The poor man's dollar and the rich man's dollar are the same size. The meals they purchase may not be; the hours of anxiety they remove may not be; the place they occupy in a life may be separated by everything that poverty means. Ordinary judgment crosses that distance readily. It says that the dollar matters more where there is less to spare. But the science that has put utility at the center of value encounters, at this apparently simple comparison, a limit of its own construction. It can describe how each man chooses. The question is what entitles it to put their satisfactions on the same scale.
A ranking within a life supplies no exchange rate between lives. If a woman prefers the house with a garden to the house without one, the numbers ten and five can represent her order; so can a hundred and ninety-nine. Nothing in the bare ranking tells us that the first difference is five units of pleasure, or the second one. Still less does it say how either difference compares with her neighbor's relief at obtaining a secure room. An ordinal utility function is faithful when it preserves the order it was made to represent. It does not become an instrument for comparing intensities because the order has been written in numbers. The gulf opens at the moment the numbers belonging to separate people are treated as though they had been calibrated together.
A change of units alone can reverse an unweighted social sum. In an invented comparison, arrangement A gives two people utility numbers of four and one; arrangement B gives them three and three. Add the numbers and B wins, six against five. Now multiply the first person's numbers by three, leaving the second person's alone. Every preference of both people is preserved: the first still prefers A, the second still prefers B. Yet the unweighted total now favors A, thirteen against twelve. No experience has changed. No choice has changed. Only the ruler has changed, and the supposed social verdict has changed with it. A rule whose conclusion turns on such an arbitrary unit is using information the observed rankings never supplied.
This was the nerve Lionel Robbins touched when he challenged the familiar argument from diminishing marginal utility to redistribution. Even if an additional dollar brings a smaller increment of satisfaction as one person's income rises, that is a statement about one person at different incomes. To compare that increment with another person's gain requires something further. The first person's diminishing curve does not, by itself, tell us where the second person's curve belongs. Robbins treated the transfer argument as dependent on an interpersonal valuation that positive economic analysis could not establish. His objection concerned what the premises could establish: they did not settle which person's gain or loss was larger.
There is a discipline in this refusal, and a danger in enlarging it. The discipline is to keep a convenient representation from impersonating a measurement. The danger is to conclude that no warranted comparison between people is possible because a particular representation does not contain one. The absence of interpersonal information from an ordinal model is a fact about the model's information. It is not a proof that hunger, illness, exhaustion, or the opportunities of a life admit no public evidence. Nor is the fact that a comparison involves judgment a reason to regard all judgments as equally groundless. We do not need a universal unit of suffering to recognize every difference between security and destitution. We do need to say what the comparison rests on.
Robbins himself did not draw the conclusion that economists must retreat from ethical life. In the preface to his second edition he explicitly resisted the interpretation that his argument required such abstention. His demand was that a value judgment should be acknowledged where it entered, rather than passed off as a deduction from economic analysis. That demand has force whichever distribution one favors. A defense of the existing claims is no more entitled to disappear inside the language of science than a proposal to alter them. If the evidence does not uniquely determine the moral weight of a person's gain, it does not uniquely determine that the present allocation ought to stand. The uncertainty belongs to the comparison, not exclusively to the person asking for change.
One response is to make the missing premise explicit. Suppose we agree to use comparable measures of well-being and to give equal increments equal social weight wherever they occur. We can then ask what a transfer does to the sum under that convention, and what evidence supports the comparison. If we instead give priority to a person below a threshold, or recognize a claim that cannot be traded away for somebody else's greater enjoyment, we have chosen a different social rule. These are substantial differences. Calling all of them utility maximization would conceal the very decision that needs to be made. Even in the invented example, rescaling the first person's utility need not reverse a previously specified social judgment: the weight on that rescaled utility can be divided by three. The judgment survives when its units and its weights are kept together. What fails is the pretense that an unweighted sum was neutral before those units were chosen.
A second response is to ask less of comparison without giving it up. Amartya Sen argued that social judgment need not wait for a complete, exact ranking of every possible interpersonal gain. Information may rule out some arrangements while leaving others unresolved. Severe deprivation may be recognizable without assigning its victim a precise number of utils; evidence about health, mobility, education, and the practical freedom to act may matter even when reports of contentment are difficult to compare. A person can adapt her expressed wants to a life of restricted possibilities. Taking her reports seriously does not require treating those reports as the whole of her condition. The alternative to a fictitious precision can be a reasoned partial judgment, with the unresolved cases still unresolved.
Money does not remove the difficulty. It gives the market a common unit, but the unit measures a command over goods, not an equal increment of well-being in every hand. The amount someone will surrender to secure a change depends on what else that money would have done for her. A large bid can express an intense preference, ample means, or some combination; a small bid can coexist with an urgent need. The earlier plate on the willing buyer followed this filter through the purse. Here its implication is sharper. Adding dollar valuations may be useful for a specified economic comparison. To read the addition as an unweighted sum of human benefit requires a further argument about the relation between dollars and lives. The common currency of exchange does not close the gulf merely by giving it a price.
The choice reveals an order within a life. The weight given to that life must still be answered for.
On what warrant, then, may a science say that the poor man needs the dollar more? It may establish the conditions the dollar would relieve, examine what the recipient can do with it, test an explicit account of diminishing benefit, and expose the assumptions by which one person's gain is compared with another's. It may contribute greatly to a judgment without pretending that the judgment arrived concealed in a demand curve. The gulf is neither an excuse for indifference nor a license for invented measurement. It is the place where the evidence about people meets the reasons for counting them. The next plate asks how far economics can go when it avoids that meeting altogether, certifying an arrangement through comparisons that never cross from one life to another.