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The Quality of Life$

Martha Nussbaum and Amartya Sen

Print publication date: 1993

Print ISBN-13: 9780198287971

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198287976.001.0001

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John Roemer: Distributing Health: The Allocation of Resources by an International Agency

John Roemer: Distributing Health: The Allocation of Resources by an International Agency

(p.358) John Roemer: Distributing Health: The Allocation of Resources by an International Agency
The Quality of Life

Paul Seabright

Oxford University Press

Abstract and Keywords

Seabright comments on two issues in Roemer's paper: (1) the comparison of theory with practice when technologies are changing over time is more difficult than Roemer implies; and (2) while he is in agreement with the enterprise of developing normative rules and using them to assess the practice of policy‐makers, Seabright believes that Roemer needs a more persuasive rule than the leximin allocation rule.

Keywords:   leximin rule, monotonicity, resource allocation, technologies

It is rare for contributors to the literature on social choice theory to discuss how a social choice rule might be implemented in a practical policy‐making context. It is rarer still for them to examine the practice of political institutions to see how these measure up to the standards prescribed by theory. In his paper John Roemer offers us the pioneering combination of an axiomatic argument in social choice and a practical study of the allocation of resources by the World Health Organization (WHO). He discusses a set of criteria that he believes a satisfactory resource allocation rule for such an agency may be constrained to satisfy; he then shows that only one rule satisfies all the criteria. He argues that the practice of the WHO diverges from the rule; and he leaves us guessing whether to conclude that the agency's practice should be adapted to fit the rule better, or our criteria for a rule adapted to match the constraints of practice. It is a stimulating paper whose example I hope will be widely emulated. I shall confine my comments to two issues: first, it is harder than he implies to compare theory with practice when technologies are changing over time; second, and more important, while I support the enterprise of developing normative rules and using them to assess the practice of policy‐makers, I wish that he had discussed a more persuasive rule than the leximin allocation rule, some of whose unattractive features deserve a more conspicuous exposure than he gives them.

Roemer begins by imposing restrictions on the kinds of budget allocation rule that can be judged acceptable. There are seven axioms: Pareto optimality, the independence of ancillary information, monotonicity, symmetry, consistency of resource allocation across dimension, the deletion of irrelevant countries, and the domain condition. It is worth noting straight away that the domain condition is less demanding than it appears, because of the restriction that the technologies u i(.) be represented by concave functions. Roemer's defence of this assumption for the WHO's programmes is not very convincing: of course the functions u i(.) become concave at some level, but they may well contain convex segments, and actual resource allocation problems may find countries on these convex segments. Given the importance of infrastructural investment (which typically displays increasing returns) in reducing infant mortality, the relevance of Theorem 1 to real‐world problems is not quite clear.

Several of the seven axioms raise important issues, but here I shall concentrate on monotonicity (I disagree that ‘the axioms can be seen as either quite weak . . . (p.359) or quite reasonable, or both’, but have no space to pursue the point here). Monotonicity is the only axiom that appears to have been violated by the practice of the WHO to date, according to the evidence in Roemer's Table 1. Even here he argues that some apparent violations of monotonicity are really due to changes in accounting procedures. The sole clear case of violation, he contends, was in 1984–5, where in spite of a fall in the total budget the budgets for some regions increased. Now one of the regions whose real allocation increased was Africa. The continent at this time was going through considerable turmoil: the world had only recently become aware of the importance of Africa's AIDS epidemic, there were threats to food supplies from poor harvests and civil disturbance in a number of areas, and falling commodity prices had delivered a major blow to many countries' economic prospects. In terms of Roemer's economic environments, this means that their technologies had changed (alternatively, one could say that their country‐specific resources had been cut back). Either way, we cannot judge, from the rise in their real budget allocation at a time when the total WHO budget was falling, that the monotonicity axiom was violated. Roemer does not, in any case, attach great significance to this (he argues that the spirit of monotonicity pervades much of the agency's practice). My point is merely that even if we can establish clearly whether or not the agency is following a particular rule (WHO clearly does not follow leximin), diagnosing axiom violation on the basis of the evidence realistically available may be much harder than Roemer makes it appear. His enterprise, though important, is also difficult.

The points I have made so far are largely matters of emphasis. But the shortcomings of the leximin rule are a more serious matter. Roemer discusses an attractive alternative to leximin, namely population‐weighted utilitarianism. It should be noted that this is not actually utilitarianism, but rather a rule for allocating resources that has some structural features that are similar to utilitarianism properly so called. Instead of maximizing total utility this rule recommends maximizing the total number of infant lives saved. As Roemer points out, the shortcomings of utilitarianism (its indifference to the boundaries between persons, for instance) are not obviously applicable here: saving infant lives would seem to be valuable irrespective of where the infants are situated, and the boundaries between nations morally irrelevant to that end. He provides no further argument against population‐weighted utilitarianism, so presumably he considers its failure to satisfy the monotonicity axiom the most likely reason for its failure to find favour with the WHO. This would be a satisfactory outcome only if our intuitions in favour of the monotonicity axiom were more compelling than our intuitions in favour of maximizing the number of infant lives saved. Are they?

To see whether they are we can do no better than to examine an example in which population‐weighted utilitarianism violates monotonicity. Consider two countries: in the first, infant mortality is neither very high nor very low, and its causes are a familiar mixture of poor sanitation, low nutrition, shortages (p.360) of primary health care, and low educational levels. Most of the obvious infrastructural investments in lowering infant mortality have already been made, however, and significant extra resources would be required to lower it significantly further. In the second country, infant mortality is considerably higher: in addition to the familiar causes (the state of poverty and infrastructure is roughly the same in the two countries), the second country also suffers from a serious endemic water‐borne disease. Since the country is criss‐crossed by rivers, lakes, and canals the cost of eradicating the disease by destroying its habitat would far exceed the total available resources in both countries. There is an alternative cure using genetic engineering to eradicate the parasite that breeds in the water, but initially the cost of this technology is prohibitively high. At a certain date, however, there is a significant fall in the price of the genetic engineering technology. This corresponds with an increase in the total resources available to the two countries. It also means that investing resources in the second country produces dramatically greater reductions in infant mortality than before. Provided both countries had previously been recipients of WHO aid, population‐weighted utilitarianism would prescribe that some resources be diverted from existing programmes in both countries towards the programme of parasite eradication. A consequence of this would be that the resources allocated to the first country would decline, in spite of the increase in total resources. This would be an entirely reasonable outcome, since that increase in total resources had made possible the assault on a pressing problem that could not be effectively tackled before.

The monotonicity axiom would rule out this reasonable response. Worse still, the leximin principle would have meant that the first country received no resources at all from the WHO. If the second country had a higher infant mortality rate than the first, the leximin principle would have prescribed that the second country should receive all the available resources so long as the returns, however small, were not precisely zero. So expensive and wasteful programmes of eradicating waterways in the second country might have saved a few hundred infants per year while hundreds of thousands died in the first country through lack of a programme to spread information about oral rehydration therapy. The leximin principle is inexorable. If Liechtenstein (say) were to be afflicted with an AIDS epidemic that lowered its infant mortality rate below that of China or India, then so long as expensive nursing care, by prolonging the lives of AIDS‐infected infants, could make marginal reductions in their mortality rate, WHO aid to China and India would be diverted in its entirety to Liechtenstein (I an assuming that Liechtenstein is a member of the WHO). Leximin can be described as favouring heroic and almost futile programmes over effective and productive ones, so long as the former are not absolutely futile and so long as they occur in sufficiently blighted countries. In turn this makes the boundaries between countries of crucial importance: epidemics may ravage infant lives in regions of China without provoking the tiniest reallocation of resources, but a similar outbreak in Mauritius could (p.361) have major effects on the budget. Nothing could be better calculated to provoke secessionist movements in Bombay, Bangkok, or even (who knows?) the Bronx.

In the end it is unclear how much force an axiomatic argument of this kind should have. Roemer's introductory discussion of the monotonicity axiom, for example, suggests that it is justified not on ethical but on pragmatic grounds, due to the fact that countries contribute as countries to the budget of the WHO. On the other hand, he later discusses the way in which population‐weighted utilitarianism has exerted an influence on the decision‐making of the WHO, albeit in tension with other principles. This might be taken to imply that the monotonicity axiom is not an inscrutable given of the political situation, in which case its ethical shortcomings are of relevance after all. One thing this shows is that using social choice theory to illuminate policy‐making is fraught with uncertainty: to what degree must theorists take themselves to be articulating the preferences of policy‐makers, and to what extent may they legitimately seek to influence those preferences? An instructive contrast is with Roemer's own justly influential article ‘Equality of Resources Implies Equality of Welfare’,1 whose formal argument has a very similar structure to the present one. That article (apart from bringing insights from bargaining theory powerfully to bear on a problem in social choice) draws out the consequences of a particular form of egalitarian social theory. It shows that egalitarianism with respect to resources implies egalitarianism with respect to welfare, provided resources are interpreted sufficiently broadly to enable differences in utility functions between agents to be ascribed to different endowments of ‘internal’ resources. Egalitarianism with respect to welfare has itself some disturbing consequences (the presence of a single severely disabled person would justify diverting enormous resources to that person so long as the marginal welfare benefit of doing so were not quite zero). But it is clear what Roemer's argument establishes: one theory (already articulated by others, notably Ronald Dworkin) implies another, and those who espouse the first should espouse the second if they also accept the auxiliary assumptions. Here, however, it is less clear what the argument of this paper establishes: a set of axioms, which may or may not characterize the principles guiding resource allocation in an international agency, implies an allocation rule that does not characterize the agency's actions—and probably should not, in any case. Should we reform the agency or the principles? The answer is probably that we should reform both. At any rate, the theorem's claim ‘to answer definitively the policy problem of the international agency’ is untenable as long as its conclusion favours leximin. The question of what policy should replace leximin remains very much an open one.


(1) Quarterly Journal of Economics, 101 (1986), 751–82.