An ethical minefield. Stepping from the worst to the best population ethical theories

About ten years ago, during my studies in moral philosophy, I encountered the area of population ethics. It is clearly one of the most tricky areas in ethics, a minefield of very counterintuitive conclusions. But it is also one of the most important areas, because it strongly influences very important decisions that deal with huge problems such as human extinction, animal farming and wild animal suffering. Population ethics tells us how much we should care about future people. As the number of those people can be huge, a lot is at stake with population ethics.

Population ethics is an extension of welfare ethics. Welfare ethics deals with problems where different situations involve people with different welfare levels. For example, in one situation, everyone is moderately happy, in another situation, those people are extremely happy, except for one person who is extremely miserable. Which situation is the best? A concern for justice implies that the first situation is preferable. Population ethics deals with problems where different situations involve different people having different welfare levels. The question of justice becomes much more tricky in population ethics.

In the early days of my PhD-research in moral philosophy, after many hours of work, I formulated my favorite population ethical theory. But a year later, around 2012, I learned that it was a mistake, as I discovered that my favorite theory contained counterintuitive implications. It was one of the first times that I had to change my mind, give up my favorite theory and destroy my own work. (I later learned that Ashem and Zuber called this theory ‘rank-discounted utilitarianism’ and defended it in their 2012 and 2014 articles, right at the time I changed my mind about this theory. Problems with this theory were mentioned by Budolfson and Spears.)

A few years later, in 2014, I defended my PhD-dissertation about animal ethics, which contained another population ethical theory that strongly relates to average utilitarianism (although as the name ‘positive number-dampened power mean prioritarianism with negative total utilitarianism’ suggests, a lot more complicated than average utilitarianism). But another few years later, I realized that this new theory was horrible again. So I had to start all over again, kill my darling a second time, and look for another favorite population ethical theory. I started drifting around from theory to theory.

In 2018, I came up with a new theory, which I called variable critical level utilitarianism (but perhaps is better called autonomous critical level utilitarianism, as explained below). I still consider it as a very good and promising candidate, but knowing how difficult it is to avoid very counterintuitive implications, I’m not so confident anymore. And a few weeks ago, I found a second very promising candidate, which I call minimax net-complaint theory.

In this article, I first explain what is wrong with my previous favorite candidate: average utilitarianism. I consider this theory, which I defended in my PhD-dissertation, as the worst of the population ethical theories that are still at least a bit reasonable. Next, I describe my two favorites (up to now): autonomous critical level utilitarianism and minimax net-complaint theory.

The worst reasonable theory: average utilitarianism

Standard population ethical theories start with a social welfare function, which is a function of individual welfares. For each situation we can calculate the social welfare, and the best situation is the one that has the highest social welfare. A common population ethical theory is average utilitarianism, where the social welfare of a situation is defined as the average welfare of everyone who exists, existed and will exist in that situation. You take the sum of everyone’s welfare, divide it by the number of existing people, and that quantity should be maximized.

This theory seems simple and elegant, and could be derived from a kind of Rawlsian ‘veil of ignorance’ thought experiment: imagine that you are behind a veil of ignorance, only knowing that you will be born in the world, but not knowing who you will be. You can become anyone who exists in the world, with equal probability. Now you can decide the welfare distribution of all existing people. If you want to maximize your expected welfare, which is reasonable, you end up with average utilitarianism.

However, I now consider average utilitarianism as the worst of all reasonable population ethical theories, because it faces several problems and counter-intuitive implications.

  • The dominance addition problem: increasing the welfare of extremely happy people by adding very happy people, is not good. Suppose in situation 1, a person has welfare level 100, whereas in situation 2, that same person has welfare 110 and an extra person exists who has welfare 84. Hence, the first person is happier, the extra person is also very happy, no-one is worse-off, and the total happiness almost doubles. Yet, situation 2 now has an average welfare of 97, which is lower than 100 and hence not preferred by the average utilitarian.
  • The dependence problem: whether or not it is good to add happy people, depends on the welfare of unaffected people. In taking the average, we have to include e.g. past generations, wild animals or even aliens on distant planets. Suppose in situations 1 and 2 described above, there exists an extra person who is unaffected by the choice between situations 1 and 2. That means in both situations, that person has the same welfare, say 100. The average welfare in situation 2 now equals 98, which is lower than the average in situation 1, which equals 100. Hence, in this case choosing situation 2 is not allowed, as in the dominance addition problem described above. However, suppose that unaffected person has welfare 10 in both situations. Now the average welfare in situation 2 equals 68, which is higher than the average in situation 1, which equals 55. If the unaffected person has a low welfare, adding the extra person in situation 2 is good. Hence, whether we decide whether procreation is permissible, we first have to know the welfare of everyone else who existed, exists and will exist in the universe. If we learn about the existence of a large population of unaffected people, a situation that was once better than another, might become worse.

Sadistic and repugnant conclusions. If the unaffected beings are much more numerous than the people whose existence and welfare we can influence, things become even worse for average utilitarianism.

  • The sadistic conclusion. If the welfare of the unaffected people is negative: adding extra people with negative welfare becomes good. Suppose there is a huge population of extremely miserable people, such that the average welfare is -100. Adding an almost as extremely miserable person with welfare -99 would slightly increase the welfare and hence would be good, even if all the other people are unaffected.
  • The repugnant conclusion. If the welfare of the unaffected people is positive but very small, then it would be good to strongly decrease the welfare of one person by adding a huge number of people with lives barely worth living (i.e. a very low welfare slightly above zero). Suppose the average welfare is 0,1, and one person has a high welfare of 100. Now thousands of extra people are born, all with very low welfare 0,2. But by adding those people, that one happy person gets a very low welfare of 0,2 as well. Everyone now has a very low welfare, but still, the average welfare increases slightly. Or, if we discover the existence of a huge population of aliens with lives barely worth living, humans would have a strong duty for extreme procreation, decreasing our welfare by adding lots of extra slightly happy people.
  • The sadistic repugnant conclusion. The above repugnant conclusion can become more sadistic: suppose by adding the thousands of extra people, that one happy person becomes extremely miserable, receiving a large negative welfare of -100. Even then, the average welfare increases slightly.
  • The reverse repugnant conclusion. If the welfare of unaffected people is positive and very high, adding people with high positive welfare is bad. If the average welfare is 100, adding people with welfare 90 lowers the average. This happens even when adding those people would increase the welfare of a person. Consider a slightly happy person who would become extremely happy when she has many very happy children. Increasing one’s welfare by adding many happy children would not be allowed according to average utilitarianism. Or, if we discover the existence of an extremely happy alien race, it is better for humans to stop procreating.
  • The reverse sadistic repugnant conclusion. The above reverse repugnant conclusion can become more sadistic: suppose the welfare of unaffected people is positive and extremely high (welfare +100), and one person is extremely miserable (welfare -100). We can make that person extremely happy (welfare +100) by adding a huge number of very happy people (with welfare 90). Now everyone is at least very happy, one person moves from extreme misery to extreme happiness, but the average welfare is lower, which is bad according to average utilitarianism.

We can try to avoid some of the above counter-intuitive implications, by looking for other population ethical theories. Average utilitarianism can be a starting point from which we can move towards other population ethical theories. For example, if we assume the existence of an infinitely large population of unaffected people, with a non-negative average welfare level, we arrive at critical level utilitarianism, where the average welfare of the unaffected people counts as a critical level.

In critical level utilitarianism, the social welfare function can be reduced to the sum of everyone’s relative welfare levels, whereby someone’s relative welfare is the welfare minus the constant critical level. When a person is added to the world and has a welfare above this critical level, the social welfare increases, but when the welfare is below the critical level, social welfare decreases.

A special version of critical level utilitarianism, is total utilitarianism, where the critical level is zero. This theory is susceptible to the repugnant and the sadistic repugnant conclusions.

Autonomous critical level utilitarianism

Critical level utilitarianism has many advantages. First, the social welfare function of critical level utilitarianism is simply a sum of terms, which means that the non-affected people do not matter, because they always have a constant contribution in this sum. As only the affected people count in the welfare function of critical level utilitarianism, we avoid the dependence problem. Second, as the critical level is non-negative, we avoid the sadistic conclusion. Third, when the critical level is not too low, we avoid the repugnant and sadistic repugnant conclusions. Fourth, when the critical level is not too high, we avoid the dominance addition problem and the reverse repugnant and sadistic repugnant conclusions.

Critical level utilitarianism has its problems, though. We face an arbitrariness of the choice of critical level. Some counter-intuitive implications can be avoided when the critical level is not too low, and other problems when the level is not too high. So the ideal critical level should be somewhere in the middle. However, with a medium critical level, both (sadistic) repugnant and reverse (sadistic) repugnant conclusions are still present to some degree. A low critical level gives one problem, a high critical level gives another problem, and a medium critical level gives us both problems, but with half of their strengths. Suppose we have a medium critical level, and a situation where one person suffers a lot. Suppose we can help that person, increase that person’s welfare to a high level, by adding a huge number of medium happy people with lives worth living, but welfare levels barely below the medium critical level. As they are below the critical level, that huge number of people negatively contributes to the social welfare function of critical level utilitarianism, which means we should not help that one miserable person.

My idea a few years ago, was to improve critical level utilitarianism by allowing a variable critical level. If we are faced with choices that lead to the repugnant or sadistic repugnant conclusion, we can set a high critical level in order to avoid those conclusions, and if we are faced with choices that lead to the reverse repugnant or reverse sadistic repugnant conclusion, we can set a low critical level instead. Or we can move a few steps further, by allowing complete freedom: if the choice of critical level is arbitrary, why not let people determine for themselves which critical levels they have? Autonomous critical level utilitarianism assumes that individuals can autonomously (freely) choose their own critical levels. Different individuals can have different critical levels. But also the same individual can choose to have different critical levels in different situations. And even the same individual in the same situation can choose to have different critical levels in that situation, depending on the other situations that are available. If another option becomes available, people may change their own critical levels.

The social welfare function is again the sum over all individuals of the differences of the individual welfare levels with the individual critical levels. The individual welfare level measures how strongly the individual prefers the situation, whereas the individual critical level captures the population ethical preferences of that individual.

The full flexibility in choosing critical levels may be unproductive, because people can choose to increase their critical levels to infinity. Suppose there are two situations and two people, the first person prefers situation 1 and the second prefers situation 2. To steer the outcome towards situation 1, the first person can set a very high critical level for himself in situation 2. But the second person can anticipate that and set a high critical level for herself in situation 1. Now the first person can choose an even higher critical level. This can quickly escalate, such that in both situations there is someone with an infinite critical level. In both situations, the social welfare function becomes minus infinity, and it becomes impossible to compare those situations and select the best situation that has the highest social welfare.

To avoid such problems of escalation and strategic manipulation, we can introduce some constraints.

First, individuals cannot choose a negative critical level. Choosing a negative critical level means that one is willing to be born with a negative welfare, and that is not rational.

Second, in each situation, the sum of everyone’s critical level cannot be higher than the maximum (over all available situations) of the sum (over all contingent people) of the positive welfares of contingent people. Available situations are those that are possible or feasible and can be chosen. Contingent people are people who exist in some but not in all the available situations, in contrast with necessary people who exist in all available situations. In each available situation, we can look at the contingent people who have positive welfare levels, and take the sum of those positive welfares. Finally, we can take the maximum over all available situations of those sums of positive welfares. If people choose high critical levels such that the sum of their critical levels becomes larger than this maximum, the excess critical level (the difference between the sum and the maximum) is simply not taken into account in the social welfare function.

Third, the necessary people who exist in all available situations, have to choose their critical levels from behind a Rawlsian veil of ignorance, as if they do not know which of the necessary people they will be.

Autonomous critical level utilitarianism often reduces to total utilitarianism, because in many cases, each available situation has some people who choose the maximum critical level. If all available situations have the same maximum critical level, those critical levels cancel each other out. Major exceptions are cases where total utilitarianism offers counter-intuitive implications such as the repugnant and sadistic repugnant conclusions. Consider the case of the sadistic repugnant conclusion: in one situation, one person has a high welfare and has no intention to choose a high critical level. In another situation, that same person gets a negative welfare, and a huge number of extra people are born with lives barely worth living. Those extra people are contingent people, because they did not exist in the first situation. We can take the sum of their welfare. Now, the first person, who is miserable, can set a very high critical level equal to the total welfare of the contingent people. It is as if the positive welfare of the contingent people no longer counts (because that part is subtracted by the critical level of the one person). As only the welfare of the one person counts, the first situation will be selected. In that situation, the contingent people do not exist, cannot complain and cannot set a positive critical level to steer the outcome back to the second situation.

Another implication of autonomous critical level utilitarianism, is that it is against animal farming, even if the farm animals would have a positive welfare. Consider a first situation, where humans exist but do not breed animals. These humans have a total welfare H. They can increase their welfare a little bit to H+, by breeding, raising, slaughtering and eating farm animals. Suppose those farm animals have a positive welfare overall (they live healthy happy lives on the fields and are painlessly killed). The total animal welfare is denoted as A. However, a third situation is available, where the same animals are not slaughtered, but live even longer happier lives on farm sanctuaries. Their welfare increases to A+. The animals are the contingent people, and they have maximum welfare in the third situation equal to A+. This means the animals can set a high critical level (equal to A+) in the second situation, to steer the outcome towards the third situation. But in the third situation, the humans have the lowest welfare, written as H-, because they can no longer enjoy eating meat, and now have to share resources with the animals and take care of them. So the humans set a maximum critical level equal to A+ in the third situation, steering the outcome towards the first. If in the first situation, the humans again choose a maximum critical level, all three situations contain maximum critical levels. These critical levels cancel each other, which means we end up with total utilitarianism, and this theory selects the third option. That third situation was not preferred by humans, so to avoid selecting that situation, it is reasonable for the humans in the first situation to set their critical level at zero. In the end, the first situation, without animal farming, is the best according to autonomous critical level utilitarianism.

Minimax net-complaint theory

If in a situation the necessary people set their critical level equal to the welfare of the contingent people, it is as if the welfare of the contingent people do not count. This brings us to a whole new category of population ethical theories: the person-affecting theories.

According to the person-affecting view, if a situation is better, it should be better for at least someone, and if a situation is worse, it should be worse for at least someone. Consider the repugnant conclusion again. In the first situation, a person is happy, in the second situation, that person has lower happiness and extra people with positive welfare exist. A total utilitarian says that the second situation is better, which means the first situation is worse. But there is no person existing in the first situation for whom the first situation worse. That is why total utilitarianism does not satisfy the person-affecting view.

Many person-affecting theories face a sadistic conclusion, because the contingent people do not count. Suppose we can increase your welfare a tiny bit, by adding a person to the world who has a very negative welfare. In the initial situation, you are worse-off and no-one is better-off, so the person affecting-view says that the initial situation is worse. A person-affecting theory would select the second situation where one person suffers a lot and another person is only slightly better-off.

This sadistic conclusion can easily be avoided by refining the person affecting theories, making them asymmetric. The asymmetry means that adding a life with negative welfare always makes things worse, but adding a life with positive welfare not always makes things better. In asymmetric person-affecting utilitarianism, the positive welfare levels of the contingent people are not included in the social welfare function, but the negative welfares are. If a contingent person has a negative welfare in one of the available situations, we have to consider that person as a necessary person: the situations where the person does not exist have to be treated as if the person exists and has welfare 0.

Autonomous critical level utilitarianism is asymmetric, because the critical levels are always non-negative. But it does not often satisfy the person affecting view. My second favorite population ethical theory is a more recent discovery that is also asymmetric, and satisfies the person-affecting view more often.

Suppose we have a number of available situations which we can choose. To say that a situation is better, we have to compare that situation with another situation. So let’s take two situations. Some people in the first situation would prefer the other situation, for example because they have a higher welfare in that other situation. Those people in the first situation can complain against choosing the first situation above the second. We can add up all the complaints in the first situation (against choosing the first above the second situation) and subtract the total complaints in the second situation (i.e. the complaints of all people in the second situation against choosing the second situation above the first). This is the net-complaint of the first situation relative to the second situation. For each pair of situations, we have a net-complaint that measures how much better people in those situations prefer one situation over the other. For each pair comparison, the person-affecting view is satisfied. This also means that each situation has many net-complaints relative to the other situations, one for each of the other situations. Now consider the maximum of those net-complaints of that situation. Finally, we look for the situation that has the lowest value of this maximum net-complaint. That situation is the best, according to minimax net-complaint theory: we have to minimize the maximum of the net-complaints. This selection of the best situation is closely related to the minimax Condorcet margins method in voting theory.

People can freely choose their complaints, just like people can freely choose their critical levels in autonomous critical level utilitarianism. If complaining results in the selection of a situation that is not preferred by the complainer (e.g. a sadistic repugnant conclusion), that person can choose not to complain in order to avoid selecting that situation. However, just as in autonomous critical level utilitarianism, we have to set constraints on the allowed complaints, otherwise people might choose negative or infinite complaints. Just like the critical level should always be non-negative, a complaint should always be non-negative. And the maximum complaint of a person in situation 1 relative to situation 2 equals the personal harm: the welfare of that person in situation 2 (assumed to be zero if the person does not exist in situation 2) minus the welfare of that person in situation 1. If a person does not exist in a situation, that person off-course has a zero complaint in that situation.

Note that this upper constraint on a complaint assumes that we can identify the same person in two different situations. But that brings us to a tricky area of personal identity. It is not always possible to clearly determine whether a person in one situation is the same person in another situation. Are you the same person as that person in a very different situation, that has your name and your parents, but a completely different life? Imagine after your birth you were raised in another country, speaking another language, having another education, having completely different life experiences, having other memories, having other atoms in your body, developing other preferences, having your genes altered, having chips implanted in your brain, and so on. There is no objective truth to this notion of personal identity: we cannot objectively determine which persons are identical. But, we can allow people to determine for themselves whether they identify with a person in another situation. In your actual situation, you can identify yourself with a person that lives in another situation, but with one condition: that person in the other situation should not already be identified by someone else in your actual situation. If you believe to be mister X in situation Y, and I also believe to be that person, then you and I have a problem. Only one of us is allowed to identify with mister X, unless we believe that you and I are the same person.

With this being said, we can look at an application of minimax net-complaint theory, that resembles the above example of animal farming. Consider an existential risk that can cause the extinction of humanity, such as extreme climate change. In the first situation, we do nothing against that risk, which means we are the last generation and humanity goes extinct. In this situation, we have welfare H. In the second situation, we partially mitigate that risk, which means humanity survives, but future generations face harsher living conditions due to the catastrophe. This would be the case of non-extreme climate change. As the current generation doesn’t face mass extinction, we are happier (welfare H+). The future generations could still have lives worth living, but with low welfare A. Those future generations are comparable to farm animals with net-positive lives in the above example of animal farming. But there is a third situation, comparable to the farm sanctuary situation mentioned above. We can increase our efforts, sacrifice our welfare, to mitigate the catastrophe and completely eliminate the risk, such that future generations would live very happy lives (welfare A+). Due to our efforts, however, we get a much lower welfare (H-), perhaps lower than in the first situation.

The tricky point is that our efforts to mitigate climate change have an influence on who will exist in the far future. If we change our behavior, we might have other children, and other grandchildren. That means the future generations in the second situation are not the same individuals who would exist in the third situation. If they would not exist in the third situation, the future generations in the second situation cannot complain against selecting the second situation, as long as they have a positive welfare in that situation. Concerning the current generation of humans, they can complain against selecting the first or the third situations, because they get a higher welfare in the second situation. Hence, the second situation has the lowest net-complaint, which should be chosen.

However, it is possible that some future people in the second situation identify themselves with future people in the third situation. Then they can complain against selecting the second situation, because their counterparts in the third situation are better-off. If they complain, we may have an intransitivity here that is a characteristic of person-affecting views: situation 2 is better than 1 (according to the current generation), situation 1 is better than 3 (according to the current generation), and situation 3 may be better than situation 2 (when future generations in situation 2 complain). This can be represented as a cycle with three nodes representing the three situations, and three directed links between the nodes, representing the net-complaints between situations. We can easily make this theory transitive, simply by cutting the weakest link in the cycle. The strength of a link is measured as the net-complaint. Hence, the situation with the lowest net-complaint will be selected. This is the minimax net-complaint theory.

Expressed mathematically, with minimax net-complaint theory, assuming everyone chooses their maximum allowed complaints, situation 2 is selected when A>max{A+-H-H++2H; A++H-2H++H}, i.e. when the welfare of the future generations in situation 2 is sufficiently high. Situation 3 is selected when H<min{(H++H)/2; 2H-H++A+-A}, i.e. when the welfare of the current generation in situation 1 is very low. Situation 1 is selected when H>max{(H++H)/2; 2H+-H-A++A}. The same goes of-course for the above animal farming problem: situation 2 with happy farm animals is the best only when those farm animals are sufficiently happy (i.e. when A is very high).


I have two favorite population ethical theories: autonomous critical level utilitarianism and minimax net-complaint theory.

Autonomous critical level theory selects the situation that has the highest sum of relative utilities (summed over all individuals existing in that situation), whereby a relative utility is the utility of a person in a situation minus a critical level chosen by that person in that situation. The critical levels capture the population ethical preferences of people and are constrained: an individual critical level cannot be negative, and the sum of critical levels in a situation cannot be higher than a maximum value which equals the maximum total welfare of contingent people who do not exist in all available situations. In many cases, this variable critical level utilitarianism resembles total utilitarianism, but it allows to avoid the most counterintuitive sadistic and repugnant conclusions of total utilitarianism.

Minimax net-complaint theory selects the situation that has the least amount of maximum net-complaint, whereby a net-complaint of a situation versus a second situation measures how much people in the first situation complain against selecting the first situation over the second situation, minus the complaints of people in the second situation against selecting the second situation over the first situation. The complaint of a person can be freely chosen, but should be between zero and the personal harm (the difference in utility of that person between the two situations).

Both theories avoid the counterintuitive implications such as sadistic and repugnant conclusions. When it comes to the animal farming problem, the situation without breeding of farm animals is selected, unless the farm animals are very happy and would not complain against them being used for consumption, or unless the situation with animal farming has a higher total welfare than all other available situations. When it comes to the existential risk problem, we should maximize risk mitigation and maximize the welfare of future generations, unless future generations have a sufficiently high welfare or would not complain when we do not maximize future welfare, or unless such level of risk mitigation is too costly for current generations (where ‘too costly’ is determined by all the welfare levels of both current and future generations in all possible situations).

Given two favorite theories, which one should we choose? One option is that we apply both theories and determine the optimal situations according to both theories. If the two optimal situations are different, we can have a democratic majority vote which one of them we should choose.

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2 reacties op An ethical minefield. Stepping from the worst to the best population ethical theories

  1. Pingback: The problem of possible populations: animal farming, sustainability, extinction and the repugnant conclusion | Stijn Bruers, the rational ethicist

  2. Pingback: My top ideas of 2021 | Stijn Bruers, the rational ethicist

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