Interpersonal Comparison of Utility

Interpersonal Comparison of Utility in Health Economics

An interpersonal comparison of utility is a welfare judgement made across people, holding for example that one patient is worse off than another, or would gain more from a treatment than someone else would. Comparisons of welfare levels differ from comparisons of welfare gains, and decision rules need different kinds. In health economics the question sits beneath every summary measure that adds benefits across patients, including total QALYs in cost-utility analysis and net benefit in cost-benefit analysis. Much of the debate between welfarist and extra-welfarist evaluation turns on where comparisons are allowed, in individual utility or in health itself.

Robbins and the case against comparing satisfactions

The modern debate starts with Lionel Robbins's Essay on the Nature and Significance of Economic Science of 1932. Robbins examined the argument that, because of diminishing marginal utility, an extra pound means less to a rich person than to a poor one, so transfers of income towards the poor that do not appreciably affect production raise total satisfaction. He accepted that each person can rank alternatives and that the orderings of different people can be set side by side. He denied that the magnitudes behind those orderings can be compared between people, and concluded that there was no way of comparing the satisfactions of different people.

Robbins did not say such comparisons should never be made. He described the assumption that people in similar circumstances are capable of equal satisfaction as a convention, justifiable on grounds of convenience or by appeal to ultimate standards of value but not by positive science, and he classed the comparison as normative. On his account, an argument that redistributing health care spending towards poorer groups raises total welfare is an ethical argument and has to be defended as one.

The objection shaped the new welfare economics. Hausman, in the Stanford Encyclopedia of Philosophy, explains that identifying welfare with preference satisfaction makes interpersonal comparisons questionable, so few economists defend maximising total welfare, with Harsanyi and Ng among the exceptions. Economists looked instead for judgements that need no comparison, such as the Pareto improvement and the potential Pareto improvement behind cost-benefit analysis. Brouwer, Culyer, van Exel and Rutten describe the Paretian tradition as holding comparisons to be impossible, meaningless or unscientific, and contrast it with the Bergson and Samuelson social welfare function, which makes comparisons once a normative choice about distribution has been made.

Comparing levels and comparing gains

Harsanyi separates comparisons of utility levels, such as whether one patient is worse off than another, from comparisons of utility differences, such as whether one patient gains more from a change. A utilitarian sum needs differences to be comparable, because adding gains is meaningful only if everyone's gains are in the same units. A Rawlsian maximin rule needs levels to be comparable, because it must identify the worst-off person.

Sen gave these ideas a formal shape, which Christian List sets out in terms of the rescalings of each person's welfare function that are taken to leave its information unchanged.

$$W^{*}_{i} = a_{i} W_{i} + b_{i}, \quad a_{i} > 0$$

where $W_i$ is the welfare function of person $i$, $W^{*}_{i}$ is a rescaled version treated as carrying the same information, $a_i$ is a scale factor and $b_i$ is a shift of origin. If $a_i$ and $b_i$ may differ between people, welfare is cardinal within each person but nothing can be compared across people. If the scale factor must be one common number $a$ while the shifts may differ, gains and losses become comparable.

List's main assumptions differ in what they allow.

List records that Arrow held interpersonal comparison of utilities to have no meaning, and explains that once level or unit comparisons are admitted, rules exist that satisfy analogues of all of Arrow's conditions. In a welfare setting the impossibility can therefore be traced to a lack of interpersonal comparability.

A cardinal scale for one person does not on its own permit comparison. Harsanyi notes that von Neumann and Morgenstern utilities, the basis of expected utility and the standard gamble, give one person's utility differences a behavioural meaning, but the second row of the table shows that comparisons between people remain undefined.

Where health economic evaluation makes the comparison

Cost-benefit analysis is often said to avoid interpersonal comparisons, since it asks only whether gainers could compensate losers. Brouwer and colleagues argue that applied cost-benefit analysis in fact compares people in money, giving each uncompensated gain or loss an equal unit weight whoever bears it, with net utility expressed through willingness to pay and ability to pay. A screening programme valued at the sum of stated willingness to pay counts a pound of benefit to a wealthy person the same as a pound to a poor person.

HM Treasury's Green Book (2026) states that an extra GBP 1,000 of income is more valuable to a low-income household than to a high-income one, reflecting the diminishing marginal utility of income, and lets analysts weight costs and benefits by the group that bears them.

$$w_g = \left( \frac{Y_{n}}{Y_{g}} \right)^{1.25}$$

where $w_g$ is the welfare weight for group $g$, $Y_n$ is the median equivalised household income of the national population, $Y_g$ is the median equivalised household income of the group, and 1.25 is the Green Book's estimate of the elasticity of marginal utility of consumption. Weighted estimates must be presented alongside unweighted ones. For health effects the Green Book uses one willingness-to-pay value per QALY, GBP 70,000 in 2020-21 prices, based on average values from representative samples of the population, so a QALY is valued the same whoever gains it.

Cost-utility analysis makes the comparison in health instead of money. The NICE manual (PMG36, section 4.3.4) bases the valuation of health-related quality of life on public preferences from a representative sample of the UK population, and its reference case (table 4.1 and section 6.2.10) gives an additional QALY the same weight whatever the other characteristics of the people receiving it, except in specific circumstances. Summing QALY gains then treats a gain of 0.1 QALY as the same size for any patient, which is a comparison of units, while ranking patients by health shortfall is a comparison of levels.

Brouwer and colleagues place this at the centre of the welfarist and extra-welfarist divide. Welfarist applied work normally treats comparisons of individual utility as impossible, whereas extra-welfarism explicitly allows comparisons, but in characteristics such as health and capabilities, not in utility. They observe that one may not know whether an unhealthy person has less utility than a healthy one, but one does know that the unhealthy person has less health, and that measures such as the QALY make comparison within the health domain practical.

Worked example with two patients and two programmes

All numbers here are illustrative. A commissioner can fund programme X or programme Y, each affecting patients A and B. Each index is on that patient's own scale.

1. Utilitarian ranking on the original scales. The sums are 60 + 20 = 80 for X and 50 + 35 = 85 for Y, so Y is preferred. Choosing Y over X costs A 10 units and gives B 15.

2. Maximin ranking on the original scales. B is worst off under both programmes, at 20 under X and 35 under Y, so Y is preferred again.

3. Rescale B without unit comparability. If units are not comparable, B's index could equally be halved, giving 10 under X and 17.5 under Y. The sums become 60 + 10 = 70 for X and 50 + 17.5 = 67.5 for Y, so X is now preferred although nobody's health or preferences have changed.

4. Shift B without level comparability. If levels are not comparable, 50 could equally be added to B's index, giving 70 under X and 85 under Y. A is now worst off, at 60 under X and 50 under Y, so maximin also switches to X.

5. Impose unit comparability. Multiplying both indices by a common factor of 2, with any separate shifts, makes A's loss 2 × 10 = 20 and B's gain 2 × 15 = 30, a net gain of 10 for Y. The shifts cancel because only differences enter, so the utilitarian verdict stays with Y.

6. A money version with Green Book weights. Scheme P yields monetised benefits of GBP 1,200,000 to a group with median equivalised income of GBP 45,000, and scheme Q yields GBP 1,000,000 to a group with median income of GBP 18,000, against a national median of GBP 30,000. Unweighted, P is preferred. The weights are (30,000 / 45,000) raised to the power 1.25, which is 0.602, and (30,000 / 18,000) raised to the power 1.25, which is 1.894. Weighted benefits are 1,200,000 × 0.602 = about GBP 722,000 for P and 1,000,000 × 1.894 = about GBP 1,894,000 for Q, so Q is preferred.

7. Interpretation. Without comparability the welfare numbers cannot rank options that create gainers and losers (steps 3 and 4). The unweighted total in step 6 also embodies a comparison, one that sets every pound equal, and a different comparison reverses the decision.

Reading results that rest on a comparison

Every cost-effectiveness or net benefit result is conditional on its built-in comparison. An incremental cost-effectiveness ratio below the threshold is usually read as health gained exceeding health displaced elsewhere in the NHS, an opportunity cost argument that counts health equally between the patients who gain and those who lose. NICE committees may consider other factors and decision modifiers and, in exceptional circumstances, a different QALY weighting, but PMG36 (section 6.2.10) requires such departures to be supported by reason, coherence and available evidence. Reporting weighted and unweighted Green Book estimates does the same for money, and equity-weighted analysis and distributional cost-effectiveness analysis show for health how results change when some gains count for more.

How the idea relates to neighbouring concepts

A Pareto improvement needs no interpersonal comparison. The potential Pareto test was designed to avoid one but, on Brouwer and colleagues' reading, brings in an equal-weight comparison in money. A social welfare function states the comparison, and its form depends on the comparability assumption accepted. Distributional weights, such as the Green Book welfare weights, write the comparison as numbers. The equity-efficiency trade-off arises only once comparisons are allowed, since without them gains for one group and losses for another share no common measure.

Common misreadings and limits

Most errors come from assuming that a method avoids the comparison when it has only made it implicitly. The comparison is then left unstated and untested.

1. Cardinal scaling implies comparability. A cardinal scale for each person, such as one from the standard gamble, leaves comparisons between people undefined unless a common unit is also assumed.
2. Cost-per-QALY analysis avoids the issue. It makes the comparison in health by giving every QALY equal weight.
3. Cost-benefit analysis avoids the issue. It weights each pound equally, which Brouwer and colleagues describe as an interpersonal comparison in monetary terms.
4. Robbins ruled comparisons out of policy. He ruled them out of positive science and accepted that they could be justified by convenience or by ultimate standards of value.
5. Comparisons are meaningless because they can be wrong. Harsanyi argues that the difficulty is exaggerated for ordinary goods and harms, and that fallible comparisons are not meaningless ones.
6. Any currency of welfare is equally defensible. List notes that comparisons based on preference satisfaction may treat expensive tastes and adaptive preferences unfairly, and that resource-based or functioning-based currencies may be less morally problematic, part of the extra-welfarist case for comparing health.

Sources

• Brouwer WBF, Culyer AJ, van Exel NJA, Rutten FFH. Welfarism vs. extra-welfarism. Journal of Health Economics. 2008;27(2):325-338. https://doi.org/10.1016/j.jhealeco.2007.07.003
• Harsanyi JC. Interpersonal utility comparisons. In: The New Palgrave Dictionary of Economics. 2nd ed. Palgrave Macmillan; 2008. https://doi.org/10.1057/978-1-349-95121-5_1119-2
• Hausman DM. Philosophy of economics. In: Stanford Encyclopedia of Philosophy. Substantive revision 4 September 2018. Section 6. https://plato.stanford.edu/entries/economics/
• HM Treasury. The Green Book (2026). Updated 28 October 2026. https://www.gov.uk/government/publications/the-green-book-appraisal-and-evaluation-in-central-government/the-green-book-2026
• List C. Social choice theory. In: Stanford Encyclopedia of Philosophy. Substantive revision 14 October 2022. Sections 3 and 4. https://plato.stanford.edu/entries/social-choice/
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Table 4.1 and sections 4.3.4 and 6.2.10. https://www.nice.org.uk/process/pmg36
• Robbins L. An Essay on the Nature and Significance of Economic Science. London: Macmillan; 1932. Chapter VI, pages 121 to 125. https://cdn.mises.org/Essay%20on%20the%20Nature%20and%20Significance%20of%20Economic%20Science_2.pdf