Negative egalitarianism, a view about the value of equality, says that the less inequality, the better the outcome.Footnote 1 More specifically, how good an outcome is with respect to equality is a function (and there can be more than one, to be sure) of the number of pairwise relations of inequality. This has been the standard view about the badness of inequality. But more recently an alternative view has been suggested. According to positive egalitarianism it is not only inequality that detracts from the goodness of outcomes but also equality that adds to it. Here is positive egalitarianism (henceforth PE) as formulated by one of its main proponents, Gustaf Arrhenius:
PE: The egalitarian value of a population is a strictly decreasing function of pairwise relations of inequality and a strictly increasing function of pairwise relations of equality.Footnote 2
This proposal constitutes a new and exciting take on the value of equality. Among other things it seems to generate the correct judgement on a number of challenging cases. Consider for example the following:
Case One: Proportional extension of the population
A is a society that has two classes of individuals, between which substantial inequality obtains. As we move to B and then C, this society expands, and expands proportionally, retaining all the while the same original gap. Accounts of inequality that are based on measuring the average of all pairwise gaps, such as the well-known Gini coefficient for example, say that the inequality remains the same in all three societies. But that seems wrong. As Larry Temkin has persuasively argued, there is a strong intuition that things are actually getting worse with respect to equality in the move from A, through B, to C. Retaining the exact same gap all the while the society keeps growing in fact implies that things are worse in terms of inequality.Footnote 3 PE captures this intuition. Although the number of equal relations increases in the move from A to C, the number of unequal relations increases at a much greater rate. PE thus improves on average measures of inequality such as Gini.
Here is another case that PE seems to get right. Consider the following:
Case Two: Mere addition of better off individuals
In A we have two individuals, one better off and one worse off. In B, another better off individual has been added. And the process is iterated all the way to Z. Here, many share an intuition that Z is better than A (and better than B). (I myself don't share that intuition but set that aside for now.) The Gini measure captures this. But notice that in contemplating the move just from A to B we might actually think that things are getting worse. After all, there is only one added relation of equality, but the number of relations of inequality has been doubled. PE registers this important nuance. It says that Z is better than A (and B), on account of the much greater number of equal relations, but that A, in turn, is better than B. The negative value of doubling the number of unequal relations trumps the addition of just one relation of equality.Footnote 4
PE seems to get the right results in some tough cases, where average measures like Gini, and other additive measures like negative egalitarianism, do not. At the same time, PE has already attracted some criticism. In particular, it is recognized, including (to their credit) by its own proponents, that it is vulnerable to two main objections. One objection says that according to PE we have a reason to bring into existence equally situated individuals, even when they would lead lives that are worth not living. But it seems implausible that we would have such a reason. Call this the Sadistic Conclusion. The other objection says that according to PE, the egalitarian value of a perfectly equal population increases still with the addition of more and more equally situated individuals, even when this is at the cost of the level of well-being dropping drastically (although still remaining positive). That is, provided sufficiently great numbers of new equally situated individuals are brought into existence, the huge drop in quality of life does not detract from the goodness of the outcome. This has become known as the Egalitarian Repellent Conclusion.
My aim in this article is to try to move the debate forward a little bit by assessing attempts to deflect these two long-standing objections. My claim is that none of these responses and amendments successfully rescues PE from its weaknesses. If so, I want to show, PE does not offer a plausible view of the value of equality. Although the bottom-line itself is rather discouraging, I do believe much of the subplots this inquiry throws up along the way should be of considerable interest to both egalitarians and students of population ethics.
I. The Sadistic Conclusion
Here then is the first long-standing objection to PE. PE entails that we have a (pro tanto) reason to bring into existence pairs of equally situated individuals, even if these individuals will be equal in leading lives that are so horrible that they are worth not living. But it seems counter-intuitive to think that we have any reason, let alone an egalitarian one, to bring into existence lives that are worth not living.Footnote 5
How may positive egalitarians respond? I want to explore here three new potential lines of defence. First, proponents of PE may concede the embarrassing implications of the Sadistic Conclusion, but then overcome it by restricting their view such that it would not apply to cases of negative welfare; second, they may bite the bullet and deny that the Sadistic Conclusion is all that embarrassing or, alternatively, that there is something attractive about it nevertheless; or third, they may concede the objection but point out that the only other rival view (negative egalitarianism) is susceptible to an even worse objection. I take these in turn.
i. The restrictive approach
The first line of defence that positive egalitarians may employ to repel the Sadistic Conclusion consists of restricting the scope of their view. A couple of replies might come under this heading.
One answer, and this is something Arrhenius has offered himself, is that proponents of PE (such as himself) would do well to set aside negative welfare. The positive value of equal relations, he says, applies only to equal pairwise relations that occur at positive welfare.Footnote 6 If such a restriction were to be applied, PE would no longer yield a Sadistic Conclusion. But I think we should quickly dismiss this response, and not only because Arrhenius himself, later on, does not seem to put much faith in it. I think this response is extremely ad hoc, and for two reasons. First, we ought to be suspicious, in general, of any view that is restricted in this manner. Lives not worth living represent a challenge to many a view, and it would not do simply to dismiss the challenge by restricting the view (to lives worth living). Negative egalitarianism, for one, applies across the board, to lives worth living and to those that are not. Think, to give another example, of an ex ante utilitarian view, and consider the following case (from Arrhenius himself in a joint paper with Orri Stefansson):Footnote 7
Here, we have the choice between with certainty having a population of very high welfare in A, or the prospect of having, with probability P, which is very high but smaller than 1, a population (B) of the same size but with very negative welfare and, with probability 1−P, a much larger population (C) with positive but very low welfare. For a large enough population B, ex ante utilitarianism would recommend the lottery over the for-sure population A. If B is large enough, then the aggregate value of its prospective welfare, the slight chance of it coming about notwithstanding, outweighs the negative aggregate value of C, the immense chance of it coming into being notwithstanding. This is a serious challenge to a utilitarian view that incorporates prospects (rather than just outcomes) into its currency of distribution. Suppose now that a proponent of ex ante utilitarianism were to meet Arrhenius and Stefansson's objection by asserting that her view simply does not apply to negative welfare. I think we would rightly see this as extremely ad hoc.
To avoid being ad hoc proponents of the restrictive strategy must explain why the positive value of egalitarianism obtains only for lives that are worth living. The reply that ‘doing so will prevent embarrassing consequences for the theory in question’ is of course not a very good reason. As Parfit has said with regard to similar matters, ‘we cannot justifiably reject strong arguments merely by claiming that their conclusions are implausible’.Footnote 8 Similarly, I think, one may not restrict the application of one's view only because doing so will deliver it from difficult implications. There must be some independently good reason for such a restriction, lest it be ad hoc. Let me give an illustration to this second point by alluding to another egalitarian view. The view known as Conditional Egalitarianism seeks to escape the embarrassing implications of the levelling down objection by stipulating that equality is valuable only when there is at least one individual that it (equality) benefits. Proponents of conditional egalitarianism provide a detailed account of the ‘intimate’ relation between equality and utility gains (or ‘beneficence’), and person-affecting reasons more generally. Whether you find that story convincing (I myself don't)Footnote 9 is a different matter. The point, rather, is that proponents of Conditional Egalitarianism do realize that to restrict their view without providing a background story and justification would be ad hoc. To sum up the point, to suggest that the positive value of equal relations should be restricted just to those individuals who lead a life that is worth living is hopelessly ad hoc. It is a bit like saying, to paraphrase Nils Holtug, that equality is valuable, but only on Wednesdays.Footnote 10 At the very least, then, we need a good reason (apart, that is, from avoiding embarrassing implications for one's own view) to believe that proponents of PE could avail themselves of this restrictive version of their view.Footnote 11
As mentioned, Arrhenius himself does not seem to put much stock in this first answer, and indeed in a later paper (this time co-authored with Julia Mosquera) he handles the problem slightly differently. Arrhenius and Mosquera say there that PE may assign neutral value (that is, zero) to equal relations when they obtain at negative welfare. This slight amendment would be successful in not committing the PE to having a reason in favour of bringing into existence an egalitarian society of miserable individuals.Footnote 12 I think this is a better response in that it does not have recourse to an arbitrary and ad hoc restriction of the view to only certain relations (those occurring above the threshold for life worth living). However, this still strikes me as only slightly better than the previous reply, and for a similar reason. Namely, we ought to be given a reason, beyond avoiding difficult implications, for assigning a zero value to equal relations that occur below the threshold for life worth living. To avoid being ad hoc, in other words, positive egalitarians must at least tell us why their function behaves in such a way according to which below zero welfare it generates zero value of equality. But unless and before one is given such a reason one cannot escape the conclusion that this is again rather ad hoc. We shall return to discuss the shape of the PE function in section II.
ii. Biting the bullet
The second line of defence available to proponents of PE is simply to bite the bullet on the Sadistic Conclusion. I can think of two variants here. Friends of PE may, to begin with, simply deny that there is anything remotely embarrassing about the Sadistic Conclusion. Alternatively, they may concede that all things considered bringing into existence pairs of individuals with lives that are equally worth not living is indeed bad, but that doing so is better in at least one respect.Footnote 13
The first response, I think, is not a very hopeful strategy. Taken on its own a view that says that there is value to be had by bringing into the world individuals with lives that are by definition worth not living cannot but be embarrassing. Denying that there is anything wrong with the Sadistic Conclusion seems to me like a non-starter. Instead, what proponents of PE might do is to concede that while all things considered it would be wrong to bring about an egalitarian society of miserable individuals, there is still at least one respect in which doing so would nevertheless make things better. After all, they might say, egalitarians in general and negative egalitarians in particular are themselves quite accustomed to this line of response in their deflection of the levelling down objection (LDO). Famously, the standard egalitarian reply is that levelling down might be on the whole worse, but better in one respect.Footnote 14 Why cannot the PE similarly say that while bringing about a world of equally suffering individuals is undesirable all things considered, it is still valuable in one respect?
In contrast to the restrictive approach, there is certainly nothing ad hoc about this line of response. As mentioned, this is one, perhaps the major, strategy employed by negative egalitarians in repelling LDO. Indeed, proponents of standard (negative) egalitarianism are often at pains to point out that critics are not always careful to differentiate between things being better all-things-considered and them being better in one respect. As a consequence, large tracts of egalitarian defence have had to be devoted to directing attention to this very distinction. There would be something good about levelling down the rich to the level of the middle class, egalitarians assert, even if this may not be desirable all things considered. Consequently, in recent years quite a bit of egalitarian thought has gone into spelling out and explaining precisely how levelling down improves things in one respect.Footnote 15 Can proponents of PE do the same? Do we have reasons to accept that bringing about an egalitarian society of wretched individuals is better even in one respect?
Proponents of PE are not very forthcoming with providing such reasons, and perhaps that is because it is rather difficult to come to grips with our intuitions in such extreme scenarios. Nevertheless, we can try to provide a thought experiment on their behalf. Consider the following. Suppose a couple in the very early stages of a pregnancy undertakes some scans and tests only to confirm every parent's worst fears. The child that would be born will, with certainty, be of very low, indeed negative well-being. It will have a life worth not living. Most of us think that this gives us an overwhelming (in most people's view decisive) reason not to go through with the pregnancy. Suppose then that the physician contacts the couple shortly after to say that there has been a terrible mistake. The quality of life of the unborn will indeed be as negative, but instead of one foetus the couple in fact is going to have twins. In short, it is twins, and they are expected to have the exact same level of negative well-being. It is incredible, in my view, that this new information should make egalitarians go: ‘now, hang on, that changes everything!’ It is incredible, in other words, to think that the new information should give us (us, impartial observers, let alone these poor parents) a pause, be it the slightest, to reconsider our original judgement. If anything, it is quite the opposite. (I have my own speculation as to what the underlying mistake that leads PE down this stray road is, but I shall reserve it for the concluding section.)
My claim, then, is that contra PE the news about it being twins should not give egalitarians a pause, even the slightest one. There is no egalitarian reason, no matter how defeasible, in favour of bringing into existence life that is worth not living. But is this a fair criticism? Compare with negative egalitarianism and levelling down. Take for example Temkin's famous immortality berries.Footnote 16 Crucially, there are enough such berries for only half the given population. Suppose you think that all things considered this would be absolutely wonderful. A new frontier has been crossed for humankind, not to mention the wonderful things that these Methuselahs could enjoy (say, all the new bird species they could add to their Western Palearctic List). Suppose now the egalitarian planner comes to testify before the decision-makers on legalizing these berries and reminds them of the large, indeed immense, inequality that would ensue. And suppose further that the decision-makers do decide to go ahead with legalizing the berries. Surely then the fact about the immanent inequality ought to give them some pause. In fact, for such a plan to go ahead without due consideration for the ensuing inequality would be hugely immoral (for one thing, because dismissive of the non-enhanced individuals). Can the PE point to a comparable pause-giving moral fact in the twins’ pregnancy case? This is very doubtful.
Let me consider a final reply to my claim in this sub-section. Friends of PE may respond that even though on the whole they would agree that refraining from LDO requires a more substantial ‘pause for thought’, still the case of the miserable twins, extreme as it is, gives some pause for thought. It is this. On the ideal known as ‘relational egalitarianism’ we all benefit from living in a society of equals. ‘Positively, egalitarians seek a social order in which persons stand in a relation of equality. They seek to live together in a democratic community, as opposed to a hierarchical one.’Footnote 17 This ideal of egalitarianism stresses individuals’ equal standing and relations, rather than their equal bundles. You might say, then, that coupled with ‘relational egalitarianism’, PE does show that things are made better in one respect by proliferating the number of equal relations in society, even though all things considered we might refrain from doing so (on account of the Sadistic implications).Footnote 18 Let me say something about this. Think of negative egalitarianism first. One indication that levelling down makes things better in one respect is that its absence leaves the worse off with a complaint. Other things being equal, this complaint might be drowned by other considerations (including the suggestion that levelling down might make the disadvantaged herself even more worse off, in absolute terms, than she would otherwise be). In contrast, refraining from bringing into existence pairs of individuals who have equal levels of lives worth not living leaves no trace of complaint in the world. This is the case, I want to say, even when the ideal of relational egalitarianism is brought into the fray. For according to leading proponents of relational egalitarianism, ‘there can be no injustice, without an injury to someone's interests’.Footnote 19 Refraining from bringing the miserable twins into existence constitutes no such injury (on the contrary). I therefore think that even coupled with the logic of relational egalitarianism there is no respect in which the Sadistic Conclusion makes things better.
iii. The levelling out (counter-) objection
The third and final line of defence open to proponents of PE in deflecting the Sadistic Conclusion might be to say that the only other game in town, namely negative egalitarianism, does no better with respect to that very objection. If so, the objection does not help in telling one rival telic view from the other. It goes like this. Suppose, PE proponents may concede, that it is true that positive egalitarians cannot but recommend bringing into existence individuals with lives that are worth not living. That, they continue, is not nearly as bad as what, upon reflection, negative egalitarians recommend. For negative egalitarians are in fact committed to eliminating inequalities by eliminating the very ‘offending’ individuals (say, bumping off all but the better off individuals in a society). This extreme case of levelling down (what we might henceforth call levelling out) individuals with good lives is surely harder to stomach than the implication of bringing into existence individuals with lives worth not living, or so goes the response.
This is an important counter-objection.Footnote 20 Let me say, nevertheless, why I think that ultimately it does not work. Let us start by observing that egalitarians must be at least minimally pluralist about value. It has long been noticed that any plausible egalitarian view would have to register not just equality but also welfare (or beneficence). If this were not the case then egalitarians would have no more reason to prefer a distribution of (200, 200) to (100, 100), say.Footnote 21 Notice, this concern for beneficence is required not in order to escape standard cases of levelling down; it is required to escape what I have elsewhere called gratuitous levelling down. It is, no wonder, a pretty minimal requirement.Footnote 22 Consider now levelling out. Notice, to begin with, that when both options – levelling down and levelling out – are available there is no apparent reason to prefer the latter. There is no reason, that is, why for egalitarians (Ω, Ω) would be better than (200, 200), say. This, I think, is true for all egalitarians (especially bearing in mind the minimal requirement of value pluralism with regard to beneficence). It follows that egalitarians only have reason to recommend levelling out when levelling down is for some reason unavailable. After all, there is no apparent (negative) egalitarian reason to prefer having no individuals to having individuals living in complete equality. So far so good.
The levelling out objection, then, only applies when levelling down is for some reason unavailable. Now, negative egalitarians could say that it is pretty hard to think of any practical impediments to levelling down. Whatever your currency of egalitarianism is (income, resources, welfare) it is difficult to see why it would be impossible to reduce a better off person's bundle. Still, there is at least one type of cases I can think of where levelling down is indeed blocked, namely inequalities between past and future generations. It is this:
If the former were well off, and the latter expected to be worse off, the only avenue open for negative egalitarians would have to be levelling out, or in other words (near) extinction. These are extreme cases, to be sure, but that is beside the point. The levelling out objection to negative egalitarianism, I concede, stands. But now observe that where levelling down is indeed impossible – as in the case of better off past generations – positive egalitarians would be similarly disposed. That is, just like negative egalitarians, they would be forced to recommend levelling out. That is so because, as you will recall, PE comprises not just the positive value of equality but also the negative value of inequality. In the choice between huge inequalities between well off past generations and worse off future generations, and a perfect equality that existed in the past, PE likewise will, with one exception, favour the former. The only way in which PE can avoid levelling out here is to ensure that future generations are not only perfectly equal but also populous enough. In this way, the positive value of the numerous low-level pairwise relations of equality may outweigh the significant inequalities with past generations. Given that, ex hypothesi, the original problem stemmed from future generations having far fewer resources than past generations, the PE solution of further increasing the population must therefore entail a further reduction in their level of well-being. It implies, in short, a Repugnant Conclusion:
Where does this leave us? We have seen that in the one case where negative egalitarians would favour levelling out (inequalities between better off past generations and worse off future ones), PE would be either likewise disposed or, alternatively, avert it by means that are arguably equally embarrassing (a repugnant conclusion, on which more in the next section). It is therefore plausible to say that whereas the Sadistic Conclusion is a major reason against PE, the levelling out objection is no reason to prefer one view over another.
Let us add one more thing before concluding this long section. I want to say that there is an important difference between the Sadistic Conclusion and the levelling out objection. It is a difference that may be best revealed when contemplating both objections taken all things considered. All things considered, the Sadistic Conclusion is, it is safe to say, undisputedly repugnant. On the whole, bringing into the world lives that are so miserable that they are worth not living cannot be a move for the better. It is not clear, however, that the same is true for levelling out. Consider this:
A is a perfectly equal society, with billions of people, all living very happy lives. B contains a population of the exact same dimension as in A, plus a much smaller population of worse off individuals. It does not seem absurd, to me at least, to propose that moving from A to B would be a move for the worse, as far as the value of equality is concerned. I think that is pretty obvious. Moreover, it does not even seem preposterous to suggest that the move from A to B would be a move for the worse, all things considered. In other words, in contemplating those few worse off individuals with low (yet positive) welfare, it does not seem absurd to say that all things considered it would be better to refrain from bringing them into existence. The reader and myself may not agree on this intuition, but I think the example at least establishes that, unlike the Sadistic Conclusion, the repugnance of levelling out is not beyond dispute.
II. The Egalitarian Repellent Conclusion
It has been pointed out (to his credit, by Arrhenius himself, among others)Footnote 23 that PE has the following curious implication. Consider Case Three, where in world A ten billion individuals, say, are leading very satisfying lives, and in perfect equality. For any such population A we could then imagine a much larger, perfectly equal population Z with much lower (although still positive) well-being. To simplify things suppose also (although this is not crucial for our main worry) that Z contains the exact same amount of aggregate utility as A.
Case Three: The Egalitarian Repellent Conclusion
Negative egalitarians, it is easy to see, judge both populations to be equally good, at least as far as the value of equality is concerned. Both contain zero inequality. PE in contrast, judges Z to be better than A, with respect to the value of equality. That is because world Z contains so many more pairwise relations of equality (and the same amount of inequality as well as total welfare as A). (In all likelihood, they would also judge Z as better than A all things considered, because it contains the same aggregate utility, but set that aside.) But to judge Z as better than A (not just all things considered, but even just with respect to equality) seems counter-intuitive. This has become known as the Egalitarian Repellent Conclusion. Notice that the repellent conclusion is more repellent than its more famous cousin, the Repugnant Conclusion. According to the repugnant conclusion, in Case Three, utilitarians would be indifferent between A and Z. PE takes the further step of actually favouring Z. This is a tough bullet to bite and proponents of PE would presumably want to show that their view does not, in fact, entail this very repellent egalitarian conclusion.
I can think of two main strategies for avoiding the Egalitarian Repellent Conclusion (henceforth ERC). One involves placing an upper limit on the value of equality, while the other centres on making the egalitarian value sensitive to the absolute level of welfare at which it obtains.
i. The capped model
The first strategy open for positive egalitarians in responding to ERC is to place some cap on the value of equality. Placing an upper absolute limit on values was famously proposed by people like Larry Temkin as a possible strategy for meeting the challenge presented by Derek Parfit's aforementioned Repugnant Conclusion.Footnote 24 On this suggestion an outcome gets a score on each of its various aspects (utility, equality, desert, Maximin, perfection, etc.). Importantly, however, there is an upper limit on that score (as in competitions of gymnastics or in decathlon, say). In other words, there is a limit to how good a state of affairs is on each of these aspects. For example, world A containing as it does ten billion individuals all living in near bliss is a world saturated with utility. Adding a million individuals all living just above the zero level (the level of welfare at which life ceases to be worth living) would not make that world better. The ‘capped model’ (as it is known) captures this intuition. The original world has already scored a perfect score on the utility index, so adding the million additional lives cannot improve it. The same idea can be applied to how good things are with respect to equality. On the current proposal, a state of affairs can score a very high mark in terms of equality, so much so that an increase in the number of pairwise equal relations would not earn it a higher score in terms of the value of equality. We can see how this model could help proponents of PE deflect ERC. World A, one could say, already scores the perfect score on the value of equality because it contains billions of people living in perfect equality. If there is such a thing as an upper limit on the value of equality then there is a question whether Z could actually improve on A with respect to the value of equality. Consequently, it is not obvious that PE is committed to judging Z better than A, and so not committed to ERC.
The Capped model has far-reaching implications for value theory in general, and I cannot hope to do it justice within the narrow scope of this article. Nevertheless, I do want to register two reservations about it and their application here. One thing to notice is that whatever you might think of the capped model, negative egalitarianism need never have recourse to this controversial mechanism. On negative egalitarianism there is a very clear, and not at all arbitrary, cap on the disvalue of inequality, namely zero. A state of affairs cannot get better, from the point of view of negative egalitarianism, when there is no inequality.Footnote 25 (2, 2) is as good as (2, 2, 2, 2), and as good as (−9, −9, −9, −9, −9) for that matter. Negative egalitarianism has no need for the soothing effect of the Capped model.
Here is a second concern, one that proponents of the Capped model were honest enough to raise themselves. The point is this. The Capped model seems to have attractive results when it comes to positive values (say, of utility), but less so when it comes to negative values. Many of us, that is, may be willing to go along with the suggestion that the value of utility follows a concave function, with value diminishing the more utility there already is, until the point where further gains in utility do not translate into an increase in goodness. But crucially, we might have different intuitions regarding negative utility.Footnote 26 Imagine a world with ten billion people suffering the most horrendous lives ever lived. Adding a million, or even a thousand more tortured individuals commonly strikes us as worse. If the only thing we could do in this new situation were to help those extra thousand individuals (or even one!) and ensure that they do not suffer we intuitively think that we ought to grab that opportunity. There does not, in other words, seem to be a cap on how bad things are. This is true for utility, and I think it is also true for inequality. When Barack Obama left the White House the US still had socio-economic inequality that was pretty bad on any conceivable measurement of the OECD. But crucially, in the days and months to come that inequality could and would become worse. There is, in other words, no apparent limit to how bad things can be with respect to inequality. This brings back the question whether it is really the case that there is a cap on how good things can be. Perhaps all that there is, then, is a failure of our imagination when it comes to goodness on a large scale, a failure which, interestingly, we do not suffer from when thinking about how bad things can be.
ii. Welfare-level sensitive egalitarianism
Let us, then, look at the other strategy for avoiding ERC. It consists of supplementing basic PE with the following addition. ‘How valuable equal relations are might arguably depend on the level of welfare involved’.Footnote 27 In a more recent paper, Arrhenius and Mosquera further add that this could ‘be achieved by aggregating the value of equal relationships at high welfare levels linearly while the value of equal relationships at low positive levels is aggregated by a strictly concave function with an upper limit’.Footnote 28 This slight revision helps the PE avoid ERC. For if equal relations are more valuable the higher individuals’ level of welfare then it may well be the case that A, although having fewer relations of equality than Z, is still the better outcome (with respect to equality, that is, not just all things considered). Making the value of equality sensitive to welfare levels may well deliver PE from ERC.
I want to offer some reasons to be doubtful about incorporating welfare-level-sensitivity into PE. Let us start with a couple of technical wrinkles. I want to stress: nothing I say in this paragraph constitutes a rebuttal of welfare-sensitive PE. Rather, these are just a couple of implications worth bearing in mind. First then, notice that by introducing this welfare-level-sensitivity proponents of PE would have to abandon the neat formulation of their view that appears at the top of this article. That is, of course, no hindrance to the view itself, but we do need to observe that the view defended is no longer the clean formulation above. Second, observe the following asymmetry within the new PE formulation. There is discontinuity between the application of the linear function (applying to high levels of welfare) and the application of the concave function (applying to low levels of welfare). What could that boundary be (such that drawing it would not be ad hoc)? How do we know when to stop applying a linear function and start applying the concave function? One option could be to draw the line at the zero level of welfare. But as we already saw, there is at least one reason this cannot be the case, namely that proponents of PE in fact hold that their view either does not apply to negative welfare, or that a function of another kind entirely (one with zero value) applies there. Again, like the first point this is not an insurmountable challenge to PE, but at the very least it forces the PE into incorporating some threshold (perhaps a sufficientarian one?), thereby muddying their otherwise neat egalitarian view.
These were just some technical difficulties, and no doubt they could be overcome. My substantive rebuttal begins now, and it begins by observing the shape of the function proposed by the PE in response to ERC. The suggestion, as we saw, is that egalitarian relations are more valuable at higher levels of welfare. However, apart from the attractive feature of avoiding an uneasy implication (ERC) for the original view, what exactly is the justification for adopting this particular shape of the function? Why, we might ask, should egalitarian relations be more valuable the higher the welfare at which they obtain? Indeed, this is quite puzzling. If anything, one would have expected things to go precisely the other way around. That is, arguably equal relations matter more at lower levels and have a diminishing marginal value the higher up we go.Footnote 29 We commonly think that the inequality between the lowest (first) centile and the fourth centile of the population, say, is more alarming, morally speaking, than inequalities at higher levels, say the inequality between Warren Buffet and Bill Gates. In fact, it is precisely those latter inequalities (those occurring at very high levels) that are often employed by critics to try to embarrass egalitarianism and to support rival views (e.g. sufficientarianism).Footnote 30 The particular shape of the PE function, then, clashes with a widely held egalitarian intuition that, if anything, there is more value to equality at the bottom than at the top.
Indeed, in the original paper introducing PE Arrhenius himself takes this very position (that equality matters more the lower the welfare of the parties to it), and one arguably diametrically opposed to the one he seems to endorse in response to ERC. There he writes that we might reasonably want an index for the badness of inequality that would ‘take into account that, for example, differences at low levels matter more than differences at high levels’.Footnote 31 It is therefore all the more puzzling that he now adopts what seems like the opposite view.
Now, in Arrhenius's defence, there is a way to dissolve the apparent inconsistency. Perhaps the thought is that while inequalities matter more at low levels, equalities matter more at higher levels.Footnote 32 This would certainly get rid of the inconsistency. But can this suggestion really work? Let us take a very simple example to test this. Think of the following set:
(9, 8, 3, 2)
Suppose that we then have one more unit of welfare to allocate. Who should receive it? The latest formulation of PE tells us (roughly) that if we give it to the worse off person (the fourth from the left) we would minimize the disvalue of inequality, while if we gave it to the second person (from the left) we would maximize the value of equality. This makes for a very puzzling recommendation. This does not show the view to be incoherent, I concede, but this implication of it strikes me as exceedingly implausible.
I said ‘roughly’ earlier because in the particular example just reviewed the case is not as clear cut, and for the following reason. By awarding the extra benefit to the fourth person (the worst off one) we would be minimizing inequalities between her and all other three members. While, if the benefit were given to the second person we would achieve equality at the top but exacerbate inequalities further below. One way to control for that and isolate the clash between inequalities at the top versus inequalities at the bottom is to introduce uncertainty into the proceedings. Think of the following case:
Here we have two individuals, Anne and Betty, and two equiprobable states of the world, S1 and S2, one representing lower level inequality and one representing upper level inequality. My intuition (which I will say more about in the next section) is that as egalitarians, and given the uncertainty regarding which condition Anne and Betty in fact occupy, we ought to give the extra benefit to Betty, on pain of the risk of S1 materializing. That is, the risk of exacerbating inequalities at the bottom outweighs the equal risk of exacerbating inequalities at the top. Or at least, that is my intuition. If you share that intuition (which you may well not), then you must observe that it clashes with PE. For here the latest suggestion of PE would be indifferent between awarding the extra benefit to Anne or to Betty. I find this position to be a strange one for an egalitarian to hold.
The suggestion that a positive egalitarian could combine the view that equalities matter more at the top while inequalities matter more at the bottom leads to counter-intuitive implications. But to show this I have brought uncertainty into the picture. And you might think that this introduces a complication that is not quite fair in evaluating PE. In reply, I concede that uncertainty introduces all sorts of complications here. But I also think, first, that these complications apply across the board, that is, across both rival views. And second, I think that given the peculiar nature of the suggestion in question, introducing uncertainty is the only way one could isolate the two effects (weighing inequalities at the top versus inequalities at the bottom) and test our intuitions about them. For those readers who are still uncomfortable about introducing uncertainty here, I would propose the following alternative thought experiment. Suppose that you were persuaded (unlike the present author) by Derek Parfit's famous Divided Worlds example,Footnote 33 and thought that inequalities existing on two sides of the yet-uncrossed Atlantic Ocean did not matter, morally speaking. And suppose further that in the Americas the distribution was (2, 3) and in Europe (8, 9). You now have an additional unit to spare. Should you, as an egalitarian, benefit the worse off in America or the worse off in Europe? On Arrhenius's latest formulation one would have to be indifferent, and I find this extremely counter-intuitive (again, while bracketing the moral disvalue of the inequality across the Atlantic).
PE may not, we conclude, avert ERC by adding sensitivity to welfare levels.
III. Can negative egalitarians be welfare-level-sensitive?
For positive egalitarians to incorporate welfare-level-sensitivity into their view would have counter-intuitive results. But there is an important reply that proponents of PE may raise here. They may point out that the rival view, negative egalitarianism, is itself also welfare-level-sensitive, and so may not employ this feature to debunk another view. After all, it has been a mainstay of Temkinite egalitarianism that the disvalue of inequality is inversely correlated with welfare levels. Negative egalitarians, one might plausibly say, could hardly criticize positive egalitarians for something that they themselves are complicit in. Indeed, Temkin himself devotes a whole chapter of Inequality to arguing that on his version of egalitarianism inequalities of the same size are worse, the worse off (in absolute terms) individuals are.Footnote 34 This understanding could give rise to what some have called ‘egalitarianism-cum-priority’ (Rabinowicz)Footnote 35 or ‘prioritarian egalitarianism’ (Mosquera).Footnote 36 That is to say that the disvalue of unequal relations follows a priority-like concave function that decreases the higher the welfare. Let me concede right away that I think Temkin is absolutely right on that score. Suppose we agree then that negative egalitarianism is welfare-level-sensitive. If so, isn't it inconsistent to criticize PE for incorporating welfare-level-sensitivity while allowing negative egalitarianism to do just that?
I want to say that there is an important sense in which welfare-level-sensitive NE is distinct from welfare-level-sensitive PE. Begin by observing that fixing level-sensitivity to the badness of inequality makes a lot of sense. Consider the following:
A (100, 200) B (1100, 1200)
C (100, 100) D (1100, 1100)
Consider first the difference between A (100, 200) and B (1100, 1200). There is a strong intuition that even though the size of the gap (or ‘complaint’) is identical, still the inequality in A is worse than the inequality in B.Footnote 37 Welfare-level-sensitive negative egalitarianism captures this. It says that inequality is worse, the worse off individuals are. And that is because the worse off people in A have only a third of society's resources, while the worse off people in B control almost half of the resources in their society.Footnote 38 This makes a lot of sense. Inequality is worse at lower levels because it implies (for the worse off) a smaller share of the pie. But the same logic, it is easy to see, does not apply for PE. If you are concerned with the size of one's share, then that is no reason to think that equality at C (100, 100) is more valuable than the equality in D (1100, 1100). In short, negative egalitarianism is sensitive to welfare levels because the size of one's share matters. Negative egalitarians have a good reason to appeal to level-sensitivity; a reason that PE manifestly lacks.
Now, someone might say that the size of individuals’ shares matters also on PE, and that is because any equally sized deviation from the said equalities [C (100, 100), D (1100, 1100)] will matter, and matter differently. That is true, but this says nothing yet about the value of the equality at hand. (And that is especially true for those like Arrhenius who seem to divorce the value of equality, which on his account is directly correlated with welfare levels, from the disvalue of inequality, which for him is inversely correlated with welfare levels.) This is important. While eradicating the inequality in A (100, 200) is more urgent than eradicating the inequality in B (1100, 1200), that does not mean that the equality in D is more valuable than the equality in C. A proponent of PE might insist, saying that it is the case that the equality in D is better than the equality in C because it is a more stable one. That is, an equally sized deviation (from equality) would undermine D less than it would C. The equality in D is therefore more valuable because more stable. But this again is not persuasive. The only meaning in which the equality in D is more stable (and hence valuable) is that it protects against an inequality that is of less disvalue. The alleged PE value therefore piggybacks on the disvalue of inequality. It (the purported value of equality) adds nothing distinctive.
Proponents of PE owe us some account about why the value of equality should vary along the level of welfare, and in the particular shape they ascribe. I conclude that PE encounters a repellent conclusion and that responses put forward by its proponents are unhelpful.
Conclusion
There are at least two critical tests PE must surmount: the Sadistic Conclusion and the Egalitarian Repellent Conclusion. I have tried to show that recent attempts by proponents of PE to overcome these are unsuccessful.
But where, we might ask, does PE go wrong? Surely, the idea that there is something good about equality is not that far-fetched. Moreover, perhaps Parfit was right after all to quip that the distinction between the goodness of equality and the badness of inequality is ‘pedantic’.Footnote 39
I agree that PE is not far-fetched, but I also think that it is still ultimately wrong. And I want to speculate where exactly it might have gone awry. Jan Narveson is famous for his often quoted anti-utilitarian critique according to which we have a duty to make individuals happy, but not to make happy individuals.Footnote 40 I actually think he is wrong about that (at least if we substitute ‘valuable’ for ‘have a duty’). But I also think there is a parallel here that has some truth to it. For egalitarians, it is clear that there is value in making societies just (or equal). But it is much less clear to me that there is value in creating just (or equal) societies de novo.Footnote 41 Far from being pedantic, this might make all the difference in the world. All egalitarians, negative and positive, believe that there is value in eliminating inequalities. But is there value to bringing about new relations of equality (when doing so does not entail eliminating existing inequalities)? The persistence of the Sadistic Conclusion and the Egalitarian Repellent Conclusion suggest that there is not.Footnote 42
