagnoses and various prescriptions involve an equal measure of folly. But they do all embrace, sometimes in association with other errors and sometimes in isolation, the fundamental doctrine which economists have long known by the name of the "work-fund fallacy." They all assert that, if Smith and Jones do less work or do no work at all, there will be more left over for Brown and Robinson: if foreigners stop making motor-cars for our markets, or if prisoners stop making clothes, or if tramway conductors work six hours instead of twelve, by so much is room made for "the unemployed" to be "absorbed." This doctrine has so wide a currency and is, withal, so plausible, that it needs to be examined with considerable care.

What makes the doctrine plausible is the fact that it contains an element of undoubted truth. It is true that, if foreigners or prisoners are prevented from sending to our markets a particular type of goods, say steel billets, there will be more employment available in the particular English industry which is engaged in making these things. And this is not merely a temporary incident, to disappear again so soon as people have adapted themselves to the new conditions. On the contrary, there is every probability that the extra employment available in the particular industry affected will be permanent. As regards each industry separately there is, speaking roughly and practically, a fixed work-fund. What more natural than the inference that such a fixed work-fund also exists as regards all a country's industries collectively? Consider more particularly the case of workpeople engaged in industries subject to severe foreign competition. They see, maybe, orders which their own employers were willing and eager to supply, going again and again to foreign firms. On special occasions, when their own firm has an exceptional spell of success with its tenders, they experience the full glory of a boom. Meeting other workpeople in other occupations, they find that the case is the same with them.

Each trade knows perfectly well that, if foreign competition with its product were cut off, there would be more work available in it for native hands; and each trade believes its neighbours, when they assert that the case is similar with them. If only, they argue, we could work shoulder to shoulder, and, by political action, keep the foreigner out, there would be work available for us all, and unemployment would become an evil of the past. And reasoning of an exactly similar kind is open to those persons whose products compete with prison-made goods, or those who are desirous of employment in industries where the workmen at present work long hours: if these hours were only halved there would be room for the employment of twice as many men. Now, it is easy to show that the reasoning process by which these results are attained is defective in point of logic. All arguments, which infer that, because a given policy, if applied to A alone, would benefit A, if applied to B alone, would benefit B, and, if applied to C alone, would benefit C, therefore, that policy, if applied at once to A, B and C together, would benefit them all, involve what logicians call the fallacy of composition. A famous and orthodox illustration of this fallacy is provided by the industry of picking pockets. If a number of men sit round a table, it is evidently true that Smith, by taking the purse of his left-hand neighbour, will gain; Jones, by doing likewise to his left-hand neighbour will similarly gain; and so on throughout. But it is fallacious to infer from this that, if every member of the group picks the pocket of his left-hand neighbour, the group as a whole will gain. The secret of the fallacy is, of course, that, in the transition from the effect upon each to the effect upon all, the possibility is ignored that the gain which a policy, when pursued by Smith alone, yields to Smith, may only be obtainable at the cost of corresponding loss to others. The popular argument about unemployment, which was set out above, embodies this defect, and fails, therefore, to establish the conclusion at which it aims. For, from the fact that there is (substantially) a fixed work-fund from the standpoint of each industry separately, it does not follow that there is a fixed work-fund from the standpoint of all industries together.

...

It would, however, be unwarrantable to conclude that, because the reasons which popular thought offers in defence of any thesis are invalid, therefore, that thesis is untrue. If it were a good ground for rejecting an opinion that many persons entertain it for bad reasons, there would, alas, be few current beliefs left standing! As a matter of fact, however, conclusions are often right when the reasons adduced by their supporters are ridiculously wrong. It is not undesirable to walk under a builder's ladder because to do so is, in some magical manner, "unlucky"; but those who dislike the impact of accidentally descending bricks will, nevertheless, do wisely to refrain. Indeed, the reasoning process, which seeks to rebut a conclusion merely by disproving the cogency of a particular argument used in its support, itself involves a fallacy to which logicians have given a name — the fallacy ignoratio elenchi. We are not, therefore, entitled to cut short our inquiry concerning unemployment and the fixed work-fund at the point reached so far. It is still necessary to inquire by direct study whether the extra employment, which would be made available in a particular trade by cutting off the competition of foreigners or prisoners in respect of that trade, would be net extra employment, or would be balanced by a corresponding loss of employment in other industries.
The ineffectiveness of the reasoning we have hitherto been reviewing is easily explained. That reasoning fails to penetrate beneath the surface of appearance to the essential under- lying causes. Economists, however, are acquainted with a more adequate analysis. Let us take the point of view of those workpeople in the country who are unemployed, and for whom it is contended that the exclusion of competing imports, the prohibition of prison-labour and the reduction of the normal hours of work would create employment. Why are these people unemployed? They are unemployed because, at the wage they ask, there is no demand for their services, and, unless the wage they ask is lowered, they can only cease to be unemployed if such a demand comes into being. But whence can such a demand come? It can only come from the general income of the country, that is to say, from the product of the labour and capital of the rest of the community. It follows that the exclusion of competing imports, the prohibition of prison-labour and the reduction of the normal hours of work can create employment for them on one condition and on one condition only; namely, that these devices succeed in rendering the labour and capital of the rest of the community more effective in production. The prohibition of prison-labour is certain not to do this, and must necessarily have the opposite effect. The reduction of the normal hours of work will do it or will fail to do it, according as the extra leisure increases the workers' efficiency more or less than in proportion to the reduction of hours.