The Moral Arbitrariness of the Location of the Thresholds
As we have seen, a standard objection to sufficiency principles is that it seems difficult to set the threshold level non-arbitrarily. It is rarely noticed, however, that the same criticism may be directed towards the priority view. In its standard formulation, the priority view says that it matters more to benefit people the worse off they are. Irrespective of the problems we have raised (and that have been raised elsewhere) regarding the priority view, its plausibility will to a large extent depend on exactly how much more it matters to benefit people the worse off they are. And if x times more, why x times more and not y times more or z times more? It may seem obvious that it matters more to benefit a patient with severe cancer than a patient with a seasonal cold but how much more is less obvious. Likewise, with regard to DTP, it seems obvious that severe cancer is below the lower threshold and the seasonal cold is above it. But it is less obvious exactly where the threshold should be set. However, if one believes that the priority view may be specified in this respect (whatever methodology one finds appropriate for such specification), it seems no less reasonable to allow for thresholds, even if set roughly (perhaps some vagueness should be allowed).Footnote 16
Moreover, it seems that the constraint that DTP establishes on certain kinds of aggregation is achieved quite non-arbitrarily and clearly. Although it may be vague, uncertain, and to some extent arbitrary exactly where to set the threshold between being worst off and moderately badly off, and between being moderately badly off and best off, the distance between being worst off and best off is significant and clear.
Even though DTP does not ascribe absolute priority to people below the lower threshold as standard sufficiency principles do there may still be cases where quite small differences play a decisive role for priority setting.Footnote 17 For example, if there is an individual A just below the lower threshold and an individual B just above this threshold standard sufficiency ascribes absolute priority to A. In contrast, in such a case, DTP may imply that B outweigh A. Now, suppose next that there is also a group C just above the upper threshold. In a choice between A, B and C DTP implies that since there are still needs that are unmet among the worst off the first choice is between A and B. Suppose next that DTP implies that A should be treated and suppose further that A was the last person among the worst off. Since there are now no unmet needs among the worst off tradeoffs between the moderately badly off and the best off are allowed. In such a case DTP may imply that C outweighs B. In this case, one might argue that it is arbitrary that DTP implies that A has absolute priority over C but B does not.
First, note that this case would only arise in very specific circumstances as DTP prescribes that everyone (including A) among the worst off should be treated before treating C can be an option. Hence, this scenario is only possible when A is the last one among the worst off.
Second, if one is concerned about letting small differences play a decisive role in determining decisions for priority setting we should again compare DTP to other views. For example, the priority view may have similar implications. Suppose we have ascribed a certain moral weight to benefits accruing to the worse off and suppose again the choice between A, B and C. A may be just badly enough to outweigh the benefits accruing to the individuals in C but B may be just below the margin to do so. Once again, DTP is not in a worse place than the priority view stated by itself.
The Arbitrariness of the Number of Thresholds
One may ask what determines the number of thresholds. For one thing, there seems to be some intuitive appeal in the idea that there is something very different between the very severe conditions and the mild ones and that this difference is worth taking seriously from a moral point of view.Footnote 18 DTP can account for this difference because of its multiple thresholds.
Secondly, DTP employs two thresholds in order to avoid certain outcomes that cannot plausibly be implied by a principle of need, without prohibiting aggregation altogether. One may ask if this normative work could be done by a single upper threshold. It seems as if a possible outcome of DTP is that the best off remain untreated as there may always be something that could be done for the worst off. If this is the case, why not settle with an upper threshold and employ absolute priority to people below it? We could simply accept that the best off often remain untreated and that the priority view holds below. Let us call this view Upper Threshold Priority (UTP). Note that UTP would not be more favorable than DTP to the worst off but worse than DTP for the best off. UTP implies that the best off should be treated if and only if there is nothing more that can be done for the worst off and the moderately badly off. However, DTP leaves room for a tradeoff between the best off and the moderately badly off, given that there is nothing more that can be done in order to further fulfil the needs among the worst off.
Although we have focused on the moral importance that principles of need ascribe to benefitting the worst off in this paper, a principle of need should do more than that. A well-constructed principle of need should also have the resources to handle normative questions that concern the moderately badly off and the best off.
Thirdly, even though DTP avoids outcomes where the best off outweigh the worst off, it may still prescribe outcomes with a similar formal structure. For example, there may be some group at 0.79 that outweighs people at 0.1. One may take this as a reason to add a third, or perhaps a fourth, threshold. This would decrease the distance between the worst off and people that may outweigh the worst off. Even though there is no problem (in principle) with additional thresholds, such a reduction in distance between thresholds would undermine a substantial normative claim that DTP, constructed with two thresholds, accounts for. The advantage of employing two thresholds, and no more, is that it accounts for the moral importance of the difference between health states among the best off and the worst off. As one increases the number of thresholds one decreases the extent to which DTP plausibly accounts for the moral importance of this difference.
A Temptation for a Comparative Approach
One may argue that the underlying intuitive appeal of DTP is not the absolute position of the thresholds but the difference between the worst off and the best off. It may be that DTP appeals to an egalitarian intuition according to which tradeoffs between people who are sufficiently far away in relation to each other should be avoided. Voorhoeve  sketches a view that he refers to as Aggregate Relevant Claims (ARC) and that is similar to DTP in several respects. Much like we do in this paper, Voorhoeve aims to construct a distributive principle that accounts for the view that it seems right to aggregate some claims but wrong to aggregate others. However, while ARC is similar to DTP in several ways, it also differs in a number of important respects. In the following we shall consider a number of points made by Voorhoeve .
First, Voorhoeve’s primary aim is to construct a principle that can account for the view that while it seems right to aggregate some claims it seems wrong to aggregate others. The project undertaken in this paper is to construct the best version of a need principle with a primary focus on aggregation. ARC and DTP may have similar implications regarding how to allocate health care resources. However, the moral basis for why a given resource allocation ought to be done is different. ARC aggregates claims whose strength is dependent on (a) the increase in well-being, and (b) the level of well-being from which this increase takes place . Need-based claims are also dependent on (a) and (b) but the interpretation of (b) is different: need-based claims are best understood as non-comparative as they are based on people’s absolute levels and have an independent standing of the relation to other people’s needs [15, 16]. Therefore, while need principles may be plausibly specified in terms of a concern for the worse off (the priority view) as well as sufficiency principles, the idea that need is about the strength of claims in relation to the strongest competing claim seems counterintuitive. Accordingly, ARC is not a plausible specification of a principle of need.
Second, while ARC bans tradeoffs on the basis of (a) as well as (b), DTP bans tradeoffs on the basis of (b) alone. Hence, DTP effectively rules out the possibility that the best off benefit at the expense of the worst off. ARC seems open to this possibility if the size of the benefit accruing to the best off is large enough [see e.g. 43, p. 68 Fn 6]. Hence, DTP seems to say something stronger than ARC, namely that no amount of benefits accruing to the best off can outweigh benefits accruing to the worst off.
Third, one might argue that Voorhoeve is better placed than DTP to answer the objection from arbitrariness. He offers the following rationale for ARC. The claims that are not appropriate for aggregation are referred to as irrelevant. The relevance of a claim is dependent on whether the tradeoff would be permissible from the personal perspective of the person with the strongest claim [see 43, p. 72]. Voorhoeve argues that although the actual degree of permissibility will vary among individuals there will be some ideal degree that should be considered appropriate [43, p. 73]. This proposed rationale for ARC reflects, according to Voorhoeve, a respect for the separateness of persons. DTP does not make reference to the separateness of persons. Rather, it says that, from a third person perspective, there seems to be some degree of being badly off that should have absolute priority over mild conditions. It seems as if also adherents of ARC are pushed towards a similar explanation as they appeal to an ideal appropriate degree of permissibility. Hence, ARC does, in the end, justify the aptness of tradeoffs from a third person perspective, just like DTP does. Therefore, it is not the case that ARC is in a better position than DTP to handle the issue of arbitrariness.
The Moral (Ir)Relevance of Benefits Accruing to the Well Off
Frankfurt  provides a reason for a sufficiency principle rather than principles of equality in the following way: “We tend to be quite unmoved, after all, by inequalities between the well-to-do and the rich” [11, p. 146]. Crisp  argues in much the same way for his move from priority to sufficiency when he says that “…any version of the priority view must fail: when people reach a certain level, even if they are worse off than others, benefiting them does not, in itself, matter more” [8, p. 754]. In other words: even though the priority view does account for the diminishing moral importance of benefits there still seems to be some cut off point for when benefits have no, or significantly less, moral importance [see also 5].
Does this objection have any relevance for constructing a principle of need for health care priority setting? While DTP prohibits tradeoffs between the best off and the worst off, it still employs the priority view within the groups. Hence, there may be some group among the best off at, say, 0.98 that trumps some other group among the best off at, say, 0.99. This implication seems analogous to the problem sketched by Frankfurt and Crisp. However, the objection is no reason to reject the argument put forth in this paper since we assume that there is an optimal level of health. The objection just does not seem to be relevant to principles that employ currencies of which there is an optimal level. While DTP implies that some amount of ill-health carries less moral weight, there is no amount of ill-health that carries no weight. Hence, there is nothing strange in claiming that a sore throat ought to outweigh a slightly sore throat.
For a principle to guide priority setting in health care it must be able to rank the goodness of all possible distributions (i.e., it must be transitive in the deontic sense).Footnote 19 One might argue that DTP cannot do that. Consider the following series of choices (a–c) in the following three cases (i–iii). In each case, there are two alternatives of which only one can be chosen.Footnote 20
We can either (a) provide a minor (but not trivial) benefit to one individual among the worst off or (b) provide large benefits to a hundred thousand people among the moderately badly off. In such a case DTP implies that we ought to (b) treat the moderately badly off.
We can either (b) treat the hundred thousand among the moderately badly off or (c) provide large benefits to a billion people among the best off. In this case DTP implies that we ought to (c) treat the billion people among the best off.
However, DTP is not supposed to allow that the best off benefit at the expense of the worst off. Therefore, it seems as if we should choose to (a) benefit the individual among the worst off rather than (c) treat the billion people among the best off.
It may seem as if DTP cannot answer what ought to be done here. It seems as if we cannot avoid acting wrongly. This cannot be acceptable for a distributive principle. However, DTP does have implications for such cases. In case (i) it is correct that DTP implies (b) rather than (a). However, in case (ii), DTP implies (c) rather than (b) if there is nothing more that can be done in order to further fulfil the needs among the worst off. Hence, DTP only implies the tradeoff suggested in case (ii) if there are no unmet needs among the worst off that can be met. Therefore, as alternative (a) is on the table, case (iii) is never actualized. This means that the worst off have absolute priority over the best off.