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Unweighted lotteries and compounding injustice: reply to Schmidt et al
  1. Alex James Miller Tate1,2
  1. 1 Centre for Medical Law & Ethics, King's College London, London, Greater London, UK
  2. 2 Philosophy, King's College London, London, UK
  1. Correspondence to Dr Alex James Miller Tate, Centre for Medical Law and Ethics, King's College London, London WC2R 2LS, UK; alexander.miller_tate{at}


I argue that Schmidt et al, while correctly diagnosing the serious racial inequity in current ventilator rationing procedures, misidentify a corresponding racial inequity issue in alternative ‘unweighted lottery’ procedures. Unweighted lottery procedures do not ‘compound’ (in the relevant sense) prior structural injustices. However, Schmidt et al do gesture towards a real problem with unweighted lotteries that previous advocates of lottery-based allocation procedures, myself included, have previously overlooked. On the basis that there are independent reasons to prefer lottery-based allocation of scarce lifesaving healthcare resources, I develop this idea, arguing that unweighted lottery procedures fail to satisfy healthcare providers’ duty to prevent unjust population-level health outcomes, and thus that lotteries weighted in favour of Black individuals (and others who experience serious health injustice) are to be preferred.

  • allocation of health care resources
  • COVID-19
  • distributive justice
  • minorities
  • Public Health Ethics

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Selective rationing policies, unweighted lotteries and compounding injustice

In an extremely important recent paper,1 Schmidt et al argue that dominant ventilator rationing guidance, based in significant part on survival odds as determined by a patient’s Sequential Organ Failure Assessment (SOFA) score, compounds prior structural injustice experienced by Black patients by tending to deprioritise them for ventilator access. The SOFA does this because it incorporates creatinine levels into the assessment, without controlling for pre-existing structural injustices that may result in higher creatinine levels in Black populations.1 2 Policies that instead (or also) use the presence of certain pre-existing comorbidities to prioritise ventilator access have the same problem; they fail to control for the disproportionate likelihood that Black patients will have those comorbidities, as a direct result of prior structural injustices and socially determined health inequalities.3

I fully agree with Schmidt et al on this point, and find the account of ‘compounding injustice’ they cite in support of it enlightening. According to Hellman,4 an actor’s action or policy compounds prior injustice just in case,

  1. The actor involves themselves in or ‘interacts with’ (p.4) the injustice or its effects in such a way as to bear some responsibility for it.

  2. The action amplifies the effects of the injustice in the sense of making its effects more severe or spreading them into a new context or ‘sphere’ (p.4).

Both requirements are clearly met in the case of the rationing guidance policies analysed by Schmidt et al. First, medical professionals and/or the institutions that set and enforce the policies involve themselves in Black individuals’ prior experiences of health injustice by making the injustices’ effects (higher creatinine levels and/or certain comorbidities) part of the criteria for deprioritising people for ventilator access. That is, the effect of a prior injustice is part of the institution’s reason for deprioritising certain individuals.4 Second, the effects of the initial injustice are clearly amplified by the policy’s effects. Since ventilators can be life-saving, and so being deprioritised for access to one can equate to a death sentence, the rationing policies transform poorer baseline health (the result of structural injustice) into an inflated risk of death. They make the effects of prior injustice relevant to whose lives are saved now; when a Black patient suffers and dies due to being refused a ventilator, they do so in part because of the prior injustice they have faced, so the effects of the prior injustice now additionally include being deprioritised for ventilator support.

Schmidt et al 1 rightly focus their attention on policies that prioritise on the basis of survival odds and postdischarge life expectancy, since such policies have been implemented and endorsed across the USA5 and the UK,6 as well as within the Bioethics literature that emerged throughout 2020.7–9 Briefly, however, they also suggest that a policy that prioritised people for ventilator access via an unweighted lottery would also compound past health injustice for back patients. They1 write, referring to their fictional case of two Black patients, James and Martin, and one White patient, John,

…a lottery could give everyone a seemingly equal chance. However, there is no baseline equality: James’ and Martin’s poor health reflects historical and structural disadvantages, and conversely, historical and structural advantages shaped John’s better health…An unqualified lottery would therefore simultaneously further increase John’s past advantage, and reaffirm and compound James’ and Martin’s prior disadvantage. (p.1, emphasis mine)

If we assume that Hellman’s4 is the correct account of what it is to compound injustice, then this claim seems to be strictly incorrect. An unweighted lottery policy does not involve itself in past structural injustice, since, if James and Martin are deprioritised by such a lottery, neither their past experiences of injustice nor the effects thereof are the reason for this. Moreover, when a person is deprioritised by an unweighted lottery, this is not because of the injustices they have previously suffered, since the lottery is, by design, indifferent to individuals’ pasts. So, in such a situation, individuals’ past experiences of injustice are not amplified by the lottery policy either.

Some might take this as a sign that there is no mishandling of past injustices when it comes to using an unweighted lottery to prioritise ventilator access. This would be an error. Although unweighted lotteries do not compound past injustice (in Hellman’s sense)4 they do violate a duty to prevent further inequity, as I explain below.

Lotteries and the duty to compensate

It has recently been argued10 11 that lotteries are generally preferable to selective rationing policies, since any attempt to prioritise on the basis of survival probability (or similar health metrics) (1) predictably distribute the burden of avoidable mortality and morbidity unjustly onto elderly and disabled populations10 12 13 (as well as, derivatively, other disadvantaged populations, including Black populations, with proportionately higher rates of prospect-altering disability and chronic illness3), and (2) wrongly treat the healthcare claims of those patients most urgently in need of medical attention (again, disproportionately those who are old, disabled, or members of groups with proportionately higher rates of prospect-altering disability/chronic illness) as being weaker than those with whom they are competing for resources.10 11 This would be so even if the measures used were adjusted for measures of social deprivation, or somehow altered so as to track only survival odds and not (simultaneously) the effects of structural injustice, as Schmidt et al 1 recommend. This is because, though a huge improvement on the status quo, such a system will still unfairly discount the claims of those who, by natural misfortune alone, are likely to be sicker when being considered for ventilator support in a way that reduces their odds of surviving to come off it (eg, the immunosuppressed or those with already damaged lungs).10 11 Natural misfortune (as captured by the most robust and injustice-adjusted measures of survival probability) no more weakens one’s claims on healthcare than unjust discrimination does.

I don’t have space to further defend this position here (see reference for my considered view).10 But what should lottery defenders say about Schmidt et al’s challenge to unweighted lotteries? Despite the fact that I do not think unweighted lotteries compound the effects of health injustice in Hellman’s4 sense, I thank Schmidt et al for the spirit of their corrective. Previous work has missed a very troubling feature of unweighted lottery procedures.

Unweighted lottery procedures violate healthcare providers’ duty to prevent, where possible, unjust health outcomes in Black populations (and other populations experiencing health inequity as a result of structural injustice). This duty is distinguished from the duty to avoid compounding injustice in two main respects. First, it is a duty to prevent an undesirable outcome, not to refrain from enacting a particular kind of wrong. Second, it involves leveraging the population-level effects of allocation frameworks to correct for past injustices, rather than merely trying to avoid making their effects worse. That healthcare providers have a duty of this sort follows from so-called ‘social justice’ prioritarian principles.14 Healthcare providers have a duty to correct for unequal health outcomes that are the result of systematic injustice (ie, unjust health outcomes) by prioritising those worst affected by them. This may include treating claims on healthcare resources made by those who experience serious health injustice as stronger than others’.

While systematic injustices are not implicated in the process of selecting individuals for treatment by unweighted lottery, they are implicated in rates of hospitalisation in need of a ventilator,15 and thus, in conditions of scarcity and an implemented lottery policy, rates of being entered into a lottery for a ventilator (or ‘lottery exposure’) as well. Unweighted lotteries will result in disproportionate (according to overall population size) numbers of Black people, and others exposed to prior systematic injustice, being deprioritised for ventilator access relative to White counterparts, simply as a function of lottery exposure. If proportionately more Black people are entered into unweighted lotteries, then proportionately more will invariably ‘lose out’. In this case, injustices previously done to individuals are not amplified (in Hellman’s4 sense), since neither past injustices nor the effects thereof affect any individual’s position in the priority order. Yet population-level injustice is amplified in this way, as a function of lottery exposure, because population-level overexposure to lotteries is allowed to translate into disproportionately poor population-level health outcomes.

While healthcare providers cannot plausibly equalise baseline rates of lottery exposure by themselves, they can adjust for it by weighting the lotteries in favour of Black people, as well as members of other social groups at disproportionate risk of lottery exposure as a result of health injustice (ie, by treating such groups’ claims on healthcare as stronger than others’ in virtue of the health injustice they have faced). This could be achieved by using Area Deprivation Index data,16 just as Schmidt et al suggest using such data to ‘correct’ prioritisation procedures based on survival odds. Since weighting these lotteries will prevent or mitigate disproportionately poor health outcomes in these populations arising as a result of prior health injustices, providers are duty-bound to do so, on social justice prioritarian grounds.14 Thus, healthcare providers have a duty to correct for prior health injustice by weighting lottery-based allocation procedures in favour of those who experience it.

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I thank Harald Schmidt for a helpful exchange on this paper, and for encouraging me to submit at as a response.



  • Contributors AJMT is the sole author.

  • Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

  • Competing interests None declared.

  • Provenance and peer review Not commissioned; externally peer reviewed.

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