This competition entry has been selected for publication by the Forum team.
Kollin, Clifton, DiGiovanni, and Macé (2025) propose two “bracketing” theories for recovering altruistic action guidance under cluelessness, formalizing a response that DiGiovanni (2025) had earlier viewed sympathetically but raised doubts about. On bottom-up bracketing, we set aside beneficiaries for whom it is indeterminate which option is better, and then aggregate over the remaining beneficiaries. On top-down bracketing, we instead evaluate the largest subsets of beneficiaries for which the comparison is determinate. Although bottom-up bracketing yields Kollin et al.’s intended verdict in the motivating donation case (Against Malaria Foundation > Make-A-Wish Foundation, despite long-term cluelessness) and satisfies Super-Strong Pareto, the authors reject it because it fails to extend their baseline consequentialist relation and, in particular, violates Statewise Dominance.
I argue that this rejection is ill-motivated. In their central counterexample to bottom-up bracketing, one person is determinately better off under option A than option B, while neither A nor B is determinately better for the other people. Bottom-up bracketing therefore chooses A. B wins under top-down bracketing only because the other people’s individually indeterminate welfare comparisons are pooled before determinacy is assessed. But if individual persons are the basic sources of altruistic reasons, the bottom-up order is more plausible: Assess each person’s complete represented prospect first, and only then aggregate the resulting person-attributable contrastive reasons (i.e., reasons to prefer A rather than B). Infinite cases reinforce this by showing that anonymous, non-contrastive aggregation can erase morally important facts about how the individuals fare. The resulting view rejects unrestricted Statewise Dominance. This does not undermine its status as an impartial, altruistic, welfarist, and entirely consequence-focused theory; whether it counts as “consequentialist” depends on how narrowly that label is defined.
This defense of bottom-up bracketing also answers DiGiovanni’s (2025) worries about bracketing: Persons’ complete prospects provide a non-arbitrary, morally motivated decomposition of consequences, and indeterminate person-attributable comparisons do not supply any contrastive reason in either direction. Bottom-up, person-centered bracketing can thus preserve principled impartial action guidance where total expected welfare remains indeterminate.
In a final bonus section, I draw out an implication suggested by the infinite cases considered: that DiGiovanni’s epistemological approach—set intuitions and heuristics aside, reason from “first principles”—should lead him to question whether the notion of impartial altruism is as determinate as he assumes it is. In particular, there are scope-insensitive views that can lay equal claim to being impartial, altruistic, welfarist, and entirely consequence-focused. This leads to a troubling kind of moral uncertainty whose analysis and resolution I leave for another day.
Even if we cannot determine whether A or B produces greater total expected welfare, A may be determinately better with respect to some consequences, while the remaining consequences are too unclear to favor either option. Perhaps those consequences can be “bracketed,” leaving us with a reason for A and no reason for B.
Kollin, Clifton, DiGiovanni, and Macé (2025) distinguish two bracketing procedures. Bottom-up bracketing first identifies the beneficiaries for whom the comparison between A and B is determinate, sets aside the other beneficiaries, and then aggregates over those who remain. Top-down bracketing instead searches for the inclusion-maximal subsets of beneficiaries relative to which the comparison is determinate, and ranks an option above another only if all inclusion-maximal bracket sets weakly favor it and at least one strictly favors it. The authors describe bottom-up bracketing as prima facie compelling and show that it yields their intended verdict in the motivating Against Malaria Foundation vs. Make-A-Wish Foundation case: Against Malaria Foundation is more choiceworthy, even if we are clueless about either option’s long-run effects.
The authors nevertheless favor top-down bracketing because only top-down extends their baseline expected-total-welfare relation. This relation respects the principle of Statewise Dominance (which we will define momentarily). Bottom-up bracketing violates Statewise Dominance, and the authors reject it for this reason (pp. 15–20). Their discussion turns centrally on the following case:
| e | ¬e | |
| A | (1, 10, 0) | (1, 0, 10) |
| B | (0, 0, 20) | (0, 20, 0) |
The options are A and B, and the agent has maximally imprecise beliefs, i.e., their credal set permits every probability p ∈ [0,1] for the state e, where p = P(e). The state is assumed to be independent of the choice between A and B. The three entries in each vector represent the welfare of persons 1, 2, and 3, respectively.
For person 1, the comparison is simple: EU_1(A, p) = 1, EU_1(B, p) = 0. A is therefore determinately better for person 1 than B, regardless of which admissible probability is used. For person 2, A is better when p > 2/3, while B is better when p < 2/3. Similarly, for person 3, A is better when p < 1/3, while B is better when p > 1/3. Therefore, for persons 2 and 3, neither option is determinately better than the other, nor are they determinately equal.
The Super-Strong Pareto principle says that if A is determinately better for at least one person and B is determinately better for no one, then A is better overall (or more choiceworthy). That condition holds here: A is determinately better for person 1, while B is neither determinately better for person 2 nor for person 3. Bottom-up bracketing reaches the same verdict. It brackets the persons for whom the comparison is indeterminate, retains person 1, and chooses A.
This procedure violates Statewise Dominance, which says: If the aggregate value of B’s outcome is at least as great as that of A in every state, and greater in at least one state, then B is better overall (or more choiceworthy). In the above case, aggregate welfare ranks B above A under both e and ¬e: B yields total welfare 0 + 0 + 20 = 20, while A yields 1 + 10 + 0 = 11, in either state. B therefore statewise dominates A. It does not personwise pareto-dominate A, however, since person 1 is worse off under B in both states.
Bottom-up bracketing respects Super-Strong Pareto but violates Statewise Dominance. By contrast, top-down bracketing violates Super-Strong Pareto but respects Statewise Dominance. The top-down procedure bases its overall verdict on what is best for the inclusion-maximal subsets of individuals for which the agent is not clueless, i.e., for which the comparison is determinate. In the above case, the full set {person 1, person 2, person 3} is the unique inclusion-maximal set relative to which the comparison is determinate: B yields expected total welfare 20 under every admissible probability, while A yields 11. Top-down therefore chooses B.
Kollin et al. (2025) want their bracketing theory to be an extension of consequentialism (p. 18). Since consequentialism entails Statewise Dominance, they favor top-down over bottom-up bracketing. (Cf. Mogensen 2024 for a related view on consequentialist versus nonconsequentialist theories.)
The bottom-up procedure arguably takes persons (or individuals) more seriously as moral patients. Consider the above case again. From person 1’s represented ex ante welfare standpoint, A is determinately better than B. Person 1 therefore would be “begging” us, as it were, to choose A (given our beliefs about how our decision will affect her), and would object to our choosing B on personal welfare grounds. For persons 2 and 3, by contrast, neither option is determinately better. They may have important conditional interests pointing in both directions, but neither has a contrastive reason to prefer A rather than B or B rather than A, nor would they object to either choice. (If the choice were theirs, they had only their individual welfare interests in view, and our credences, they could rationally choose either option.) If one person provides us with a determinate reason to prefer A over B, while no person provides us with a determinate reason to prefer B over A, then impartial altruists should arguably choose A. This is the thought behind Super-Strong Pareto.
If this is sound, Statewise Dominance is not a universal requirement of impartial altruistic choice. In cases like the above, it fails. And its failure is no mystery: It is perfectly intelligible based on person-centered contrastive reasons. (Cf. Clifton 2025 on reasons-based choice.) The top-down approach—which upholds Statewise Dominance—requires us to ignore these reasons and pool the people first, before making any comparisons. But individual persons are the fundamental welfare-bearers whose individual comparative perspectives determine whether things are better, worse, or neither. Our theory should therefore determine what each person’s represented prospect supports before pooling the individual stakes across persons.
What we have here, in effect, is a clash between different dominance principles: Personwise Dominance (Super-Strong Pareto) and Statewise Dominance. Kollin et al. (2025) side with Statewise Dominance by default (p. 18), but this is underargued. While it is plausible that consequence-focused, welfarist impartial altruism must respect suitable dominance principles, the choice between them depends on the basic object of altruistic concern, i.e., the basic source of altruistic reasons (see section 3.5 below). If individual persons are the basic object of altruistic concern, Personwise Dominance is the more plausible default.
Kagan (2015, p. 471ff., cf. Van Liedekerke 1995) discusses an infinite shift case that highlights the problem with pooling people before making any comparisons. (Recall that Statewise Dominance directs us to do just that.) Consider an infinite line of people at the following welfare levels:
..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
The choice is between world W1 and world W2. In W1, exactly one person occupies each integer welfare level. In world W2, the very same people are each 100 units (or arbitrarily many units) better off. The anonymous set of welfare levels is unchanged. Both worlds contain exactly one person at every integer level. An evaluation sensitive only to that anonymous distribution is therefore hard-pressed to avoid the conclusion that neither world is better than the other, or more choiceworthy. (See Nebel 2026 and Muñoz 2026 for discussion of anonymity principles.) Yet every individual is much better off in W2. Each individual therefore provides us with a strong contrastive reason to prefer W2 over W1, and each is begging us to choose W2, as it were. Personwise Dominance principles (Pareto) rank W2 above W1, and Kagan says he “cannot take seriously” (p. 473) the contrary verdict. The lesson is not merely that infinite totals misbehave. Person-attributable comparisons preserve morally decisive information that anonymous distributions erase. Each person, given their comparative perspective on the choice, provides us with a strong contrastive reason to prefer W2 over W1.
Similarly, consider a choice between (1) saving persons p1, p2, p3, p4, ... and (2) saving persons p0, p1, p2, p3, p4, ... (i.e., two countably infinite sets of people, where the former is a proper subset of the latter), with all else being equal. If we pool the people first, we face pressure to conclude that neither option is better than the other: A straightforward total welfare comparison tells us that each option saves countably infinitely many lives. If, instead, we ask about each person’s contrastive welfare stakes first, we can distinguish the options immediately: Only p0 has a contrastive stake, and it favors (2). Hence, we choose (2).
Such cases do not by themselves establish bottom-up bracketing under cluelessness. They support the prior claim on which bottom-up bracketing rests: Individual identities and contrastive individual welfare stakes provide us with morally relevant information that anonymous welfare distributions can erase. Once that is granted, the natural procedure is to determine what each individual’s complete prospect supports before aggregating across persons.
In his post on metanormative bracketing, DiGiovanni (2025) writes:
“... we might worry that it’s ad hoc to infer ‘the clueless view gives us no reason to choose’ from ‘the clueless view says the relative choiceworthiness of a and b is indeterminate’. Should we rather say the clueless view gives us an indeterminate reason to choose, and so we still can’t resolve infectious incomparability? I think the reasoning we just went through supports the ‘no reason’ perspective: Metanormativity is a different level of analysis than first-order normativity. If view n doesn’t consider a more or less choiceworthy than b, it seems natural to say that n doesn’t ‘have a complaint’ against choosing either a or b. And thus, n’s verdict has no weight in the choice between a and b.”
I must admit that this passage’s dialectical status was somewhat unclear to me. But if I’m not misinterpreting it, it may provide internal support for the person-centered rationale behind bottom-up bracketing defended above. DiGiovanni seems to argue that separate normative views are the appropriate units of metanormative deliberation. This suggests that we should ask whether and how each view compares the options, and base our overall verdict on the view-level verdicts. When a view regards A and B as incomparable, it has no objection to (or complaint against) our choosing either option, and we can therefore bracket it out.
This recommends the bottom-up procedure. First determine, for each separate normative view, whether and how it ranks A and B; then bracket out the individually incomparable views and aggregate over the others. This is structurally parallel to person-centered bottom-up bracketing: First determine, for each separate person, whether and how their complete represented prospect ranks A and B; then bracket out the individuals with incomparable verdicts and aggregate over the others.
DiGiovanni’s metanormative choice rule, however, is top-down rather than bottom-up. Under it, a metanormative bracket-set is any subset of normative views for which the options become comparable after aggregating the views in that subset. The rule then considers the inclusion-maximal such subsets. Consequently, an individually incomparable view need not be bracketed out: It may remain inside a maximal bracket-set if combining it with other views produces a determinate aggregate comparison. In this way, a normative view can be made to weigh in on a choice even though it is itself silent (indeterminate) on the choice. This seems inadequate.
Last but not least, the idea and language of “complaints” applies even more naturally at the first-order level, namely: to separate persons. If a person’s welfare determinately favors A over B, given our credences, she could object to/complain about our choosing B, on personal welfare grounds. Why not, therefore, hold that when an individual person has no contrastive stake in a choice, she provides us with no reason either way, and can thus be bracketed out? This is what bottom-up bracketing does.
Top-down bracketing, by contrast, can “force” an individual person to weigh in on a choice even though she is herself silent on (indeterminate about) the choice at hand, given our credences. (The person may remain inside a maximal bracket-set if combining her with other persons produces a determinate aggregate comparison.) If and to the extent that persons and their welfare-based individual perspectives are the basic objects of altruistic concern, this seems inadequate.
DiGiovanni (2025) writes:
“There are many different ways of carving up the set of ‘effects’ according to the reasoning above, which favor different strategies. For example: I might say that I’m confident that an AMF donation saves lives, and I’m clueless about its long-term effects overall. Yet I could just as well say I’m confident that there’s some nontrivially likely possible world containing an astronomical number of happy lives, which the donation makes less likely via potentially increasing x-risk, and I’m clueless about all the other effects overall. So, at least without an argument that some decomposition of the effects is normatively privileged over others, [we won’t have] much action guidance.”
Person-centered bottom-up bracketing avoids this objection. The decomposition is fixed independently of the desired verdict: The basic units are individual moral patients, and we assess each person’s complete represented welfare prospect under A and B—including all represented direct, indirect, near-term, and long-term effects—before asking whether either option is determinately better for them. We do not bracket “the long-run effects”; we bracket a person only when their complete represented prospect supplies no contrastive reason either way. An astronomical happy future therefore favors B only insofar as it makes some individuals’ prospects determinately favor B. (See section 3.6 for a comment on population ethics and nonidentity.)
Top-down bracketing also avoids DiGiovanni’s cherry-picking worry: Rather than selecting a convenient subset, it considers all inclusion-maximal determinate subsets. But top-down bracketing introduces new procedural choices that invite arbitrariness worries again: Why inclusion-maximality, rather than maximum-cardinality, say? And why unanimity among maximal sets? Why should a singleton and a set containing almost everyone have equal veto power?
DiGiovanni (2025) writes:
“Should I interpret [the bracketing verdict] as, ‘I ‘expect’ A to have systematically better effects than B, impartially speaking’? In particular, should I consider the impartial altruistic argument for choosing A over B to be as strong as if ‘all the other effects’ canceled out in expectation? Arguably not. I still care about those other effects, whether or not I can determine which strategy they recommend. I think that, properly disentangled, these effects give me some reasons in favor of A, some in favor of B, and it’s indeterminate how to weigh these reasons up. So I’m not sure I see the moral urgency [of the bracketing verdict].”
This reasoning threatens to prove too much by generalizing from cluelessness to the case of ordinary uncertainty. Suppose A directly saves a life, while its long-run effect is either an enormous benefit or an enormous harm to an astronomical number of people, each with a well-justified probability of exactly ½. Subjective expected-value reasoning says to choose A: The long-run effects cancel out in expectation, even though in actuality A may deterministically lead to the enormous harm and B to the enormous benefit. “Properly disentangled,” the effects would give us reason to favor B (though we don’t know this). So why, we might ask, consider the situation as morally urgent as if the effects canceled out (in actuality, not merely in expectation)?
But if that does not trouble us, it is unclear why indeterminacy should. While exact cancellation and bracketing differ epistemically—the former establishes an expected difference of zero, while the latter establishes no determinate direction—both leave us without a long-run contrastive reason for either option. Under both exact cancellation and bracketing, the moral importance of A derives from the determinate reason provided by the person saved.
The proposed person-centered rationale for bottom-up bracketing involves Super-Strong Pareto. Hedden (2024) argues (p. 589) that a weighing model of reasons fails to support Super-Strong Pareto (while it does support Weak and Strong Pareto). To the extent that such a model is independently plausible, Super-Strong Pareto may remain unjustified.
Kollin et al. (2025) have replied (p. 15) that this argument is question-begging, given that there is “no single ‘weighing model’ of reasons to fall back on.” I believe this reply to be on the right track but incomplete. (I also directionally agree with Kollin et al.’s replies to the various objections against Super-Strong Pareto from cyclicity, p. 13–16.) A weighing model of reasons is highly attractive, especially under a welfarist view of the content of our reasons. As argued above, the reasons provided to us by the welfare stakes of moral patients are plausibly contrastive: The better off an individual is in option A relative to option B, the stronger the reason to choose A rather than B (and the stronger the individual’s objection to our choosing B). The proposed model says to weigh up all such person-attributable contrastive reasons. This entails Super-Strong Pareto: If A is determinately better for at least one person, that person supplies a contrastive reason to choose A. If B is determinately better for no one, the respective people supply no contrastive reasons. Hence, weighing the contrastive reasons yields the verdict that A is better overall (or more choiceworthy).
On this person-centered model, unresolved considerations within a person’s prospect are not independently exported into an interpersonal aggregate. They must first resolve into a settled person-attributable comparison. If neither option is determinately better for a person, her prospect supplies no directional reason at the interpersonal stage. The justification, again, is that persons and their welfare-based perspectives on the choice at hand (as represented by the decision-maker), rather than subpersonal considerations or state-contingent fragments of personal prospects, are the basic objects of moral concern and the sources of welfare-based reasons.
Kollin et al. (2025) reject Personwise Dominance (Super-Strong Pareto) and side with Statewise Dominance on the grounds that “consequentialism” requires Statewise Dominance (p. 18). As mentioned, while it is true that consequence-focused, welfarist impartial altruism must respect suitable dominance principles, the choice between them depends on the basic object of altruistic concern, i.e., the basic source of altruistic reasons. If individual persons are the basic objects of concern, Personwise Dominance (Super-Strong Pareto) is more plausible.
Nonconsequentialists have often complained that consequentialism, and utilitarianism in particular, fails to respect persons, their “separateness,” and their distinct comparative perspectives on the world by treating them merely as intrinsically unimportant “receptacles of value.” If I thought this objection were sound, it would trouble me enough that I would hardly be attracted to consequentialism. (But it is unsound, or at least avoidable—cf. Chappell 2015, who argues that “to avoid treating people as replaceable, utilitarians should be token-pluralists who see each person’s welfare as a distinct final good, rather than (separateness-violating) token-monists who see the aggregate welfare as the only final good.”) What attracts me to impartial altruism is the idea of equal concern for every single individual, and the aim of making their life go better rather than worse, by their own lights. Consequentialism, I would hope, is consistent with this. In any case, however, a theory that sides with Personwise Dominance over Statewise Dominance can be impartial, altruistic, and entirely focused on welfare consequences (for people). Whether this counts as “consequentialist” ultimately depends on how narrowly that label is defined.
Clifton (2025) writes:
“It looks to me like bracketing with spacetime locations has a much better shot at being action-guiding than bracketing with persons. Despite the importance of this point, a proper discussion is beyond the scope of this post and our paper, though I’ve tried to put some intuition in a footnote.[7: Personal identity is fragile, such that many persons exist only in worlds where we take a particular action. For example, personal identity depends sensitively on the timing of conception, and through many chaotic pathways our actions affect the times at which future persons are conceived. (The point may be familiar from the nonidentity problem for person-affecting ethics.) This creates a problem: we can construct a maximal bracket-set based on ‘all the happy people who would exist if we do A’ and another based on ‘all the happy people who would exist if we do B,’ where these sets favor different actions. Since bracketing only favors A over B if A is better than B for all maximal bracket-sets, this would leave us still indecisive between A and B. ... <how spacetime locations as value-bearers may avoid such difficulties> ... ]”
I must admit I did not entirely follow the reasoning here. Clifton seems to suggest that top-down bracketing generates distinctive nonidentity-related problems if persons (instead of spacetime locations) are chosen as value-bearers. Suppose he is right that top-down bracketing must entail that A: create p1 at welfare level 10 and B: create p2 at welfare level 5 are equally choiceworthy. Perhaps, on a person-centered approach to ethics, that is simply true (cf. Boonin 2014 and Pummer 2024): If we choose B, we will have made it the case that (i) no actual person has negative welfare, which they could object to on personal welfare grounds, and (ii) all actual persons have the maximum amount of positive welfare they could have had. (Person p2, once she exists, will have no welfare-based objection to our choosing B: We could not have made her better off. Nor will p1, who will not exist.) On a person-centered approach, we may therefore have maximized people’s welfare in the sense that matters.
However, person-centered views have other theoretical options in population ethics, too. Let me illustrate this for person-centered bottom-up bracketing. In variable-population contexts, it must be based on some moral account of what person-indexed contrastive reasons, if any, option-dependent people supply across existence and nonexistence under uncertainty. Once such an account classifies each person’s prospect as favoring option A rather than B, B rather than A, tying, or having no direction, bottom-up bracketing proceeds just as in fixed-population cases: It retains persons whose comparison is determinate, brackets those whose comparison is indeterminate, and aggregates over the retained persons (i.e., weighs up the contrastive reasons supplied by them).
Clifton goes on:
“If it’s true that only spacetime location-based bracketing is action-guiding, that’s unfortunate, because spacetime locations don’t seem morally relevant! (You might or might not consider persons to be morally relevant -- maybe they, too, are just containers of experience-moments -- but spacetime locations definitely don’t seem to be.) We would be left with a tradeoff: Morally well-motivated but doesn’t get the intuitive answers in terms of action guidance (persons) vs. morally poorly-motivated but gets the intuitive answers (spacetime locations).”
But what intuitive answers, in terms of action guidance, does person-centered bottom-up bracketing fail to get? Also, even if it were true that person-centered views cannot avoid counterintuitive implications about action guidance, shouldn’t Clifton’s reasons-based approach side with what’s morally well-motivated (persons as value-bearers)?
Finally, Clifton writes:
“Interestingly, this is closely analogous to the situation in infinite ethics. Prominent theories of infinite ethics also depend on locations of value. (For example, we might want our theory to satisfy a ‘Pareto principle’ which says that an infinite world World 1 is better than another World 2 if it is better than World 2 at each location of value.) And it turns out that theories of infinite ethics based on persons also lead to much more widespread incomparability than those based on spacetime locations (Askell (2018), Wilkinson (2021)).[8] The implausibility of incomparability in the cases he considers leads Wilkinson to develop an approach to infinite ethics based on spacetime locations. We may have in infinite ethics a surprising source of support for spacetime bracketing?”
It seems to me that we do not—quite the contrary, as we have already seen in section 2. While Askell supports Clifton’s descriptive claim that person-based Pareto principles generate widespread incomparability, she rejects his intended inference (like many other authors in the infinite ethics literature). She defends person-based Pareto and accepts the resulting incomparability rather than adopting a more complete spacetime ordering without independent moral justification: “Ethics is concerned with the wellbeing of people. It is not particularly concerned with the pattern of utility across spacetime.” (Askell 2018, p. 84)
Furthermore, it is unclear how the mere fact of widespread incomparability renders the situation in infinite ethics “closely analogous.” This depends on the kind of incomparability at issue. Consider, for instance, the following comparisons involving countably infinite sets of people:
(i) saving persons a1, a2, a3, ... = saving persons b1, b2, b3, ...
(ii) saving persons b1, b2, b3, ... < saving persons b0, b1, b2, b3, ...
Proposition (i) is hard to deny; it seems to follow from impartiality (whatever impartiality is, precisely). (ii) follows from person-based Pareto. Now, add a transitivity premise:
(iii) If X = Y and Y < Z, then X < Z
The conjunction of (i), (ii), and (iii) entails the conclusion
(iv) saving persons a1, a2, a3, ... < saving persons b0, b1, b2, b3, ...
But this is false. Instead of (i), we could have started with the proposition “saving persons a1, a2, a3, ... = saving persons b0, b1, b2, b3, ...”, on grounds of impartiality.
What gives? If, like many authors in the literature, we wish to preserve transitivity, the most plausible way out is
(i)* saving persons a1, a2, a3, ... || saving persons b1, b2, b3, ...
(iv)* saving persons a1, a2, a3, ... || saving persons b0, b1, b2, b3, ...
In other words, we introduce widespread incomparability (between any sufficiently disjoint infinite sets of people). But this sort of incomparability seems to me unrelated to problematic failures of action guidance.
Finally, in footnote 8, Clifton encourages the reader to consider Wilkinson’s (2021) Firing Line and Saving-a-Child-from-Traffic cases. As far as I can tell, person-centered bottom-up bracketing handles the latter without any noteworthy difficulties. The former is as follows: Infinitely many persons are lined up in front of us. We can either let every second person in the line be killed, or let every fifth person be killed. Wilkinson thinks the former option is worse, and uses this in an argument for spacetime locations over persons (as value-bearers). The option that kills every second person, he claims, kills more people in a sense that matters: It kills people that are more densely positioned over the line.
I disagree. Between the option of every second person dying and every fifth person dying, there is an overlap containing people who are sadly doomed anyway: {p10, p20, p30, p40, ...}. These people have no contrastive stake in the choice, so that they provide us with no contrastive reasons. Similarly, some people are safe either way and have no contrastive stake in the choice for this reason: {p1, p3, p7, p9, p11, ...}. We can affect the fates of {p2, p4, p6, p8, p12, ...} and {p5, p15, p25, p35, p45, ...}. Let us relabel the people in the former set as follows: {a1, a2, a3, a4, a5, ...}, and relabel the people in the latter set as follows: {b1, b2, b3, b4, b5, ...}. We have no net reason to prefer saving either set over the other.
In conclusion, let me draw out an implication suggested by the infinite cases just considered: that DiGiovanni’s epistemological approach—set intuitions and heuristics aside, reason from “first principles”—should lead him to question whether the notion of impartial altruism is as determinate as he assumes it is. In particular, I will briefly argue that some scope-insensitive views can lay equal claim to being impartial, altruistic, welfarist, and entirely consequence-focused. This may induce a particularly troubling kind of moral uncertainty concerning impartial altruism itself.
Consider, again, the above argument for widespread incomparability:
(i) saving a1, a2, a3, ... = saving b1, b2, b3, ...
(ii) saving b1, b2, b3, ... < saving b0, b1, b2, b3, ...
(iii) If X = Y and Y < Z, then X < Z
Therefore:
(iv) saving a1, a2, a3, ... < saving b0, b1, b2, b3, ...
But (iv) is false. As discussed, one way out is to introduce incomparability and maintain that “saving a1, a2, a3, ... || saving b1, b2, b3, ...”. Another way out is to deny the transitivity premise (iii). Given the arguments Kollin et al. (2025) offer in defense of cyclicity (p. 13ff. and p. 22ff.), denying (iii) should be viable a fortiori; it commits us to a milder form of intransitivity, not to outright cyclicity.
The problem is that this may leave scope-sensitivity unjustified. Some people believe that impartial altruism should be scope-insensitive, i.e., that the numbers should not count (e.g., Taurek 1977 and Timmermann 2004). If you can save person a1 or persons b0 and b1 but not all three, either option is permissible, or you must perform an impartial lottery (regarding the latter, cf. the literature on probabilistic social choice rules, e.g., Intriligator 1973, Fishburn 1975, Pattanaik and Peleg 1986, and contemporary proponents such as Florian Brandl). The standard argument against such views, and for non-probabilistic scope-sensitivity, has run roughly as follows (e.g., Kavka 1979, in response to Taurek 1977):
(i) saving a1 = saving b1
(ii) saving b1 < saving b0 and b1
(iii) If X = Y and Y < Z, then X < Z
Therefore:
(iv) saving a1 < saving b0 and b1
This argument generalizes to any natural numbers m < n of people in the conclusion. Scope-insensitive views have two ways out. The first is to introduce incomparability: “saving a1 || saving b1.” The second is to deny the transitivity premise (iii). If these moves are legitimate in the infinite domain, why would they be illegitimate here? In other words, what is our reply to scope-insensitive altruists who make these moves—quite consistently—in the finite domain as well?
Such arguments create pressure to conclude that all we have is a mere intuition favoring (or disfavoring) scope-sensitivity—cf. Muñoz (2024). As Muñoz argues, scope-insensitive views can lay equal claim to “counting each person for one.” The scope-sensitive view that we are required to save b0 and b1 over a1 gives each person an equal additive vote. The scope-insensitive view that we may permissibly save b0 and b1 or a1 gives each person equal veto power to block a requirement to save the other side. The scope-insensitive view that we are required to perform an impartial lottery gives each person an equal probabilistic vote, i.e., equal probabilistic influence over the outcome. It is disputed whether, in the b0 and b1 vs. a1 case, this should lead to a (½, ½) lottery or to a (⅔, ⅓) lottery between the options, i.e., whether one should toss coins or draw lots. While lotteries violate non-probabilistic scope-sensitivity, they can be individually stakes-sensitive: If b0 and b1 each have less personal welfare at stake than a1, the lottery should plausibly be proportionally weighted in a1’s favor.
Hence, scope-insensitive views can be impartial, altruistic, welfarist, and entirely consequence-focused (i.e., they can deny the moral relevance of distinctions such as doing/allowing, intending/foreseeing, etc.). One might object that lottery procedures depart from an exclusive focus on welfare consequences. But consequentialist, scope-sensitive aggregation, or stakes-weighted additive voting, is a social choice procedure too (cf. Henning 2023). Nor does the justification for lotteries need to involve fairness. Lotteries can be justified as an impartial social choice rule within welfarist beneficence.
Though I cannot argue for this here, I share DiGiovanni’s epistemological aversion to relying on mere intuitions, best guesses, or heuristics. This leads me to ask: Why, precisely, must impartial altruists be scope-sensitive? The above arguments suggest that the notion of equal consideration may be quite indeterminate. This threatens to induce a troubling form of moral uncertainty that affects the heart of impartial altruism. I leave its conceptual analysis, implications for cluelessness, and resolution as an exercise for the reader.
I’m one of the judges of the competition. My comments shouldn't be taken as a full review of a post. And, unfortunately, I won’t have capacity to comment on every post or engage with all replies. Thanks so much to everyone who entered!
I find the case for bottom-up bracketing very well-argued and compelling.
I’d like to see more engagement with non-identity issues that threaten the action-guidingness of bottom-up bracketing.