A common currency promises to make unlike things answerable to one another. An hour of leisure can be set beside a cleaner river, the river beside another room, the room beside the time spent earning it. Utility gives this promise its most abstract form: whatever the goods may be, a person's ranking can sometimes be represented by numbers, and the preferred arrangement receives the higher number. Money then offers a practical language in which to ask how much of one thing the person would surrender for another. Yet these are different achievements. A numerical ordering, a willingness to pay, and a judgment about the worth of a life require different grounds. The convenience of writing each as a number can conceal the distance between them.
A ranking supplies less arithmetic than its numerical appearance suggests. Suppose a person places three available arrangements in the order A, B, C. Scores of three, two and one represent that order; so do scores of a hundred, two and one. In the first representation, the intervals happen to be equal. In the second, the upper interval is ninety-eight times the lower. Both tell us which arrangement comes first, and neither, by that fact alone, tells us how much pleasure separates them. The numbering has made a comparison legible without making the distances measurable. Nor has it established a rate at which every component of the arrangements can be exchanged for money. That further question concerns the person's choices as compensation, circumstances and available alternatives change.
A monetary measure can nevertheless be precise within a specified choice problem. If a household would surrender at most six dollars for an improvement and remain as well off by its own ranking, six is a meaningful measure of its willingness to pay. The amount refers to the whole comparison: its resources, the improvement, the alternatives and the circumstances in which the question is asked. An increasing relabeling of the utility index leaves that indifference unchanged. The dollars are therefore more than an arbitrary set of utility numbers. But they remain dollars the household can afford to give up. A different income can change the monetary measure while leaving the improvement itself unchanged.
A small illustration shows purchasing power entering the scale. Give two people the same stipulated utility function: the square root of their remaining money, plus one unit if a particular environmental improvement occurs. One has a hundred dollars and the other ten thousand. The first can surrender nineteen dollars for the improvement and retain the original score: the square root of eighty-one, plus one, is ten. The second can surrender a hundred and ninety-nine: the square root of nine thousand eight hundred and one, plus one, is a hundred. Before any payment, the improvement adds exactly one unit to each person's score on the common scale we have assumed. Their monetary bids nevertheless differ by more than ten to one. The example makes the assumption of comparable utility explicit so that the divergence can be seen; actual choices do not supply that common scale merely by supplying two prices.
Cost-benefit analysis carries these monetary comparisons into a common decision. Its attraction is practical: a proposed road, treatment or regulation affects several people in several ways, and a decision cannot be avoided simply because the effects differ. Kaldor's compensation argument asked whether those who gain could compensate those who lose and still retain a gain. That test describes a possibility for rearranging resources. It leaves a further choice about whether compensation will actually be paid. A favorable sum can identify room for a mutually acceptable arrangement without identifying the arrangement that the decision will deliver. The accounting becomes misleading when the possible payment is allowed to stand in for the missing payment.
The test also depends on what has entered the account. A worker compelled to leave a familiar occupation may require more than replacement earnings to accept the change. A neighborhood may lose access to a place around which its common life has formed. Kaldor himself recognized that losses of this kind belonged in the compensation question. Including them is a serious attempt to learn what a change costs the affected people. It does not guarantee that an answer can be elicited reliably, that the relevant payment is feasible, or that the affected people regard the proposed exchange as permissible. The difficulty has to be specified. A missing price, an uncertain estimate, a disagreement about authority and a refusal to trade describe different obstacles.
A protected value can instead be treated as a condition on the decision. Suppose a community requires a minimum standard of drinking water and compares the costs of all the feasible ways of meeting it. The standard excludes some proposals; monetary appraisal helps select among the rest. The community has made a substantive judgment about the boundary within which trade-offs may occur. It can still ask whether a cheaper method meets that boundary, whether a supposed improvement shifts harm elsewhere, or whether the resources could achieve more protection in another use. Giving a value protection does not make the costs of protecting it disappear. It changes the role those costs are permitted to play.
Incomplete comparison offers another possibility besides either a universal price or a complete refusal to decide. Two arrangements may differ in education, health and freedom in ways for which no agreed single weighting is available. A third arrangement may improve one of those dimensions and worsen none. The third can be preferred to the arrangement it improves even while the first pair remains unresolved. Sen's account of partial comparability gives this form of judgment a place within reasoned evaluation. One need not pretend that every disagreement has already acquired a numerical answer in order to recognize improvements on which the available reasons converge. A common decision can be disciplined while its ordering remains incomplete.
The choice of a currency therefore belongs inside the argument about value. Unweighted dollars give a useful account of monetary gains and losses under stated conditions. Distributional weights introduce a judgment about whose dollars should count more. A welfare index introduces judgments about its dimensions, scales and aggregation. A right or threshold can limit which exchanges are admissible before any of those sums is taken. Each approach makes some features prominent and can leave others obscure. The relevant question is what the measure permits the decision-maker to see, and what grounds justify acting on that view. A number helps when its meaning remains attached to the comparison that produced it.
A common currency makes a comparison possible; it does not make the comparison innocent.
Utility can organize choices among unlike goods without discovering a substance into which every good dissolves. Money can make the sacrifice involved in one exchange explicit without settling the justice of all exchanges. The currency is strongest when the account travels with it: whose choice, whose resources, which alternatives, which losses, which further judgment. Once those questions are kept visible, the demand for a single scale becomes a proposal that can be examined. What is lost in making the incomparable compare is whatever the chosen account has omitted and the decision still requires. The argument remains open.