We distinguish between strong and weak equality. The most straightforward view of health equity is strong health equality, where every person or group has equal health. In the normative literature on inequalities in health, however, there is almost unanimous agreement that strong equality of health is an unattainable and unattractive goal and should therefore be avoided or modified. For example, in a recent summary of the normative literature on this issue, Asada concludes that:
"Strict equality for all, however, is not an attractive view for various reasons. For example, it denies personal choice. It would be unrealistically expensive. Moreover, it would be unachievable because some determinants of health are beyond human control. Unlike political liberty, strict equality in health for all would not be a feasible nor agreeable goal." 
Brock expresses a similar view in somewhat different words:
" [...] some commitment to equality is a central feature of nearly all theory of justice, with most of the dispute being in what respects should people be equal. However, whatever the relevant arguments, strong objections exist to a fundamental commitment to equality in outcomes or conditions, both in general and as the basis for a special concern for the worst off."  (emphasis added).
Rejecting strong equality of health, the question then becomes when we can reasonably diverge from strong health equality. Below, we will examine four widely held objections to strong equality of health: (1) the levelling down objection, (2) only those inequalities that are social are unjust, (3) individual responsibility, and (4) the problem of biological or technological limitations. On the basis of the examination of these four objections, we defend the weak principle of health equality as a backbone of our proposed framework of fair health distribution.
Levelling down objection
Health economists, Culyer and Wagstaff, in a widely cited article, define an equitable distribution of health care as "simply one which gives rise to an equal distribution of health." They immediately add the following qualification: "Of course, this will almost certainly have to be qualified by a side condition that greater equality cannot be achieved by reducing the health of some as a deliberate act of policy" . This qualification is a response to a common objection to strong equality, the levelling down objection. Parfit has argued that egalitarians should not be concerned about strong equality, but rather be concerned with giving priority to the worst off . No one would argue that we should "blind the sighted to equalize health states with the blind".
Daniels defines the goal of "equity in health" partly in response to the levelling down objection:
"One natural way to understand the goal of equity in health--the goal of health egalitarians--is to say that we should aim, ultimately, to make all people healthy; that is, to help them to function normally over a normal lifespan. Pursuing equality means "levelling up"-- bringing all those in less than full health to the status of the healthy."
We accept the argument that levelling down is never a good thing, but we hold that equality often is. As we demonstrate in the last section, when weak equality and trade-off considerations are combined properly in a pluralist theory of fair distribution, egalitarians can still promote the value of equality. This argument is grounded on a pluralist moral view . Levelling down will never be judged as a good thing for egalitarians if we adopt a pluralist theory that integrates distributional concerns with overall goodness . Equality is not the only value egalitarians promote, but equality is so important that we should not reject it.
Only those inequalities that are social are unjust
Arguably, the strongest objection historically to defining health equity as strong equality in health has been that health is a natural good and cannot be redistributed by institutions (such as the health care system or more broadly, a welfare system) in the same way as income. Many scholars think the distinction between naturally and socially created inequalities is of moral importance. Fairness or justice is concerned only about socially created inequalities, not naturally created inequalities.
This distinction goes back to Rawls, who, more than 35 years ago, distinguished social goods from natural goods and suggested that health should be considered as a natural good . Health cannot be distributed in the same way as political rights or income. Although Rawls' ideal theory did not discuss the distribution of health and health care at all (Rawls famously assumed disease and disability away and stipulated that the parties in the original position are fully cooperating members of society over a complete life), the view of health as a natural good has survived up to this day. From these two assumptions combined (that health is a natural good, and that the parties in the original positions have normal capabilities of their complete lifespan), it follows, for instance, that a severe mental disability is not a concern for justice [Attempts at extending or modifying these assumptions in Rawls can be found in Daniels (1985/2007) and Pogge(1989). Daniels does not build upon Rawls' original assumptions].
Does this distinction between social and natural goods indeed hold, and is it morally relevant and useful? We shall not attempt to review the very interesting debate about the correct interpretation of Rawls' view on this issue, but rather question the factual premise this debate presupposes . In our view, this distinction is irrelevant in thinking about when inequalities in health are unjust.
First, health is primarily a social good. In the world we live in today, the basic institutions of society determine to a large extent the level and distribution of health. According to statistics from the World Mortality Report, life expectancy in many countries has increased by as much as ten years since the early 1970s . This change is mediated through social factors such as economic growth, technology, reduced inequalities, knowledge and investment in public health and health systems. The WHO reports that life expectancy at birth ranges from 77 (for males) and 82 (for females) in Norway to 41 (for both males and females) in Malawi . Natural factors probably play a minor role in explaining this difference. The health of peoples, or nations, is not something given but fundamentally shaped by how societies are organized and how the benefits of cooperation are shared. We know that Malawi is a much poorer country than Norway, and that the social determinants of health (including health care and public health) are unequally distributed between and within the two countries. The literature on the social determinants of health has, convincingly in our view, demonstrated that social factors are dominantly associated with inequalities in health [39, 40]. Health is, then, a concern for social justice.
Second, in most cases it is not possible to distinguish between natural and social causes of disease. Diseases, such as cardiovascular disease or cancer, typically result from the complex interaction between genetic and environmental factors (widely understood to include many of the social determinants of health) [41, 42]. A person may inherit genes that increase the risk for, say, cardiovascular disease, but this risk is substantially modified by personal behaviour, the environment and culture, and the basic institutional structures in which that person grows up. Singling out one etiological factor as natural and others as social is in practice difficult, if not impossible.
Third, natural and genetic inequalities in health are actually taken seriously in health policy and clinical practice. Convincing arguments are needed to depart from this view. For example, women who have inherited the BRA1 gene that increases their lifetime risk for breast and ovarian cancer by up to 70-80% are typically treated with more concern than others, not less. Indeed, why should genetically inherited disease (caused by the natural lottery) be given less or no priority compared to those who acquire a disease because they live in poverty or lack basic education? Whether risk is associated with unfair social circumstances or is the result of the natural lottery, it affects well-being, opportunities and freedom to the same degree. Disease and risk of disease are not in the same category as the colour of our eyes or beauty in our judgment of social obligations. In clinical practice, no one would consider whether a condition is caused by social or natural factors as a decisive reason for different prioritisation. Practice does not make a thing right, but if we consider principles against well-considered intuitions in reflective equilibrium, this widely held intuition should be considered seriously .
Finally, the implications of the distinction between natural and social factors are counterintuitive and not normatively attractive. Some people have low life expectancy because they are poor, lack education and employment. Others may have low life expectancy, even if not so poor, because they happen to be in a natural setting where there are a lot of malaria-carrying mosquitoes. Should this "natural fact" be a factor against a justice concern? "Freedom from malaria" is one of Sen's paradigmatic examples of what an egalitarian theory should focus on . We agree. If anyone thinks that freedom from malaria should not be a concern for justice, it is probably a mistaken expression of the underlying intuitions that there are some health inequalities we cannot, as a society, do anything about. Consider the situation in the early 1980s before the existence of HIV was known, before its ways of transmission was known and before antiretroviral treatment was developed. The fact that some people died prematurely from AIDS at that time could not be considered unfair, because the disease was not possible to prevent or treat.1 Being free from malaria (and HIV today), on the other hand, is a concern for justice because society does have the knowledge and the means to prevent and treat them. In our view, the relevant distinction is whether the institutions of society can respond adequately to a disease or not, which we will elaborate below - not whether the causes are natural or social.
The upshot of this discussion is that most health inequalities should - as a starting point - be considered unjust. The division between health as a natural and a social good is not possible to define. Neither is it morally relevant. [Of course it would be judged unfair if they had been denied access to preventive measures. That many people died prematurely was also a reason to fund HIV research.]
Individuals should have some responsibility for inequality
Another widely held objection to strong health equality is personal responsibility. Temkin, though his work does not focus specifically on health, proposes the following view of which inequalities are of moral concern: "Egalitarians generally believe that it is bad for some to be worse off than others through no fault or choice of their own" . Sen also argues that the issue of personal responsibility has some bearing on the issue of health inequalities:
"What is particularly serious as an injustice is the lack of opportunity that some may have to achieve good health because of inadequate social arrangements, as opposed to, say, a personal decision not to worry about health in particular. In this sense, an illness that is unprevented and untreated for social reasons (because of, say, poverty or the overwhelming force of a community-based epidemic), rather than out of personal choice (such as smoking or other risky behavior by adults), has a particularly negative relevance to social justice." 
Similarly, liberal egalitarian theories of distributive justice argue that a central goal of public policy should be to secure all individuals equal opportunities. All equal opportunity approaches argue that society should eliminate inequalities that arise from factors beyond individual control. One prominent position argues that equal opportunity requires that all inequalities that arise from factors outside the agent's control in the social and the natural lottery, such as a person's natural and genetic abilities should be eliminated, but that inequalities or costs that arise from factors under the agent's control should be accepted .
Applied to the context of health the principle of equality implies that all individuals who make the same choices should be treated as if they were identical with respect to all factors outside their own control. This view holds that natural inequalities (associated with, for example, genetic factors) should be a concern for egalitarian justice.
A common misunderstanding of liberal egalitarianism is that these theories argue that individuals should be held responsible for the consequences of their choice. In the context of health this would imply that all inequalities in health are counted as fair if the agent in question could have avoided bad health outcomes by making different choices. However, the principle of responsibility states that individuals should be held responsible for their choices, not for the consequences of their choices [46, 47]. It is only in the special case where the outcome only depends on the individual's choices and not on any other factors (including the responsibility of society) that this principle implies that individuals should be held responsible for the consequences of their actions. To hold people responsible for the actual consequences of their choice would therefore be to hold them responsible for too much . The implication of the principle of responsibility on the concept of health equality is therefore in practice limited.
Interestingly, health systems of liberal societies generally embody this (correctly understood) principle of responsibility. We discourage people from practising "irresponsible" health behaviours, such as smoking, unsafe sex, and sedentary life styles, through public health and health promotion. For some behaviours, we make people responsible for their action by imposing taxes (e.g., tax on cigarettes) or making them illegal (e.g., seat belt laws). But our health systems do not treat the reckless and the sensible differently.
Strong equality is unachievable because of limitations of biology and technology
The final objection to strong health equality commonly found in the literature relates to considerations about biological and technological limitations. Many definitions of health inequity proposed by health science researchers suggest that inequalities in health are fair if those inequalities are unavoidable. Whitehead and Dahlgren explicitly incorporate unavoidability in their definition. Similarly, the pragmatic definition of health equity adopted by the International Society for Equity in Health in 2000 focuses on remediability: "Equity in health is the absence of systematic and potentially remediable differences in one or more aspects of health across socially, demographically, or geographically defined populations or population subgroups" . Furthermore, though not as explicit as the two definitions above, Gakidou, Murray, and Frenk, in their proposal for measuring health inequities across countries for The World Health Report 2000, consider health inequalities caused by factors amenable to human interventions as unjust [4, 27].
The concern for unavoidability in the health equity literature echoes the idea of shortfall equality developed by Sen and Anand for the human development index . They are concerned about the fact that some people are more efficient converters of resources or goods to well-being (or health) than others . Anand and Sen explain:
"In those cases in which human diversity is so powerful that it is impossible to equalize the maximal levels that are potentially achievable, there is a basic ambiguity in assessing achievement, and in judging equality of achievement (or of the freedom to achieve). If the maximal achievement of person 1 -- under the most favourable circumstances -- is, say, x, and that for person 2 is 2x, then equality of attainment would invariably leave person 2 below her potential achievement." 
As an alternative to strong or attainment equality, Anand and Sen defend shortfall equality (for a more extended discussion and some reservations, see ). This view can most easily be illustrated by reference to gender inequality: There is a commonly observed gender difference in life expectancy of about 2-5 years (researchers disagree about the correct figure), favouring women . In a society where life expectancy is, for example, 60 years for men and women, this equality in life expectancy by sex would be judged equitable if strong equality is the normative standard, while it is inequitable if shortfall equality is the standard.
The key question is: if strong equality is not feasible, should egalitarians be concerned about strong equality or equal shortfall from what is feasible? In short, should we be concerned about all health inequalities (measured from an equal baseline), or only shortfall inequalities (measured from a baseline defined by what is possible)?
We agree with Anand and Sen, that equity concerns inequalities that are avoidable. Although they do not clearly define when we should consider inequalities to be unavoidable, the term often includes limitations of biology, technology or knowledge. Anand and Sen refer to limitations of biology when they defend shortfall equality in the case of men and women as illustrated above. Our view of biological limitations is that, whether they are functional or mental limitations, egalitarians should not count them as legitimate shortfalls. Above, we argued against the view that only those inequalities that are social are unjust. In health policy and clinical practice, we take natural inequalities in health seriously and consider them as important as social inequalities in health. Inequalities due to biology are examples of natural inequalities, and we do not see why gender deserves special consideration among many other biological factors, such as genetics.
It appears reasonable, on the other hand, that egalitarians should be concerned about limitations caused by the level of technology or knowledge available. The implications of this departure from strong equality are probably substantial as technological limitations change over time. To repeat our example from above, using shortfall equality as the standard, people dying prematurely from HIV/AIDS in the early 1980s (before the aetiology of the disease was known) were suffering tremendously, but their tragically reduced life expectancy was not unfair. Given the medical advancement for HIV/AIDS treatment in recent decades, however, the same amount of suffering and premature death now is quite rightly considered inequitable.
We believe the idea of shortfall equality applied to technological limitations reflects a sound principle and well-considered moral intuitions that many people hold regarding equity -although what such limitations entail requires further clarification.
Statement of the weak principle of health equality
The discussion above on four objections to strong health inequality suggests the following. First, health equity should not be improved by "levelling down," that is, making people less healthy. The objection loses force if concern for equality is integrated with concern for average health as required by a pluralist theory of fair distribution. Second, when considering which health inequalities are unjust, distinguishing social and natural factors is morally irrelevant. Third, health inequalities are acceptable if they are derived completely from choices that free and fully informed adults make. But such health inequalities are extremely rare, and in practice, individuals cannot often be held responsible for health inequalities due to choice. Finally, health inequalities are fair if they are associated with technological limitations on further health improvements.
Taken together, we propose a definition of weak health inequality: every person or group should have equal health except when: (a) health equality is only possible by making someone less healthy, or (b) technological limitations exist to further health improvements. In other words, the weak principle of health equality suggests that health inequalities that are amenable to positive human interventions are unacceptable.