1. DEFINITIONS AND PUZZLES

Assume that there is a benefit which can be more or less equally distributed to individuals in the population, and the problem here is not to define what this benefit should be (this is the topic of a different, and no less interesting, part of political philosophy), but how it should be distributed, or, more precisely, how to rank different distributions which may differ in terms of the total quantity as well as of how the benefit is shared among individuals. For instance, is a = (2, 3, 5) better than b = (1, 4, 4)? Let us call this a social ranking. It is important to distinguish disagreements about the social ranking from disagreements about the reasons supporting the social ranking. Only the former have practical implications and are directly relevant for the policy-maker.

An egalitarian is supposed to be someone who cares about equality, and considers that ‘it is in itself bad if some people are worse off than others’ (Parfit Reference Parfit1995: 4). Temkin (Reference Temkin2000) writes that the egalitarian not only cares about equality but seeks equality per se, as a ‘non-instrumental’ goal. These definitions are puzzling. First, there is essentially one way to define equality, assuming that the quantity to be equalized is well defined, but there are many ways of measuring inequality. Two egalitarians may disagree on whether distribution A is more unequal than distribution B. There should be a minimal definition of what it means to care about equality, in terms of how inequality is measured. For instance, one may propose the Pigou–Dalton principle of transferFootnote ² as a minimal condition that a reasonable measure of inequality should satisfy, but even this is somewhat controversial, since there exists inequality measures which do not satisfy it. The minimal egalitarian statement that seems to be adopted is that unequal distributions have something bad that equal distributions do not have. For instance, Temkin (Reference Temkin2000: 2) says that ‘the core, fundamental tenet of substantive non-instrumental egalitarianism is that it is bad for some to be worse off than others’. But this minimal egalitarianism says almost nothing about the shape of the social ranking. Maybe it implies that the best distribution of a given amount of benefit is the egalitarian one. But, apparently, this is not a bone of contention between egalitarians and prioritarians. Now, does it imply anything about the comparison of unequal distributions, or about the comparison of distributions with different total amounts of benefits? One may suspect that, through this minimal egalitarian statement, the discussion is already shifting from the shape of the social ranking to issues of foundation, reasons and ethical intuitions.

Moreover, the secondary distinction between Intrinsic Egalitarianism and Instrumental Egalitarianism seems again, and even more clearly, to bear only on the reasons for, not on the content of, the social ranking. A social ranking only makes comparisons between distributions, and cannot yield the judgement that one distribution has something that ‘is in itself bad’ (the formula used by Parfit in his definition of egalitarianism). Therefore, two observers may propose the same social ranking to the policy-maker, but it may be that for Parfit and Temkin only one deserves the full egalitarian label, namely, the one who loves equality in a non-instrumental way. This distinction is, however, irrelevant to the actual choice of policies.

The Priority View says that equality has no value, and that, however, people who are worse off should have priority. ‘Benefiting people matters more the worse off these people are’ (Parfit Reference Parfit1995: 19). At first glance, this seems to be just saying that individual weights should be (positive and) inversely related to the individual initial levels of benefits.

But, in fact, it seems that most authors are keen on insisting on a non-relative definition of ‘worse off’. People who are badly off will have a great weight not because they are worse off than others, but just because they are badly off. This definition is even more puzzling than the definition of egalitarianism. First, any notion of priority is relative. If the Priority View has nothing to do with comparisons between individuals, it should have a different name. But surely one cannot avoid interpersonal comparisons of some kind in the current setting.

Second, suppose that two individuals are equally well-off. Is it possible for one to have priority over the other, according to a social ranking compatible with the Priority View? That seems implausible. But if they have equal priority, then necessarily an individual who is worse off than another one will have greater priority, in virtue of the rule that priority increases with how badly off the individual is (considered in isolation). This implies that even if there is an ‘Absolute’ Priority View to be distinguished from a ‘Relative’ one, both views give priority to worse off agents over better off agents, although for different reasons.

Does this mean that there is no substantial distinction here? Maybe not. One may guess that the idea that the importance of an individual should not depend on his relative position actually means that the social good must be measured as the sum of weighted individual benefits, and that every individual's weight must depend only on that individual's level of benefit. (In other words, for the economist reader: the social ranking must be represented by an additively separable social welfare function.) If that is so, then the Priority View, in its Absolute construal, is quite restrictive. It excludes the non-additive representations of separable rankings, and all the rankings based on the maximin, the leximin, the Gini social welfare functions, etc. However, as mentioned by Parfit (Reference Parfit1995) and Temkin (Reference Temkin1993), one can still accept the maximin and the leximin as limit cases of this approach (although the maximin is not separable). In conclusion, the main feature of the Priority View which may bear on the content of the social ranking is this separability of individuals. Parfit (Reference Parfit1995), in particular, argues that the Priority View is special in the fact that it need not ask ‘How well off is everyone else?’ when comparing distributions for two individuals.

From Table 1 it is obvious that, as far as the content of the social ranking is concerned, prioritarianism is but a special case of egalitarianism. Several authors, however, have argued that egalitarians are actually committed to more special views, and should reject separability or the Pareto principle (which, roughly, requires weights to be positive). This issue is partly terminological. One could define egalitarianism as rejecting separability. One could as well define egalitarianism as rejecting the Pareto principle. I prefer to stick to the broader, and somewhat more conventional, definition given above. The substantial issue, then, is whether by giving equality an intrinsic value, egalitarians are committed to special social rankings which differ from prioritarian rankings. It is hard to see why this should be the case, and the examples discussed in the sequel illustrate this point.

Table 1.

Defining characteristics of Egalitarianism and Prioritarianism and their rationales.

2. THE PRIORITY VIEW IMPLIES INSTRUMENTAL EGALITARIANISM

Before addressing these issues, an easy point can be recalled. It has been acknowledged by Parfit (Reference Parfit1995) and other authors that the Priority View actually implies an instrumental preference for equality. This point can be explained in a graphical way with some of the economist's tools.

If worse off individuals have priority, then the social ranking satisfies the Pigou–Dalton transfer principle applied to social rankings, which says that a transfer of a given amount from an agent to another who is worse off (even after transfer) yields a socially preferred distribution.Footnote ³ Indeed, by the definition of priority, it is a good thing to make a transfer of benefit from an individual to another who has greater priority (before as well as after the transfer). Since priority is allotted to those who are worse off, it is a good thing to make a transfer from a better-off to a worse-off individual, which is precisely the Pigou–Dalton principle.

Therefore, the Priority View, both in its Absolute and Relative versions, implies the Pigou–Dalton principle for social rankings. And this principle implies that the best distribution of a given total quantity of benefit is the egalitarian one. The Priority View has a bias toward equality, and this has been recognized by all authors.

But something more precise can be said. If the social ranking is continuous,Footnote ⁴ then a social ranking based on the Priority View, and more generally any social ranking satisfying the Pigou–Dalton principle (for social rankings), can be represented by a function which depends on the average (or total) amount of benefit, and on an inequality index satisfying the Pigou–Dalton principle (for inequality). This function takes on the following shape:

\begin{equation*} W\, = \,B\, \times \,(1 - {\it IN}) \end{equation*}

where B is the average level of benefit (or the sum total), and IN the inequality index.

The proof is extremely simple. Choose W to be the function that represents the social ranking and that satisfies the property that whenever a distribution is egalitarian, then W equals B. The existence of such a function relies on the continuity condition, and that technical part is skipped here. Then one immediately sees that defining IN by ${\it IN}\, = \,1\, - \,(\frac{W}{B})$ yields a sensible inequality index, because IN = 0 whenever the distribution is egalitarian, and IN satisfies the Pigou–Dalton principle because any Pigou–Dalton transfer increases W while leaving B unchanged, so that IN decreases. Now, reversing the definition of IN, one gets W = B × (1 − IN), as had to be proved.

How can the Priority View be considered to give no value at all to equality while it can be represented as a combined function of the average (or total) amount of benefit and of an inequality index? Prioritarians who claim to be totally indifferent about inequality are actually relying on a precise inequality measurement. The fact that they do so in a purely instrumental way should not hide this fact.

3. A PRIORITARIAN WILL ALWAYS FIND SOME EGALITARIANS ON HER SIDE

While looking for a case in which egalitarians and prioritarians would necessarily disagree, Parfit (Reference Parfit1995) imagined an example in which additional benefits are given to the population, in such a way that the situation of the worse off improves but, on the other hand, inequality seriously deepens. In a similar vein, Hausman (Reference Hausman2015) proposes to consider ‘two changes that increase total benefits by the same amount. In one there are more benefits to the very worst off, while in the other there is a greater decline in inequality’.

But Hausman mentions that his example will entail a disagreement between an egalitarian and a prioritarian only if inequality is ‘measured in some way other than by focusing on the very worst off’. This is clearly right, and refers to the possibility that the egalitarian has such a strong aversion to inequality that the fate of the worst off essentially wholly determines the inequality evaluation. Similarly, in Parfit's example, the improvement of the situation of the worst off implies that for some egalitarians inequality has indeed been reduced, and not increased, so that they will in fact agree with the prioritarians.

This argument deserves to be spelled out. Consider, first, a case where the very worst off receive an incremental benefit. When the fate of the very worst off improves, one can always find egalitarians with a strong enough inequality aversion who favour this distribution. Because the definition of inequality is ambiguous, due to the multiplicity of inequality measures, one can simply never find an example where, in a non-controversial way, the situation of the worst off improves while inequality rises. The distribution with higher benefits for the worst off will have a Lorenz curve which starts above the curve for initial distribution, and therefore one can find an inequality index, satisfying the Pigou–Dalton principle, which judges that inequality is lower in the first distribution. This may be clearer with a numerical example. Consider a = (2, 10, 13, 15) and b = (1, 13, 13, 13). One might be tempted to say that b is more equal than a. But the Lorenz curve for a will (up to a factor 1/40) have a graph with coordinates on the y-axis at (2,12,25,40), which starts above the curve for b, (1,14,27,40). Because the two curves cross, one can find an inequality index favouring a and another one favouring b.Footnote ⁵

Consider, now, a more general case where some prioritarian prefers some distribution. Because, as shown in the previous section, the prioritarian's preference can be expressed by a function B × (1 − IN), there is nothing that prevents an egalitarian from adopting the same preference.

In short, a prioritarian will always find an egalitarian who advocates the same social ranking. When comparing distributions with the same total amount of benefits, the prioritarian will agree with any egalitarian who measures inequality with the same index that is implicit in the prioritarian's social ranking.

4. BROOME’S EXAMPLE

Broome (Reference Broome1991, Reference Broome2015) has proposed another, more sophisticated example that suggests a policy conflict between egalitarianism and prioritarianism. This example has to do with a two-individual population, and involves a policy g which entails either (1,1) or (2,2), with equal probability, and a policy h which entails either (1,2) or (2,1), with equal probability, too. As far as ex ante prospects are concerned, both policies yield the same egalitarian distribution of uncertain benefits: 1 or 2 with equal probability, for every individual. But one sees that policy g entails more egalitarian results, ex post, than policy h. Therefore, one may think, the egalitarian should prefer g while the prioritarian who cares only about individual good in isolation should be indifferent between the two policies.

I agree with Broome (this issue) that it is indeed very likely that prioritarians will feel compelled to be indifferent between the two policies, while many egalitarians would strictly prefer policy g. But this example is problematic because it is not formulated in the basic framework that was introduced above. It raises the difficult issue of how to assess individual and social good under uncertainty.

The theory of social decisions under uncertainty is quite complex and is still a battlefield. It cannot be properly dealt with here. The only point I will make in this section is that there are many competing views on the matter, and that Broome's example does not cut a line between separable and non-separable social rankings, but between different ways to deal with uncertainty.

Before going to the heart of the matter, let me introduce a third policy in this example, namely, policy j which entails (2,1) with certainty. Notice that, compared with policy h, this policy yields the same distribution of benefit ex post, namely 1 to one individual and 2 to the other, but is ex ante less fair because the individual prospects are unequal in j and equal in h.

One can distinguish three different approaches to social decisions under uncertainty. The ex ante approach first computes individual expected benefits (or utilities thereof), and then applies a social ranking to the distributions of expected benefits. This approach entails a strict preference for h over j whenever the social ranking displays some inequality aversion, because the expected benefits with h and j are respectively (1.5,1.5) and (2,1). But it cannot distinguish g from h, because these two policies yield the same distribution of expected benefits, namely (1.5,1.5).

The second approach is the ex post approach, which first computes the level of social welfare in every state of nature, with a particular function W representing the social ranking that is applied under certainty, and then computes the expected value of W. The ex post approach cannot distinguish between h and j whenever the social ranking is indifferent between (1,2) and (2,1), which is normally the case for an impartial observer, because one then has equality between the expected values of W under h and j, respectively:

\begin{equation*} \frac{{\rm 1}}{{\rm 2}}{W(1,2)}\,{\rm + }\,\frac{{\rm 1}}{{\rm 2}}{W(2,1)}\,{\rm = }\,{W(2,1)} \end{equation*}

But it can entail a strict preference for g over h if the function W is not additive. For instance, if W = B × (1 − IN), then one gets under policy g (assuming that B is, say, the total benefit):

\begin{equation*} \frac{{\rm 1}}{{\rm 2}}W{\rm (1,1)}\,{\rm + }\,\frac{{\rm 1}}{{\rm 2}}W{\rm (2,2)}\,{\rm = }\,{\rm 3,} \end{equation*}

whereas under policy h one gets:

\begin{equation*} \frac{{\rm 1}}{{\rm 2}}W{\rm (1,2)}\,{\rm + }\,\frac{{\rm 1}}{{\rm 2}}W{\rm (1,2)}\,{\rm = }\,{\rm 3}\left( {{\rm 1}\, - \,{\it IN}(2,1)} \right)\,{\rm < }\,3. \end{equation*}

Notice that this shows that a strict preference for g over h is possible with a separable social ranking, since as shown previously, the formula B × (1 − IN) can very well represent a separable ranking.

One sees that none of the two above approaches is able to entail a strict preference for g over h and for h over j. The third approach tries to do just that, and the various proposals which have been made so far essentially consist in computing a weighted average of the values of social welfare obtained with the first two approaches.Footnote ⁶ This entails the desired result because in this example it is always the case that one of the approaches is indifferent, so that the strict preference displayed by the other approach makes the difference. But the proposals are rather vague, and it seems that a lot remains to be done as far as this third approach is concerned.

Where do prioritarians and egalitarians stand in these matters? If a prioritarian is supposed to be indifferent between g and h, this means that he/she must either adopt the ex ante approach, or one of the other approaches with an additive W. Is this likely? Broome (Reference Broome1991, Reference Broome2015) and Rabinowicz (Reference Rabinowicz, Egonsson, Josefsson, Petersson, Ronnow-Rasmussen and Persson2001) argue that it would be odd for a prioritarian who relies partly or totally on the ex post approach not to take an additive W. The reason is that otherwise the social ranking over prospects (instead of outcomes) would not be separable. Which means that the comparison between two policies might then depend on the benefit level of agents who are unaffected by the alternative. But it is not absolutely obvious that the prioritarian desire for separability should extend from outcomes to prospects. Indeed, it may matter, when considering an agent at a certain level in one state of nature, to know that in another state of nature, there is another agent at the same (or some other) level. For instance, in the example under consideration here, although the two individuals face the same prospect in h as well in g, the observer is sure that one will be badly off in h, whereas with policy g, there is a chance of avoiding this (at the cost of risking that two end up badly off). This difference may matter even without introducing the kind of comparisons between individuals that prioritarians want to avoid.

Let us now turn to egalitarians. If an egalitarian is supposed to prefer g to h, this means that he/she must adopt one of the last two approaches, and rely on a non-additive W. It is actually plausible that most egalitarians would like to find a criterion that values g over h and h over j, which means that the third approach only would suit them. But it would be sectarian to declare non-egalitarian anyone who expresses some inequality aversion but adopts the ex ante approachFootnote ⁷ or an additive W. And recall that a preference for g is compatible with a separable (but not additive) W.

In conclusion, in the current context in which we lack a full-fledged theory of social decision under uncertainty, it is hard to tell exactly where prioritarians and egalitarians should stand. Broome's example will probably divide most prioritarians and most egalitarians, but it really cuts through issues of ex ante versus ex post and of additivity versus non-additivity of W, and does not directly bear on the issue of separability of the social ranking (over outcomes).

5. THE LEVELLING DOWN OBJECTION AND THE PARETO PRINCIPLE

The egalitarian approach is criticized by prioritarians on the grounds that it implies that an egalitarian distribution is better in some respect than an inegalitarian distribution, even if everyone is worse off in the former. Egalitarians are horrible sadists who claim that there is something good in equality even achieved at the price of universal sacrifice.

There are several parts in the answer to this objection. One is that insofar as prioritarians give instrumental value to equality, as shown above, they should also be subject to a similar criticism. Because the prioritarian has preferences representable by B.(1 − IN), when a change of distribution makes this product decrease in spite of an decrease in IN, the prioritarian must admit that the change is for the worse in spite of something good happening on the IN side.

Second, to give equality some value does not imply that it overrides all other values, in particular a general quest of well-being for all. As acknowledged by most authors, it is perfectly possible to combine egalitarianism with the Pareto principle,Footnote ⁸ for instance, and the Pareto principle immunizes the social ranking from judging that levelling down is, all things considered, desirable. Actually, it is easy to see that any egalitarian who adopts the Pareto principle, and who measures inequality in a way compatible with the Pigou–Dalton principle, will have a social ranking in which all individuals have a positive weight (by the Pareto principle) and the weight of worse off individuals is greater (by the Pigou–Dalton principle). The reason for this latter point is that a transfer from a better-off to a worse-off agent will be considered a good thing (it reduces inequality without affecting the total benefit). This means that the worse-off agent has priority. This is strangely reminiscent of social rankings based on the Priority View, although separability between individuals may or may not be satisfied by the egalitarian ranking.

Third, once levelling down is, all things considered, condemned as bad, there is nothing repugnant about saying that equality, in and of itself, is a good feature of a levelled-down distribution. Prioritarians, in particular, cannot, in the same breath, say that equality is an instrumentally good feature of the lower distribution and that it would be repugnant to view equality as intrinsically good in the levelled-down distribution. Nonetheless, Temkin (Reference Temkin2000) devotes a lot of space to discussing the ‘Slogan’, according to which ‘one situation cannot be worse than another in any respect if there is no one for whom it is worse in any respect’. But this principle is obviously absurd, and the example of levelling down precisely shows why. There may be something (but not everything) better in an equal distribution, instrumentally or intrinsically, even if everyone is worse off (in every respect) in it.

Finally, one must do justice to two intuitions that may be misleading. One is that whenever a value is combined with another value in a pluralist view (as with the pluralist egalitarian combining preference for equality with the Pareto principle), there must be cases where either value overrides the other one. For instance, there must be cases where his preference for equality will force the egalitarian to violate the Pareto principle. This is simply wrong. The elegance of a pluralist view is precisely that it may respect the two values in all cases. And this is perfectly possible for the combination of preference for equality with full respect of the Pareto principle (see the next section for details).

The second misleading intuition is that whenever two views are based on different foundations (such as the equality view based on a preference over distributions and the priority view based on a concern for the badly off), there must be some possible worlds where the two views lead to opposite practical judgements. Again, this is clearly wrong. There are many different arguments supporting the Pareto principle, but they cannot lead to practical disagreement because they yield the same principle. Similarly, a pluralist (that is, a Paretian) egalitarian and a prioritarian may exhibit exactly the same social ranking, albeit for different reasons. But there is no way of making them disagree on practical issues, and this is so simply because they have the same ranking.

6. OLDER DEBATES

Several decades ago, another debate took place about egalitarianism, which bears some superficial similarity with the equality-priority distinction. It had to do with the fact that utilitarianism, which seeks to maximize the sum total of benefits, can be criticized for ignoring inequality. But, on the other hand, a strong preference for egalitarian distributions might hurt the Pareto principle. This latter issue is apparently similar to, but has actually little to do with, the levelling down objection. The levelling down objection is raised against the idea that a lower, but egalitarian, distribution is better in some respect. The above Paretian objection was against the idea that a lower, egalitarian, distribution could be better, all things considered. The levelling down objection is not really about the shape of the social ranking, whereas the Paretian objection is.

Since the Pareto principle is quite appealing, one would like the social ranking to obey it, but at the same time to exhibit some aversion to inequality. The solution has been found in the neoclassical theory of consumption, in which similar features are captured by the elasticity of substitution. And it has quickly been found that the maximal aversion to inequality that is compatible with the Pareto principle is displayed by the maximin criterion, or better,Footnote ⁹ by its lexicographic version, the leximin criterion. In welfare economics, as well as in the theory of Rawls, the maximin (or leximin) criterion has then been adopted as yielding the most egalitarian among reasonable (that is, Paretian) social rankings.

Contrary to the equality-priority luxuriance, these notions are very relevant to the policy-maker, because they bear on the shape of the social ranking. (In health economics, their implications have been examined by Olsen (Reference Olsen1997).) Although most authors accept the Pareto principle and would have the policy-maker focus on the choice of an appropriate degree of inequality aversion (is the maximin criterion too extreme when it says that (2,3) is better than (1,1000)?), Temkin (Reference Temkin1993, Reference Temkin2000) argues that equality might be so important as to override the Pareto principle in some cases. In relation to health, he proposes an example which involves an immortality pill that, maybe, should not be marketed if it has an effect only on a minority of people. The example would imply, say, that (1,1,1,1,1,1) is better than (1,1,1,1,1,1000). This example is extreme and, of course, unrealistic, but it remains an interesting question whether such conflicts between equality and Pareto may occur in real policy issues.

In the economics literature, the conflict between equality and Pareto has appeared more severe in the uncertainty context, when Pareto is applied in terms of unanimity of people's preferences. For instance, modify Broome's example slightly, and consider policy h ⁺ which yields either (1.01,2.01) or (2.01,1.01). It gives individuals better prospects ex ante (either 1.01 or 2.01) than policy g (either 1 or 2), so that if these figures are congruent with individual utilities, both individuals will ex ante prefer policy h ⁺ to policy g, no matter how they handle decision-making under uncertainty (they need not be expected-utility maximizers). Yet an egalitarian might still prefer policy g to policy h ⁺. This example is somewhat special, and more commonly, the conflict takes the following shape: The egalitarian wants to force individuals to insure more than they spontaneously would, in order to avoid the ex post inequalities that risk-taking entails. For instance, the individuals might prefer h ⁺ to a policy yielding (1.5,1.5) for sure, whereas the egalitarian might prefer the latter.Footnote ¹⁰

A related but different issue has been the introduction of separability of individuals in the social ranking. It has never been doubted by economists that (intrinsic or instrumental) preference for equality is fully compatible with separability of the ranking (over outcomes). Are they wrong? Recall that separability merely says that the social judgement about a change affecting a subpopulation does not depend on the rest of the population. This property is clearly not incompatible with egalitarian values. The prioritarian rejection of equality as an intrinsic value does imply separability, but separability does not require rejecting equality, and an egalitarian may also like separability.

Let us be more precise on this matter. The prioritarian rejection of equality is usually interpreted as implying that social good (or welfare) is an additive function of individual benefits:

\begin{equation*} f(b_1 )\, + \, \cdots \, + \,f(b_m ), \end{equation*}

and this in turn implies that the social ranking is separable. There is a partial converse: Separability, under conditions of continuity, implies that the social ranking can be represented by an additive function. This converse is doubly partial. First, it does not imply that social good can be measured, and if it can, that it is an additive function (only that it is an increasing transformation of an additive function). Second, it is not obvious that adopting an additive function as a measure of social good implies that equality has no intrinsic value. Even if the latter point were true, the egalitarian who likes separability would not be forced to adopt an additive function as a measure of social good, and for practical purposes there is actually no need to measure social good, because a social ranking is all that is needed for decision-making. As pointed out by Broome (this issue), the prioritarian formulations about measuring social good and the social value of individual benefits are troublesome, and may involve distinctions that are practically impossible.

In economics, most authors think that separability is a desirable feature, at least because it considerably simplifies the social ranking and its application to subpopulations, but there are interesting social rankings, such as those derived from the Gini coefficient, which are not separable, and display a non-separability that seems to reflect an interesting concern for the distribution, for instance a sensitivity to how individuals are ranked. Although Parfit (Reference Parfit1995) and Broome (Reference Broome2015) certainly exaggerate when they claim that egalitarians must be committed to a non-separable social ranking, a lot remains to be done about the foundations of this controversial property.Footnote ¹¹