Critical‐level Sufficientarianism*

Sufficientarianism is a general class of distributional principles that assign absolute priority to those below a threshold level that represents a minimally acceptable standard of well-being. This topic has received an increasing amount of attention in the recent literature.11 See, for instance, Crisp 2003; Huseby 2010; Shields 2012, 2016. The notion of sufficientarianism can be traced back to Frankfurt who writes that "[w]hat is important from the point of view of morality is not that everyone should have the same but that each should have enough."22 Frankfurt 1987, pp. 21–2. This theory relies on the existence of some threshold value of sufficiency: if an individual's well-being is above the threshold, then he or she is deemed to have enough. In this article, we employ an axiological approach to identify a class of sufficientarian principles. Our starting point is the notion of absolute priority, a requirement that we consider to be at the very core of sufficientarian ideas. Absolute priority postulates that attention is to be focused on those whose well-being is below the threshold, and the utilities of those above the threshold only matter as a tie-breaker if the criterion to be applied below the threshold fails to be decisive. The feature that is novel to our approach is that we combine this fundamental sufficientarian principle with axioms that have a distinctly utilitarian flavor. This allows us to develop a sufficientarian theory that is based on utilitarian principles. Our most important observation is that our theory, which we refer to as critical-level sufficientarianism, necessarily follows as a consequence of adding the absolute-priority requirement to utilitarian axioms. The critical-level sufficientarian criteria represent an adaptation of critical-level generalized utilitarianism, a theory of justice that originates in the literature on population ethics. Critical-level generalized-utilitarian population principles are introduced in a fundamental contribution by Blackorby and Donaldson.33 Blackorby and Donaldson 1984, pp. 20–2. It employs a fixed critical level of utility that represents the level of well-being such that adding a person at that level does not change moral goodness, provided that no one else's utility is affected by this population augmentation. Our principles lexically apply critical-level generalized utilitarianism to those below the threshold first and, if this criterion results in equal goodness, use a critical-level generalized-utilitarian principle above the threshold as a tie-breaking device. In a sense, our theory can be seen as a refinement of Crisp's proposal which has been examined axiologically in a recent contribution by Hirose.44 Crisp 2003, pp. 755–63; Hirose 2016, pp. 62–4. Brown's absolute sufficientism is a special case of critical-level sufficientarianism.55 Brown 2005, p. 213. Section II reviews important variants of sufficientarianism that appear in the previous literature. The properties that we impose on sufficientarian principles are defined and defended in Section III. They include a formulation of a version of absolute priority compatible with most approaches that can be found in the requisite literature. The other properties that we impose are characteristic of generalized utilitarianism. Section IV presents the definition of our critical-level sufficientarian rankings as adaptations of the critical-level generalized-utilitarian population principles, and then provides the main result of the article—an axiomatic characterization of critical-level sufficientarianism. In Section V, we use well-established transfer principles to identify the subclass of our principles that are compatible with these conditions. Section VI concludes, and more formal statements of our properties as well as the proof of our characterization result appear in the Appendix. Frankfurt recommends "to distribute the available resources in such a way that as many people as possible have enough or, in other words, to maximize the incidence of sufficiency."66 Frankfurt 1987, p. 31. His proposal, which is based on the number of those above the threshold, is characterized in a framework that focuses on opportunities (or chances of success) by Alcantud et al. 2019. See also Roemer 2004 for an assessment. Since Frankfurt restricts attention to a fixed population, it does not matter whether the absolute number of people above the threshold is considered or a relative notion (which divides this number by total population size) is employed.77 Frankfurt 1987. Of course, this distinction is crucial once the population is permitted to change. Consider, for example, a society comprised of 100 individuals. Among them, 40 individuals are above the threshold. Suppose now that 100 additional individuals are born, and 20 of these are above the threshold. The absolute number of individuals who have enough increases, but their number relative to total population size decreases. Thus, an absolute-number interpretation suggests that this addition is desirable, whereas a relative-number sufficientarian approach recommends against this population augmentation. Frankfurt's formulation is criticized by Casal who writes that "the thesis favors a world overpopulated with individuals just above sufficiency, and perhaps containing many far below that line, over a less crowded world where everybody is very well off."88 Casal 2007, p. 298. Casal suggests that a natural extension of Frankfurt's criterion to a variable-population framework consists of the ratio of the number of people above the threshold and the total number of individuals in the society.99 Ibid.; Frankfurt 1987. This proposal corresponds to the head-count poverty index if the threshold of sufficiency is interpreted as the poverty line. A second point raised by Casal is that "Frankfurt's statement remains implausible as it requires raising one individual from slightly beneath to slightly above the threshold, even when doing so involves placing an unlimited number of individuals who were previously also just beneath the threshold far below it. Moreover, the statement requires raising a million and one from just below to just above the threshold rather than one million from intense deprivation to paradisiacal conditions."1010 Casal 2007, p. 298. This second criticism focuses on the poor performance of Frankfurt's sufficientarian account when it comes to distributional sensitivity—the depth of insufficiency is not taken into consideration by Frankfurt's criterion. Our axiomatic analysis examines these observations from a novel perspective. We propose an axiologically more appealing formulation of the head-count approach and argue that, even in this alternative incarnation, it suffers from serious limitations; see Section III. A distributionally sensitive version of sufficientarianism is proposed by Crisp, who advocates the view that "[b]elow the threshold, benefiting people matters more the worse off those people are, the more of those people there are, and the greater the size of the benefit in question."1111 Crisp 2003, p. 758. His formulation can be regarded as an attempt to incorporate some aspects of prioritarianism into a theory of sufficientarianism. Crisp suggests resolving trade-offs between people below and above the threshold in a way so that "absolute priority is to be given to benefits to those below the threshold" but "[a]bove the threshold, or in cases concerning only trivial benefits below the threshold, no priority is to be given."1212 Ibid. According to this proposal, a small progressive transfer from the rich to the poor is considered to be morally desirable. There are three axiological requirements in Crisp's notion of sufficientarianism, namely, (1) absolute priority is assigned to the aggregate utility of those below the threshold; (2) among those below the threshold, a transfer from a relatively rich person to a relatively poor person is morally desirable; and (3) a transfer among those above the threshold does not change goodness according to the sufficientarian ranking. The second and third requirements are variants of transfer principles, which can be traced back to early contributions in welfare economics; see Section V. We note that (2) is not satisfied by Frankfurt's formulation. The first requirement is compatible with both Frankfurt's and Crisp's approaches, and we use it as part of our core axiological principle of sufficientarianism. Crisp's proposal does not generate a complete ranking of the requisite distributions of well-being, however.1313 Ibid. For example, if a person above the threshold drops below the threshold as a consequence of a progressive transfer, none of Crisp's three prescriptions applies. We note that a progressive transfer of this nature poses an important moral question within the sufficientarian context. Frankfurt's formulation does not comply with the requirement that such a transfer is to be deemed desirable, a feature criticized by Casal.1414 Frankfurt 1987; Casal 2007. Brown proposes a criterion that he labels absolute sufficientism in the context of evaluating well-being distributions for a fixed population.1515 Brown 2005. A natural extension of his criterion to a variable-population framework turns out to be a special case of our proposal. This is also echoed in Hirose's contribution, which extends Crisp's approach by closing the gaps that are not covered by Crisp's proposal.1616 Hirose 2016, p. 62. Neither Brown nor Hirose provide an axiomatic characterization of their sufficientarian accounts. In contrast, we formulate a set of properties which we argue are appealing for a notion of sufficientarianism, and derive a general class of sufficientarian principles which includes those of Brown and of Hirose as special cases; see Section IV. Casal points out a shortcoming of Crisp's approach that raises a fundamental issue for sufficientarian theories in general; she writes that "[a]ccording to Crisp's principle, if granting a nontrivial benefit to somebody below the threshold required bringing the rest of humanity down to the compassion threshold, we are required to do so. This requirement is counterintuitive with either a high or a low threshold."1717 Casal 2007, pp. 298–9; Crisp 2003. One possible solution to this problem is to abandon the idea of giving absolute priority to those below the threshold. An alternative—more subtle—resolution is provided by Casal.1818 Casal 2007. In particular, Casal introduces a two-threshold approach, proposing that "the multilevel view grants absolute priority to individuals below a low threshold and then grants them some priority until they exceed a higher threshold."1919 Ibid., p. 317. Casal suggests that, although an individual whose utility is between the two thresholds is not accorded absolute priority, such a person is given a higher moral weight than those who are above the higher threshold. Thus, only the lower threshold identifies a dividing line between those who have absolute priority and those who have not. An advantage of this approach is that it allows a trade-off between the rich and the middle classes. We note that Casal's two-threshold formulation (or a variant thereof) can be taken care of by means of our proposal. It turns out that critical-level sufficientarianism can achieve the objective of the higher threshold without formally using multiple thresholds; see Section V. Benbaji considers the possibility of defining more than two thresholds but does not assign absolute priority to anyone; in his own words, "absolutism is clearly counterintuitive."2020 Benbaji 2005, p. 321. See also Benbaji 2006. Rather, his position is that "benefiting people matters more, the more priority lines there are above the utility level at which these people are, the more of these people there are, and the greater the size of the benefit in question." Thus, Benbaji's contribution departs from those of the authors mentioned earlier in that there is no threshold that defines an absolute line of priority. Indeed, his proposal advocates a subclass of the generalized-utilitarian principles, as we illustrate in Section V.2121 See also Blackorby et al. 2005a, ch. 4. We treat utility as an indicator of lifetime well-being and use the two terms interchangeably. An individual's utility is a numerical representation of goodness for that individual. That is, it corresponds to what Broome and Vallentyne call personal goodness and prudential goodness, respectively.2222 Broome 1991, 2004; Vallentyne 1993, p. 105. It specifies not only the order of goodness but also its intensity. We assume that utilities are interpersonally comparable. The threshold is a utility level , assumed to be fixed. Our main purpose is to propose a sufficientarian criterion that ranks utility distributions, paying special attention to individuals who are below a given threshold level. Specifically, we consider several morally appealing properties of an ordering of utility distributions and identify the class of orderings that satisfy these axioms. It is essential to perform comparisons across different population sizes; without being able to do so, intertemporal comparisons are virtually impossible. Therefore, we define a sufficientarian ordering as a complete and transitive relation that is used to compare any two utility distributions and , where the two (finite) population sizes and may differ. Throughout this article, we ignore the identities of individuals in utility distributions so that given two utility distributions and with the same population size, it can be the case that and represent the utility levels of different individuals. Therefore, the sufficientarian orderings we consider are impersonal moral-goodness relations. The impersonal nature of our criteria is explicitly postulated by the axiom of anonymity. A discussion of the anonymity axiom in a welfarist setting is provided by Blackorby, Bossert, and Donaldson.2323 Blackorby et al. 2005a, ch. 3, 2005b. We denote a sufficientarian ordering by , and we interpret to mean that is at least as good as from a sufficientarian perspective. The better-than relation associated with is defined as if and only if and not and, likewise, the corresponding as-good-as relation is given by if and only if and . We note that, for the sufficientarian orderings advocated in this article, it does not matter whether those at the threshold level are considered part of the disadvantaged or the advantaged—the criteria turn out to be neutral with respect to this choice. This is a desirable feature because it lends a degree of robustness to these orderings. We now propose several properties that we argue are desirable for a sufficientarian ordering. To make the article easily accessible to non-specialists, we present the requisite definitions in a relatively non-technical manner; a more formal treatment is provided in the Appendix. All of these properties other than absolute priority are satisfied by generalized utilitarianism, the variant of the utilitarian principle that employs transformed utilities. When combined with absolute priority, which we consider to be a core requirement of sufficientarianism, we obtain a class of sufficientarian orderings that have their foundation in the ideas underlying utilitarian theories of justice. As is common in the literature, we give absolute priority to those below the threshold. This means that, whenever a sufficientarian criterion indicates that one distribution is better than another for the people whose utilities are lower than in both distributions, the former is ranked as better than the latter, independent of the utilities of those equal to or above the threshold. However, those whose utilities are higher than or equal to may matter when it comes to breaking ties: if two distributions are equally good for those below in both distributions, then (and only then) their ranking is determined by those at or above the threshold. This is consistent with what Casal refers to as a positive thesis, stipulating that it is morally important that people have enough.2424 Casal 2007, pp. 297–9. Its companion, a negative thesis, claims that improving people's well-being above the threshold is morally irrelevant. The positive thesis is supported by sufficientarian ideas that appear in the works of Crisp and of Brown, for instance.2525 Crisp 2003; Brown 2005. Wiggins argues that "it is pro tanto unjust if … the greater strictly vital need of anyone is sacrificed in the name of the lesser needs of however many others."2626 Wiggins 1998, p. 43. In an earlier contribution on basic needs, Braybrooke states that "before the Minimum Standards of Provision have been met, even the tiniest increment of provisions for needs will offset any amount of provision for other things."2727 Braybrooke 1987, p. 206. The assumption that absolute priority is to be given to people below the threshold is viewed by most contributors as being at the core of the doctrine of sufficiency. We acknowledge, of course, that this judgment is not unanimous; consider, for instance, Benbaji's rejection of absolute priorities.2828 Benbaji 2005, 2006. Benbaji's point is well taken. However, it seems to us that some notion of absolute priority is at the core of sufficientarianism, and Benbaji may have in mind a theory that more resembles a prioritarian view. We follow the part of the literature that subscribes to the absolute-priority view, which is why we state this principle as our first basic property. To express the notion of absolute priority in terms of the sufficientarian ordering , suppose there are two population sizes and , corresponding to a distribution composed of people with utility below or at and people with utility above or at the threshold, and a distribution that contains people with utility below or at and people with utility above or at . Now consider the subpopulations and in which everyone is below or at the threshold. If the sufficientarian ordering ranks to be better than , the first part of the absolute-priority requirement demands that be better than , independent of the utility values of those above or at the threshold—namely, the subpopulations and composed of and people, respectively. Thus, the property says that, under the circumstances just described, if we have , then we must also have . The second part of absolute priority says that if the distributions of the subpopulations and are equally good according to , the ranking of and is determined by the ranking of and . We reiterate that, as mentioned earlier in this section, it does not matter whether we count those at the threshold among the disadvantaged or not, and this is reflected in the following statement of the property. Absolute priority.For all population sizes , and , for all distributions , , , and , if all and all are less than or equal to , and all and all are greater than or equal to , then This property is compatible with the proposal of Crisp.2929 Crisp 2003. Brown's absolute sufficientism (which constitutes a special case of our proposal) satisfies this requirement.3030 Brown 2005. The original formulation by Frankfurt, which compares states on the basis of the number of those who are above the threshold, does not satisfy this priority requirement—and neither does its relative counterpart.3131 Frankfurt 1987. This observation does not mean that absolute priority is incompatible with Frankfurt's idea. Consider an ordering under which a distribution is better than another if the number of individuals strictly below the threshold for the former is smaller than that for the latter. We call this ordering the dual Frankfurt ordering, and it is identical to Frankfurt's original proposal (and its relative version) if the total population is fixed. However, these orderings are different when two distributions with different population sizes are compared. Note that the dual Frankfurt ordering does satisfy absolute priority. In this sense, a suitable variant of Frankfurt's counting approach is capable of satisfying absolute priority. Moreover, this property accommodates the notion of absolute priority given to those below the lower threshold in Casal's two-threshold approach.3232 Casal 2007, p. 317. In addition, absolute priority is consistent with positive and negative theses. The first part reflects a positive thesis as well as a negative thesis in the sense that the utilities of those above the threshold are irrelevant as long as there is a strict ranking based on those who are below. The property of anonymity requires very little discussion. It is a fundamental equal-treatment condition that ensures that the criterion applied to assess utility distributions from a sufficientarian perspective does not depend on the labels assigned to the individuals in a given population. For example, anonymity demands that the four-person utility distributions and are equally good according to the sufficientarian ordering because one can be from the other by means of the note that , , , and . In any to the utility labels in a distribution to a distribution that is equally all population sizes and for all distributions and , if is by a to the utility labels in , then . rather property is the We that the principle is not See, for example, 1993, pp. requires that be in the sense that if everyone is at least as well off in one distribution than in another with at least one individual being better the former distribution is better than the according to . all population sizes and for all distributions and , if for all with at least one strict then . We note that if is there are two distributions and with the same population such that for all with at least one strict but is not morally better than . This is a general of the by p. that can be by welfare levels of the to those of the and argues that this a fundamental of a of namely, what he refers to as Ibid., pp. It is to see that any ordering is to the same In this sense, can be regarded as the of the All of the variants of Frankfurt's proposal to satisfy This is a fundamental with Frankfurt's head-count approach from an axiological point of Frankfurt 1987. properties are to the of the utilities of those who are is, those whose welfare is the same in two on the sufficientarian ranking. In a variable-population there are several variants of such a on whether they apply across different population See Blackorby et al. 2005a, ch. In the context of this article, it is to attention to distributions a fixed number of this is the case because the condition is enough in the of our other most the absolute-priority In our those who are are the individuals who the same levels of utility in the distributions to be compared. The property demands that the relative ranking of such of distributions does not depend on the utilities of these is, if they are equally in both their levels of well-being are irrelevant for the ranking. As an consider two distributions and with a total population of in The individuals with the utility levels are the between and either of the two distributions, they the same utility says that if the utility levels of the are from to in both distributions, the relative ranking of the two should That is, is at least as good as if and only if is at least as good as . properties are essential in an intertemporal setting because they out the of the well-being of individuals who no on the ranking. A critical position these of is by 2016. are also in with other they that the criterion to be used has an properties that the criteria in question are in individual well-being is taken into consideration without to on the For a see Blackorby et al. 2005a, ch. all population sizes and , and for all distributions , , , and , As an there no between and part of absolute that the requires that the be independent of the subpopulations of people below or at the threshold if those subpopulations are deemed equally even if combined with part of absolute priority, does not part of absolute priority. The properties introduced in this are robustness conditions. they that small in a utility distribution do not to in the ordering . In our we two of these properties applied below and above the threshold, to the feature of the absolute-priority those below the threshold have absolute priority, it is possible that a small change in utility to a in the goodness This can if we from a of below the threshold to a that is by the threshold and to the utilities above the threshold as Therefore, the requisite properties must be to distributions that are at or or at or above the threshold level . of orderings that these properties are orderings such as According to if the person in a distribution has a higher utility than the person in another the former is better than the latter. If the individuals in two distributions have the same level of well-being, then the utilities of the are and so of the of from the to the these principles to satisfy properties of this Suppose that and are two distributions of the same population size and everyone is at or below the threshold in both and , and that is better than according to the sufficientarian ordering . below the threshold requires that any distribution of the same population size that is to is also better than , provided that everyone in is also at or below the threshold. below the all population sizes and for all distributions , , and such that everyone is at or below the threshold in all three distributions, suppose now that and are two distributions of the same population size and everyone is at or above the threshold in both and , and that is better than according to the sufficientarian ordering . above the threshold requires that any distribution of the same population size that is to is also better than , provided that everyone in is also at or above the threshold. above the all population sizes and for all distributions , , and such that everyone is at or above the threshold in all three distributions, Our proposal is to use critical-level sufficientarianism to the moral goodness of utility There is axiological for this criterion because the requisite orderings are the only that satisfy all of the properties introduced in the previous A critical-level sufficientarian ordering is based on the of the between transformed utilities and the transformed threshold level. the of transformed utilities there clearly is a to generalized-utilitarian However, generalized utilitarianism, the orderings introduced do not these across all of in with the absolute-priority principle that at the of our sufficientarian approach, they first compare the of of the transformed utilities from the transformed threshold level for individuals below the threshold. if this results in a between two distributions, the of the of the transformed utility over the transformed threshold level for individuals above the threshold is as a criterion. Thus, as to in the our approach utilitarian principles with sufficientarian ideas. To define the critical-level sufficientarian we

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