Contractualist alternatives to the veil of ignorance

Some of the strongest criticisms of the original position have come from contractualists sympathetic to egalitarianism. In “Contractualism and Utilitarianism,” Thomas Scanlon objected that, without special assumptions, choice under uncertainty justifies maximizing the average rather than the minimum, and is thus compatible with the least advantaged suffering serious avoidable hardship. Yet Scanlon also argued that the difference principle is unreasonably strict in its single-minded focus on raising the least advantaged position without regard to the size of forgone benefits in other parts of the distribution.1

Scanlon went on to develop a contractualist theory of moral obligation, not of social justice.2 More recently, he has discussed the reasons for objecting to economic inequality, defending a “weaker” version of the difference principle.3 Yet, as Jacob Barrett has argued,4 Scanlon is not entirely clear about the content of his alternate principle. Nor has he explained exactly how it is derived from the requirement of invulnerability to reasonable rejection.

Others have worked out what has become known as the “complaint model” of reasonable rejection, building on Scanlon's suggestions about how we might accommodate a limited form of aggregation while preserving the main thrust of contractualism's individualism.5 However, this model has been developed primarily in the context of moral rather than political philosophy, with a focus on problems of rescue, not decisions about the basic structure of a political society. The result is that there still isn't a Scanlonian theory of justice.

Choice from behind a veil of ignorance forces one to imagine what it would be like to be in someone else's disadvantaged position, but it also permits one to gamble—for the sake of a greater expectation—that one is unlikely to end up in that position. The complaint model of reasonable rejection requires not only that I consider your situation, but that I withdraw my own complaint if it is (much) smaller than yours.7 Since everyone in my position should do the same, it won't matter if there are more of us in my position than in yours. The complaint model is subject to a number of objections, but I will argue that most of them do not arise with respect to choices about the design of the basic structure of society, assessed in terms of the lifetime prospects associated with different social positions. As the basis for a theory of distributive justice, however, the complaint model is insufficiently egalitarian. Minimizing the maximum complaint does disallow many relatively trivial gains higher up in the spectrum of advantage from outweighing one serious loss lower down. However, once we relax lexical priority, the complaint model can also prevent many smaller gains lower down from outweighing one larger loss at the top end.

The article develops an egalitarian alternative to the complaint model, based on a competing account of role reversal. Instead of asking a person to withdraw their complaint when it is not close enough in size to the biggest complaint, we can ask them whether they would be willing to insist upon their complaint regardless of which position they were to occupy in the alternative that would obtain were their complaint accepted as decisive. This invariant complaint model of reasonable rejection yields something like the difference principle, the exact formulation depending on what kind of prima facie complaints we permit. It doesn't yield any way of watering down the strictness the principle assigns to benefiting the least advantaged, although in the special case of collective decisions about the basic structure of society, this strictness is more plausible than it seems.

Section I interprets Scanlon's recent discussion of economic fairness in light of his earlier critique of Rawls. Here, I use the single-biggest complaint model to respond to Barrett's criticism that if Scanlon rejects maximin, he must accept that greater aggregate benefits can justify extra inequality that doesn't benefit everyone. Section II argues that the main criticisms of the complaint model aren't relevant in the context of distributive justice, but that this model is insufficiently egalitarian. Section III develops the invariant complaint model, and explores whether it is too restrictive of aggregation.

One of the distinctive features of the difference principle is the strictness it attaches to raising the least advantaged social position, even (1) by small amounts at the expense of greater decreases in other positions, and even (2) for fewer people, at the expense of more numerous losses in other positions.

Regarding (1), Rawls's general conception of justice was that inequality should benefit all, but the difference principle focuses on the worst off. The principle either permits or mandates inequalities that must either benefit, or merely not harm, the least advantaged.8 The permissive interpretation reflects Rawls's claim that if all existing inequalities raise the worst off, the distribution is “just throughout,” while the mandatory view reflects the claim that when the level of the least-advantaged position is maximized, the distribution is “perfectly just”.9 In either formulation, the difference principle assigns lexical priority to raising the lowest position over raising higher positions.

For example, [1,10] < [2,3] even though a gain of 1 for Low is smaller than a loss of 7 for High. And [1,10,20] < [2,5,10], even though a gain of 1 for Low is smaller than losses of 5 + 10 = 15 for Mid and High. The difference principle thus limits aggregation across positions at different levels. The strictness of this priority may seem reasonable, if we are dividing benefits created by social cooperation amongst cooperators. However, when there are more than two positions and the factual assumption of “chain connection” fails,10 it's possible that extra inequality that raises the lowest position will lower intermediate positions, as in the case of [1,5,10] versus [2,3,20]. Requiring that everyone benefit from increased inequality would preclude maximizing the minimum, in this case, but Rawls denied that the better off should have a veto over gains for the worst off.11

Regarding (2), the difference principle applies primarily to collective choices about the basic structure of a political society, based on the lifetime expectations of different social positions. The principle therefore restricts aggregation with respect to different numbers of persons. The distributions [1 1 1 1 1, 5] and [1, 5 5 5 5 5] are identical, from the point of view of the representative members of different positions, while [2 2 2 2 2, 3] ranks above [1, 9 9 9 9 9].

These two limits on aggregation make it unlikely that the difference principle would be selected from behind a veil of ignorance. Before Rawls, Harsanyi argued that choice under uncertainty about one's position would lead to maximizing average utility.12 Yet this principle could leave the least advantaged in serious avoidable hardship. Rawls blocked this result by denying the parties knowledge of probabilities, or even the assumption that they had an equal chance of being anyone, forcing them to use the maximin criterion of choice. Yet he justified these exclusions by the claim that the parties' choice must be justifiable to others, not just prudential.13

Scanlon denied that choice under uncertainty identifies principles that are impartially acceptable,14 emphasizing other aspects of the original position: that one can only enter agreements one would be willing to keep come what may (the “strains of commitment”)15; and that principles of justice are ones it would be rational to choose if one's place in society were to be assigned by one's enemy.16 The fundamental question is not what principles it would be rational for an individual to choose if uncertain about their position, but what principles can be accepted (non-heroically, without supererogation) from any position, on the part of parties wanting to find rules acceptable from all of the positions the rules generate.

There is a gap, however, between “acceptable from any position” and “most acceptable to the least advantaged position.” Despite their rejection of utilitarian aggregation, Rawls's contractualist critics rejected the strictness of the difference principle. Nagel denied that gains for the worst off should be lexically prior to gains for the better off; it was “more reasonable” to employ a sliding scale of urgency, depending on the level at which the gains occur. Nagel also argued that at some point numbers must count. He considered a choice between (1) “preventing severe hardship” for a few and (2) “preventing less severe but still substantial hardship” for many.17 For example, assume that 0–4 counts as severe hardship, while 5–9 counts as moderate hardship, and that there are a lot more people in Low than in Bottom:

In such a case, Nagel suggested, it might be right to pick A, even though it doesn't maximize the minimum.

Scanlon followed Nagel, at least with respect to aggregation across levels. Contractualism directs our attention to the fate of the worst off, but does not always require us to maximize their expectations; it all depends on how badly off the least advantaged are, and how the gains of someone in this position compare to the losses of the representative members of higher positions.18 A self-interested chooser ignorant of what position they will occupy, but knowing that they have an equal chance of being anyone, might rationally gamble on a principle (“A”) that promised very good outcomes on average, while leaving a small group in extremely bad circumstances. The “losers” under A could reasonably reject this choice, Scanlon argued, if there were an alternative (“E”) in which no one need be so badly off, even if this alternative had a lower average outcome.19 Yet the complaint of the worst off under A still had to be “weighed” against the complaint of those who would do worse under E, Scanlon said.

When the worst off are not so badly off, and small gains for them will lead to large losses for those higher up, the complaint of the worst off may not be decisive. Even if we accept that [1,10] < [2, 3], for example, we might think [11,20] > [12,13] if, at this higher level, Low's sacrifice doesn't involve hardship (or [11,100] > [12,13], if one is tempted to say the loss of 7 from 20 to 13 isn't big enough to justify forgoing the gain from 11 to 12. Rawls admitted that the difference principle wasn't intended to apply to such cases, which involve a high ratio of losses for the better off to gains for the worse off—cases that wouldn't arise (he claimed) when prior principles are satisfied.20

In Why Does Inequality Matter?, Scanlon defends a less demanding version of the difference principle.21 Economic inequality can be objectionable because of its causes as well as its consequences, in particular when it arises from an economic system that is unfair,22 as suggested by the recent rise in high-end income inequality in English-speaking countries.23 One worry about such inequality is that it may lead to political domination. Yet objections based solely on the consequences of income inequality “fail to account for the sense many have that the recent rise in inequality is objectionable in itself, apart from whatever effects it may have.” A social system is fair, Scanlon says, when it takes into account the interest of every participant “in having a greater share in the fruits of cooperation.” Shares need not be equal, but each person's interest must be “given equal standing.”24

One criterion of fairness is Rawls's difference principle, which Scanlon initially formulates in terms of the permissive “just throughout” version of the principle: “a basic structure S is just only if the inequalities it involves are to the advantage of those in the worst off social position,” which is to say only if any reduction in inequality would worsen the situation of the representative member of the least advantaged position.25 However, Scanlon goes on to say that many people object to the current CEO–worker pay gap, “even though they do not accept anything as demanding as Rawls's Difference Principle.”26 Scanlon's view is that in order for a basic structure to be just, inequalities must be either ineliminable without violating basic liberties, or “required in order for the economic system to function in a way that benefits all,”27 which he calls “a relatively weak” interpretation of the idea that inequalities must be to everyone's advantage. Rawls's interpretation is “stronger” because “it requires that a system that generates inequalities must not only benefit all, but must benefit those who have less as much as possible.”28

The description of Rawls's principle as requiring that we benefit the worst off as much as possible suggests that Scanlon might be dissenting from the maximizing/perfect-justice versions of the difference principle, in favour of an inequality-permission/just-throughout formulation. In that case, however, Scanlon would be defending a principle that is more egalitarian than Rawls's, in that it permits us to forsake potential increases in the lowest position for the sake of greater equality. For example, in the feasible set [1,1], [2,3], [3,5], [2,7], the just-throughout/inequality-permission version of the principle permits us to choose [1,1] and [2,3], as well as [3,5].

Alternately, the description of Rawls's principle as requiring that inequality must benefit the worst off as opposed to benefiting everyone suggests that Scanlon might be requiring that extra inequality raise all positions, not just the least advantaged. Again, that would make Scanlon's alternative principle more egalitarian rather than less. When chain connection fails, requiring that extra inequality raise all positions rather than just the lowest can lead us to select a more equal distribution that fails to maximize the minimum, as we saw above with respect to [1,5,10] versus [2,3,20].

Barrett interprets Scanlon as requiring both that inequality must benefit all, and that we must take advantage of all universally advantageous inequalities. In other words (reversing the order of these conditions, for consistency with what will follow), we require any extra inequality that would benefit all, and we demand that all existing inequality does benefit all. Barrett points out that when chain connection fails, this combination of demands is inconsistent. I will simplify his analysis so as to bring out what I think are the core issues in an intuitive way, using one of his central examples:29

This principle also generates menu-dependence, in that the ranking of A versus B depends on whether C is feasible, a failure of contraction consistency (a version of the independence of irrelevant alternatives). When C is feasible, A and B are both unjust, as described above, but when C is not feasible, A becomes just, because B is not better for all, nor more equal than A.

The substantive upshot is that in order to justify inequalities that don't benefit all, Scanlon must either appeal to greater total benefits, or revert to maximin. Since the extra inequality of B:[5,5,100] over A:[3,6,6] doesn't benefit all, the only reason for preferring B, if maximin is off the table, is utilitarian efficiency.31

We can avoid this result by interpreting Scanlon as wanting to weaken the priority the difference principle assigns to benefiting the worst off, rather than wanting to require that extra inequality raise every position. Scanlon's discussion of having to weigh the losses of the representative better-off party against the gains to someone in the least-advantaged position (cited above) was the inspiration for what has become known as the complaint model of reasonable rejection. According to this model, a person's complaint against a given principle is measured by their shortfall in well-being or advantage relative to their best alternative, discounted by the level at which the shortfall occurs. A person can reasonably reject a principle when her complaint is greater than anyone else's. The principle is thus to minimize the single biggest complaint.32

According to Alex Voorhoeve, the complaint model appeals to role reversal, in that the comparison of one's own complaint against those of others involves putting oneself in their shoes.33 When I see that my complaint against a certain principle/distribution is weaker than your complaint against the alternative that I favour, I should withdraw my complaint. And when every similarly situated individual does likewise, what results is a theory that limits aggregation.

On the complaint model, the choice between A:[3,6,6] and B:[5,5,100] must be made by minimizing the single biggest shortfall, which is 94 for the third position in A, as compared to a shortfall of 1 for the second position in B:

The complaint model prefers B, not on the basis of minimizing the sum of complaints, but on the basis that Z's complaint against A is stronger than Y's complaint against B.

I note in passing that there is another way of construing the appeal to role reversal. In the choice between A:[3,6,6] and B:[5,5,100], instead of saying that Y should put themself in Z's shoes in A, and withdraw their complaint against B because it is smaller than Z's against A, we could say that if Y objects to B, Y should be willing to accept A no matter what position in A they might occupy. Y isn't willing to do that, because 3 < 5. But nor is Z willing to sustain their objection to A in face of role reversal in the alternative, B, because 5 < 6. The only objection that is invariant with respect to permutation of positions in the alternative is that of X. X objects to A, and is willing to accept the alternative come what may, even if they should remain in the least advantaged position in B. I will return to this invariant complaint model of reasonable rejection below.

A variant of the single-biggest complaint model that Parfit calls the “Close Enough” view picks up on Scanlon's suggestion that aggregation might be appropriate if complaints are close in size: for example, one death versus many cases of paralysis.34 On this model, we aggregate when the gap in shortfalls falls below some threshold. Voorhoeve defends a view of this kind, which he labels by the imperative “Aggregate [only] Relevant Claims (ARC).” As in the simple complaint model, the size of a complaint depends on the size in the shortfall of advantage relative to one's best alternative, discounted by level. Yet “a claim is relevant if and only if it is sufficiently strong relative to the strongest competing claim.”35 The rule is thus to minimize the sum of shortfalls if the difference between shortfalls is less than a certain threshold, but otherwise to minimize the single biggest shortfall. In short, minimize the single-biggest post-threshold complaint, otherwise minimize the sum of complaints.

The virtue of the close-enough version of the complaint model is that it accommodates common intuitions.36 On the one hand, if we have to choose between saving one from death and many from a headache, we save the one from death, no matter how many headaches there are. On the other hand, if the choice is between saving one from death and many from quadriplegia, there will be some value of “many” for which we should save the many (a variant of Nagel's choice between preventing a few cases of severe hardship versus preventing many cases of hardship).

One problem with the single-biggest complaint model is that when applied to distributions across specific individuals, it can rank an anonymously Pareto superior distribution above an anonymously inferior distribution. Here is a case based on Parfit's musical chairs.37

The biggest shortfall is 3 for Individual 1 in A, hence the complaint model ranks B > A, even though anonymized B = [0,1,2,3,4], while A = [1,2,3,4,5]. This problem results from the fact that the feasible set involves only two of the many possible permutations; if everyone could be assigned to any share, the maximum shortfall for every distribution would be the same (5). The problem is not relevant for my purposes, since I am concerned with social justice understood as a matter of distributions over positions generated by an institutional scheme, not distributions over named individuals.

A second problem with the complaint model is that it will make our choices menu-dependent, because the size of a person's complaint against a distribution depends on their shortfall relative to how well they could do in their best alternative, which will depend on what other options are in the feasible set. This is easiest to see if we swap elements for rows, such that the set A:[1,5], B:[3,4], C:[2,8] is represented as:

Here, shortfalls are measured by vertical distances to the top option in a column. The complaint model ranks A above B when C is feasible, even though Low's AB gap of 2 is bigger than High's BA gap of 1, because High's complaint against A is measured relative to C, at 3. Thus the exclusion of C from the feasible set will lead to a reversal of the ranking of A versus B. The competing invariant complaint model doesn't have this consequence; Low objects to A, and is willing to accept either position in both B and C, so it doesn't matter whether C is feasible.

The use of a relevance threshold can also induce menu-dependence, even in cases that would otherwise be free of it, because it can affect whether the gap in complaints falls below the threshold. Consider the case A:[1,8], B:[5,6], C:[3,9], with only one person in Low but many in High:

Whether C is feasible won't affect who has the biggest shortfall in this case, because One's AB shortfall is bigger than both Many's BA shortfall and Many's AC shortfall. Suppose we set our threshold at 2, however, such that if the difference is less than 2 we aggregate (minimize the sum of the shortfalls), whereas if it is equal to or greater than 2, we don't aggregate (but minimize the maximum shortfall). When A and B alone are feasible, the difference in shortfalls is 4 for One in A versus 2 for Many in B, which is a gap of 2, so we don't aggregate, but minimize the biggest shortfall, with the result that B > A. When C is feasible, however, the shortfalls for the Many in B are now calculated relative to C, at 3, reducing the difference in shortfalls to 4 versus 3 = 1, which is below the threshold. Now we add up the Many shortfalls of 3 in B (relative to C), with the result that A > B, a reversal.

Whether or not menu-independence is a criterion of rationality is controversial. When choosing between types of pie, as in the case of Sidney Morgenbesser's famous anecdote, it does seem irrational. My preference for apple over blueberry shouldn't depend on whether cherry is on the menu. In other situations, however, it can make sense to engage in “positional choice,” where what matters is not just the value of each option assessed independently, but their positions relative to other options that might have been chosen.38 The taste and nutritional value of the apple don't depend on how many other apples are in the bowl, but what the choice says about my attitudes towards others does (if there is only one left, I should ask if anyone else wants it, not just take it). Menu-dependence is not necessarily irrational.

The intransitivity of the relevance relation creates a further problem when our options contain diverse sets of harms, such that there is a question about how they should be matched.39 Suppose that we can save one of two groups, A and B, and that while minor harms are relevant to moderate harms, and moderate to serious, minor are not relevant to serious (because they are not “close enough”). Suppose further that 1 serious = 10 moderate, and 10 moderate = 100 minor (though, of course, 1 serious > any number of minor, because of the threshold). If we were just considering 1 serious harm versus 10 moderate harms, it would be permissible to save either. Adding more individuals facing minor harm to Group B than to Group A should lead us to save Group B, thinking incrementally, which involves comparing across the same rows in the table below:

However, the 1000 minor harms in Group B compete with 1 serious harm in Group A (now comparing different rows, diagonally), and minor aren't relevant compared to serious; while the 2 minor harms in Group A compete with 10 moderate harms in Group B, and minor are relevant compared to moderate, inclining us towards saving A. We could opt for considering all minor claims irrelevant, even the 2 in the left-hand column that don't compete with the 1 serious claim, but then both options would be permissible even if we added minor harms to Group B alone.

Although this debate raises many interesting puzzles, they are not relevant in the context of questions of social justice, where what is at stake are decisions about the basic structure of society based on the lifetime expectations associated with different social positions. From this perspective, we are never dealing with choices between options that involve named persons moving between positions, but always anonymous positions distinguished only by their place in a ranking.

A fourth problem with the single-biggest complaint model is that it may be overly restrictive of aggregation in cases involving risk.40 The rule of minimizing the maximum complaint correctly forbids painful, involuntary medical experimentation, because we don't sum its many social benefits, but just compare one of them with the harm to the person experimented on. Yet minimizing the maximum complaint seems overly restrictive of risk-imposing activities we ordinarily take to be acceptable. A great number of people benefits from flying on planes, but a very small number of never-plane-travellers is hit by crashing planes. Still, we think air travel is permissible “because the number of those killed by it who did not stand to benefit from it is so small, and a ban on it would impose a significant (though smaller) burden on a huge number.”41

Rahul Kumar points out that there are intrinsic objections to the permissibility of non-consensual use of a person's body in the experimentation case, but not in the flight case.42 Thus we could forbid experimentation even if we had to give up plane travel. Still, that's a big cost. Kumar uses the quasi-institutional aspect of contractualist morality to argue that whether someone has been wronged depends on the risks to which they were exposed, not the eventual outcome.43 Moral obligations are based on rules for the general regulation of behaviour, given standard types of situations as identified by information to which a diligent agent would normally have access. As a result, the moral rules governing risky conduct must be rules that apply ex ante. Jeb the Amish farmer, who lives in a sparsely populated area under a flight path, ends up being harmed, but the question is whether he was wronged by the risk prior to its eventuating. If the risky activity is regulated to reduce risk, and if those who end up being harmed or their families can claim compensation, the risks are not so great compared to the benefit the representative flyer would forgo were flying prohibited.

Kumar does not invoke the “close enough” complaint model's limited permission of aggregation, which by itself would not be sufficient to reach the desired result. When combined with an ex ante approach, however, the addition of an aggregation threshold makes the case easier to deal with. Even if one risk would outweigh one forgone benefit from flying, we need only argue that the difference is close enough, and we are permitted to aggregate.

My main objection to the single-biggest complaint model, as the basis for a principle of distributive justice, is that it is insufficiently egalitarian. It is, of course, the point of the model to relax the strictness that the difference principle assigns to benefiting the worst off, in particular in high-ratio cases above the level of hardship, where a small gain for the worst off comes at the expense of a large loss for the better off, as in the case of [11,20] versus [12,13] or, even more so, [11,100] versus [12,13]. There are other cases, however, in which the complaint model's resistance to aggregation makes it objectionably inegalitarian.

If all we care about is the single greatest shortfall, it's possible that it will occur in the highest position, and so outweigh multiple smaller shortfalls lower down in the scale.

Here, each of the Many ought to put themself in the shoes of the better-off One, and so withdraw their complaint against A. In this case, the complaint model accepts extra inequality that worsens the position of the least advantaged. Such cases bring the complaint model's restriction on aggregation to bear against inequality-reducing benefits to the worse off.

The same situation can arise with multiple positions each represented by one individual:

The biggest shortfall is Top in B, at 15–8 = 7, while each of Bottom, Low, Mid, and High faces a shortfall of 3 in A. The greater inequality of A worsens all lower positions, for the sake of an individually greater gain to the top position. Here, the complaint model prefers extra inequality that only benefits the best off! The reason the complaint model generates this result is that it does not assign lexical priority to gains for the less advantaged, but limits aggregation, preventing many smaller gains lower down from outweighing one larger loss above.

The complaint model's discounting of shortfalls by the level at which they occur attenuates, but does not eliminate this problem. Up until now, I have ignored the issue of what variable these numbers represent. In a Rawlsian framework, they are shares of an index of social primary goods—for example, income and wealth holding constant the amount and difficulty of work required to generate it, and perhaps also the degree of autonomy and voice one can expect in the workplace—based on the lifetime expectations of the representative members of different positions. The moral urgency of increasing a position's expected share of these goods depends on its level. It's very bad not to have any social primary goods, in terms of one's ability to develop and exercise one's two moral powers, but increasingly less important to have more.

Putting the same point in Scanlonian terms, the size of a person's complaint about forgone benefits is a function of both the absolute size of their shortfall and the level at which it occurs.44 For example, we might define the moral value of a level of well-being to be the square root of raw well-being, and then calculate shortfalls in that scale.45 Thus, in the case of A:[1,16,49] versus B:[9,25,36], although minimizing the single biggest raw shortfall would rank A > B, taking the square root yields A:[1,4,7] versus B:[3,5,6], which reverses the ranking, because Low's shortfall of 2 in A is larger than High's shortfall of 1 in B.

For any discounting short of lexical priority, however, we can simply consider more extreme cases. For example:

This case is one of my original counter-examples, but with all values squared. Top's complaint after we take square roots is still 15–8 = 7, which is bigger than each of the other transformed complaints, which are all 3. Such cases are sufficiently counter-intuitive to make it worth considering the invariant complaint model of reasonable rejection.

The core cases that motivate contractualist resistance to aggregation are ones in which the sum of the many smaller gains higher up shouldn't outweigh a larger loss lower down. For example:

One's shortfall of 9 in A is meant to be much more urgent than each of the Many's shortfall of 1 in B. Each of the Many ought to put themself in One's shoes, and so withdraw their own, weaker claim, assuming the gap in shortfalls is above the threshold.46 The many smaller shortfalls don't sum to outweigh the single more serious shortfall.

The same is true in the case of multiple positions, each represented by a single individual:

According to the single-biggest complaint model, each of Low, Mid, High, and Top should put themself in Bottom's shoes, recognize that Bottom's shortfall in A is much more significant than theirs in B, and so withdraw their complaints against B. In such cases, the complaint model's resistance to aggregation rightly favours reducing inequality and benefiting the worst off. Is there another way to capture this intuition, which doesn't have the inegalitarian consequence I objected to above? Yes. We could say that each of Low, Mid, High, and Top ought to withdraw their claim to A because their objection to B—that they could be better off in A—is one that they are only willing to press if they can be guaranteed not switching places with Bottom in A.

The invariant complaint model of reasonable rejection is inspired by Scanlon's discussion of Rawls's enemy-assignment description of the original position, and Amartya Sen's 1970 chapter on equity and justice, in particular his treatment of Patrick Suppes's “more just than” relation.47 It is a common idea that one can't complain of someone else's violating a norm unless one accepts that in the relevant circumstances the norm would apply to oneself as well.48 This reciprocity condition on complaints of misconduct suggests that we could think of universal acceptability in terms of objections that survive role reversal. The general idea is to interpret reasonable rejectability in terms of objections that are sustainable in face of all permutations of positions. A prima facie objection will be sustained if the person making the objection would be prepared to affirm it regardless of which position they might come to occupy in the alternative that will obtain if their objection is accepted as decisive.

This alternate construal of the role-reversal test yields a different result in the counter-example cases I discussed earlier. Consider the multi-position case:

One might object that this procedure assumes that one can only object to staying in one's current distribution, whereas in principle one could also object to leaving this distribution for another. Top opposes leaving distribution [1,2,3,4,15] for any of the other positions in [4,5,6,7,8]. Doesn't this objection survive role reversal? No, because that's not the relevant comparison. If Top is objecting to leaving [1,2,3,4,15], then they should be willing to sustain that objection regardless of what position they end up in in the distribution that will obtain if their objection is accepted, which is [1,2,3,4,15], not [4,5,6,7,8].

If the only prima facie objections we permit are about forgone benefits, the result is the maximizing, “perfect justice” version of the difference principle. Thus, in the case of [1,1], [2,3], [3,5], [2,7], Low can object to [1,1], [2,3] and [2,7] that they could be better off in [3,5], and Low is willing to sustain these objections regardless of what position they will occupy in [3,5], that is, even if they stay in the Low position. In contrast, although High can object to [3,5] (that they could be better off in [2,7]), High is not willing to sustain that objection should they end up in Low in [2,7].

Scanlon maintains that individuals can complain about unfairness, not just about their own level of well-being or advantage.49 Complaints of unfairness don't violate the individualist constraint so long as they are complaints about arbitrary inequality that one suffers when one is on the bottom end of the inequality, as opposed to complaints about the aggregate level of inequality, which takes into account all positions. It will be objected that if we permit objections to inequality, we are indulging sentiments of envy. Egalitarians argue that inequality can be intrinsically objectionable, however—not all inequality, with respect to any units of comparison and any variable, but specific kinds of inequality: for example, “undeserved, nonvoluntary, inequalities” in well-being or access to advantage.50

If we allow both kinds of complaints, the invariant complaint model will lead to constrained maximin, whereby we balance the two kinds of complaints from the perspective of the least-advantaged position. In the comparison between [2,3] and [3,5], Low has two prima facie objections: to [2,3], that they could be better off in [3,5], and to [3,5], that they would experience less inequality in [2,3]. The question is whether the gain for Low in moving from [2,3] to [3,5] is worth the increase in inequality. It seems plausible that it is, because the gain is relatively large compared to the increase in inequality, and it occurs at a low level. If the gap were greater and occurred at a higher level, however, that might not be true. Consider a high-ratio case involving a Pareto improvement above hardship: [11,20] versus [12,100]. Here, maximin favours [12,100], but Low might judge that the gain of 1 in [12,100] is not worth the extra inequality.

If we accepted only objections to extra inequality, the invariant complaint model would simply minimize inequality with respect to the lowest position—admittedly, not a very plausible view. We might accept only objections to extra inequality, but allow that gains can outweigh inequality, however, which would generate the inequality-permission, justice-throughout version of the difference principle. There are other possibilities. We could accept (as prima facie complaints) objections to excess hardship rather than to forgone benefits in general. We might also accept complaints about inequality, but not above a certain level: for example, between millionaires and billionaires.51

The invariant complaint model of reasonable rejection provides a better rationale for the difference principle than does choice from behind a veil of ignorance. If what we care about is justifiability to all—that is, from all positions—then it makes sense that complaints (against a particular principle/distribution) should be invariant with respect to permutations of positions in the alternative. In a choice between A and B, if you object to A, then you should be prepared to accept B regardless of what position in B you occupy. Only the (all things considered) complaint coming from the standpoint of the least-advantaged position will satisfy the condition of being invariant with respect to all possible permutations in the alternative.

The invariant complaint model has a major limitation, however, which is that it is uncompromising with respect to aggregation, both across levels and numbers of persons. The single-biggest complaint model relaxed the stringency the difference principle attaches to raising the representative member of the least-advantaged position in two ways: by not giving complaints lower down lexical priority, and by allowing aggregation across different numbers of persons when complaints are close enough in size. The invariant complaint model has no similar mechanism. Consider a case I used to illustrate Nagel and Scanlon's desire to relax lexical priority above hardship: [11,100] versus [12,13]. Low has prima facie objections to [11,100] based on forgone benefits and extra inequality. The combined objection is sustained in face of role reversal, since Low would be better off and suffer less inequality in either position in [12,13]. In contrast, although High has a valid prima facie objection to [12,13], that they could be better off in [11,100], this objection does not survive role reversal; High is not willing to press their objection regardless of the position they will occupy in [11,100], since were they to occupy Low in [11,100], they would be worse off. This version of the role-reversal test gives strict priority to increases in the level of the lowest position over increases for higher positions.

How much of a problem are these high-ratio cases? Recall the primary rationale for maximin, in the context of questions of social justice.52 In designing the ground rules of social life, we are dividing benefits created by social cooperation across the different positions into which one can be born, each of which plays a functional role in the overall division of labour. While individuals will vary in their degree of initiative and responsibility, the representative member of each position makes the same contributive effort, and so deserves an equal share, unless unequal shares can increase the size of the smallest share.

High-ratio cases are most problematic if we think about the difference principle (incorrectly) as a social norm to govern local interactions. Situations may arise in which a worse-off individual can pay a small cost to confer a much larger benefit on a better-off individual. We want people to take advantage of opportunities for efficient beneficence, in part because what goes around may come around, and in part for the expressive significance of it being common knowledge that people care about each other.53 One problem with experimental tests of the difference principle, such as Frohlich, Oppenheimer, and Eavey,54 is that they may elicit expressions of situational social norms justifiable by the consequences of their generally being followed, whereas the principle is meant to be the ultimate standard of assessment for collective decisions about the basic structure of society, based on lifetime expectations associated with different social positions.

The other case that may seem to be a problem for the invariant complaint model is that of risky but generally beneficial activities, such as flying. If we compare ex ante risks of harm to forgone benefits, the single-biggest complaint model handles these cases, especially if we permit aggregation when complaints are close enough. The invariant complaint model does not have this allowance for summing comparable complaints, and so puts more weight on the case for adopting an ex ante approach. In the context of questions of distributive justice, however, the greater strictness of the invariant complaint model with respect to aggregation is less of a problem, because in this context a global definition of positions is appropriate.

The flying case involves a local definition of the relevant positions. The objection to permitting flying comes from the non-flyer who will be hit by a crashing plane, while the objection to forbidding plane travel comes from the individual who likes to go on vacation to Europe. For the permissibility of driving, the positions would be drivers versus non-drivers; for the permissibility of e-scooters, scooterers versus non-scooterers, and so on. It might be that in each of these dimensions, the objection of the non-user hit by a user is more serious than the objection of a would-be user not permitted access to the device in question. If we go one by one, applying the contractualist procedure to each local position in abstraction from the others, however, we'll quickly end up in a situation where no one can do anything, which would be very demanding. It might not be too much to ask people not to fly, but it would be a lot to ask them not to drive, bicycle, run, and so on, either. Each of these prohibitions might be justified separately on the grounds that some non-driver might be hit by a driver, some non-cyclist hit by a cyclist, or some non-runner hit by a runner. These activities are to some extent substitutes, such that the cost of prohibiting two is more than double the cost of prohibiting each alone. Minimizing the maximum objection based on local positions may preclude mutually beneficial exchanges of risk. I may not fly, but you may not drive. I might be willing to accept the risk of your flying because you accept the additional risk of my biking.

More fundamentally, there is no guarantee that minimizing the maximum objection associated with each component of the institutional system separately will minimize the maximum overall (or global) objection. From the perspective of distributive justice, which is my concern, that's what's relevant. It would be irrational to insist on minimizing the maximum objection for each policy individuated in a fine-grained way, based on local definitions of positions, if we faced multiple situations in which small gains for the lowest position created by the policy in question are associated with large losses for higher positions. On trade, for example, local definitions of positions might be workers in firms exposed to foreign competition versus workers in firms not exposed to competition. On intellectual property, the positions might be artists and inventors versus consumers. And so on. If for each policy choice we maximized the minimum income for the local positions in question, and if in many cases a small increase for the local minimum position came at the expense of a large decrease for higher positions, we might end up much poorer overall, with a global minimum position (for example, workers without high school education) lower than it would otherwise be.

The main contribution of this article has been to analyse the implications of three different ways of thinking about role reversal within contractualism: rational choice under uncertainty, minimizing the single-biggest post-threshold complaint, and requiring complaints to be invariant with respect to permutations of positions in the alternative. Although choice from behind a veil of ignorance requires that one put oneself in the shoes of others, it also allows one to gamble that one will not experience their fate. The veil of ignorance won't support maximin, unless we arbitrarily deny the parties the assumption that they have an equal chance of being anyone. Maximin has always seemed too strict, however.

Thus the challenge for contractualists has been to formulate an alternate account of mutual justifiability, which generates a more plausible distributive principle. The single-biggest complaint model asks each to put themself in the shoes of others, and to withdraw their own complaint if it is (much) smaller than the biggest complaint. This model can disallow many small gains on the part of the better off from outweighing fewer individually larger losses for the worst off, while permitting aggregation when complaints are close in size, as in Nagel's case of small gains to the worst off coming at the expense of larger losses to the next worst off. Yet the principle of minimizing the maximum above-threshold complaint is insufficiently egalitarian, I suggested, since once we relax lexical priority, this model's resistance to aggregation can lead us to prefer a benefit for the best off at the expense of inequality-increasing losses to lower positions.

The invariant complaint model of reasonable rejection provides better support for the difference principle than does choice under uncertainty. This model requires that one be willing to insist on one's complaint even in face of positional permutation in the distribution that will hold if one's objection is accepted as decisive. This model does not provide any ground for weakening the priority the difference principle assigns to benefiting the worst off, as compared to benefiting the better off. Yet this strictness is more plausible than it seems, when applied to lifetime expectations of overall social positions.

I would like to thank Jacob Barrett, Kerah Gordon-Solmon, Rahul Kumar, and Alex Motchoulski for their very helpful comments on earlier drafts of this article.

None relevant.

There are no potential conflicts of interest relevant to this article.

The author declares human ethics approval was not needed for this study.