Summary

Pains vary in their severity and duration. When one pain is longer-lasting but less intense than a second pain, the most straightforward way to compare how much disutility they cause is to multiply how much longer by how much less severe the first pain is than the second pain. The present report investigates whether this mathematical approach (a) is sufficient for making cause prioritization decisions, (b) requires some amendments, or (c) is fundamentally flawed.
Many writers believe that the moral badness of pain scales non-linearly as its severity increases. Some even believe that unbearable pain is always more urgent to relieve than bearable pain, no matter how much briefer it is. It is possible to amend the mathematical approach to account for the former possibility. Accommodating the latter possibility requires ignoring duration when comparing pain above a certain severity threshold to pain below that threshold.
So long as unbearable pain does not receive infinite weight in cause prioritization, long-lasting pain can matter more than severe pain when (a) the duration difference is very large, (b) the long-lasting pain is sufficiently severe to render most moments more bad than good, or (c) the long-lasting pain is severe enough to chronically prevent pleasure.
Health economics is the only field to our knowledge that appears to have an explicit research program evaluating how individuals trade off the severity and duration of pain. Incidentally germane studies from other fields are difficult to find efficiently.
- Extant evidence suggests interactions between severity and duration on preferences.
- Heterogeneity in how people weigh severity and duration is a potentially large validity threat to discovering an appropriate mathematical formulation from aggregate data
All alternatives or refinements to the mathematical approach are based on intuitions that are reasonable but are not incorrigible. There are cognitive and behavioral factors that could bias people towards overvaluing or undervaluing either duration or severity.

Epistemic Status

This report was the product of about six weeks of research, and as such may overlook relevant research or philosophical considerations that we did not find or have time to consider. Later on, we spent about a week’s worth of work revising the report in light of new comments but did not add any new sections.

A mathematical calculus for pain?

How should effective altruists decide whether to prioritize interventions that alleviate severe but relatively brief suffering or instead those that alleviate longer-lasting but less severe suffering? Different authors appear to weigh the severity and duration in diametrically opposed ways. In their report on the welfare of broiler chickens in industrial farms, Schuck-Paim et al. (2022) write that “preventing or alleviating the most extreme forms of pain and suffering is an ethical priority, of greater urgency than alleviating less severe states of suffering, regardless of how long they last” (Chapter 8, p. 39). Thus, they endorse focusing on eliminating practices that induce extreme pain, such as ineffective stunning before slaughter, over mitigating chronic issues that are less severe, such as lameness. For others, the duration of pain is more important than its severity. Norwood and Lusk’s (2011) review of welfare issues for farmed animals downplays slaughter: “In this chapter, we tended to focus primarily on the everyday life of farm animals. Animal advocacy groups will often mention a myriad other issues such as the transportation and slaughter of livestock. These issues, while important, are temporary experiences for the animals” (chapter 5, p. 69). Blanton (2021) defends raising beef cattle on the grounds that most cattle enjoy grazing the pasture. While not dismissing welfare issues in feedlots, he argues “the time spent in pens, feedlots, and rendering plants…accounts for a small part of cattle’s lives and in many cases practically none at all.”

One could attempt to circumvent the debate by using a mathematical approach to combine severity and duration into a single index. Jeremy Bentham, the founder of modern utilitarianism, suggested that we can multiply units of intensity of pleasure or pain by their duration to determine their utility (Mitchell, 1918, p 165). For example, if one pain is eight times more severe than another and lasts twice as long, then the first pain is 16 times as bad. Hungerford (2018) illustrates how to use the mathematical approach to compare the badness of a severe pain and a long-lasting pain: “Say, for example, that shackle to slaughter, a chicken’s death takes 30 seconds. The rest of her life is 135,360 times that length. That means, according to this argument, that for slaughter to be a worthy focus, a chicken’s death must be 135,360 times worse than her life on the farm.”

Pain definitions

Understanding how to compare severity and duration is relevant to the aggregation of any valanced state. However, the present investigation focuses primarily on pain. There is no guarantee that the relationship between severity and duration for pain generalizes to other negative affective states. For simplicity, however, the words “pain” and “suffering” will be used interchangeably in this report, and conclusions regarding specific types of physical pain will be tentatively assumed to apply to other types of physical pain and other sources of negative valence.

Pain is defined by the International Association for the Study of Pain as, “an unpleasant sensory and emotional experience associated with, or resembling that associated with, actual or potential tissue damage.” Acute pains are generally caused by the stimulation of specialized sensory receptors in the peripheral nervous system known as nociceptors. Nociceptors can respond to high temperatures, low temperatures, pressure, and to chemicals including those released during tissue damage. Each of these different ways of causing pain has unique sensory qualities.

Ratings of pain intensity do not perfectly track pain’s unpleasantness (Price, 2002). Researchers have shown that stimulus intensity can be correlated both with ratings of intensity and unpleasantness, but the two have different power functions. In particular, the unpleasantness of pain increases more slowly at lower stimulus intensity levels, but increases at a greater rate at higher levels of stimulus intensity. For purposes of comparing the moral impact of severity and duration, it is the unpleasantness of pain that matters. The term “severity” will always be used in the present report to refer to unpleasantness rather than stimulus intensity.

When it comes to chronic pain, definitions become a little more difficult. Chronic pain is often defined in medical practice as pain that lasts for more than three months. Clearly, this is a heuristic designed to capture general differences between short-term pains and long-term pains; there is no magic transformation that occurs to pains at the 3-month mark. The distinction that the definition is supposed to convey is that while “normal” pains are adaptive and provide a protective function for organisms, chronic pains persist even after they are no longer serving a protective function. This can be due to the peripheral nervous system continuing to send pain signals even after tissue damage has healed or due to connections between brain regions that continue to signal pain.

The neurophysiology of chronic pain turns out to be different from that of acute pains. For example, Hashmi et al. (2013) write that as pain transitions to chronic pain it tends to involve more of the emotional circuits in the brain. And so-called neural signatures of pain designed to assess acute pains do not correctly identify chronic pains (Davis et al., 2017, pgs. 629-630). The fact that there may be differences in how chronic pains and acute pains are expressed in brains could have implications for their impacts on the welfare of individuals. But so long as the unpleasantness of chronic pains and acute pains can be measured along the same scale, it should be possible to compare them.

Finally, the current report treats long-lasting pains generically, despite the fact that different sources of long-lasting pain have different etiologies. While the term “chronic pain” is typically used to refer only to the abovementioned internal changes, ongoing inflammation is also a source of long-lasting pain, as is an environment that contains painful stimuli that are impossible to avoid (Bennett, 2012). Accordingly, this report uses the terms “chronic” and “long-lasting” interchangeably.

Reasons to Prioritize Severity

Questions about Bentham’s approach for aggregating severity and duration have been raised as far back as his intellectual successor John Stuart Mill. Though Mill’s discussion was focused on pleasure rather than pain, he responded to contemporary objections to utilitarianism by introducing the idea that there might be qualitative differences between different types of pleasures which preclude the possibility of merely “summing up” lesser pleasures to the point where they outweigh qualitatively superior pleasures (Mill, 1861/2006). In particular, Mill was responding to the claim that utilitarianism should be regarded as “the doctrine of swine” because pigs could experience as much pleasure as humans. A recent formulation of the same objection can be found in Roger Crisp’s (2006, pgs. 630-631) thought experiment Haydn and the Oyster:

You are a soul in heaven waiting to be allocated a life on Earth. It is late Friday afternoon, and you watch anxiously as the supply of available lives dwindles. When your turn comes, the angel in charge offers you a choice between two lives, that of the composer Joseph Haydn and that of an oyster. Besides composing some wonderful music and influencing the evolution of the symphony, Haydn will meet with success and honour in his own lifetime, be cheerful and popular, travel and gain much enjoyment from field sports. The oyster’s life is far less exciting. Though this is a rather sophisticated oyster, its life will consist only of mild sensual pleasure, rather like that experienced by humans when floating very drunk in a warm bath. When you request the life of Haydn, the angel sighs, ‘I’ll never get rid of this oyster life. It’s been hanging around for ages. Look, I’ll offer you a special deal. Haydn will die at the age of seventy-seven. But I’ll make the oyster live as long as you like’.

The upshot of this thought experiment is supposed to be as follows: the utilitarian should endorse the life of the oyster, since the duration of pleasure would eventually ensure that the oyster’s pleasure outweighs that of Haydn’s. However, the assumption is that most people would reject this tradeoff. Therefore, there must be something wrong with the standard hedonistic utilitarian calculus.

Mill predated this precise formulation by several centuries, but in response to this type of objection, he argued that there are in fact qualitative differences between pleasures, such that if certain conditions are met, “we are justified in ascribing to the preferred enjoyment a superiority in quality, so far outweighing quantity as to render it, in comparison, of small account” (Mill, 1861/2006, Chapter 2). Mill is proposing a radical discontinuity (Griffin, 1986, p. 85) between pleasures such that enough of pleasure A can outweigh any amount of pleasure B.

Several scholars have proposed something similar when it comes to instances of extreme suffering. A central idea of suffering-focused ethics is that no amount of pleasure can compensate for suffering. However, many of these same scholars also endorse the claim that no amount of minor suffering can be equivalent to instances of extreme suffering. Vinding (2020), for example, writes the following: “I claim there is a lexical difference between the moral disvalue of these two: a single instance of such extreme suffering is worse and more important to prevent than arbitrarily many instances of such mild suffering” (p. 88). And Leighton (2011) writes, “One person suffering intensely, such as at the hands of a torturer, is qualitatively different and … incomparably worse than a million people suffering from a mild hangover” (p. 85).

Giving infinite weight to severe harms would require going beyond a simple mathematical approach to computing moral badness. Also, a practical danger of giving infinite weight to very severe harms is that it would reduce diversification in cause prioritization. Although one could justify diversification among the plausible candidates for the most severe pain when it is not clear which is the most severe, the much more numerous causes of clearly less intense pain will go entirely neglected.

A radical discontinuity, however, is only one possible way to accommodate intuitions about the relationship between extreme and moderate pains. For instance, if the most severe pains receive finite weights, then at worst they will receive too little attention but will not be neglected entirely. Moreover, it could be that, beyond a certain stimulus intensity, pain severity scales so quickly that in practice severe pains are worse than even extremely long-lasting mild pains. This idea was captured in a quote from Jamie Mayerfeld (1999, pgs. 134-5) who argues that:

as suffering increases in intensity, the urgency of preventing it rises at a faster rate than its intensity. If I think about suffering of a serious, fairly intense kind, and then think about another kind of suffering that is four times more intense, I think that it would be better to experience far more than four hours of the less intense suffering than to experience just one hour of the more intense suffering. The less intense suffering is preferable to the more intense suffering even though the total quantity involved (intensity multiplied by duration) is greater.

Reasons to Prioritize Duration

One way to justify prioritizing long-lasting pain over severe pain would be if mild pain gradually gets much worse because it goes unaddressed, such as when hunger becomes starvation. A second way is if the awareness that chronic suffering will remain unceasing makes it seem unbearable, thereby increasing its severity (Vinding, 2020, p. 72). A third possibility is if the difference in duration was larger than the difference in severity.

The present report does not elaborate on these cases further because they do not require any refinement of estimating moral badness by multiplying severity and duration. Instead, this section focuses on two ways in which long-lasting pain of sufficient severity could chronically impede positive states. First, pain can be severe enough to make any given moment of that pain more bad than good. If that pain is long-lasting, then it becomes possible that life as a whole will be hedonically net-negative. In this case, prioritizing long-lasting pain could make sense because severe but brief pain does not necessarily negate the totality of an individual’s net-positive experiences.

Second, even if long-lasting pain is not severe enough to render moments net-negative, they could be severe enough to erode the capacity for positive experience. Insofar as intense pain evolved to prevent individuals from engaging in unnecessary activities that would exacerbate an injury, positive experiences are typically the first to be deferred. Indeed, Alonso and Schuck-Paim (2021) define disabling pain partly in terms of its effect on pleasure: “Most forms of functioning or enjoyment are prevented as the direct result of pain. Symptoms are continuously distressing. Individuals affected often substantially reduce activity levels and refrain from moving” (p. 2). On simple hedonistic views, net-positive moments are the only experiences that make existence morally better than non-existence, since non-existence is entirely devoid of suffering; they likely also play a large role in making life worth living on many other theories of value (though only some and not all suffering-focused views). Thus, net-positive experiences are necessary to counterbalance the badness of net-negative experiences. This point has been made frequently in the context of the problems faced by individuals with brief lives. For instance, Ng (1995, pgs. 270-271) suggests that wild animals that die before getting to enjoy mating probably do not have lives worth living. But an analogous claim applies to long lives: Long-lasting pain can limit how many pleasures individuals can pursue, making it possible that net-negative experiences will predominate. For example, broiler breeders are kept consistently very hungry, causing them to postpone positive activities (Nielsen et al., 2011). In humans, chronic fatigue syndrome can make carrying on a social life and performing previously enjoyable activites impossible (Boulazreg & Rokach, 2020), potentially explaining part of the condition’s association with death by suicide (Roberts et al., 2016). In contrast, very mild chronic pain, such as from a slightly stiff neck, probably does not ruin any pleasurable activities, and thus would not have moral weight over and beyond the sum of its parts.

Most humans’ behavior seems more consistent with trying to balance risk and reward rather than avoiding extreme suffering. Huemer (2008, pgs. 909-910) argues that small risks of horrible outcomes are tolerable because forgone gains accumulate over time when safety is adopted as a blanket policy. He makes this point about avoiding death, but the same reasoning applies to extreme pain:

Consider the common intuition that a single death is worse than any number of mild headaches. If this view is correct, it seems that a single death must also be worse than any amount of inconvenience…this suggests that we should greatly lower the national speed limit, since doing so would save some number of lives, with (only) a great cost in convenience. Yet few support drastically lowering the speed limit. Indeed, one could imagine a great many changes in our society that would save at least one life at some cost in convenience, entertainment, or other similarly ‘minor’ values. The result of implementing all of these changes would be a society that few if any would want to live in, in which nearly all of life’s pleasures had been drained.

Even chronic pain that does not quite spoil individual moments can nevertheless have detrimental effects on how much pleasure individuals will experience. Although a sub-optimal experience at any one moment is no tragedy, a markedly reduced ability to experience pleasure can become unacceptable when accumulated over time.

The upshot of long-lasting pain taking on greater significance when it rises above a certain severity threshold is that comparing the badness of two pains by multiplying their severity and duration will be insufficient. Instead, we must represent the fact that duration has less impact on moral badness when severity is low than it does when severity is high.

Extant Empirical Evidence

So far the cases for prioritizing severe pain over long-lasting pain and vice versa have depended more on philosophical intuition than empirical evidence. However, one might worry that philosophers’ intuitions are unreliable guides to value relative to the unarticulated collective wisdom that ordinary people have gained through experience. Accordingly, a complementary approach to learning how duration and severity interact to produce moral badness involves conducting large empirical studies of laypeople’s preferences. Similarly, we could use behavioral experiments to try to elicit the revealed preferences of nonhuman animals.

Human psychology and animal welfare science

Ideal direct evidence includes experiments in which subjects endure either a longer, mild pain or a shorter, intense pain. After four weeks of searching for direct evidence from the animal welfare science and human psychology literature, it seems likely that such evidence either does not exist or is difficult to find. Neither of these possibilities would be entirely surprising, given that most behavioral scientists are not occupied with the cause prioritization decisions under consideration here.

One animal welfare science question that is sometimes framed as a trade-off between severity and duration is how quickly to stun farmed animals using carbon dioxide. For instance, Shuck-Paim et al. (2022) writes, “The greatest challenge with the use of CO2 stunning is finding a good balance between the time to the onset of unconsciousness and the amount of distress for [broiler chickens]; while the faster provisioning of high concentrations of CO2 will lead to loss of consciousness more swiftly, it can be highly aversive” (Chapter 8, p. 22; see an identical framing in Gerritzen et al., 2013, p. 42). The consensus among animal advocates appears to be that slowly increasing the concentration of C02 prevents all severe pain with only a small increase in time to unconsciousness (e.g., Eyes on Animals, 2019, pgs. 13-14). However, this conclusion was not based on observing which type of stunning chickens would rather endure.

Health economics

Health economists directly compare the badness of alternative health outcomes. For instance, the so-called disability weights used to compute disability-adjusted life years are calculated by having people judge whether someone who has a given health state is more or less healthy than somebody else who has a second health state. Health states that are more often ranked as causing a greater loss of health receive larger weights. However, by design, the duration of both problems is assumed to be the same. Therefore, even though different health states have different typical durations in everyday life, the disability weights represent the relative severity of the health states only. Similarly, quality-adjusted life years, often elicited by having people make trade-offs between longer periods in a given health state and shorter periods free of that health state, implicitly regard severity and duration as of equal importance.

The most direct evidence that severity and duration interact in producing moral badness comes from studies finding that there is a maximum duration that people are willing to endure severe health states, beyond which they would rather be dead but before which they would rather remain alive (Stalmeier et al., 2007; Scalone et al. (2015). These results could be taken to show that respondents interpret severe health states as an unceasing stream of net-negative moments, which is worse than just dying quickly and painlessly. Yet, respondents who indicate a maximum duration of endurable suffering usually prefer at least a short certain duration of suffering over immediate death. Plus, Craig et al. (2018) found that respondents regarded moderately severe states as better than being dead, even though they have decreasing value beyond a year.

An alternative way to interpret maximum duration of endurability blurs the distinction between severity and duration—viz., it could be that severe illness begins to feel unbearable simply because it is unceasing. For example, one respondent in Gudex and Dolan (1995) said of more severe states, “you would not mind them for a month but 10 years wouldn’t be bearable for you or your family” (p. 6). The accuracy of this assumption is debatable. To wit, Myers et al. (2003) found that those living a given health state longer did not grade it as worse than patients with a more recent onset, though this may be because they did not have a large sample of patients with highly severe health states.

The main ambiguity in this literature is preference heterogeneity: Even if researchers discover a functional form that performs well in predicting how severity and duration interact to produce preferences at the aggregate level, there is no guarantee it will at the individual level (Craig et al., 2018). Jonker and Norman (2022) found that the majority of respondents in a discrete choice experiment made choices as if they add duration and severity together to estimate aversiveness, whereas only a minority act as if they multiply them. Assuming this finding is not an artifact of the study design, it could imply that no single correct mathematical model of how to combine severity and duration into a moral badness judgment can be readily inferred from the general population.

Methodological Challenges

It was much easier to find research that speaks to the barriers of empirically determining whether severe pain is more or less urgent than long-lasting pain. Indeed, it seems possible that these barriers help explain why there is so little germane research. In this section, we describe these barriers and suggest potential solutions.

Uninformed preferences and distorted preferences

There was one topic within health economics that did not speak to the relative importance of severe pain and long-lasting pain, but did raise questions about whose judgments matter most: The discrepancies between general populations and patient populations in their valuations of health states. The general population tends to regard health states that severely impair quality of life as worse–sometimes worse than being dead!– than do the patients who experience those health states (Bernfort et al., 2018; Schneider, 2021). The difference in valuation gets larger as health states get more severe (McPherson et al., 2004). This might suggest that intuitions that people set the bar for what is unbearable too low, consistent with the hypothesized role of affective forecasting errors in health valuation studies (Walasek et al., 2019). If so, then even if one grants that unbearable pain does deserve special attention, one would want to exercise humility when judging that a certain experience causes unbearable suffering. An alternative (but not mutually exclusive) explanation is that the general population overestimates how much health states erode the capacity for positive experience. In particular, the general population may not realize the extent to which people with even severe physical limitations can find new activities to replace ones they can no longer do, hone their skills in domains where they can still perform, and adopt new but equally rewarding goals that they can still achieve (Helgesson et al., 2020, p. 1471). If so, then there is a risk of prioritizing the relief of chronic pains on a faulty assumption that they have squelched all opportunities for positive experiences. It is an open question whether uninformed preferences on net bias cause prioritization towards severe or long-lasting pain.

If personal experience with a pain is requisite to accurately evaluating it, researchers can prioritize studying people who have actually experienced health states that vary in terms of their severity and duration, although recruiting such individuals will likely prove expensive and inefficient. For non-human animals the issue is less tractable because some of their pains that are of the greatest concern result in death (e.g., live-shackle slaughter). It is worth noting, however, that whether to trust general or patient populations is a source of controversy. Some researchers worry that patients in severe health states are in denial about how poorly their lives are going or no longer recall what a fully healthy life was like (Helgesson et al., 2020, pgs. 1474-1478). It might be that there is no privileged source of information on severity, and that it can only be inferred indirectly by triangulating the views of different groups with biases that together cancel each other out.

Heat of the moment

The most straightforward way to test whether individuals are more averse to severe pain or long-lasting pain would be to force them to choose between the two. However, interpreting avoidance behavior as revealing the worst choice in terms of overall welfare impact is complicated by the fact that pain severity may have evolved to signal how much priority should be devoted to current welfare threats right now (Walter & Williams, 2019). Although organisms possess mechanisms such as hypersensitivity to orient them to long-term threats that were recurrent in their ancestral environments, the novel long-term threats that modern humans and farmed animals face are not likely to modulate pain.

If the severity of short-term pain plays a larger role in valuation than the totality of consequences of each outcome, then preferences could be biased towards avoiding severe pain even if the long-lasting pain produces worse consequences, all things considered. For example, Tomasik (2013) introspects on his own preferences to prioritize the severity of pain: “I think small amounts of very bad suffering are far more serious than lots of mild suffering: We’re willing to trade mild suffering for mild pleasure even when enduring the mild suffering, but if the suffering becomes intense enough, we might not accept it in return for any amount of pleasure, at least not in the heat of the moment” (emphasis added). But what an individual wants in the heat of the moment may be determined not by the long-term consequences for welfare, but instead how aversive an outcome will be at any one moment. Put another way, individuals may have limited volition to choose outcomes that result in severe pain. For instance, only about 30 percent of those who have ever seriously considered ending their own lives ever attempt to do so (Schreiber et al. 2021). One plausible reason is that the pain tolerance necessary to be capable of suicidal behavior is distinct from the desire to end life (May & Victor, 2018). Joiner (2010, p. 6, emphases added) writes:

Self-preservation is a powerful enough instinct that few overcome it by force of will. The few who can have developed a fearlessness of pain and death…People get used to such things by having repeatedly experienced them, often through previous self-injury, but other painful experiences serve too…time and time again [there are] people who report that they genuinely desired to die by suicide, but that their bodies would not allow it.

For those who can more easily endure acute suffering, there is a stronger association between suicidal ideation and suicide attempt (Anestis & Capron, 2016). And the more intense suicidal ideation is at its worst point, the more likely a suicide attempt will occur (Law et al., 2016). That is, short-term intense pain of a suicide attempt becomes less of a deterrent to enacting a preference to die the worse the chronic suffering of living is.

One way to mitigate (but probably not eliminate) the influence of volition on preferences would be to ask individuals whether they would rather endure severe or long-lasting pain without having to initiate and maintain that option themselves. For instance, a conditional place preference test (e.g., Adcock & Tucker, 2020) would enable subjects to express their preference, at which point the experimenters could administer the pain.

Duration Neglect

An alternative way to avoid reliance on volition, at least for studies of humans, would be to rely on retrospective evaluations of experiences that vary in duration and severity. However, research on duration neglect suggests that severity is more salient when people recall past experiences. Most famous in demonstrating this are experiments involving the peak-end effect. In these experiments, subjects are asked to undergo painful procedures such as a colonoscopy or holding one’s hand in cold water. In one condition, the painful procedure would be cut off abruptly but relatively early. In the other condition, the painful procedure would continue past the point where it was cut off in the other condition, gradually decreasing but still rated as painful by subjects. Surprisingly, however, when asked to evaluate their experiences retrospectively, subjects preferred the condition where they had more pain, that is pain that continued beyond the cutoff. They preferred the condition with a greater area under the pain curve.

A broad lesson of this research program was that the severity of pain at its peak and at the end of the experience tend to be more salient to subjects than the duration of the pain. One way to interpret this “duration neglect” is to regard the near-exclusive focus on severity as a bias preventing preferences from mapping onto well-being, which should boil down to severity times duration. Daniel Kahneman, who was involved in the initial experiments demonstrating this effect, later argued that we should distinguish “decision utility” (the factors that people value when making decisions) from “experienced utility” (the balance of pleasure and pain) and suggested that the latter was more important (Kahneman et al., 1997).

Imagination Failures

Many people imagine severe pain as feeling unbearable, whereas long-lasting pain does not seem to make the same impression. Although this could be evidence that duration matters less than severity, it could also be that humans have a harder time imagining very long durations because, unlike severe pains, it is impossible to mentally simulate long-lasting pain in a short period of time (Liersch & McKenzie, 2009, p. 304). This would presumably not be a major issue if people could cognitively appreciate just how much total pain would result from iterating a shorter duration of pain a large number of times. However, humans suffer from scope neglect in many domains, whereby very large numbers are not processed much differently from merely large numbers. Huemer (2008, p. 915) argues that scope neglect is responsible for the devaluation of long durations of pleasure:

Stuart Rachels and Larry Temkin hold that some intense pleasures are ‘lexically better than’ any mild pleasure, meaning that no amount of mild pleasure is as good as a given, short duration of the intense pleasure…people’s intuitions seem to shift when the length of the ecstatic experience is shortened: a mere second of ecstasy seems inferior to a thousand years of mild pleasure. This can be explained by a particular error theory: we have difficulty grasping very long time periods. The duration of a mild pleasure that is really superior to fifty years of ecstasy is too long for us to adequately grasp; hence, we fail to appreciate its superiority. To alleviate this problem, we may replace the fifty years of ecstasy with a very short (but still clearly graspable) period of ecstasy—say, one second—and then ask whether we can imagine a superior experience consisting of protracted mild pleasure. When we thus change the example to improve the reliability of our intuition, the ecstatic experience no longer seems categorically better.

Scope neglect could explain away the special status that some writers accord to unbearable pain. Tomasik (2019) acknowledges that it might explain his intuition that a day in Hell would be worse than any amount of time in Heaven. A standard strategy to increase scope sensitivity is to increase the vividness of the stimuli that accompanies the larger option (Dickert et al., 2015). In the present context, this could involve specifying the myriad life events that long-lasting pain would impact, its knock-on effects that worsen the severity of pain, and so on.

Ethical constraints

Administering pain in research settings that is severe enough to match those experienced by individuals in real life will understandably face roadblocks from ethical review boards. But using less intense pain makes the generalizability of subjects’ preference for severe pain over long-lasting pain questionable, especially if individuals increase the weight attached to severity as it increases. In contrast, if individuals apply a linear weighting to how severity relates to moral badness, then findings from comparisons among less severe pains should generalize to comparisons among more severe pains so long as the ratio of the difference in severity remains the same.

Severity: Cardinal or ordinal?

A final issue is whether the mathematical approach is doomed from the start because it assumes that severity is cardinal and that its units can be known. One reason to be optimistic about these assumptions is that researchers have ostensibly developed ratio scales of pain severity for at least low-to-moderate levels of stimulus intensity (e.g., Price et al., 1983), although we did not vet these efforts carefully. On the other hand, a general framework for assigning any given pain to a meaningful unit seems like a far-off goal. Browning (2022) laments the fact that most existing farmed animal welfare scoring systems are on an ordinal scale (pgs. 10-11), and that ostensibly cardinal systems do not obviously meet evidential standards for ratio measurement (p. 14).

It may be that the entire range of pain severity can be put on a ratio scale, and all it will take to do so is a dedicated research effort. An alternative possibility, however, is that pain is itself an ordinal trait. Bentham worried that it was not possible to quantitatively compare qualitatively different pleasures and pains (Mitchell, 1912, pgs. 168-172). Collingwood (1933, pgs. 72-73) was skeptical that even different gradations of a single type of pain qualify as cardinal:

As I move my hand nearer to the fire, I feel it grow hotter; but every increase in the heat I feel is also a change in the kind of feeling I experience; from a faint warmth through a decided warmth it passes to a definite heat, first pleasant, then dully painful, then sharply painful; the heat at one degree soothes me, at another excites me, at another torments me. I can detect as many differences in kind as I can detect differences in degree; and these are not two sets of differences but one single set. I can call them differences in degree if I like, but I am using the word in a special sense, a sense in which differences of degree not merely entail, but actually are, differences of kind.

The ordinality of severity would rule out a simple mathematical approach entirely. It is consistent with but does not entail that some pains are so severe that they outweigh all lesser pains regardless of duration. If severity is in reality cardinal but scientists have just yet to measure it on a ratio scale, then adopting a mathematical approach to pain severity is no more problematic than the myriad other ordinal scales that psychologists use to approximate an underlying continuum (Markus & Borsboom, 2013, chapters 2-4).

Future Directions

The abovementioned suggestions for how to overcome the methodological barriers in the last section are only based on a few weeks of thinking them through. It seems likely that subject matter expertise in pain in experimental settings is necessary to identify the most innovative solutions, especially for studies of non-human animals. To facilitate this effort, we are planning on hosting a workshop in which animal welfare scientists, pain scientists, and philosophers will attempt to develop new methodologies to test whether farmed animals and laboratory animals treat the severity or duration of pain differently when making aversiveness judgments.

Acknowledgements

This research is a project of Rethink Priorities. It was written by William McAuliffe and Adam Shriver. Thanks to David Moss, Jason Schukraft, Marcus A. Davis, and Travis Timmerman for helpful feedback on earlier versions of this report. A special thanks to Michael St. Jules, who provided comments on earlier drafts and quality control on the penultimate draft. If you like our work, please consider subscribing to our newsletter. You can explore our completed public work here.

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