Equality-tempered prioritarianism

Prioritarianism and misery for the ultra-rich

According to prioritarianism, the only thing that improves a state of affairs is an improvement in welfare. In this, prioritarianism agrees with many traditional axiologies, including classical utilitarianism. Prioritarianism’s distinctive feature is its weighting. Prioritarianism is a tempering of the classical utilitarian axiology: all welfare benefits improve a state of affairs, but marginal benefits to worse-off persons improve a state of affairs more than marginal benefits to the better-off. ¹ Hence, prioritarianism delivers a distinctive concave prioritarian value curve: the marginal value of welfare benefits decreases as the welfare of beneficiaries increases. Of course, prioritarianism is open to interpretation: no one has yet produced a precise account of the relative concavity of this value curve. ² For the purposes of this paper, I will leave this interpretive issue aside.

One way to capture the prioritarian idea is by way of a piece of terminology. Call a “welfare unit” a marginal welfare benefit of arbitrary size. In increasing the welfare of x from 10 to 12, there is an increase in two welfare units. Given this terminology, prioritarianism holds that a welfare unit is worth more if its recipient is worse-off. On a prioritarian view, all welfare units are valuable, but, in every case, a welfare unit for x is worth less than a welfare unit for a person slightly worse-off than x. As beneficiaries get better-off, the marginal value of welfare units (i.e., marginal welfare benefits) diminishes asymptotically to zero. ³

As I indicated above, prioritarianism—despite its vague specification—appears to successfully capture a number of intuitions that drive people away from utilitarianism and toward a form of egalitarianism. Egalitarianism seems plausible, in part, because egalitarianism generally treats the interests of the worse-off with priority in comparison to the interests of the better-off. However, although this is a general feature of egalitarianism, it is not universal; equality is sometimes increased by making the worse-off worse-off—in particular, if this is a necessary side-effect of increasing equality. However, prioritarianism seems to capture the plausibility of treating the worse-off with priority without this overwhelming downside.

However, although prioritarianism is plausible, it has a serious problem I would like to consider here. Call any person with an extraordinarily high welfare level a member of the “ultra-rich”. Now consider the following proposition:

Misery for the Ultra-Rich: There is some number of ultra-rich persons, such that the value of a minor benefit granted to each would outweigh the disvalue of moving one person from a life worth living to a life of absolute misery.

Misery for the Ultra-Rich, as stated, is vague. I have not specified what it means to be “ultra-rich”; I have not precisely specified the notion of a “minor benefit”, nor have I said anything about what it means to be in “absolute misery”. Although I will say more about the “ultra-rich” later, I leave the remaining terms vague; the general idea here should be relatively straightforward. Those interested in a more precise formulation of Misery for the Ultra-Rich are free to fill in the details as they prefer. No matter how these details are filled in, however, it seems clear to me that a very small benefit for very well-off individuals should not trade-off against a disastrously poor life, no matter how many very well-off individuals there are.

A number of views could potentially reject Misery for the Ultra-Rich. One important example is leximin. Leximin holds that benefits for any worse-off person lexically dominate benefits for any better-off person; in comparison to welfare units for the better-off, welfare units for the worse-off are of absolute axiological priority. Leximin solves Misery for the Ultra-Rich: because benefits to the worse-off are absolutely prior in value, it is not the case that there is some finite number of benefits to the best-off that would be sufficient to outweigh burdens for the worse-off.

Although it solves Misery for the Ultra-Rich, leximin has been rightly criticized as too extreme. Richard Arneson (referring to “maximin”) notes that a leximin-style view:

…would prefer the outcome which a single worst-off person gains a penny’s worth of benefit at the cost of the loss of thousands of dollars for each of thousands of the better-off. A maximin rule introduces a strict lexical priority for the interests of the worst-off, however slight, when they conflict with the interests, however great, of the next worst-off. Lexical priority relations among moral values are strong medicine and perhaps are very rarely, if ever, justifiable. They are especially difficult to justify if the value given lexically lower priority really has value at all. In the context of the distribution of social benefits as assessed by social justice principles, leximin is implausibly extreme. ⁶

It might be responded that if Misery for the Ultra-Rich is really unintuitive, leximin cannot be too extreme: our intuitions appear to support just this kind of lexical priority in denying Misery for the Ultra-Rich. After all, no amount, no matter how large, of minor benefits for the ultra-rich can outweigh the disvalue of misery for one. However, leximin goes far beyond the denial of Misery for the Ultra-Rich, as Arneson notes. Consider the possibility that to benefit one member of the worst-off class, who is doing very poorly, all members of the next worse-off class, who are doing quite badly themselves, must sacrifice nearly everything that makes their lives even barely worth living. Insofar as leximin implies that such a distribution would be better, leximin delivers unacceptably strong results, and should be rejected.

A second option is to return to egalitarianism. Call “strong egalitarianism” the view that the betterness of states of affairs is based only on the extent of improvements in equality between these states of affairs (perhaps admitting the value of welfare as a tie-breaker). This form of egalitarianism would have the power to render Misery for the Ultra-Rich false. The value of any equality-improving welfare unit cannot be outweighed by any equality-worsening welfare unit. Worsening the worse-off for the benefit of the better-off is surely, on any serious view of the nature of equality, an exacerbation of inequality.

However, strong egalitarianism succumbs to serious problems. One such worry is the classic:

Leveling-Down Objection: Egalitarianism holds that there is something good about simply reducing the welfare levels of the better-off class, without benefiting anyone. ⁸

Furthermore, on straightforward assumptions about the nature of inequality, sometimes a necessary feature of improving the lot of the worse-off is increasing inequality, for example in cases in which the worse-off can be made better-off only by also making the better-off better-off. So, for instance, if one person is living in misery, and a necessary side-effect of relieving her misery is to grant an even larger improvement to a well-off person, strong egalitarianism would rank this transfer as a value loss, even though both the worse-off person and the better-off person improve. Call this result “Misery for Equality”. In accepting Misery for Equality, strong egalitarianism proves unacceptable.

One way to avoid the leveling-down objection is to adopt a version of “conditional egalitarianism”. This family of views declares that equality is intrinsically valuable, but only conditionally; an egalitarian state of affairs is more valuable than an inegalitarian state of affairs in a way that depends on further features of those states. Andrew Mason prefers a version of conditional egalitarianism such that equality is valuable for its own sake if and only if at least one person is better-off as a result of equality. Mason writes: “When some benefit from equality, we should value it for its own sake even though its value is partly grounded in its benefiting some. If no one benefits from equality, then it lacks non-instrumental value.” ⁹ This view is extensionally equivalent to a view described by Bertil Tungodden and Peter Vallentyne under the heading “Paretian egalitarianism”. As stated by Tungodden and Vallentyne, Paretian egalitarianism is the conjunction of a concern for a weak efficiency requirement with a concern for equality. On this view, whenever two states of affairs are Pareto-incomparable (i.e., one state of affairs is better for some and worse for others than the other), “equality is determinative of justice.” ¹⁰ (These views are equivalent given that both views will declare an egalitarian improvement worse only if it is worse for at least one and better for none. In all other cases, egalitarian improvements are better. Insofar as conditional egalitarianism is a family of distinct views—a variant of which I explore below—it will be convenient to refer to the view outlined by Mason and Tungodden and Vallentyne as “Paretian egalitarianism”.)

Paretian egalitarianism can successfully avoid Misery for the Ultra-Rich and Misery for Equality. Because equality determines the relative betterness of states of affairs only in cases in which equality makes at least one person better-off, Misery for Equality is avoided; in that case, no one is made better-off as a result of equality. Secondly, because the transfer discussed in Misery for the Ultra-Rich renders some better-off, others worse-off, this transfer is Pareto-incomparable, and hence equality reigns. Thus, on Paretian egalitarianism, it does not improve a state of affairs to make a worse-off person worse-off for the sake of minor benefits for the better-off. Despite these victories, however, this view should be rejected. Paretian egalitarianism yields verdicts we have already used to reject other principles including, for example, leximin. According to Paretian egalitarianism, a very minor benefit for a worst-off person would seem to justify any amount of losses for the better-off, so long as the resulting state is more egalitarian. Imagine, for instance, that one very poor person could be granted a penny’s worth of benefit, but only at the cost of robbing all individuals who live even marginally good lives of that which renders their lives worth living at all. It would seem that, in this case, the penny’s worth of benefit justifies such an enormous cost to those who, already, barely get by (assuming, for example, that everyone ends up equally poorly off). If this verdict is extreme enough to justify rejecting leximin, it is extreme enough to justify rejecting Paretian egalitarianism.

Call the last family of views that solve Misery for the Ultra-Rich, “threshold-laden”. Threshold-laden views set a particularly important line of welfare achievement, and declare that benefits below the line are to take absolute priority to benefits above the line. Important examples of threshold-laden views are Roger Crisp’s recent version of a sufficientarian doctrine, ¹¹ and Campbell Brown’s “threshold prioritarianism”. ¹² For Crisp’s version of sufficientarianism, worse-off persons below a certain threshold would take absolute priority to better-off persons above that threshold. Assuming the threshold is placed somewhere between misery and the position of the ultra-rich, this view solves Misery for the Ultra-Rich. The main difference between Brown’s and Crisp’s views is that Crisp’s view is indifferent to distributions above the threshold, while Brown’s treats distributions among super-threshold and sub-threshold welfare units as weighted on a prioritarian scale, while admitting that sub-threshold welfare units are of absolute priority to super-threshold welfare units. ¹³

However, a threshold-laden view is difficult to sustain plausibly. The first worry is that this view comes with an analogue of Misery for the Ultra-Rich. Imagine, for instance, that some person is living a good life above the line, but could be lowered to just above the threshold (barely achieving whatever line of important significance is identified by the threshold-laden view in question) for the benefit of miniscule welfare gains for some finite amount of people who are even better-off than the ultra-rich (call this “Sufficiency for the Mega-Rich”). In other words, we simply shift the persons involved in the original Misery for the Ultra-Rich case higher on the scale. I submit that this is no more plausible than the original Misery for the Ultra-Rich, especially given that most sufficientarian views will set the all-important threshold at a relatively low level. ¹⁴

However, there is a deeper problem here. Threshold-laden views lack an adequate rationale. To see this, consider the moral strength of the threshold on a threshold-laden view. For either version, a microscopic benefit to a person just below the line would be enough to outweigh massive benefits for any amount of people just above the line. ¹⁵ Although I do not regard this verdict as implausible in all cases (surely the plausibility depends, in part, on where one sets the threshold), its strength requires an equally strong rationale. Threshold-laden views declare that the moral weightiness of the threshold is licensed by the importance of a particular line of welfare achievement, and its importance. However, it seems difficult to defend one particular line of welfare achievement as having enough relative importance to manage such a strong evaluative conclusion. ¹⁶ Roger Crisp, for instance, suggests that the proper line should be set at “the point at which [a person] has a level such that [she] can live a life which is sufficiently good.” ¹⁷ However, this response is not particularly helpful—it does not specify a particular welfare achievement that (a) is plausible as a description of a life as “sufficiently good”, and (b) could plausibly bear the evaluative weight required of it by threshold-laden views. As it stands, threshold-laden views seem in need of a stronger rationale, one that would select a welfare level of importance enough to license a conclusion sufficient to reject Misery for the Ultra-Rich.

So what to do? Prioritarianism succumbs to Misery for the Ultra-Rich and hence should be viewed with a strong degree of suspicion. However, we have seen reason to be skeptical of virtually all ways to reject it. Of course, these problems are well-known, and well-discussed. However, they are significant enough, I think, to warrant an expanded catalog of potential alternatives. In the remainder of this paper, I argue that prioritarianism and egalitarianism can work together to establish a view that avoids Misery for the Ultra-Rich without the problems we have so far uncovered in alternative views.

The basic idea: equality-tempered prioritarianism

In this section, I briefly outline the main idea behind my proposed amendment to prioritarianism. The resulting view has the advantage of being relatively simple. Of course, nothing comes so easy. The view I present here comes along with some serious problems and will be revised in light of these problems below. It is helpful, however, to state the basic idea here for heuristic purposes.

To illustrate the general idea, assume that the following principle is true:

Egalitarianism: improvements in the equality of a state of affairs are intrinsically valuable.

For instance, consider the difference between two states of affairs, each containing two persons: A: {x: 100, y: 10}; B: {x: 55, y: 55}. B is better. But why? It appears that an entirely natural answer to the question is that B’s distribution is equal; A’s is not. Although egalitarianism is not the only view that can support B’s betterness (virtually any non-utilitarian view can do the same), egalitarianism does so in a particularly intuitive, straightforward way. It seems too roundabout, for instance, to declare that B is better because a move from A to B treats the worst-off with priority, or that benefits to the worse-off are worth more, hence rendering B better than A. Speaking in terms of bare intuition, equality has at least pro tanto value: value that does not necessarily track the overall value of states of affairs, but value nonetheless. If this is correct, the assumption that equality should play a role in the betterness relation is—at least for the moment—justified. Hence, if we assume also that improvements in overall welfare are valuable along a prioritarian axiology, the resulting view is pluralist: both welfare (according to prioritarian weighting) and equality are intrinsically valuable.

Of course, the grand dilemma of any pluralist axiology is the problem of weight. If Egalitarianism is true, we have a choice about how to weigh the value of equality against other values. However, because prioritarianism weighs marginal welfare units along a concave value curve, there will be no single answer concerning how much equality is worth in comparison to marginal welfare benefits. However, progress can be made if we can figure out, in some suitably benchmark case, the comparative value of a single inequality-increasing welfare unit in comparison to the equality it decreases. The following point is critical. Confining our discussion to inequality-increasing welfare units, if the value of these units diminishes asymptotically to zero as beneficiaries get better-off, there will be some point at which the disvalue of inequality will overtake the value of a marginal welfare unit. However, if this is correct, we can reframe the question of the relative value of equality and welfare this way: at what level of welfare do we believe that an increase in equality is more important than an additional welfare unit for an individual at that level of welfare? I propose the following: the negative value of inequality is enough to outweigh one inequality-increasing welfare unit for the Ultra-Rich. A welfare benefit for the ultra-rich does not improve the overall value of a state of affairs if that welfare unit increases inequality (decreases equality). Hence, we are left with a view that treats the value of equality as having the power to outweigh additional welfare units for very well-off individuals. Call this view Equality-Tempered Prioritarianism (ETP).

It would do to express this idea technically. Let A ( w 1 , w 2 ) be an interpretation of the betterness relation between two states of affairs w 1 and w 2 . If A is positive, w 2 is better than w 1 , vice versa if A is negative. For ETP, A will be a function, first, of the prioritarian value of the first state of affairs as compared to the second ( P ( w 1 , w 2 ) ) , and second, of the comparative level of equality or inequality of the first state of affairs as compared to the second ( E ( w 1 , w 2 ) ) :

E T P : A ( w 1 , w 2 ) = f ( P ( w 1 , w 2 ) , E ( w 1 , w 2 ) ) .

So far so good. However, three questions arise. Firstly, what is the function f ? Secondly, how is P determined, given the input of two states of affairs and, thirdly, how is E determined, given the input of two states of affairs? Taking these in reverse order, E will be a determination of the comparative equality of w 1 and w 2 . If w 2 is less egalitarian than w 1 , the value returned will be negative; if w 2 is more egalitarian, the value returned will be positive. ¹⁸ P is, obviously, simply determined by the prioritarian value curve, that is, the weighted aggregate welfare of w 2 minus the weighted aggregate welfare of w 1 .

Now to f. Because ETP declares that both welfare (according to a prioritarian value curve) and equality are intrinsically valuable, the overall comparative value of two states of affairs will be an aggregative function of their comparative prioritarian value scores and equality scores. However, it is important not to weigh equality too heavily in comparison to its partner input. As briefly noted above, the basic idea of ETP is that the value of increasing equality should be no less than the value of a welfare unit for an individual who barely meets the threshold of the ultra-rich. If that is correct, then, the aggregative function f should weigh E by a factor equivalent to a welfare unit for a member of the (just barely) ultra-rich. If we define the prioritarian weighted value of a welfare unit for a member of the (just barely) ultra-rich as W u r , then, as a first pass:

f = P + ( W u r E ) .

Here is how this view solves the problem of Misery for the Ultra-Rich. ¹⁹ For prioritarianism, the value of a particular welfare unit will always be positive; however, the value of individual welfare units will diminish as the welfare score of the beneficiaries increases. If this is correct, for every inequality-increasing welfare unit (a welfare unit the addition of which renders E negative), the overall value of that welfare unit will be less than its weighted prioritarian value, insofar as the intrinsic disvalue of the resulting inequality will be added to its weighted prioritarian value (given that ( W u r E ) will be negative for any negative value of E). However, if this is correct, at some level of welfare, the positive value gained by a particular inequality-increasing welfare unit granted to an individual at that level will not be enough to counteract the negative value of the resulting inequality, and hence the comparative value of that particular welfare unit (A) will be negative. As defined here, this point is set at the level of the ultra-rich. Hence, given that each minor welfare benefit granted to a member of the ultra-rich is inequality-increasing, these welfare benefits will not, on balance, contribute to the comparative value of the state of affairs in question.

It would be helpful at this point to say a little more about who the ultra-rich are. Although I will not offer any precise theory, we have the tools in place to answer this question. Notice that identifying the ultra-rich will depend in large measure on our intuitions concerning Misery for the Ultra-Rich. The main problem with Misery for the Ultra-Rich is that the people provided a minor benefit at the cost of misery for one are comparatively extremely well-off. If so, at some lower level of welfare n, it will be plausible to say that for these individuals a minor benefit can, in substantial numbers, outweigh the cost of misery for one. If this is correct, a determination of who counts as a member of the ultra-rich will simply be a determination of those for whom minor benefits will, and those for whom minor benefits will not, at some magnitude, outweigh misery for one. This will in turn determine how we assign the value of E in comparison to P.

Some may complain, surely correctly, that the difference between individuals for whom minor benefits can outweigh major burdens for the worse-off and individuals for whom minor benefits cannot outweigh major burdens for the worse-off is vague, far more vague than ETP allows. Ultimately, any particular assignment of the relevant ultra-rich threshold may seem arbitrary. While this is correct, simply because any particular line may seem arbitrary does not entail that there is no such line. Unless we are to commit to an unacceptably indeterminate axiology, at some point we must say that minor benefits for these people, and not people slightly better-off, can outweigh major burdens for the worse-off. Refusing to do so either commits us to Misery for the Ultra-Rich, or to a wide swath of individuals for whom the axiological status of welfare benefits is, in essence, in limbo. Both conclusions should be avoided.

At this point, it is worth comparing ETP to threshold-laden views. ETP is committed to the claim that benefits to people below a certain threshold (the threshold of the ultra-rich) are absolutely prior to inequality-increasing welfare units for those above the threshold. Thus ETP is, in a sense, a threshold-laden view. However, ETP avoids both problems with the threshold-laden views I discuss above. Firstly, Sufficiency for the Mega-Rich poses no problem for ETP, and for two reasons. (A) because ETP’s threshold is set comparatively high, even if it would make a state of affairs better to reduce a person above the line to just above the line for the sake of minor benefits to those wildly above the line, this seems comparatively innocuous. The problem for sufficientarian views is that the sufficientarian threshold is set, as noted above, at a comparatively low level. However, (B) even if this were a problem, because on ETP any increase in equality improves a state of affairs more than welfare benefits for those above the threshold would have, exacerbating inequality above the threshold is always worse; above the threshold, ETP becomes a version of strong egalitarianism and hence Sufficiency for the Mega-Rich, on ETP, is false. Secondly, recall that threshold-laden views are required to offer a rationale strong enough to support the claim that any finite number of super-threshold welfare units cannot outweigh the smallest relevant amount of sub-threshold welfare units. ETP, however, can offer a comparatively strong rationale: the rationale for the threshold designated by ETP is not the overwhelming importance of a single welfare achievement (which seems far too meager to defend the strong implications of sufficientarianism), but, simply, that the value of equality will eventually overtake the value of welfare units assuming that the value of welfare units are evaluated according to the concave prioritarian value curve. ETP is a natural outcome of a dual commitment: a commitment to a prioritarian weighting of welfare units, and a commitment to the non-zero value of equality. If we accept Egalitarianism and accept the claim that marginal welfare benefits for the better-off decrease asymptotically to zero, we are committed to the claim that, at some level of welfare n, the non-zero value of an increase in equality outweighs the non-zero value of a marginal welfare benefit at n. Hence, for ETP, the rationale is simple: the conjunction of prioritarianism and Egalitarianism.

However, if this is true, we appear to have rejected Misery for the Ultra-Rich without rejecting prioritarianism in favor of a view that embraces the implausible conclusions of views I explored in the second section. In addition, it is worth noting that the value of equality in most cases is dormant in terms of the all-things-considered better-than relation. However, as the prioritarian value curve dips, it dips below the value of equality; equality thus regains its bite in a manner sufficient to defeat Misery for the Ultra-Rich.

Leveling-down: equality-tempered prioritarianism defended and revised

Because ETP is equality-tempered prioritarianism, it comes equipped with standard egalitarian baggage. The heaviest piece of which is the Leveling-Down Objection. I will take this objection in two stages; I consider, firstly, ETP’s evaluative attitude toward leveling-down the ultra-rich. Secondly, I consider ETP’s stance when it comes to leveling-down the worse-off. Indeed, as a warning, although ETP substantially tempers the excesses of strong egalitarianism, some structurally similar absurdities arise on ETP. Hence, or so I shall argue, we should slightly alter one component of ETP.

Leveling-down the worse-off and Misery for Equality

Now let us turn to ETP’s attitude toward leveling-down the worse-off. Here matters turn ugly. Insofar as ETP accepts Egalitarianism, ETP appears committed to the claim that leveling-down those who are extremely poorly off is a pro tanto value improvement. However, even if leveling-down is plausible in cases in which welfare units are absolutely insignificant, it would appear strange to say that leveling-down the worse-off makes a state of affairs better to any degree at all.

To be honest, I share the intuition that leveling-down the worse-off can be good in no respect whatsoever. However, the problem gets much, much worse. Recall Misery for Equality. Strong egalitarianism does not simply license leveling the better-off down to the standard of the worse-off, it licenses leveling-down both the better-off and worse-off if that would have a net benefit in terms of overall equality. So, for instance, if the only way to improve the equality of a state of affairs is to worsen the condition of the better-off class and the worse-off class (while worsening the condition of the better-off class to a greater degree), this would be embraced by strong egalitarianism. Misery for Equality is substantially tempered by ETP, but it remains. Given the prioritarian value curve, every inequality-increasing benefit for the ultra-rich is an all-things-considered value loss. Thus, at some point the aggregate value loss of inequality-increasing welfare units for the ultra-rich will be enough to outweigh the value gain granted by giving a benefit to a worse-off person. For instance, if we are forced to choose between E: {x: 10; y: 1000} and F: {x: 11; y: 10,000}, the loss of value in terms of inequality might be enough to outweigh the gain in welfare for x, hence leading us to prefer E to F. ²¹ Furthermore, take G: {x: 10; y: 100,000} versus H: {x: Misery; y: 1000}. Given the value gain in terms of equality as a result of moving the better-off from mega-rich to simply ultra-rich, H appears favored by ETP. Indeed, it is not the case simply that there is something good about so doing. Rather, it is all-things-considered better to level-down even the worse-off for a comparatively gigantic improvement in equality when those equality-improvements come at the cost of the ultra-rich. Hence, although ETP tempers Misery for Equality, it remains.

However, I think ETP can be salvaged by rethinking our commitment to the value of equality. Given the problems noted (firstly, that ETP retains the implausible claim that there is at least something good about leveling-down everyone, even the worse-off, and, secondly, the remaining vestiges of Misery for Equality), it would appear that the axiological relationship between the prioritarian welfare value of a given state of affairs and the equality or inequality of that state of affairs is substantially more complex than is currently represented by ETP. As stated, ETP accepts Egalitarianism, which grants equality non-zero value however it arises. However, this appears not to be an adequate representation of considered judgment. In particular, it would seem more plausible to rule out the value of equality in cases in which an increase in equality makes the worse-off worse-off, or where a decrease in equality makes the worse-off better-off. So rather than accepting that equality is intrinsically valuable (and inequality intrinsically disvaluable) in all contexts, we should adopt a version of conditional egalitarianism. However, rather than adopting the Paretian iteration discussed above, we should say that equality contributes to the relative value of two states of affairs only if an increase in equality (or a decrease in inequality) does not make the worse-off any worse-off. ²²

To express this more precisely, I need to make use of a Boolean operator, C ( w 1 , w 2 ) , which assigns a score (1 or 0) determined by two factors, viz., the difference in welfare units for the worse-off between the specified states of affairs ( W O ( w 1 , w 2 ) ) , ²³ and whether there is an aggregate increase or decrease in equality between those two states of affairs (which I have already defined as E ( w 1 , w 2 ) ) . When (WO < 0 and E > 0) or (WO > 0 and E < 0), C = 0; otherwise C = 1. With this defined, A can be expressed as follows:

E T P : A ( w 1 , w 2 ) = f ( P ( w 1 , w 2 ) , C ( w 1 , w 2 ) , E ( w 1 , w 2 ) ) .

The relevant function f is thus defined:

f = P + ( C ( W u r E ) ) .

Under this formula, the value of equality is in operation only when either the interests of the worse-off are unaffected, or when the interests of the worse-off are advanced by an increase in equality. In all other cases, that is, when the worse-off are made better-off by inequality, equality plays no role in the betterness relation.

Two points are worth mentioning about this proposal. Firstly, in accepting a form of conditional egalitarianism, rather than a more straightforward egalitarianism, I deny that equality is intrinsically valuable in cases in which the worse-off stand to lose by an increase in equality. If this is correct, the view I advocate has the resources to deny that there is anything valuable about leveling-down the worse-off. In cases in which the worse-off lose, equality has no intrinsic value at all. However, I think this is significant. Some might believe that accepting this form of conditional egalitarianism is implausibly ad hoc (more on this objection in the next section). However, if, as it is plausible to believe, we should reject even the pro tanto value of leveling-down in cases in which the worse-off stand to lose, we should be inclined to accept conditional egalitarianism rather than a more straightforward egalitarianism as a proper representation of our disposition toward the value of equality. Generally speaking, it is plausible to hold that equality is valuable. However, this holds only when the worse-off are not made worse-off by equality. If this is correct, the view just stated is no more ad hoc than the basic idea, articulated in the third section.

Secondly, I have not properly identified the “worse-off”. However, my preference here is to remain neutral between potential methods by which to assess the point at which an individual’s welfare has the power to render it the case that equality is not intrinsically valuable. For the record, I favor an absolute conception of the “worse-off”. In particular, a natural suggestion is that the worse-off should include anyone who falls below the level of the ultra-rich. However, there are other methods. One could identify a “worse-off” individual as someone below the mean, or someone below some other identified absolute threshold. ²⁴ How best to set the line will, of course, require investigation into our considered judgments. I leave this investigation for another time.

One note before I conclude. As it stands, ETP is a general account of the nature of the “better-than” relation. However, I have not offered any general proof that my proposal has a number of important technical features. For instance, I have not argued that my proposal guarantees that the better-than relation will be transitive. However, whether my view is ultimately transitive must depend on the interpretation of a number of elements of ETP between which I remain ecumenical here, including the proper theory of equality or inequality, the assignment of the “worse-off”, etc. The view as stated guarantees neither transitivity nor intransitivity, ²⁵ and hence, if we wish to guarantee one or the other, we should be careful to interpret the missing elements in ways that guarantee the transitivity (or intransitivity) of the better-than relation, as suggested by ETP.

Conclusion: Is equality-tempered prioritarianism ad hoc?

ETP has substantial virtues in comparison to the views I have considered so far. Unlike un-tempered prioritarianism, ETP can solve Misery for the Ultra-Rich. Unlike leximin, ETP holds that it does not improve a state of affairs to grant a very minor benefit to the worst-off at the expense of very substantial burdens for the sake of people who are themselves very poorly off. Unlike strong egalitarianism, ETP (as revised) avoids the most problematic instances of leveling-down. In addition, unlike threshold-laden views, ETP does not commit to a transposed version of Misery for the Ultra-Rich, nor can it fail to offer an independent rationale for the strong axiological conclusions it posits.

In conclusion, I discuss an important objection I have so far (mostly) left to the side. Someone might claim that the view I offer is ad hoc. After all, why should we believe that not only is the better-than relation characterized by a generally prioritarian weighting of human welfare, but also the (conditional) value of equality? What independent reason is there to believe this view?

I have already argued that to accept the intrinsic value of equality is independently plausible. However, if equality is intrinsically valuable, we must determine some method by which to weigh the value of equality in comparison to the value of welfare improvements. However, then why not do so in a way that solves Misery for the Ultra-Rich? If equality is valuable, and welfare is valuable according to the prioritarian value curve, the value of equality must exceed the value of welfare units at some point. ²⁶ Why not address the comparative weight of these values in a way that best suits our considered judgments? The basic idea behind ETP, as outlined in the third section, then, is not ad hoc.

Of course, I accept a revised version of the basic idea; I accept a non-Paretian conditional egalitarianism rather than Egalitarianism. Hence, ETP is not ad hoc only if the rejection of Egalitarianism in favor of a conditional egalitarianism is not ad hoc. However, once again, it is not. My version of conditional egalitarianism responds to the considered judgments that I, and I hope the reader, will have concerning Misery for Equality, and the implausible result that leveling-down the worse-off will improve a state of affairs in at least some respect. Conditional egalitarianism, or so I claim, is a more plausible representation of considered judgment than Egalitarianism. Of course, if the objection on the table is asking for a further rationale than conformity to considered judgment, I am afraid I cannot offer one. However, I confess to finding this very little reason to be concerned about the fate of ETP. The view I advocate solves Misery for the Ultra-Rich, without the implausible results of leximin, strong egalitarianism, or threshold-laden views. This result is of course not enough to guarantee the truth of ETP. However it is, at the very least, strong enough to get it a place at the table.