Weighted sufficientarianisms: Carl Knight on the excessiveness objection

Abstract Carl Knight argues that lexical sufficientarianism, which holds that sufficientarian concerns should have lexical priority over other distributive goals, is ‘excessive’ in many distinct ways and that sufficientarians should either defend weighted sufficientarianism or become prioritarians. In this article, I distinguish three types of weighted sufficientarianism and propose a weighted sufficientarian view that meets the excessiveness objection and is preferable to both Knight’s proposal and prioritarianism. More specifically, I defend a multi-threshold view which gives weighted priority to benefits directly above and below its thresholds, but gives benefits below the lowest threshold lexical priority over benefits above the highest threshold.


Introduction
Sufficientarianism holds that providing enough, or as close to enough as is possible, is an important distributive goal (Casal 2007;Shields 2012). 1 We can distinguish two types of this view.Lexical sufficientarianism holds that providing enough is lexically prior to other distributive goals (Frankfurt 1987: 31;Dorsey 2008: 437).Alternatively, weighted sufficientarianism holds that providing enough is nonlexically prior to other distributive goals (Benbaji 2006: 334-338;Shields 2012: 108).Put differently, lexical sufficientarianism holds that providing enough trumps all other distributive goals, whereas weighted sufficientarianism rejects such strong priority.
In a recent article, 'Enough is too much: the excessiveness objection to sufficientarianism ', Knight (2022) argues that lexical sufficientarianism is excessive because it requires too much in various distinct ways. 2 It requires that providing enough justifies any losses, no matter how large, and no matter to how many beneficiaries, above the threshold; it requires that providing enough justifies complete insensitivity to concerns for responsibility and desert; and it requires that any distribution above the threshold, no matter how unequal or unfair, must be allowed if doing so promotes providing enough.
Knight concludes by discussing 'responsibility-catering weighted sufficientarianism' (for short: 'luck sufficientarianism'). Luck sufficientarianism holds that a distribution is more just if it gives weighted priority to providing enough, increasing overall advantage, benefitting the worse off, and being sensitive to individual responsibility.According to Knight, such weighted sufficientarianism tackles the excessiveness objection while maintaining a distinctive commitment to providing enough as an important distributive goal.However, because luck egalitarianism and other types of weighted sufficientarianism still forgo large advantages above the threshold for the sake of providing enough, Knight rejects luck sufficientarianism in favour of prioritarianism.
In this article, I will assume with Knight that sufficientarians should prefer weighted sufficientarianism to lexical sufficientarianism.But Knight's discussion of weighted sufficientarianism aims only at responding to the excessiveness objection.He does not explore the qualification 'weighted' in much detail.As a result, aside from luck sufficientarianism, Knight neglects alternative versions of weighted sufficientarianism that may be able to meet the excessiveness objection.In this article, I will defend such a specific version of weighted sufficientarianism, which I will argue to be preferable to both luck sufficientarianism and prioritarianism.In brief, I will defend a sufficiency view with multiple thresholds, which gives weighted priority to benefits directly above and below its thresholds, but which gives lexical priority to benefits below the lowest threshold over benefits above the highest threshold.
This article is structured as follows.In section 2, I distinguish three types of weighted sufficientarianism.In section 3, I draw on Knight's excessiveness objection to define four desiderata for distributive patterns, such as sufficientarianism and prioritarianism.In section 4, I introduce partiallyweighted-multi-threshold sufficientarianism.In section 5, I argue that this view is preferable to luck sufficientarianism and prioritarianism.Section 6 concludes.

Three types of weighted sufficientarianism
According to weighted sufficientarianism, providing enough, or as close to enough as is possible, is a non-lexically prior distributive goal, which means that it could be outweighed by other distributive goals.Though Knight presents a compelling case in favour of weighted sufficientarianism over lexical sufficientarianism, he does not explore the several ways in which sufficientarian views can be 'weighted' views.However, this is important to understand the possible sufficientarian responses to the excessiveness objection.In this section, I will distinguish three types of 'weighted sufficientarianism', which I will draw on when defending my proposal.

Fully and partially weighted sufficientarianism
The first distinction between weighted sufficientarian views is between 'fully weighted' and 'partially weighted' views.Fully weighted views hold that providing enough must be non-lexically weighted with all other distributive goals.Alternatively, partially weighted views hold that providing enough must be non-lexically weighted with some distributive goals but has lexical priority over others.There are several ways of partially including weights, and, consequently, partially weighted sufficientarianism can take several different forms.3One might, for example, say that providing enough always has lexical priority over some goal(s) but has weighted priority over other goals.Alternatively, one might sometimes give providing enough lexical priority over certain distributive goals whereas other times reject that it has lexical priority over these goals.For instance, one could give priority to benefits to those below some threshold when the alternative is benefitting the super well-off, but still give no priority to those below that threshold when comparing them with people just above it. 4 take it that Knight's luck sufficientarianism is a fully weighted view.It holds that a distribution is more just if it gives weighted priority to providing enough, increasing overall advantage, benefitting the worse off, and being sensitive to individual responsibility.If so, providing enough never trumps any of the other distributive goals.A different type of luck sufficientarianism, however, might hold that providing enough has lexical priority over at least one but not all these goals.If, for example, providing enough has lexical priority over increasing overall advantage, then if the choice is between either providing enough or increasing overall advantage, priority must be given to the former goal.But such sufficientarianism is still 'weighted' because if the choice is between providing enough, benefitting the worse off, or being sensitive to individual responsibility, these different goals must be balanced non-lexically.In those cases, providing enough does not always outweigh these distributive goals.

Weighing sufficientarian distributive goals and other distributive goals
The second distinction between weighted sufficientarian views concerns the distributive goals that providing enough is weighted against.As Knight defines it, weighted sufficientarianism holds that providing enough is a non-lexically prior distributive goal.This suggests that weighted sufficientarianism weighs various distributive goals, one of which is 'providing enough'.Luck sufficientarianism, for example, gives weighted priority to providing enough, increasing overall advantage, benefitting the worse off, and being sensitive to individual responsibility.But of course, weighted sufficientarianism could weigh other distributive goals as well (e.g.equality), or weigh only some of these distributive goals, resulting in distinct types of weighted sufficientarianism.

Weighing different sufficientarian goals
The third distinction between weighted sufficientarian views concerns how they specify priority among different sufficientarian goals.Following Knight, I started this article by saying that sufficientarianism posits providing enough, or as close to enough as is possible, as an important distributive goal.But unlike the singular 'goal' suggests, this definition entails two distinct sufficientarian goals (see also Timmer 2021: 435-439).The first goal, i.e. 'providing enough', is concerned with bringing people above the threshold.The second goal, i.e. 'providing as close to enough as is possible', is concerned with improving people's lives below that threshold.This suggests a third way in which sufficientarian views can be 'weighted', namely by specifying weighted rather than lexical priority among these two sufficientarian goals.
Knight implicitly acknowledges the distinction between different sufficientarian goals when he says that 'where it is impossible to provide enough for all, [sufficientarianism] is concerned with providing as close to enough as is possible' (Knight 2022: sec.1).Put differently, if providing enough for all is impossible, then sufficientarianism cares about providing as close to enough as is possible.In doing so, this view gives 'providing enough' lexical priority over 'providing as close to enough as is possible'.However, there are at least two interpretations of this idea that providing enough has lexical priority over providing as close to enough as is possible; neither of which is particularly plausible.
The first interpretation, call this the 'all-or-nothing interpretation', holds that if providing enough for all is impossible, then sufficientarianism is concerned with providing as close to enough as is possible.There are two problems with this interpretation.To start with, in practice, it leaves little room for 'providing enough for all'.In circumstances of scarcity, and with a threshold at even a modest level, few distributions will provide enough for everyone.In practice, then, the all-or-nothing interpretation basically focuses on providing as close to enough as is possible; it leaves little room for the idea that providing enough is a valuable goal.
Furthermore, the all-or-nothing interpretation neglects that it is intrinsically valuable if someone has enough, which many sufficientarians consider to be a core element of sufficientarianism (Shields 2012: 112-113). 5The all-or-nothing interpretation recognizes the instrumental value of someone having enough, for example if that benefits those below the threshold, and because it suggests that that person should receive lower or zero sufficientarian concern.It also recognizes the intrinsic value of everyone having enough, because that is the intrinsic value it gives lexical priority to.However, it does not attach intrinsic value to someone having enough.For that reason, sufficientarians should reject the all-or-nothing interpretation of the idea that providing enough has lexical priority over providing as close to enough as is possible.
On the second interpretation of the idea that providing enough has lexical priority over providing as close to enough as is possible, call this the 'headcount interpretation', sufficientarianism says that if providing enough for more people is impossible, then sufficientarianism is concerned with providing as close to enough as is possible.This means that we must maximize the number of people above the threshold, and only if we have done so, we should be concerned with distributions below the threshold.Unlike the all-or-nothing interpretation, the headcount interpretation recognizes the intrinsic value of someone having enough.The problem with this interpretation, however, is that it fails to capture the value of bringing people closer to the threshold even if they cannot be brought above the threshold.For instance, if the threshold is at 10 units, it may require pursuing distribution A(10,1,1,1) over B(9,9,9,9) because in A more people are above the threshold, even if in B the worse off are much better off than in A. This is seen as a crucial objection to sufficientarianism, and I believe rightly so (Casal 2007: 315-16; Shields 2012: 102-3; Knight 2022: sec.1).For that reason, the headcount interpretation must be rejected as well.
In my view, this suggests that the most plausible type of sufficientarianism posits non-lexical priority between the two sufficientarian distributive goals, i.e. 'providing enough' and 'providing as close to enough as is possible'.Such weighted sufficientarianism gives weighted priority to maximizing the number of people above the threshold and to benefitting those below it.This too is a way in which sufficientarianism can be 'weighted'.
Incidentally, so far, I have only discussed the priority among sufficientarian goals pertaining to a single threshold.However, sufficientarianism also entails different sufficientarian goals if it posits multiple thresholds, such as the multi-threshold sufficientarian view I will defend in sections 4-5.For example, suppose a sufficientarian view posits a low threshold T− and a high threshold T. In that case, 'providing enough' can mean 'providing enough to meet T−' or 'providing enough to meet T' (and similarly for 'providing as close to enough as is possible').And these different goals can clash, for instance if two people are below T− and we face the choice between either bringing both people above T− or only one of them above T.To settle such a question requires a specific prioritization among different sufficientarian goals.
To summarize, I have distinguished three ways in which sufficientarianism can be a weighted view, namely by specifying weighted priority (i) between some or all relevant distributive goals (section 2.1); and/or (ii) between sufficientarian distributive goals and other distributive goals (section 2.2); and/or (iii) among sufficientarian distributive goals (section 2.3).

Four desiderata for distributive patterns
My aim is to offer the most plausible sufficientarian response to the excessiveness objection.Knight ends up rejecting weighted sufficientarianism, including luck sufficientarianism, because it still forgoes large advantages above the threshold for the sake of providing enough.He defends prioritarianism instead as a more plausible distributive pattern.I will argue, however, that there is a weighted sufficientarian view, not discussed by Knight and not 'weighted' in the sense he defines it, that meets the excessiveness objection and is preferable to luck sufficientarianism and prioritarianism.In this section, I will list four desiderata that this view must meet, which I distil from Knight's discussion of the excessiveness objection.I then introduce and defend my proposal in sections 4-5.
Knight's excessiveness objection encompasses four different objections, each of which holds that lexical sufficientarianism requires too much by lexically prioritizing providing enough or as close to enough as is possible over other distributive goals.First, the objection about the magnitude of advantage holds that lexical sufficientarianism objectionably forgoes large advantages above the threshold for the sake of minor benefits below it (Knight 2022: sec.3).Second, the objection about the number of beneficiaries holds that lexical sufficientarianism objectionably forgoes benefits to many people above the threshold for the sake of benefits to a single individual below it (Knight 2022: sec.4).Third, the objection about responsibility and desert holds that lexical sufficientarianism objectionably considers people's actions and choices irrelevant in distributing benefits and burdens (Knight 2022: sec.5).Fourth, the above-threshold distribution objection holds that lexical sufficientarianism objectionably disregards any type of inequality or unfairness above the threshold for the sake of promoting sufficiency (Knight 2022: sec.6).
In light of these four objections, we can formulate four desiderata distributive patterns must meet.These desiderata are the following: Magnitude of advantage.A distributive pattern should not forgo large advantages above the threshold for the sake of providing enough.Number of beneficiaries.A distributive pattern should not forgo advantages to many people above the threshold for the sake of providing enough.Responsibility and desert.A distributive pattern should allow insufficiency resulting from responsibility or desert.Above-threshold distribution.A distributive pattern should be responsive to the distribution of above-threshold advantages even when not everyone has enough.
Knight suggests that luck sufficientarianism meets these desiderata better than lexical sufficientarianism because it gives weighted priority to providing enough, increasing overall advantage, benefitting the worse off, and being sensitive to individual responsibility.However, as mentioned, Knight himself already raises an objection to luck sufficientarianism and other weighted sufficientarian views, namely that they remain vulnerable to a version of the objection about the magnitude of advantage.He argues: Consider a crude version of weighted sufficientarianism that says that 1 unit of above-threshold benefit has moral value of 1, while 1 unit of below-threshold benefit has moral value of 101.This view implies that if : : : we can have individual A at 200 units and B at 99 units (200,99), or both at 100 units (100, 100), we should bring about the latter.According to the view under According to Knight, weighted sufficientarianism cannot take the magnitude of advantage into account because in cases like this it still forgoes large advantages above the threshold for the sake of minor benefits below it.Knight (2022: sec.7) therefore proposes that '[w]eighted sufficientarianism must be combined with weightings that do not give too much weight to below-threshold benefits', but maintains that prioritarianism is better able to do this, and rejects weighted sufficientarianism for that reason.
Though I agree that distributive patterns should not give too much weight to below-threshold benefits (giving 'too much' weight is, of course, wrong by definition), I reject Knight's proposal for how sufficientarians should accommodate for that desideratum.Knight proposes that instead of giving lexical priority to below-threshold benefits, such benefits should only have extra weight compared with above-threshold benefits.However, I will argue that below-threshold benefits should have both 'extra weight' and 'lexical priority'.More precisely, they should have extra weight compared with benefits just above that threshold but lexical priority over benefits well above that threshold.I develop this idea in the next section.In doing so, I will argue that such sufficientarianism can meet the four desiderata listed above and is preferable to both luck sufficientarianism and prioritarianism.

4.
A proposal: partially-weighted-multi-threshold sufficientarianism I will defend 'partially-weighted-multi-threshold sufficientarianism' (for short: PWMS).PWMS is a sufficientarian view with multiple thresholds which gives weighted priority to benefits directly above and below each of its thresholds but gives providing enough to meet the lowest threshold lexical priority over providing benefits above the highest threshold.In this section, I explain PWMS in more detail and compare it with other sufficientarian views in the literature.
PWMS has multiple thresholds, and, importantly, its highest threshold is considerably higher than its lowest threshold.Here I have no particular threshold levels in mind, but we can assume, for example, that the lowest threshold indicates the level above which people can meet their basic needs and that the highest threshold indicates the level above which people have more than enough to live a very good life.I will refer to these thresholds as T− and T, where T− refers to the lowest threshold and T refers to the highest threshold.
Furthermore, PWMS is a partially weighted view which holds that providing enough must be non-lexically weighted with some distributive goals but has lexical priority over other distributive goals.More specifically, PWMS holds that providing enough to meet T− has weighted priority over providing enough to meet T. Similarly, it holds that providing enough to meet T has weighted priority over providing benefits above T.This means, then, that if sufficiently large benefits are at stake to a sufficiently large group of people, providing benefits above T can outweigh providing enough to meet T. Likewise, providing enough to meet T can outweigh providing enough to meet T− (and similarly for 'providing as close to enough as is possible' for each of these thresholds).However, providing enough to meet T− has lexical priority over providing benefits above T.And so, if we face the choice between providing enough to meet T− or providing benefits above T, providing enough to meet T− has lexical priority.Consequently, benefits above T can never outweigh benefits below T−.
The possibility of giving lexical priority to benefits below T− in the way PWMS does is neglected by both Knight and others in the literature.To the best of my knowledge, it is simply taken for granted that if providing enough to meet some threshold has lexical priority, it must have lexical priority over everything that happens above that threshold.And, similarly, that if benefits above the threshold are lexically outweighed by below-threshold benefits, then any benefit below the threshold lexically outweighs benefits above it (for some examples, see Sales-Heredia 2003: 67-72, 85-87, 220-221;Benbaji 2005: 321;2006: 334-338;Casal 2007: 315-316;Shields 2012: 102-103;Ram-Tiktin 2012: 342-344, 347-349;2017, 156-162;Huseby 2010: 184-185, 188-189;2017: 71-73;2020: 211-213;Schuessler 2019: 150-151, 171).What I suggest here, however, is different.I propose to give providing enough to meet T− lexical priority only over what happens well above that threshold, namely above T.And consequently, that benefits above T are only lexically outweighed by proving enough below T−.
It is not difficult to see why single-threshold sufficientarian views adhere to the classical idea about lexical priority.If there is only one threshold, and if benefits below that threshold have lexical priority, then such benefits must have priority over all benefits above it.Giving lexical priority to some but not to all benefits above that threshold is only possible if multiple thresholds are in play.But PWMS is, of course, not the first multi-threshold sufficientarianism in the literature.It may therefore be worthwhile to briefly explain what my proposal adds to this literature and how it differs from other multi-threshold sufficientarian views.
Consider first the view defended by Benbaji: The multi-level doctrine of sufficiency (the anti-egalitarian priority view): Benefiting people matters more, the more priority lines [or 'thresholds', DT] 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.(Benbaji 2005: 321; see also 2006) Benbaji goes on to explain that 'the view I recommend : : : is non-absolutist.And absolutism is clearly counterintuitive.It claims that a slight increase to one person just below the threshold outweighs huge increases to any number of people just above the threshold' (Benbaji 2005: 321; for Benbaji's argument against absolutism, see 2006: 334-338).Unlike Benbaji's multi-level doctrine of sufficiency, PWMS is explicitly 'absolutist' in that it gives lexical priority to benefits below T−.But even though it is an absolutist view, it does not give lexical priority to benefits below T− over all other benefits, but only over those above T. PWMS differs from Benbaji's view in being absolutist, though not in the sense Benbaji describes.Now consider Huseby's defence of sufficientarianism.Huseby (2010Huseby ( , 2020) ) has defended two versions of multi-threshold sufficientarianism, both of which are absolutist views.Both views say that benefits below the highest threshold have lexical priority over benefits above that threshold.However, the first view, which he defends in 'Sufficiency: Restated and Defended', says that it is valuable for people to reach the highest threshold (Huseby 2010: 181-182, 184-185), whereas the second view, which he defends in 'Sufficiency and the Threshold Question', rejects that it is valuable that people reach that threshold (Huseby 2020: 213-215, 221).To put this point in a more familiar sufficientarian phrasing: the first view says that both the positive thesis, which says that it is morally important that people have enough, and negative thesis, which says that further distribution is not required once everyone has enough, refer to the highest threshold.However, the second view says that these theses refer to different thresholds: the positive thesis refers to the lowest threshold and the negative thesis to the highest threshold.
Though my proposal shares a commitment to absolutism with both of Huseby's views, it differs from them by rejecting that lexical priority should be given to any benefit below the highest threshold T. Whereas Huseby adheres to the classical idea of lexical priority, modelled after the role it plays in single-threshold views, I propose to take advantage of the possibilities that multi-threshold sufficientarianism offers in how it gives lexical priority to benefits below T−.Another difference is that, unlike Huseby's views, PWMS is agnostic about whether it is morally important that people can reach T; and it is equally agnostic about whether further distribution is required once everyone has reached that threshold.But if PWMS is specified such that it says that it is important that people reach T, then it does not have the counterintuitive implication pointed out by Benbaji that slight increases to someone just below T outweigh huge increases to people just above it.
To summarize, PWMS gives weighted priority to benefits directly above and below T− and T but gives providing enough to meet T− lexical priority over providing benefits above T. Let me now turn to why it is preferable to luck sufficientarianism and prioritarianism as a response to the excessiveness objection.

In defence of partially-weighted-multi-threshold sufficientarianism
Let us assume that except for being a partially weighted multi-threshold view, PWMS is equivalent to luck sufficientarianism in all other respects.This entails the following.As Knight defines it, luck sufficientarianism says that a distribution is more just, the more it What sets PWMS apart from luck sufficientarianism is that it adds that providing enough below T− lexically outweighs concerns for (b)-(d) above T.As a result, increases in overall advantage, improving the condition of the worse off, and individual responsibility and desert, cannot justify benefitting those above T if doing so comes at a cost for those below T−.At the same time, however, these concerns can justify benefitting those between T− and T even if that comes at a cost for those below T−.
Knight argues that luck sufficientarianism and other weighted sufficientarian views still fall prey to the objection about magnitude of advantage.For example, they prefer distribution A(100,100) over distribution B(200,99) if, say, every 1unit benefit above the threshold has a moral value of 1 and every 1-unit benefit below that threshold has a moral value of 101.This implies that a single benefit to one individual justifies a loss of 100 units for another individual, which violates magnitude of advantage.
PWMS also has this implication, especially if the benefits in question are above T.However, I consider this to be a strength of PWMS.This is because unlike luck sufficientarianism and prioritarianism, it means that PWMS is not vulnerable to the opposite version of the objection about the magnitude of advantage.The lower the comparative weight of benefits below T−, the sooner benefits to those above T− outweigh benefits to those below T−.For example, if those who already live very good lives benefit enough, this can outweigh benefits to the worst off far below T−, no matter how many people live below T− and no matter how much benefits they could receive instead.This, it seems to me, is morally problematic.PWMS avoids this by giving lexical priority to providing enough to meet T− over providing more for those above T. 6Knight might of course respond that such lexical priority invites the excessiveness objection.However, because of how it gives lexical priority to providing enough below T−, PWMS significantly mitigates the problems that lexical priority raises compared with lexical sufficientarianism.Moreover, by accepting some form of lexical priority, it avoids preferring marginal benefits to those who already live very good lives over significant benefits to those below the lowest threshold.It does so by saying that providing enough to meet T− is not given lexical priority over everything else, but only over benefits above T.Some but not all below-threshold benefits have lexical priority; more precisely, only benefits below T− have lexical priority, namely over benefits above T.
Let me end by discussing three objections to PWMS. 7The first is that it still forgoes advantages to many people above the threshold for the sake of providing enough.For instance, an extra year of high-quality life for each of a billion people above T would be outweighed by a minor utility-gain for someone below T−.I grant that this is a consequence of PWMS, if such circumstances would arise.Yet I believe proponents of PWMS should stand their ground here.A core insight of sufficientarianism is that people should be able to meet some modest threshold.PWMS gives this goal lexical priority not over all other distributive goals but over some of them, namely those pertaining to people above some high threshold.Whatever objection about forgoing large advantages can be levelled against PWMS, they apply less to PWMS than to lexical sufficientarianism.
Furthermore, the circumstances under which PWMS is supposed to give guidance seldom resemble those fantastic circumstances.As I write this, hundreds of millions of people around the world live in extreme poverty.It is hard to imagine policies or actions that would benefit only few of these people at the expense of billions of people above T. Finally, depending on the level of the threshold, there simply are not a billion people above T.For example, the number of ultra-high-net-worth individuals, which are people with a net worth of over US$30 million including their primary residence, is estimated to be around 295,450 worldwide in 2020. 8If T tracks such fortunes, such cases cannot occur.
The second objection is that as a multi-threshold view, PWMS requires an arbitrary prioritization of the interests of those just below each of the thresholds, compared with those just above each of them, unless there is a compelling rationale for each threshold.This is a greater justificatory burden than that facing single-threshold views, such as luck sufficientarianism, because it requires a defence of multiple thresholds.I have discussed the arbitrariness objection to sufficientarianism and other problems related to setting thresholds extensively elsewhere, and I will not say much about this here (e.g.Timmer 2022: sec.VI-VII; see also Timmer 2021).But multi-threshold views as such are no novelty in debates about sufficientarianism (Benbaji 2005;Huseby 2010; see also fn. 5).We can draw on these existing views to determine the level of the thresholds.
The third objection is that PWMS cannot accommodate for concerns about luck and responsibility.For instance, suppose a vindictive person below T− releases a dangerous chemical that takes a year off the lives of each of the people above T.We can now use a different chemical to either restore that year for the billion, or give a brief pleasant smell to the vindictive person.It seems like PWMS prefers the latter, which is strongly counterintuitive.Moreover, if PWMS must be a plausible alternative to luck sufficientarianism, it should be able to accommodate such concerns.
However, following Crisp (2003: 758), I consider justice-relevant benefits to be non-trivial benefits.But the pleasant smell to the vindictive person is trivial and so is irrelevant from the standpoint of justice.We must therefore assume that the chemical will non-trivially benefit the vindicative person.Would that be justified, according to PWMS?
That providing enough to meet T− has lexical priority over providing benefits above T does not justify any kind of redistribution from those above T to those below T−.The vindictive person, for example, clearly fails to treat those above T with sufficient concern and respect, and in doing so may forfeit their claim to additional benefits.Still the objection is right in that, in certain cases, people who are below T− due to their own fault will be benefitted at the expense of those above T.Here again, however, PWMS significantly mitigates the problems that such lexical priority raises compared with lexical sufficientarianism, because it is only in these specific cases that concerns for luck are lexically outweighed by concerns for sufficiency.With these qualifications in place, sufficientarians should consider the remaining concerns for indifference regarding desert and responsibility below T− to be a virtue rather than a vice of their view, as is suggested by Herlitz (2019: 932-37).Such qualified indifference is, in my view, part of the most plausible view about what justice requires regarding people who are below T− due to their own faults and choices.

Conclusion
In this article, I have discussed Carl Knight's argument that lexical sufficientarianism falls prey to the excessiveness objection.I have distinguished three ways in which sufficientarian views can be 'weighted'.And I have outlined four desiderata distributive patterns must meet in response to the excessiveness objection.Furthermore, I have defended partially-weighted-multi-threshold sufficientarianism, which gives weighted priority to benefits directly above and below each of its thresholds but gives providing enough to meet the lowest threshold lexical priority over providing benefits above the highest threshold.I have argued that such sufficientarianism is preferable to luck sufficientarianism and prioritarianism, while at the same time responsive to the excessiveness objection.
consideration, the first world has moral value of (100*1)(199*101) = 20,199 and the second world has moral value of 200*101 = 20,200.(Knight 2022: sec.7) (a) provides enough, or as close to enough as is possible, (b) increases the overall amount of advantage, (c) improves the condition of the worse off, and (d) makes distributions sensitive to individual responsibility.(Knight 2022: sec.7) Knight then categorizes the different elements of that view: (a) is the distinctively sufficientarian aspect of the view, while (b)-(d) ensure that the view accommodates the concerns with magnitude of advantage, number of beneficiaries, above-threshold distributive distribution, and responsibility and desert that standard sufficientarianism neglects.(Knight 2022: sec.7) Here, then, I will assume that like luck sufficientarianism, PWMS endorses (a)-(d).