The Problem of Measuring the Utility Gained from Taxes

A common way of understanding the history of welfare economics goes something like this. The British economist A.C. Pigou in his The Economics of Welfare (1920) argued that progressive taxes increase social welfare. By the law of diminishing marginal utility, as you accumulate more dollars, each new dollar is worth less to you than the previous one. Doesn’t it follow, then, that that if money is taxed away from a rich person and given to a poor person, total social welfare will go up? Consider, on the one hand, Jeff Bezos with his billions of dollars, and, on the other, someone who is starving and homeless. Isn’t it obvious that if the government transfers a few thousand dollars from Bezos to the poor man, there will have been a gain in utility?



According to the common understanding, another British economist, Lionel Robbins, pointed out that Pigou’s reasoning rests on a fallacy. Pigou is assuming that you can measure utility interpersonally. A dollar is valued as so-and-so many units of utility by Bezos and as another number of units of utility by the poor man, and the latter number is greater. But this calculation isn’t valid. Utility is ordinal, not cardinal. You can say that a person ranks his tenth dollar higher than his 10 millionth dollar on his preference scale, but there aren’t measurable units of utility that underlie this comparison. If you can’t measure a person’s utility, it makes no sense at all to measure one person’s utility against that of another. You can’t legitimately say, then, that a dollar gives the poor man more utility than it does Bezos. Interpersonal comparisons of utility have to be banned from welfare economics. They are unscientific. This is in fact the Austrian view of Mises and Rothbard, and it is in defense of this view that Robbins is alleged to have argued.

In fact, Robbins doesn’t say this. In his article “Interpersonal Comparisons of Utility: A Comment” (Economic Journal, December 1938), he doesn’t rule out as meaningless interpersonal comparisons of utility. He says that “My own attitude to problems of political action has always been one of what I might call provisional utilitarianism….I do believe that, in most cases, political calculations which do not treat them as if they were equal are morally revolting.”

He thus viewed with great sympathy Pigou’s proposals about taxation. But a problem confronted him. As long as we stick to one person, we can make utility comparisons that can be verified. “The assumptions of the propositions which did not involve interpersonal comparisons of utility were assumptions which had been verified by introspection or observation, or, at least, were capable of such verification.”

But this isn’t true for interpersonal comparisons. You can’t introspect someone else’s mind, and here Robbins quotes Jevons: “’I see no means, Jevons had said, whereby such comparison can be accomplished. Every mind is inscrutable to every other mind and no common denominator of feeling is possible.’”

What follows from this? Here is where the myth arises. Robbins does not say that because we can’t prove the validity of interpersonal comparisons of utility, that we therefore shouldn’t make them. To the contrary, he says that we should continue to make them. But in doing so, we should recognize that we are introducing the value judgment that we take people to have equal capacities for satisfaction. “All that I [Robbins] proposed to do was to make it clear that the statement that social welfare was increased, itself involved an arbitrary element—that the proposition should run, if equal capacity for satisfaction on the part of the economic subjects be assumed, then social welfare can be said to be increased.”

Robbins, contrary to the myth, does not want to ban proposals like that of Pigou from economics. “I confess that I was very much surprised when I found myself held up for advocating for economists the impossible and sterile virtue of never attempting to apply their conclusions—rapt astronomers of the social universe deigning no aid to navigators in search of the desired haven. All that I had intended…was that they might better realise the exact connection between the normative and the positive, and that their practice as political philosophers might be made thereby more self-conscious.”

Robbins sums up his difference from economists such as Roy Harrod in this way: “They think that propositions based on the assumption of equality are essentially part of economic science. I think that this assumption comes from outside, and that its justification is more ethical than scientific. But we all agree that such assumptions should be made and their implications explored with the aid of the economist’s technique.”

An example will serve to show the myth about Robbins in action. The philosopher Hilary Putnam says in his book The Collapse of the Fact/Value Dichotomy and Other Essays (Harvard, 2002), “it was during the depths of the Depression that Lionel Robbins, certainly one of the most famous economists in the world, persuaded the entire economics profession that interpersonal comparisons of utility are ‘meaningless.’”

Putnam thinks he is countering Robbins when he asks, isn’t it plausible “that the marginal utility of say, a thousand dollars to someone at the point of going hungry…is greater than the marginal utility of a thousand dollars to, say, Bill Gates?” Putnam admits that we can’t measure interpersonal utility scientifically, but can’t we achieve a democratic consensus relevant to policy about comparisons like that between Gates and the starving man? But that is just what Robbins thinks. Putnam, contrary to what he imagines, is defending Robbins, not attacking him. And that is a positive and not a normative judgment.

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