Pareto Improvement

Pareto Improvement and Health Policy Changes With No Losers

In health economics, a Pareto improvement is the one kind of change whose desirability needs no judgement about whose gain matters more, because someone gains and nobody loses. It is the move that takes an allocation towards Pareto efficiency, and its test is close to unanimity, because every affected patient, taxpayer, clinician and supplier must end up at least as well off as before. The test marks the boundary between decisions that economics can endorse without comparing one person's gain with another's loss, and the much larger set, including most funding decisions in a fixed health budget, that need an explicit view on who should gain and who should lose. The wider framework is on the welfare economics page.

The person-by-person test, strict and weak

A Pareto improvement is judged by comparing each affected person's position before and after a change, never by adding gains and losses together. Feldman's dictionary entry on Kaldor-Hicks compensation describes a reform that in fact, and not merely in theory, makes everyone as well off and some people better off as a Pareto improvement, and observes that such a reform would get unanimous support. Brouwer and colleagues state the same Pareto principle in terms of social welfare, which rises unambiguously only if someone's welfare rises and nobody's falls.

$$\Delta u_i = u_i(y) - u_i(x) \ge 0 \text{ for every } i, \qquad \Delta u_j > 0 \text{ for at least one } j$$

Here $x$ is the current allocation, $y$ is the proposed one, $u_i(\cdot)$ is the welfare of person $i$ under an allocation, $\Delta u_i$ is the change for person $i$, $i$ runs over everyone affected and $j$ is any one affected person. This is a weak Pareto improvement, in which some people may be unaffected, provided at least one gains.

$$\Delta u_i > 0 \text{ for every } i$$

Here every affected person $i$ gains, which defines a strict (or strong) Pareto improvement. Every strict improvement is also a weak one, but not the reverse. Arrow's 1963 paper on the welfare economics of medical care used the strict form when he stated Pareto's definition of optimality, as the absence of any allocation that would make all participants better off, and called the judgement that such a change should be made a very weak one.

The labels can mislead. In social choice theory, List's encyclopedia entry calls the condition that society prefers an option when every individual strictly prefers it the weak Pareto principle, and the version that also counts changes where some are indifferent the strong Pareto principle. The weak principle therefore concerns strict improvements, so an analysis should state which test it applies. The measure being compared also needs stating. Brouwer and colleagues note that the Pareto criterion can be applied to non-utility characteristics such as health, so a change can be a Pareto improvement in QALYs while failing the test in utility, or the reverse.

Why few health policy changes pass the test

Feldman notes that in most real policy choices a change produces some gainers, some losers and some people who are indifferent. Health care decisions fit this pattern closely. Within a fixed budget, money spent on one service is unavailable for another, so the opportunity cost of a new technology falls on patients whose care is displaced. Turner and colleagues describe a cost-effectiveness threshold that, depending on how it is calculated, can capture how much health is expected to be foregone when resources are used for an intervention, and they note that cost-benefit analyses typically fail to reflect which other health interventions may need to be displaced. When the threshold reflects the health foregone, a change that passes it produces a net health gain, which is a different claim from a gain with no losers.

The welfarist version of the test is stricter still, because it counts everyone whose welfare changes, including taxpayers who fund the change, suppliers who lose sales and staff whose work changes. Brouwer and colleagues observe that the Pareto improvement normally has little cutting power outside voluntary trading in well-regulated markets, and that relying on the Pareto criterion while refusing to compare individual welfares leads to policy paralysis. In health care, they add, it seems curmudgeonly to insist on going no further than Pareto allows, given explicit government statements such as the UK government's 1944 white paper A National Health Service, which said that access to care should not depend on ability to pay. Both cost-effectiveness analysis and cost-benefit analysis rest on decision rules that accept losers.

Changes that can qualify in health care

Some health care changes can pass the test, at least when the analysis is clear about whose welfare counts. Each of the cases below is a Pareto improvement only under stated conditions, and each fails if one affected group is overlooked.

• Removing pure waste. Care that produces no health gain can be withdrawn and its resources used to produce health elsewhere. Judged in health terms, the patients who received it lose nothing and the patients who receive the new care gain. In welfare terms, the test also requires that providers whose income falls, and any patients who valued the care for reassurance, are no worse off.
• Switching to a dominant technology. NICE's methods manual (PMG36) describes a dominated technology as one that is more costly and less effective than another technology in the analysis. Replacing it with the dominant option releases money and improves average health, and reinvesting the money can benefit other patients. The switch is a Pareto improvement only if no individual patient does worse on the new option, which average results cannot confirm (see the example below), and, in welfare terms, only if the maker of the displaced product is no worse off.
• Redistribution valued by the payers. Brouwer and colleagues note that changes in the distribution of income and wealth can themselves satisfy the Pareto criterion, for example in a society containing some altruists. Taxpayers who value other people's access to care may be better off paying for it, so a tax-funded service can in principle pass the test if every taxpayer values it at least as much as the tax paid.

Compensation and the move from potential to actual Pareto improvement

The Kaldor-Hicks test asks whether the gainers from a change could compensate the losers and still be better off. Feldman explains that the compensation is a theoretical possibility, not a fact, and that the payments, if made, would leave everyone as well off after the reform as before and some better off. He adds that Hicks did not recommend that compensation always be paid, but urged reformers to be more explicit about what compensation policies, such as adjustments of taxes, would be appropriate. A change that passes the test is therefore a potential Pareto improvement, and it becomes an actual one only when compensation is paid in full.

In health economics the compensation is usually left hypothetical. Turner and colleagues describe cost-benefit analysis as resting on a welfarist foundation in which improvements in social welfare are judged as potential Pareto improvements, and note that the criterion is almost always applied hypothetically, so some people win and others lose.

Actual compensation in health care takes two broad forms. Compensation in kind keeps losers whole without cash, as when patients who would do worse on a new treatment stay on the old one, or a service that is relocated keeps transport support for those whose journeys lengthen. Compensation in money, through prices, taxes or payments, suits welfarist analysis, where Feldman notes that compensation payments are transfers of goods or money and not of utility. Health losses are harder to reverse in health terms, because lost health cannot be returned after the event, and compensation schemes have costs of their own, so a full transfer may use up much of the gain.

Illustrative example of a dominant drug and the patients it does not suit

The numbers below are illustrative. A commissioner treats 200 patients with drug A at GBP 5,000 per patient. Drug B costs GBP 4,000 per patient. In 180 patients (subgroup 1), B yields 0.15 more QALYs than A; in the other 20 (subgroup 2), B yields 0.35 fewer QALYs than A. Nobody outside the 200 patients is affected, and saved money is held by the commissioner.

1. Switching everyone (P1). The saving is 200 x 1,000 = GBP 200,000. Subgroup 1 gains 180 x 0.15 = 27 QALYs and subgroup 2 loses 20 x 0.35 = 7 QALYs, so the net gain is 20 QALYs (27 gained against 7 lost), or 20 / 200 = 0.10 QALYs per patient. On average B is cheaper and more effective, so it dominates A, yet 20 patients are worse off.
2. Switching only those who benefit (P2). If subgroup 2 can be identified in advance at no cost, it stays on A. The saving is 180 x 1,000 = GBP 180,000 and the gain is 27 QALYs. Nobody loses and subgroup 2 is unchanged, so P2 is a weak Pareto improvement. It also yields more health than P1.
3. Making every patient gain (P3). Suppose GBP 20,000 of the saving funds closer follow-up for subgroup 2, worth 0.02 QALYs to each of them. Subgroup 2 gains 20 x 0.02 = 0.4 QALYs, the saving falls by GBP 20,000 to GBP 160,000, and every one of the 200 patients is strictly better off.
4. When subgroup 2 cannot be identified. Each patient then faces a 180 / 200 = 0.9 chance of gaining 0.15 QALYs and a 0.1 chance of losing 0.35 QALYs. The expected change is 0.9 x 0.15 + 0.1 x (-0.35) = 0.10 QALYs, so before treatment every patient expects to gain, but after treatment 20 have lost.

The example shows three things. A dominant result in a cost-effectiveness analysis is a statement about averages, so it does not establish a Pareto improvement. Holding losers harmless is a form of compensation in kind, here achieved through targeting, and in this case it raises total health as well. Judged on expected QALYs before treatment, P1 makes every patient better off; judged on outcomes, it does not.

How Pareto improvement relates to nearby ideas

Pareto improvement is a property of a move between two allocations, while Pareto efficiency is a property of an allocation from which no such move remains. A sequence of Pareto improvements continued until none remains ends at an efficient allocation, but which one depends on the starting point, and a move from an inefficient allocation to an efficient one is not necessarily a Pareto improvement, because it may harm someone on the way. The Kaldor-Hicks criterion widens the test to potential compensation. Allocative efficiency asks whether a stated objective, such as total health, is maximised, and net health benefit measures a population gain after opportunity cost. Neither asks whether any individual loses.

Common misreadings

Most errors come from treating a population result as a statement about every person, or from reading more into the test than it contains. The points below recur in health economics writing.

• A cost-saving change is a Pareto improvement. Saved money goes somewhere, and the change may still harm the patients, staff or suppliers it affects.
• A dominant option is a Pareto improvement. Dominance compares options on mean costs and effects for a population, so individual patients can still lose.
• Potential compensation is compensation. Passing the Kaldor-Hicks test leaves losers worse off unless they are actually paid.
• The weak Pareto principle refers to weak improvements. In social choice theory it refers to changes that every individual strictly prefers.
• A Pareto improvement is fair. The criterion is silent on distribution, so a change whose gains all go to the best-off group still passes. Choosing among changes that create losers needs a social welfare function or explicit equity weights.

Sources

• Arrow KJ. Uncertainty and the welfare economics of medical care. American Economic Review. 1963;53(5):941-973. https://www.aeaweb.org/aer/top20/53.5.941-973.pdf
• Brouwer WBF, Culyer AJ, van Exel NJA, Rutten FFH. Welfarism vs. extra-welfarism. Journal of Health Economics. 2008;27(2):325-338. doi:10.1016/j.jhealeco.2007.07.003. Author version: https://eprints.whiterose.ac.uk/id/eprint/3789/
• Feldman AM. Kaldor-Hicks compensation. In: Newman P, editor. The New Palgrave Dictionary of Economics and the Law, volume 2. London: Macmillan; 1998. p. 417-421.
• List C. Social choice theory. Stanford Encyclopedia of Philosophy. First published 18 December 2013; substantive revision 14 October 2022. 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). London: NICE; 2022, last updated 13 October 2026. Section 4.10.8. https://www.nice.org.uk/process/pmg36
• Turner HC, Archer RA, Downey LE, Isaranuwatchai W, Chalkidou K, Jit M, Teerawattananon Y. An introduction to the main types of economic evaluations used for informing priority setting and resource allocation in healthcare: key features, uses, and limitations. Frontiers in Public Health. 2021;9:722927. doi:10.3389/fpubh.2021.722927