II. DORSEY'S THRESHOLD VIEW

Here is a seemingly plausible argument that has as its conclusion that a large number of just slightly disvaluable states outweighs the badness of a small number of grossly disvaluable states. Dale Dorsey states this argument as follows:

John Broome points out that Continuity is too weak in the context of this argument.Footnote ⁶ His reasoning is this: consider an infinitely long chain of events, {E1, E2, E3, . . .}. Suppose each event ‘En + 1’ is worse than En. If the increasing badness of these states is correctly described by a function that approaches an asymptote, then, although the chain of bad events is infinite, there could be some bad states (i.e. the ones beyond the asymptote) that are not part of the chain. This point, I take it, is correct. It pinpoints a formal glitch in Dorsey's argument. However, it does not present a case against the spirit of the argument. An explicit, continuous chain supporting Dorsey's challenge can be constructed. Here is a slightly abbreviated version:

The problem, then, is this: on the one hand, it seems intuitive that there is no number of Slasts that is worse than a single S1.Footnote ⁸ On the other hand, the above argument seems to entail that there is some number of Slasts that is worse than a single S1 (i.e. that Lives for Headaches is true). Let me illustrate how the argument would achieve this. If Dorsey's Chain is continuous, then for each state Sn there is some number of Sn + 1s that is worse than Sn. If this reasoning holds for each two adjacent states in Dorsey's Chain, then, given Transitivity, it must hold for far-away states (e.g. S1 and Slast) as well. Consider the following statements to be an illustration of this problem:

Furthermore, given Transitivity (see above) it follows that:

If the reasoning illustrated in (1), (2) and (3) generalizes over the entire chain, then it is indeed hard to see how one can avoid the conclusion Lives for Headaches.Footnote ⁹

Dale Dorsey intends to show how this conclusion can be resisted, by showing that the above chain is not, in fact, continuous: any bad state that interferes with ‘the fulfillment of global plans’Footnote ¹⁰ is ‘strongly inferior’Footnote ¹¹ to any state that does not interfere in this way. A state S is said to be strongly inferior to some other state S ^∗ if no number of S ^∗s is jointly worse than even a single S.

Of course, as indicated, not any old plan counts. My plan to take out the garbage does not count. Rather, plans that count are ‘global’ plans that are ‘genuinely endorsed’ and that are issued in ‘full awareness’.Footnote ¹² These are ‘major plans, projects and relationships that characterize an agent's whole life or significant segments of an agent's whole life’.Footnote ¹³ Examples of such life projects include, for instance, becoming a philosopher, or becoming a trombone player.

The fact that Dorsey focuses on projects and not on quantities of one's lifespan is instructive. An account that renders any bad that shortens life by just a tiny bit strongly inferior to any other bad that does not have such an effect is wildly implausible. It is implausible, say, that ‘any extension of a person's life, however short, is better than improving the life by letting the person see the Northern Lights’.Footnote ¹⁴ Dorsey avoids these unintuitive consequences by focusing on life projects rather than quantities of life. Life projects, arguably, don't come in quantities. By definition, such projects are discrete and have rather large scope.

Let's move to objections. Consider again Dorsey's Chain from above:

States such as S1 (i.e. death) and S7 (i.e. extensive migraine) are strongly inferior to Slast (i.e. minor headache). According to Dorsey, this is because premature death and migraines interfere with one's global plans, but mild headaches do not interfere in this way.

However, defending the strong inferiority between the first and last links in Dorsey's Chain by distinguishing them with regard to life project interference is hardly enough. Strong inferiority should also hold between at least one pair of adjacent states one of which is marked by life project interference, while the other is not. In other words, strong inferiority should also hold between the worst non-life project interfering state and the most benign life project interfering state; but this just looks much less plausible. Consider the following case:

Not much seems to be lost if Bob doesn't get his favourite choice. However, the bad introduced by the headaches seems quite severe. It is overwhelmingly plausible that Ann should push the red button. Perhaps, it might be thought, we should amend Dorsey's account, ruling out the idea that Bob's choosing his second favourite option constitutes interference with his life plans. Perhaps we should say that what makes a state strongly inferior to some other state is that it prohibits one from achieving any life projects whatsoever; not just the ones one actually happens to have. This proposal will not work either, as the following example will show:

I think it is obvious that it is not reasonable for Ann to push the green button. Billions of people having to give up almost all of their projects is clearly the worse option. The general problem with Dorsey's proposal is this: wherever we set the cut-off point in Dorsey's Chain based on the fact that life projects of varying intensity are being interfered with, it just isn't plausible that two adjacent states stand in the strong inferiority relation. The examples Bob the Trombonist and Bob's Migraines are an illustration of this point. A forceful way to make the point more broadly is by way of constructing a chain analogous to Dorsey's Chain that takes interfered life projects as its values:

In Chain of Upset Life Projects, it becomes apparent that each two adjacent states do not stand in the strong inferiority relation. This entails that for all candidate notions of ‘life project interference’ it will always be implausible that one life project interference of a certain magnitude is strongly inferior to, say, a million life project interferences of a slightly lesser magnitude. Chain of Upset Life Projects reinstates the original problem; it does not provide its solution.

One might suspect that these problems are due to vagueness. One may wish to argue that terms such as ‘seriously endorsed life project’ are vague; i.e. for some things it is not determinately true or false whether they are (or aren't) a ‘seriously endorsed life project’. Accordingly, one may wish to argue that in Dorsey's Chain there is no determinate threshold we can set such that the states on the left-hand side of the threshold clearly interfere with one's projects and the states on the right-hand side do not. However, the defence continues, problems of vagueness are notorious, and, therefore, not specific to Dorsey's account.

Vagueness, I think, is not the problem. Reconsider, for instance, Bob the Trombonist. Bob's trombone-noise-related headaches make him choose his second-best option (i.e. to become a flute player). It turns out that there are lots of much less bad states a great number of which would outweigh the badness of Bob choosing his second-best option. Consider, for instance, one million people experiencing serious migraines for one month. It is easy to imagine that all of these people's seriously endorsed life plans are determinately not being interfered with. Nevertheless, we would not judge that Bob's not realizing his preferred plan trumps one million people's experiencing disastrous migraines for a month.

That said, from an intuitive standpoint, Dorsey's solution to the puzzle seemed compelling. But despite its intuitive appeal, Dorsey's account cannot withstand thorough reflection. I argued that Dorsey's theory requires strong superiority between two adjacent links in Dorsey's Chain. This, however, is implausible. I further demonstrated that the problems associated with this view are not due to vagueness. In the next section, I will analyse and reject Alex Voorhoeve's rejection of P2 of the above argument.

III. VOORHOEVE'S ARGUMENT FROM PERMISSIBLE SELF-CONCERN

In his 2014 article ‘How Should We Aggregate Competing Claims?’ Alex Voorhoeve argues that not all moral claims can be aggregated, thereby denying P2 of the above argument.Footnote ¹⁶ Voorhoeve gives a broadly contractualist rationale for the irrelevance of a certain claim: it is justified to deem claims irrelevant in an allocation case, if this can be reasonably explained to the parties whose claims are deemed irrelevant. In this section, I will present and criticize Voorhoeve's argument.

Voorhoeve holds that when weighing competing claims, only those that are ‘sufficiently strong relative to the strongest competing claim’ are ‘relevant’;Footnote ¹⁷ and only relevant claims figure in aggregation. Aggregation refers to the process of conjoining a number of claims to produce a stronger claim. Note that claims, on this picture, are not aggregatable or non-aggregatable per se; rather, certain claims don't aggregate when held against much stronger claims.

Of course, he owes a rationale for the distinction between relevant and irrelevant claims. According to Voorhoeve, an irrelevant claim is one that it would be impermissible for an agent to satisfy even if this claim were this agent's own claim. Here is a simple example in illustration of this point. Suppose Ann is faced with a decision to either alleviate headaches in 10,000,000 people or let a person die. Now she should ask herself ‘Would it be permissible for me to alleviate my headache if it entailed letting another person die?’. Presumably, Ann's claim to have her headache alleviated is not strong enough to justify letting one person die. In a broad range of cases, it is permissible to favour one's own claim over those of others. However, intuitively, there is a limit to the ‘permissible degree of self-concern’.Footnote ¹⁸ Allegedly, this limit explains why certain claims cannot be aggregated.

Voorhoeve's account is appealing from an extensional standpoint. After all, the philosophical problem discussed in this article is that there is no number of very minor disvaluable states that outweighs the badness of a severely bad state. In congruence with this diagnosis, permissible self-concern stretches quite far; only when my own claim is very weak and your claim is very strong am I not morally permitted to favour the satisfaction of my own claim. Of course, extensional correctness is but a necessary condition for the plausibility of Voorhoeve's account. Still, we'd also want a rationale for why permissible self-concern justifies non-aggregation.

Voorhoeve's account is broadly contractualist. He first argues that his account can explain why there should be unanimous agreement concerning the way claims are weighed in the relevant cases.

Therefore, everybody will agree with the prioritization of the stronger claim. I think it is true that, when comparing weak claims to very strong claims, it can be unanimously agreed upon that the strong claims take priority. However, this does not need to be a function of permissible prioritization of one's own claims. Suppose, say, a resource allocator, call her ‘A’, had to make a decision between either saving B's arm, or C's life. Presumably, if B had to make this decision it would be permissible for him to save his own arm. However, even B can agree that A is justified in prioritizing C's over A's claim. B should realize that special reasons based on permissible self-concern don't apply to A. The resource allocator is not bound by those special reasons, because it is not her own arm that she has to make a decision about. This point has been forcefully emphasized by Parfit, who argues that certain potential losses can be prioritized if they are your own losses.Footnote ²⁰ Accordingly, if B is rational, one would expect him to realize that A is not bound by reasons related to permissible self-concern.Footnote ²¹

Lastly, Voorhoeve argues that his solution

This argument, it seems to me, begs the question. If my own claims aren't strong enough to justify satisfying my own interests straight away, then this could possibly explain why an impartial third party should not satisfy my claim straight away or give both claims equal weight. However, it does not entail that an impartial third party should not give it proportional weight. Analogously, why would it not be permissible for me to give my weak claim proportional weight? Why would I not be permitted to flip an extremely biased coin in such a conflict situation? The answer, presumably, is that this would be impermissible because my claim is irrelevant. This shows that Voorhoeve's argument relies on the idea of irrelevance of certain claims, rather than explaining it.