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This is part four of a series on minimalist axiologies (i.e. axiologies that essentially say “the less this, the better”).

Every part of this series builds on the previous parts, but can also be read independently.


Population axiology matters greatly for our priorities. Recently, it has been claimed that all plausible axiological views imply certain “very repugnant conclusions” (defined below). In this response, I argue that minimalist views avoid these “very repugnant conclusions”, and that they face less repugnant conclusions than do contrasting offsetting views.

1. Are repugnant implications inevitable?

In population axiology, certain offsetting views, according to which independent bads can be offset by a sufficient amount of independent goods, face the Very Repugnant Conclusion (VRC):

A population of arbitrarily many lives with arbitrarily high welfare is worse than a population of arbitrarily many arbitrarily negative lives plus sufficiently many ε-lives that each have an arbitrarily small quantity of positive welfare (Figure 1).

Figure 1. The original VRC.
Figure 1. The original VRC.

Offsetting views also allow the ε-lives in the VRC to be rollercoaster lives that all contain unbearable suffering (purportedly counterbalanced by a sufficient amount of bliss).[1]

In particular, symmetric classical utilitarianism implies interchangeability between a non-suffering ε-life and the rollercoaster life illustrated in Figure 2 (provided that the “overall welfare” of the rollercoaster life equals ε).

Figure 2. The happiness and suffering over time of a single rollercoaster life.
Figure 2. The happiness and suffering over time of a single rollercoaster life.

Additionally, one may replace each non-suffering ε-life in the original VRC with an intrapersonal VRC life (Figure 3).

Figure 3. The happiness and suffering over time of an intrapersonal VRC life.
Figure 3. The happiness and suffering over time of an intrapersonal VRC life.

Recently, Budolfson and Spears (2018) have argued that all plausible views in population ethics imply similarly repugnant conclusions, namely that they imply either the VRC or a closely analogous Extended VRC (XVRC), which I illustrate shortly at the beginning of Section 2.

The purpose of this essay is to argue that this claim does not apply to minimalist views. In a nutshell: minimalist views avoid the VRC, can avoid repugnant XVRCs, and, at any rate, face XVRCs that are less repugnant than are the comparable conclusions faced by offsetting views.

Three claims

Budolfson and Spears (2018, pp. 31–32) make the following three claims:[2]

Claim 1:  No leading welfarist axiology can avoid the VRC.

Claim 2:  No other welfarist axiology in the literature can avoid the XVRC.[3]

Claim 3:  The XVRC is just as repugnant as the VRC.

The authors conclude that:

Repugnant implications are an inevitable feature of any plausible axiology. If repugnance cannot be avoided, then it should not be. We believe this should be among the guiding insights for the next generation of work in value theory.

Claim 1 does not apply to minimalist axiologies

The scope of Claim 1 (“No leading welfarist axiology can avoid the VRC”) is limited to ‘leading’ welfarist axiologies, that is to views that, according to the authors, are commonly-held in the axiological literature (p. 8).

These do not cover minimalist axiologies, although axiologies that are essentially minimalist have been defended, for instance, by Schopenhauer (1818/18191851), Wolf (199619972004), Fehige (1998), Breyer (2015), and Knutsson (2021b, “axiological claim”).

To the extent that the VRC seems repugnant, it is worth noting that all minimalist axiologies do avoid the VRC, and can do so neatly without relying on arbitrary or ad hoc assumptions.

Claim 2 requires that we extend the XVRC

Claim 2 (“No other welfarist axiology in the literature can avoid the XVRC”) is not straightforward to evaluate, because the original XVRC, as the authors define it, applies strictly only to views that make the assumption of independently aggregable positive utility (cf. Appendix B).

This assumption is not made by minimalist welfarist axiologies, such as antifrustrationismtranquilism, and some types of negative utilitarianism.

Yet by extending the original definition of the XVRC, we can construct minimalist XVRCs. This will be done in Section 2. After that, we can evaluate Claim 3 (“The XVRC is just as repugnant as the VRC”) for minimalist views.

Claim 3 requires comparisons

If Claim 3 were true not only for offsetting but also for minimalist views, that would support the authors’ conclusion that repugnant implications are inevitable.

Yet is it true? That is, are minimalist XVRCs just as repugnant as the VRC? Settling this question requires that we directly compare minimalist XVRCs against the VRC.

Overview of this essay

Section 2 illustrates comparable XVRCs for offsetting and minimalist views. The illustrations are categorized into three separate subsections depending on the kind of the views in question:

  1. Archimedean views,
  2. lexical views with sharp thresholds, and
  3. lexical views without sharp thresholds.

Section 3 unpacks what sources of repugnance are present in the different XVRCs, and why I exclude the element of non-creation as non-repugnant.

Section 4 evaluates the comparative repugnance of the offsetting and minimalist XVRCs within each of the three categories of views.[4]

Additionally, Section 4 explains how (at least some) minimalist views face XVRCs that are not as repugnant as the original VRC, which implies that Claim 3 (“The XVRC is just as repugnant as the VRC”) does not hold for those minimalist views.

2. Comparable XVRCs for offsetting and minimalist views

Archimedean views (“Quantity can always substitute for quality”)

Let us look at comparable XVRCs for Archimedean views. (Archimedean views roughly say that “quantity can always substitute for quality”, such that, for example, a sufficient number of minor pains can always be added up to be worse than a single instance of extreme pain.)

Figure 4 illustrates the original XVRC for Archimedean offsetting views, which goes roughly like this (cf. Budolfson & Spears, 2018, p. 19):

Rather than adding arbitrarily many lives with arbitrarily high welfare, it is better to add arbitrarily many arbitrarily negative lives and have each life in a sufficiently large base population receive an arbitrarily small quantity (ε) of positive welfare (an ε-change).

Figure 4. An XVRC for Archimedean offsetting views.
Figure 4. An XVRC for Archimedean offsetting views.

A special case of the Archimedean offsetting XVRC is “Creating hell to please the blissful”, in which every life in the base population is brought from a very high welfare to an even higher welfare at the cost of adding maximally bad lives (Figure 5).

Figure 5. Another XVRC for Archimedean offsetting views (“Creating hell to please the blissful”).
Figure 5. Another XVRC for Archimedean offsetting views (“Creating hell to please the blissful”).

In the case of minimalist welfarist axiologies, ‘welfare’ cannot refer to independently aggregable positive utility. Instead, minimalist views construe welfare as the absence of intrinsically problematic features, such as of ‘frustration’, ‘craving’, or ‘discontentment’.[5]

Yet we can nonetheless construct an XVRC for Archimedean minimalist views by defining the arbitrarily small changes (ε-changes) more generally as ε-sized improvements in welfare.

Thus, an Archimedean minimalist XVRC could go like this (Figure 6):

It is a net benefit to add arbitrarily many arbitrarily negative lives so as to barely reduce the suffering of each life in a sufficiently large base population.[6]

Figure 6. An XVRC for Archimedean minimalist views.
Figure 6. An XVRC for Archimedean minimalist views.

Figure 7 illustrates another Archimedean minimalist XVRC, which is basically what is known as the Reverse Repugnant Conclusion (cf. Carlson, 1998, p. 297; Mulgan, 2002).

Figure 7. Another XVRC for Archimedean minimalist views (the Reverse Repugnant Conclusion).  [7]
Figure 7. Another XVRC for Archimedean minimalist views (the Reverse Repugnant Conclusion).[7]

Lexical views (“Some qualities get categorical priority”)

Let us now look at comparable XVRCs within a prominent class of non-Archimedean views, namely what are known as lexical views.[8] Lexical views deny that “quantity can always substitute for quality”; instead, they assign categorical priority to some qualities relative to others.

Specifically, lexical minimalist views entail lexicality between bads, such as by (all else equal) prioritizing the reduction of unbearable suffering over any mild discomfort (cf. Vinding, 2022a). Additionally, lexical offsetting views entail lexicality between goods (of e.g. higher pleasures over lower pleasures),[9] or between goods and bads (of e.g. higher pleasures over mild discomfort).

Do lexical views face XVRCs? Notably, lexical views may question the assumption of representing welfare with a single real number to begin with. Therefore, lexical views may reject the formal framework of the Archimedean XVRC, whose definition entails arbitrarily small changes (ε-changes) to the aggregate welfare (a real number) of each life in the base population.

Yet, even if we reject the Archimedean framework, we can still reinterpret the XVRC in order to construct analogous lexical XVRCs (for both minimalist and offsetting lexical views). Let us first look at such XVRCs for lexical views with sharp thresholds, and then for lexical views without sharp thresholds.

With sharp thresholds

Consider a lexical minimalist view with a sharp threshold. For instance, one may hold that some sentient minds have a sharp breaking point at which suffering becomes unbearable, and that the passing of this point is categorically worth avoiding more than any amount of “bending without breaking”.[10]

Figure 8 illustrates an XVRC for such a view:

It is a net benefit to add arbitrarily many non-lexically bad states (of e.g. barely bearable suffering) as long as we reduce the number of lexically bad states (of e.g. unbearable suffering).

Figure 8. An XVRC for lexical minimalist views with a sharp threshold.
Figure 8. An XVRC for lexical minimalist views with a sharp threshold.

A comparable lexical offsetting view might entail all of the following claims:

  1. There is a lexical threshold between some goods (e.g. higher and lower pleasures).
  2. There is a lexical threshold between some bads (e.g. bearable and unbearable suffering).
  3. Non-lexical goods (e.g. lower pleasures) cannot compensate for lexically bad states.
  4. Some number of lexically good states can compensate for a lexically bad state.

Figure 9 illustrates an XVRC for such a view:

It is a net benefit to add arbitrarily many arbitrarily negative lives (that entail lexically bad states) so as to replace, within each life in a sufficiently large base population, a just barely not lexically good state with a lexically good state.

Figure 9. An XVRC for lexical offsetting views with sharp thresholds.  [11]
Figure 9. An XVRC for lexical offsetting views with sharp thresholds.[11]

Without sharp thresholds

Finally, it has been argued that lexical views need not be sharp like the ones that were abstractly sketched in the previous subsection. After all, perhaps a more plausible lexical view would hold that (e.g.) unbearableness comes in degrees.[12]

A “non-sharp” lexical threshold could be a range — e.g. in the intensity of suffering — between which the suffering becomes lexically bad relative to suffering above the range. This would imply that no duration of suffering above the range (e.g. “wholly bearable suffering”) can be worse than a single instance of suffering below the range (e.g. “wholly unbearable suffering”).[13]

Figure 10 illustrates a non-sharp lexical minimalist XVRC:

It is a net benefit to add arbitrarily many non-lexically bad states (e.g. wholly bearable suffering) as long as we reduce the number of lexically bad states (e.g. wholly unbearable suffering).

Figure 10. An XVRC for lexical minimalist views without sharp thresholds.
Figure 10. An XVRC for lexical minimalist views without sharp thresholds.

Figure 11 illustrates a non-sharp lexical offsetting XVRC (based on the same four assumptions made in the previous offsetting view).

It is a net benefit to add an arbitrarily large number of arbitrarily negative lives (that entail lexically bad states) so as to add one lexically good state to each life in a sufficiently large base population.

Figure 11. An XVRC for lexical offsetting views without sharp thresholds.
Figure 11. An XVRC for lexical offsetting views without sharp thresholds.

3. Sources of repugnance

Section 4 will evaluate the comparative repugnance of the above XVRCs and the original VRC.

However, let us first unpack what sources of repugnance are present in the different XVRCs.

Creating non-relieving goods for some at the price of unbearable suffering for others

Only the offsetting XVRCs entail the creation of non-relieving goods for some, at the price of unbearable suffering for others.

By contrast, the “ε-changes” in the minimalist XVRCs are arguably more plausible and less frivolous, because they are aimed at the reduction of suffering rather than at the increase of non-relieving pleasure — pleasure that has no positive roles for relieving anyone’s burden (cf. Vinding, 2020b2020c, ch. 3).[14]

Enabling rollercoaster lives that all contain unbearable suffering

Only offsetting views allow the larger populations to become rollercoaster lives that all contain unbearable suffering (Figure 2). And Archimedean offsetting views further allow the larger populations to become intrapersonal VRC lives (Figure 3).

By contrast, minimalist views reject the aggregative framework that enables the rollercoaster interpretation in the first place. Consequently, minimalist views entail only the non-rollercoaster versions of the minimalist XVRCs above, whereas the offsetting views entail those same conclusions plus their rollercoaster versions.

Making seemingly trivial changes at the price of unbearable suffering

Budolfson and Spears (2018) seem to attribute repugnance exclusively to the unbounded aggregation of arbitrarily tiny changes:

“We note that a common theme emerges, which is that any axiology that aggregates over unbounded spaces will have repugnant implications. This is the fundamental mechanism that our proofs exploit.” (p. 2) “Because all plausible axiologies permit aggregation over unbounded spaces, this means that all plausible axiologies are exposed to repugnant conclusions” (p. 30)

Clearly such aggregation is a potential source of repugnance in at least the Archimedean XVRCs for both offsetting and minimalist views. Additionally, perhaps an atom of a lexical offsetting good — such as the briefest possible experience of a non-relieving higher pleasure (the authors mention a tiny duration of Mozart) — is intuitively still roughly as trivial as is any other instance of a non-relieving good.

However, one could reasonably argue that the following three conclusions no longer apply in the case of lexical minimalist views:

1: “Either something that seems important will be outweighed by an unbounded number of initially unimportant-seeming matters, something that initially seems unimportant will unduly shape the outcome, or both.” (pp. 30–31)

This statement does not seem to hold for lexical views. After all, lexical views would not allow “something that seems important” to be outweighed by unimportant-seeming matters, nor would they allow something that initially seems unimportant to unduly shape the outcome. Specifically, extreme suffering does not seem unimportant, even if it only lasts for a short duration (Vinding, 2020c, sec. 8.12).

2: “Such seemingly-disparate axiologies as maximin and classical total utilitarianism have in common that they are both prepared to accept the cost of many arbitrarily negative lives and forgo the benefits of many arbitrarily positive lives, for the right arrangement of infinitesimal tweaks.” (p. 31)

Lexical minimalist views (uniquely) do not permit the addition of arbitrarily negative lives (nor rollercoaster lives that contain arbitrarily bad suffering), because they require that we overall reduce lexically bad states. Additionally, to “forgo the benefits of many arbitrarily positive lives” need not be a source of repugnance (a point I unpack in the next subsection).

3: “[Our argument] considers the possibility that better-off people are qualitatively different [and] considers the possibility that higher pleasures are qualitatively different. In general, because lexical views still must aggregate across people, they remain subject to repugnance.” (p. 34)

As noted, perhaps repugnant implications are inevitable for lexical offsetting views (cf. adding tiny durations of non-relieving lexical goods, however they are defined, at the price of unbearable suffering). Yet the authors do not seem to discuss lexical views that give overriding priority to the prevention of extreme bads. And such views are arguably uniquely resistant to this “trivial changes” source of repugnance.[15]


The three sources of repugnance covered in the last three subsections each entail the increase of unbearable suffering for the sake of changes that seem relatively frivolous or trivial in comparison. The original VRC and XVRC additionally entail what might seem like a fourth source of repugnance, namely the non-creation of high-welfare lives whose existence would purportedly be a great benefit for their own sake. (Let us call this the “non-creation of happy isolated lives”, which I will shortly unpack in more detail.)

A key thing to note when evaluating non-creation as a potential source of repugnance is that we need to carefully isolate our intuitions on this question — i.e. on non-creation’s independent repugnance, all else equal — from the influence of various factors that are actually external to the question itself. And when we have done so (as in my previous essays, or in the thought experiment in Vinding, 2022f), I maintain that non-creation is not an independent source of repugnance.

Let us briefly unpack some of the reasons why non-creation is plausibly non-repugnant:

  1. How repugnant is the non-creation of lives that are described as “awesome”, “flourishing”, or “full of love and accomplishments”, all else equal? Such framings of the question are quite common, which is unfortunate given that they may cause our evaluation to become strongly biased in favor of creation. After all, our practical intuitions easily associate those descriptions with lives that play positive roles for others (even on purely minimalist views of value), whereas standard population axiology counterintuitively requires that we ignore all such roles.[16]
  2. To properly respect the ‘all else equal’ assumption, we should therefore explicitly highlight that the lives in question are forever causally isolated lives that never affect any other beings in any way (e.g. that they are happy isolated matrix lives, dwellers of their closed island worlds, or the like, which clearly make no difference for others). And to further remove our potentially self-related concerns from the picture, we should imagine that no one will know whether we endorsed the creation or non-creation of those happy isolated lives, and that even we will have our memory wiped of the decision immediately after we make it.[17]
  3. For experientialist consequentialists, the question of whether non-creation is repugnant becomes a question that arguably requires a thorough phenomenological search, namely a search for non-relieving goods that constitute a positive counterpart to suffering. Yet such a counterpart plausibly does not exist (cf. Vinding, 2022c; Knutsson, 2022; see also Gloor, 2017, sec. 2.1; Sherman, 2017, pp. 103–107).[18]
  4. For preference-based views, it likewise makes sense to think of preference satisfaction as an inherently asymmetric endeavor. Singer (1980): “The creation of preferences which we then satisfy gains us nothing. We can think of the creation of the unsatisfied preferences as putting a debit in the moral ledger which satisfying them merely cancels out.”[19] Fehige (1998): “We have obligations to make preferrers satisfied, but no obligations to make satisfied preferrers. … Maximizers of preference satisfaction should instead call themselves minimizers of preference frustration.” See also DiGiovanni (2021).[20]

4. Comparative repugnance

Let us now evaluate the comparative repugnance of the XVRCs reviewed above and the original VRC. (The reader may find it useful to open a duplicate tab so as to review Figures 4–11 together with my following commentary on them.)

Tables 1–3 show how the minimalist XVRCs explored above are a proper subset of the XVRCs that are implied by the corresponding offsetting views explored above. Specifically, the offsetting views entail the minimalist implications, their (arguably more repugnant) rollercoaster or intrapersonal VRC versions,[21] and the interpersonal offsetting implications.

Notably, only the offsetting implications entail all three of the sources of repugnance that were considered in Section 3 (i.e. creating non-relieving goods at the price of others’ suffering, rollercoaster lives, and seemingly trivial changes at the price of unbearable suffering). For reasons unpacked in the section on non-creation, I do not count non-creation as a source of repugnance below.

Table 1. Implications of the Archimedean views.






Very Repugnant Conclusion (Fig 1)



rollercoaster version



intrapersonal VRC version



Archimedean offsetting XVRC (Fig 4)



rollercoaster version



intrapersonal VRC version



“Creating hell to please the blissful” (Fig 5)



rollercoaster version



intrapersonal VRC version



Archimedean minimalist XVRC (Fig 6)



rollercoaster version



intrapersonal VRC version



Reverse Repugnant Conclusion (Fig 7)



rollercoaster version



intrapersonal VRC version



Among the Archimedean implications, the offsetting XVRCs (Figures 4–5) entail more sources of repugnance than do the minimalist XVRCs (Figures 6–7). Specifically, the offsetting XVRCs entail all the same sources of repugnance as does the original VRC, with arguably no redeeming (“anti-repugnant”) elements. We can thus agree with Budolfson and Spears’ (2018) assessment that the offsetting XVRCs are just as repugnant as the VRC (i.e. Claim 3).

By contrast, the minimalist XVRCs lack the repugnance of creating non-relieving goods for some at the price of unbearable suffering for others, and the repugnance of rollercoaster or intrapersonal VRC lives that all contain unbearable suffering. Therefore, the repugnance of the minimalist XVRCs relative to the VRC depends on whether the former entail any additional sources of repugnance that are not shared by the VRC; and it appears that they do not (as argued in the previous section on non-creation), which would imply that Claim 3 does not hold for Archimedean minimalist views.[22]

(For more on “imperfect paradise” cases, see Appendix A.)

Table 2. Implications of the lexical views with sharp thresholds.


Lexical sharp




Lexical sharp minimalist XVRC (Fig 8)



rollercoaster version



Lexical sharp offsetting XVRC (Fig 9)



rollercoaster version



Among the sharp lexical views, the offsetting XVRC (Figure 9) again entails arguably all the same sources of repugnance as does the original VRC. And only the offsetting view can accept an increase in the number of lexically bad states (such as unbearable suffering), for the sake of producing non-relieving goods.

Table 3. Implications of the lexical views without sharp thresholds.


Lexical non-sharp




Lexical non-sharp minimalist XVRC (Fig 10)



rollercoaster version



Lexical non-sharp offsetting XVRC (Fig 11)



rollercoaster version



Finally, the non-sharp lexical minimalist XVRC (Figure 10) entails that no amount of sufficiently mild states of suffering can be worse than unbearable suffering.

By comparison, the corresponding offsetting view implies not only the same theoretical conclusion (Figure 10), but also the arbitrary increase of unbearable states for the sake of creating purportedly sufficient amounts of non-relieving higher goods (Figure 11). Additionally, the offsetting view again entails rollercoaster implications that would “require everyone in the chosen population to experience [arbitrarily] terrible suffering” (Budolfson & Spears, 2018, p. 19).[23]


To respond to the three claims:

Claim 1:  No leading welfarist axiology can avoid the VRC.

Minimalist welfarist axiologies do avoid the VRC. (And they also avoid the rollercoaster form of the original Repugnant Conclusion.)

Claim 2:  No other welfarist axiology in the literature can avoid the XVRC.

Minimalist views do entail modified minimalist XVRCs (cf. Figures 6, 7, 8, and 10).

Claim 3:  The XVRC is just as repugnant as the VRC.

This seems true for offsetting views. Yet the minimalist XVRCs are considerably less repugnant than the VRC.

In particular, at least the Archimedean minimalist and the non-sharp lexical minimalist XVRCs (Figures 6, 7, and 10) entail fewer sources of repugnance than does the VRC, arguably with no additional, greater sources of repugnance.

Furthermore, the XVRCs generated by minimalist views are consistently less repugnant than are those generated by the corresponding offsetting views. Minimalist XVRCs thus seem uniquely unrepugnant. This is a strong point in favor of minimalist views over offsetting views in population axiology, regardless of one’s theory of aggregation.


I am grateful for helpful comments by Anthony DiGiovanni, James Faville, Lukas Gloor, Simon Knutsson, Winston Oswald-Drummond, Michael St. Jules, and Magnus Vinding.

Special thanks to Magnus Vinding for guiding the development of this essay.

Commenting does not imply endorsement of any of my claims.


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Appendix A: Responses to the “imperfect paradise” cases

The main text already discusses why the non-creation of happy isolated lives is plausibly non-repugnant. Yet one might think that my main argument still ignores the strongest cases against minimalist views, such as “imperfect paradise” cases that entail the non-creation of arbitrarily blissful and vast paradises due to their containing more bads than does the alternative outcome (e.g. discussed here and here).

In this Appendix, I explain why “imperfect paradise” cases do not seem to constitute an additional argument in favor of offsetting views over minimalist views (beyond what is already implied by our stance on whether non-creation is repugnant). Rather, the question of whether such cases are repugnant seems divisible into two questions, both of which are already discussed in the main text:

  1. Whether non-creation is repugnant.
  2. Whether Archimedean aggregation of tiny bads is more plausible than is a lexical priority to some bads such as unbearable suffering.

Non-creation revisited

Non-creation in “imperfect paradise” cases amounts to the non-creation of arbitrarily many happy lives for the sake of preventing a single episode of slight discomfort. Yet for this scenario to pertain to minimalist views centered on overall negative states, we need to be careful not to interpret this episode of slight discomfort as something that the minimalist views would actually find to be unproblematic, such as a dip in “non-relieving bliss” from, say, “+100” to “+99”. Instead, we should imagine that this episode of slight discomfort would be experienced as an overall negative “−1” episode (cf. Vinding, 2021, What is the bad in question?). And all else equal, both offsetting and minimalist views already prefer the non-creation of an overall negative “−1” episode.

The remaining question is then whether the suffering, need, or frustration of some experience-moments can be positively counterbalanced or outweighed by the addition of subjectively perfect experience-moments elsewhere. Yet this is no different than the question, already considered in the main text, of whether there are positive counterparts to bads such as suffering (cf. points 3 and 4 in the non-creation section).

Therefore, this case adds nothing substantial to the question of whether non-creation is repugnant. A minimalist could simply respond that the non-creation of even a perfect paradise has no victims (all else equal), unlike the creation of an imperfect paradise in which the purportedly positive moments are allowed to override the unmet needs of the suffering moments (cf. DiGiovanni, 2021).

Aggregation revisited

In terms of tradeoffs and aggregation, “imperfect paradise” cases raised against minimalist views entail that a very large population of extremely happy lives that each contain a slight bad is worse than a “small hell” consisting of a much smaller population with maximally hellish lives. Yet the only difference between this case and the question of non-creation itself is that this case adds the Reverse Repugnant Conclusion (Figure 7), which is already implied by both offsetting and minimalist Archimedean views when those bads are compared against each other in isolation.

Consequently, this case arguably entails no additional element in favor of offsetting views over minimalist views in general. After all, the purported repugnance of the “imperfect paradise” case is already captured by either the repugnance of non-creation in particular, or by the repugnance of Archimedean aggregation such that we allow many tiny bads to amount to a worse problem than unbearable suffering.

Overall, the imperfect paradise cases seem to make no additional difference for the main question concerning the relative repugnance of offsetting versus minimalist views — regardless of one’s theory of aggregation — beyond what is already considered in the main text.

Appendix B: Rollercoaster lives and the Extended Very Repugnant Conclusion (XVRC)

(This section is entirely quoted from Budolfson and Spears, 2018, pp. 18–19, only annotated with some square brackets by me.)

Let us define an ε-change as a change that makes a difference in either one of these two ways:

  • ε-change: Let ε > 0 represent any small, positive quantity of well-being. An ε-change either:
    • increases the well-being of one person by ε, or
    • adds one new life of well-being ε.

One or more ε-changes can be part of an overall package of changes to a population, but to qualify as an ε-change, a change must be the only change that a particular person receives.

For example, an ε increase could involve slightly improving a tiny headache. One way to see that [an] ε increase could be very repugnant [on offsetting views] is to recall Portmore’s [1999] suggestion that ε lives in the restricted RC could be “roller coaster” lives, in which there is much that is wonderful, but also much terribly suffering [sic], such that the good ever-so-slightly outweighs the bad [according to offsetting views]. Here, one admitted possibility is that an ε-change could substantially increase the terrible suffering in a life, and also increase good components; such [an] ε-change is not the only possible ε-change, but it would have the consequence of increasing the total amount of suffering.

With this definition of ε-change in hand, we can now characterize the

  • Extended very repugnant conclusion (XVRC): For any:
    • Arbitrarily large number of arbitrarily high utility people: nh > 0, uh > 0,
    • Arbitrarily large number of arbitrarily negative utility people: nl ≥ 0, ul < 0, and
    • Arbitrarily small positive quantity of well-being: ε > 0,
  • There exists:
    • A number of ε-changes: nε, and
    • A (possibly empty) set of base population lives,
  • such that it is better to both add to the base population the negative-utility lives and cause nε ε-changes than to add the high-utility lives.

The XVRC extension from the VRC retains all of the repugnance of choosing many terrible lives over many wonderful lives for merely ε-benefits to other people. Moreover, if ε-changes are of the “roller coaster” form [which would be ruled out by minimalist views], they could increase deep suffering considerably beyond even the arbitrarily many [u < 0] lives, and in fact could require everyone in the chosen population to experience terrible suffering.


  1. ^

    For more on rollercoaster lives, see Appendix B.

  2. ^

    Budolfson & Spears (2018) is a precursor to Spears & Budolfson (2021); I discuss the former because it is more open-access than the latter.

  3. ^

    For an exact definition of the XVRC, see Appendix B. (For the main text, I will use more intuitive and less formalized descriptions of the XVRC, including extended variants of the XVRC.)

  4. ^

    In this essay, I do not focus on the relative plausibility of different views across the three categories of views on aggregation, because my main focus is on the relative plausibility of offsetting versus minimalist views in general, regardless of one’s theory of aggregation.

  5. ^

    See also Knutsson (2022) and Vinding (2022c).

  6. ^

    Thanks to Michael St. Jules for pointing out what can be seen as XVRCs for minimalist views.

  7. ^

    This is also known as the Mirrored Repugnant Conclusion, and is analogous to the much-discussed case of “Torture vs. dust specks”.

  8. ^

    Lexicographic preferences” seem to be named after the logic of alphabetical ordering. Thus, value entities with top priority are prioritized first regardless of how many other value entities there are in the “queue”.

  9. ^

    A formalism of “higher values” over “lower values” is considered in e.g. Carlson, 2007; Thomas, 2018; Nebel, 2022.

  10. ^

    More concretely, the breaking point may be equated with a supposed point at which the suffering becomes unconsentable (Tomasik, 2015). For purely minimalist views, one could imagine this to be suffering so bad that an altruistic agent cannot consent to it even for preventing similar suffering for others.

  11. ^

    A way to make each of these lexical XVRCs entail the “arbitrarily small difference” (ε) element of the original XVRC is to make them probabilistic, so that the lexically bad state in Figure 8, and the lexically good states in Figure 9, would happen only with probability ε (cf. Budolfson & Spears, 2018, pp. 12–14).

  12. ^

    Examples of non-sharp lexical views are presented in Vinding (2020a2022a) and Knutsson (2021a).

  13. ^

    At the same time, inter-intensity comparisons that take place entirely within this range could follow some Archimedean theory of aggregation. Note also that the “non-sharp” lexical XVRCs below are illustrated using only a single range, even though such views could just as well entail multiple different ranges. (Many interesting details about lexical views are best set aside here, because they apply to both minimalist and offsetting views, and hence those details have limited relevance for my goal of comparing these two classes of views.)

  14. ^

    For more on how people with minimalist intuitions may conceptualize pleasure and other purportedly positive goods, I recommend Knutsson (2022), Vinding (2022c), Gloor (2017, sec. 2.1), and Sherman (2017, pp. 103–107). For more on why minimalist consequentialist views need not have as counterintuitive practical implications as they are often claimed to have, see the previous parts of the present series.

  15. ^

    After all, it seems plausible to prioritize the reduction of certainly unbearable suffering over certainly bearable suffering (and over the creation of non-relieving goods) in theory. Additionally, such a priority is, at the practical level, quite compatible with an intuitive and continuous view of aggregation based on the expected amount of lexically bad states that one’s decisions may influence (Vinding, 2022b, 2022e).

    Thus, ‘expectational lexical minimalism’ need not be implausible in theory nor in practice, because in practice we always have nontrivial uncertainty about when and where an instance of suffering becomes unbearable. Consequently, we should still be sensitive to variations in the intensity and quantity of suffering-moments. Yet we need not necessarily formalize any part of our decision-making process as a performance of Archimedean aggregation over tiny intrinsic disvalue, as opposed to thinking in terms of continuous probabilities, and expected amounts, of lexically bad suffering.

  16. ^

    Additionally, our evaluation may be affected by factors such as what we would like to witness in the world (e.g. inspiring, beautiful, or epic lives), or by our feeling that even a theoretical acceptance of non-creation would have some undesirable implications for our lives. These, too, are subtle ways of breaking the ‘all else equal’ assumption. After all, our evaluation of the prospective lives (for their own sake) should be unaffected by the positive roles that the creation or existence of those lives could have for others, including for us.

  17. ^

    If the choice starts to feel different when we exclude these factors, this may suggest that the initial framings did indeed evoke factors whose influence was supposed to be ruled out. And this would not be surprising, as our practical intuitions are arguably not adapted to track only the subjective contents of lives, but also (and perhaps even mostly) their overall effects on others. Notably, even the standard question of whether it is “good to create happy people” may still cause a bias in favor of creation, because it may strongly evoke the relational value that these happy, intuitively prosocial people would contribute via being good friends, partners, caregivers, citizens, etc. — value whose mental exclusion may be “easier thought than done”.

  18. ^

    A key point here is to not confuse better states with “intrinsically positive states”. After all, it appears that our seemingly positive states can be understood as merely better states along a continuum that ranges from states of unbearable torment to states in which we would be perfectly tranquil or undisturbed (cf. Gloor, 2017; Knutsson, 2022). Additionally, one may argue that “intrinsically positive states” could only be reliably identified from a (perhaps very rare) flawless state to begin with, and it appears that there are plausible explanations for why we might commonly think of less troubled states as intrinsically positive.

  19. ^

    It is worth noting that Singer in his article (1980) wrote favorably of combining Preference Utilitarianism and Classical Utilitarianism. Moreover, Singer appears to have moved further toward Classical Utilitarianism in recent years (see e.g. Lazari-Radek & Singer, 2017, ch. 3).

  20. ^

    Additionally, a practical point to remember is that the (dis)satisfaction of any given preference usually has implications for the (dis)satisfaction of other preferences (contra the ‘all else equal’ assumption). Consequently, both offsetting and minimalist views are compatible with practical reasons to strongly oppose painless killing. Yet, all else equal, offsetting preference-based views seem to have the arguably implausible implication that an outcome can always be improved — and frustrated preferences outweighed — by creating (or inducing in existing preferrers) new satisfied preferences, such as an intense desire for something that is already the case (Fehige, 1998, pp. 514–515).

  21. ^

    The same point applies to the original Repugnant Conclusion (RC). Many people think that the RC is not unacceptable (Zuber et al., 2021). Yet its repugnance arguably differs greatly depending on whether we allow the population of lives that are “barely worth living” to consist of rollercoaster lives (or intrapersonal VRC lives), compared to if they do not suffer at all. Minimalist views may agree that the RC is not repugnant in the suffering-free variant, but they would object to its rollercoaster and intrapersonal VRC variants.

  22. ^

    Of course, one may still find the Archimedean minimalist XVRCs quite repugnant (even if less so than the VRC). Yet the remaining repugnant element of “​​Making seemingly trivial changes at the price of unbearable suffering” is avoided by the arguably less repugnant lexical views that give priority to the reduction of lexically bad states.

  23. ^

    The quoted part suggests that the authors do not, in fact, attribute repugnance only to the “trivial changes” source of repugnance, but also to the additional intrapersonal suffering entailed by the rollercoaster lives. And if the arbitrary increase of unbearable states (for the sake of additional, unneeded non-relieving goods) is repugnant intrapersonally, then it is presumably at least equally repugnant interpersonally.

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