Person-affecting neutral-range utilitarianism


In many examples, such as procreation, animal farming, climate change and catastrophic risks, our choices not only influence the welfare of other sentient beings in the future, but also influence their very existence. To determine what is the best outcome in such examples, we need a good population ethical theory. However, most population ethical theories face highly counter-intuitive implications, such as the very repugnant and sadistic conclusions. Forward-looking, person-affecting neutral-range utilitarianism is presented as a new population ethical theory that avoids the most counter-intuitive implications in population ethics. The theory says that we should choose the state or outcome that maximizes the sum of individual utilities (lifetime welfares), excluding the utilities of contingent people (who do not exist in all eligible states) that lie in a neutral range and subtracting the size of the neutral range from the utilities of all contingent people who have utilities above the neutral range. The theory includes a deontological ‘forward-looking’ constraint to exclude states from the choice set of eligible states that once chosen will become dominated by other eligible states. People can democratically choose the size of the neutral range, based on their population ethical preferences. This theory is a combination of critical-range utilitarianism and asymmetric person-affecting utilitarianism. It is complete (all pairs of states are mutually comparable), transitive (no cycles of preferences occur) and has a structural symmetry (positive and negative utilities are treated in the same way) that can become broken when people determine what counts as their own zero utility level.


Is it good to bring into existence a person who is extremely miserable? Is it good to drastically reduce the welfare of happy people by adding a huge population of people who have lives barely worth living? Intuitively, the answers are clear: definitely not! The first is sadistic, the second is repugnant. However, these sadistic and repugnant conclusions often appear in population ethics, the study of what are the best choices when populations are variable and choices determine the existence or non-existence of individuals.

This article presents a new population ethical theory that is probably the most simple theory that avoids the most serious counter-intuitive sadistic and repugnant conclusions. The theory lies between total utilitarianism (choose the state that maximizes the sum of utilities of everyone who exists in that state) and person-affecting utilitarianism (choose the state that maximizes the sum of utilities of everyone who exists in all available states). This theory can be called forward-looking, person-affecting, neutral-range utilitarianism.

The sadistic and repugnant conclusions

Suppose every sentient being has a lifetime welfare or utility which can be represented by a real number. If the number is negative, the individual has a life not worth living, i.e. a life consisting of mostly negative experiences. To find the optimal state, a utilitarian theory aggregates the individual utilities of all sentient beings. The state that has the largest aggregate utility is the best state that should be chosen.

There are different ways to aggregate individual utilities: we can take the sum, the average or another aggregation function of the individual utilities. What most of such aggregate utility functions have in common, is that they have an asymptotic critical level: when there is a very large background population of individuals whose utility is (almost) constant, the aggregate utility can be expressed as the sum of everyone’s relative utility. This relative utility is the individual utility minus a constant critical level. If the individual utility is higher than this critical level, the individual positively contributes to the aggregate utility.

The presence of at least one asymptotic critical level means that the aggregate utility theory faces a trilemma, as can be seen in the figure below. If the asymptotic critical level is negative, the theory implies a very sadistic conclusion: making an extremely happy person extremely miserable and bringing into existence a very large population of miserable people would be good. If the critical level is zero or positive but small, we get the very repugnant conclusion: making an extremely happy person extremely miserable and bringing into existence a very large population of people who have lives barely worth living (i.e. small but positive utilities), would be good. Finally, if the asymptotic critical level is positive and large, we get the reverse very sadistic conclusion: making an extremely miserable person extremely happy and bringing into existence a very large population of very happy people would be bad. This can also be called the ‘extreme extinction conclusion’, because it implies that extinction (causing the current generation to suffer a lot in order to avoid the existence of a large future population of very happy people) is preferable. These three conclusions are arguably the most counter-intuitive implications that we encounter in population ethics.

Counter-intuitive implications of asymptotic critical-level utilitarian theories. Width of the boxes represent population sizes, height represent utility levels, dashed horizontal lines represent zero utility, dotted horizontal lines are the asymptotic critical levels, black boxes are a large background population of unaffected people that exist in all states (i.e. both at the left and the right states), grey boxes are affected people that exist in all states, white boxes are extra people that do not exist in the states on the left. The inequality signs indicate which state has the highest aggregate utility according to the asymptotic critical-level utilitarian theories.

A first attempt: person-affecting utilitarianism

Person-affecting utilitarianism makes a distinction between necessary (or present) and contingent (or potential) people. Necessary people exist necessarily in the sense that they exist in all available states (i.e. all states that are possible or feasible and can be chosen). In contrast, contingent or potential people are individuals who do not exist in all available states. In the above figure, the contingent people are represented by the white boxes.

According to person-affecting utilitarianism, a state can only be better (or worse) if it is better (or worse) for at least someone. Consider the very repugnant conclusion: if initial state (the left state in the figure above), where everyone is happy, is said to be worse than the second, very repugnant state where someone is extremely miserable, for whom is the initial state worse? Not for the necessary people, because they are at least as well off in the initial state than in the very repugnant state. And not for the huge population of contingent people who have positive utility levels, because these people do not exist in the initial state. As we cannot point at one person who is worse-off in the initial state, a person-affecting theory cannot say that the initial state is worse.

In a person-affecting theory, the contingent people do not count. It is as if the critical level for a contingent person is no longer a constant, as in the asymptotic critical-level utilitarian theories, but equals the utility of that person in that situation. In that case, the contingent person has a relative utility equal to zero, and hence the contingent person is not included in the aggregate utility function.

Although person-affecting utilitarianism escapes the very repugnant and (reverse) sadistic conclusions, it faces two other major problems.

First, it faces another sadistic conclusion: if utilities of contingent people do not count, they also do not count when the contingent people have a negative utility. That means this person-affecting utilitarianism is neutral about adding a huge population of extremely miserable people, when everyone else keep the same utility. Adding individuals with a negative utility would not be problematic.

A second problem of person-affecting utilitarianism, is that it is indifferent between creating a life barely worth living (i.e. adding a person with a low positive utility) and creating another, extremely happy life. In both cases, before making the choice, the additional life counts as a contingent person, and hence its utility does not count.

A complete solution: person-affecting neutral-range utilitarianism

The first problem of person-affecting utilitarianism (a sadistic conclusion) can be avoided by making the person-affecting theory asymmetric: when a contingent person has a negative utility, that negative utility is fully taken into account in the aggregate utility function, whereas a positive utility of a contingent person is excluded. The critical level of a contingent person equals that person’s utility if the utility is positive, and zero if the utility is negative. Or in other words, the critical level has a lower boundary equal to zero. This gives us a procreation asymmetry: adding an unhappy life always makes things worse (all else equal), but adding a happy life not always makes things better.

The second problem of person-affecting utilitarianism can be mitigated to some degree by setting a cap on the critical level: the critical level cannot be higher than a positive upper boundary cmax. That means creating an extremely happy life (with a utility above cmax) is preferred above creating a life barely worth living (with a positive but small utility below cmax). And choosing between two lives with utilities above cmax, the life with the highest utility is preferred (all else equal).[1]  

Now we have a restricted person-affecting theory, where the critical level lies in a range between 0 and cmax. The critical level is zero if the contingent person has a negative utility, linearly increasing for small positive utility levels and a positive constant cmax for high positive utilities. As the critical level ranges from 0 to cmax, which means the range includes the neutral level of zero utility, this theory is called neutral-range utilitarianism. The theory has a neutral range of utilities for contingent people, which means that adding people who have utilities in this range does not make the world better nor worse (all else equal).

Critical-level function for contingent people in person-affecting neutral-range utilitarianism

With this critical-level function, if a contingent person has a negative utility, that negative utility fully counts in the aggregate utility function. This represents the procreation asymmetry in the person-affecting view. If the person has a positive utility below a maximum critical level, the utility doesn’t count. This corresponds with the person-affecting view. And if the utility is above the maximum critical level, the utility minus the maximum critical level counts, as in critical-level utilitarianism. Or in other words: the aggregate utility function is the sum of everyone’s utility, excluding the utilities of the contingent people who have utilities in a neutral range (between zero and a maximum critical level), and subtracting a maximum critical level from the contingent people who have utilities above the maximum critical level.

It is easy to see that this person-affecting neutral-range utilitarianism avoids the very sadistic conclusion due to the fact that the critical level function is zero at negative utilities. And it avoids the very repugnant and reverse very sadistic conclusions due to the linearly increasing ramp part of the critical-level function. If at the neutral range from 0 to cmax the critical-level function was zero (or more generally a general function strictly below the linear function with slope 1), we would face the very repugnant conclusion. And if at this neutral range the critical level function was cmax (or more generally a function strictly above the linear function with slope 1), we would face the reverse vary sadistic conclusion. With a neutral range [0,cmax] containing a linear increasing critical level function, all the sadistic and repugnant conclusions are avoided.

Person-affecting neutral-range utilitarianism is perhaps the simplest of all population ethical theories that avoid the sadistic and repugnant conclusions. There is one small complication, however: the theory requires a ‘forward-looking constraint’. If an available state, which initially seems to be the best, is later (when the state is chosen and the contingent people become necessary people) dominated by another alternative state which initially seems worse, the initial better-seeming state should be excluded from the available options of the initial decision. If you know in advance that if you choose the best state, that best state will no longer be the best state in the future, then you should not choose that best state.

Consider as an example a choice between three states. In the first state, one person exists and has a high utility 10. In the second state, the utility of this person is increased to 11, by adding an extra person at low utility 1. The third state contains the same two persons, the first person gets utility 9 and the second gets utility 4.

Suppose the maximum critical level is cmax=5. The initial choice is between three states. Person 1 is necessary, person 2 is contingent. As person 2 gets a utility below the maximum critical level, its utility does not count in the aggregate utility function. That means state 2, with aggregate utility 11+1=12, is the best. However, this choice requires bringing into existence person 2. Once that person exists, that person becomes a necessary person, state 1 is no longer an option, and a choice between states 2 and 3 remains. Including the utility of person 2 in the aggregate utility function now means that state 3 is the best, with aggregate utility equal to 9+4=13. That means state 2 becomes dominated by state 3 after the choice of bringing person 2 into existence.

If this reasoning means that we have to end up with state 3, we face the very repugnant conclusion, because we can repeat the process. Suppose we can move from state 3 to a fourth state, by adding a third person with utility 1. In state 4, person 1 may get utility 10. The aggregate utility function equals 10+4=14, which is higher than 13 of state 2. But assume there is a fifth state where person 1 gets utility 8 and person 3 gets utility 4. Once person 3 is brought into existence, that person becomes a necessary person, which means its utility counts and state 5 becomes the best. We see the utility of person 1 decreasing, from 10 in state 1 to 9 in state 3 to 8 in state 5. After a large number steps, we end up with an odd-numbered state in which person 1 has a very negative utility and all the other people have low utilities in the neutral range (i.e. below 5). This is the very repugnant conclusion.  

The only way to escape this conclusion, is by not allowing state 2 to be a member of the initial choice set. If the initial choice is between the two permissible states 1 and 3, state 1 will be chosen and person 2 will not become a necessary person. This forward-looking constraint, i.e. excluding from the initial choice set the states that will become dominated by other states once chosen, is a deontological constraint which means our population ethical theory is no longer axiological. An axiological theory only looks at the aggregate utility function over all available states and does not impose restrictions on the choice set of available, eligible states. Deontological constraints impose boundary conditions on the maximization of the aggregate utility function.

Symmetry breaking

In the previous section, the neutral range was assumed to range from utility level 0 to level cmax. As the critical values are always non-negative, it may seem that person-affecting neutral-range utilitarianism has an asymmetry (resulting in the abovementioned procreation asymmetry). However, this is not necessarily the case, due to an ambiguity in the definition of zero utility. The previous section implicitly assumed that zero utility is defined as the utility below which a contingent person would negatively contribute to the aggregate utility function, making a state worse by bringing that person into existence (all else equal). Then the neutral range becomes [0,cmax]. But we could equally define zero utility as the utility above which a contingent person would positively contribute to the aggregate utility function, making a state better by bringing that person into existence (all else equal). With this definition, the critical values are always non-positive and the neutral range becomes [-cmax,0].

The apparent asymmetry of person-affecting neutral-range utilitarianism is the result of an arbitrariness in the definition of zero utility. Although the theory is structurally symmetric, the symmetry may become broken (a bit analogous to spontaneous symmetry breaking in physics). To see this, we have to make the distinction between personal utility and contributive utility. The above paragraph referred to contributive utility: the utility that contributes to the state of the whole population (i.e. the aggregate utility function). If the contributive utility of a (contingent) person is zero, the addition of that life makes a population neither better nor worse, but equally good (all else equal, i.e. all personal utilities of other people stay the same in the situation where the contingent person does not exist). The addition of that life is neutral from an impersonal perspective, the point of view of the whole population. Personal utility, on the other hand, measures how valuable a life is according to the person who lives that life. A zero personal utility means that the person is neutral, indecisive or indifferent between living that life and non-existence (all else equal). 

Just like contributive utility has a neutral range, personal utility can have a personal neutral range as well. If personal utility is above this range, the person prefers that life above non-existence. If it is below the personal neutral range, the person prefers non-existence above that life. The personal neutral range with a non-zero height means that a person can be indecisive or indifferent between living a life and non-existence, and still be similarly indifferent if that life is slightly improved (having a slightly higher welfare).

Each person can have a different personal neutral range, with a different heights. Some people may have a very accurate idea what counts as their zero personal utility and hence have one precise personal neutral level instead of a range. But others may be more uncertain, and may prefer a vague notion of zero personal utility. In any case, we could also have a different contributive neutral range for each different person, which means cmax can be different for different people. To respect personal autonomy of people, we should assume that each person’s personal neutral range lies within their contributive neutral range (otherwise what counts as a good life for a person may count as bad for the population). One option is setting the contributive neutral range of a person equal to that person’s personal neutral range (i.e. an exact fit of the personal range within the contributive range). In that case, person-affecting neutral-range utilitarianism remains symmetric (because there is a similar ambiguity in the definition of zero personal utility as with zero contributive utility).

It is also possible that the contributive neutral range is the same for everyone and at least as large as each person’s personal neutral range. The contributive neutral range could for example be the personal neutral range of the person who has the largest personal neutral range. If a personal neutral range is smaller than the contributive neutral range, the question becomes where the personal neutral range is located within the contributive neutral range. This is where the symmetry might become broken. To respect personal autonomy of people, each person should be allowed to determine where the own personal neutral range lies within the contributive neutral range. If a person has a strong preference to avoid a sadistic conclusion, that person should choose the own personal neutral range at the lower end of the contributive range. A zero personal utility should be at the zero contributive utility. The symmetry of the theory is broken, because the person has a preference for an asymmetry. 

Determining the neutral range

A final question remains: how do we determine the size of the (contributive) neutral range? To respect personal autonomy of people, ideally people should determine for themselves how large their own contributive neutral range is (and where there personal neutral range is located in that contributive neutral range).

The size of someone’s contributive neutral range may reflect that person’s population ethical preferences, such as the preference to avoid the very repugnant conclusion.

A person’s personal utility function (and personal neutral range) represents that person’s preferences, but these preferences do not include population ethical preferences. It is difficult to represent population ethical preferences in the personal utility function, because these preferences might depend on the choice set, i.e. the set of eligible states. Given a choice set that includes a state that is very repugnant, a person might have a strong preference to avoid the very repugnant conclusion. If everyone would choose a larger contributive neutral range, that repugnant conclusion would be more easily avoided. Therefore, that person may choose a large own contributive neutral range. In this case, the size of the contributive neutral range represents the strength of the preference to avoid the repugnant conclusion.

The choice of the size of the contributive neutral range may depend on the choice set. If some states are no longer available and there is no longer a worry for a repugnant conclusion, the person might choose a smaller own contributive neutral range, to reflect a personal preference to decrease e.g. the second problem of person-affecting theories (the indifference between creating a slightly happy life and creating another slightly happier life).

The difficulty, of course, is that a contributive neutral range only matters for contingent people, and we cannot know their population ethical preferences (at least not until they are brought into existence). Therefore, we should assume that their population ethical preferences are similar to ours, i.e. to the necessary people. That means the necessary people have to democratically decide how large they set the contributive neutral range (which is now equal in size for all contingent people), given the actual choice set faced by the necessary people.  

[1] But there is still a small problem left: the theory remains indifferent between creating a life barely worth living and creating another, slightly happier life (with utility below cmax). This problem can be slightly mitigated, by introducing a small extensions of the theory, making it ‘lexical’ when there is a tie. Suppose there are multiple optimal states, having equal aggregate utility values. The aggregate utility function excludes the contingent people with small positive utilities (i.e. whose lives are barely worth living). In that case, we can break the tie by choosing the state that has the highest sum of welfares of the excluded contingent people.

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3 reacties op Person-affecting neutral-range utilitarianism

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