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Number Dampening Utilitarianism and Avoidance of the Repugnant Conclusion: Opinion Essay

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In Parfit’s attempt to create a theory of morality, labelled Theory X, which is a non-person affecting view and doesn’t allow for situations in which an intolerable conclusion could be reached, he found what he called the ‘Repugnant Conclusion’. Parfit’s original formulation of the Repugnant Conclusion was “for any possible population of at least 10 billion people, all with a very high quality of life, there must be some large imaginable population whose existence, if other things are equal, would be better even though its members have lives that are barely worth living” .

The logic behind the Repugnant Conclusion can be explained as follows: imagine a World ‘A’ with a population of 1 billion very very happy people, living fulfilling lives. Now imagine a World ‘A+’ in which there are 1 billion people of equal happiness to those in A, as well as an additional 1 billion people who are unhappy, but possess lives that are worthwhile. As the mere addition of lives worth living, given that they do not affect the lives of the current population, cannot make something worse, it follows that A+ is better than, or at the least, not worse than A.

Now imagine a World ‘B’, which has the same quantity of people as A+, but has both a higher average utility and a higher total utility than A+, although the utility of each person is less than that in A. It would be incredibly counter-intuitive to suggest that B isn’t better than A+, as the population has both a higher average and total utility. According to the law of transitivity, it follows that B is better than A. For a graphical representation of the logic thus far see appendix A.

Following this logic, we can find that C is better than B, and thus, better than A. Continuing this process, we will eventually reach a World ‘Z’, a world of “muzak and potatoes” , where people’s existence is drab and dull, but not terrible enough to not be worthwhile. However, our logic will maintain that Z is better than Y, and therefore better than A.

This leaves us with the Repugnant Conclusion, as through seemingly sound logic, we have arrived at an absurdly counter-intuitive conclusion, in which World ‘A’, where 1 billion people have a very high average quality of life, is seen to be worse than World ‘Z’, in which billions upon billions of people have an average quality of life that is barely positive. For a graphical representation of this see appendix B.

Although Parfit wasn’t the first philosopher to notice that influential moral views have counter-intuitive repercussions, such as the Repugnant Conclusion, he was certainly the one who popularised it with regards to population ethics. The Repugnant Conclusion, namely how to avoid it, has become one of the great debates of modern philosophy, at least in the realm of population ethics. This is due to the fact that the moral comparisons used in assessing the Repugnant Conclusion, are inextricably linked to the moral foundations upon which we base our present actions. In other words, our present actions, whether it be policy-making, environmental conservation or increased education, etc., will inevitably have a significant impact on the well-being of future generations as well as an influence of the size of future populations, therefore philosophers are determined to work out the best action to take.

Parfit’s admission that he had failed to construct a Theory X that was able to satisfy the parameters he had set himself, consequently drew quite a lot of philosophical attention, with a plethora of notable philosophers weighing in with their theories of how to tackle to issue. Some philosophers have argued that we should accept the Repugnant Conclusion, however, most philosophers maintain that we should attempt to avoid the Repugnant Conclusion.

Total utilitarian approaches to Theory X seem to inevitably lead to the Repugnant Conclusion, whilst average utilitarian approaches violate other principles by reaching equally intolerable conclusions such as, the Absurd Conclusion and the Sadistic Conclusion. As a result, compromise theories have begun to take prominence, the most prominent of which is Number Dampened Utilitarianism.

Number Dampened Utilitarianism, sometimes referred to as Variable Value Principles, is effectively a compromise between total and average utilitarianism such that, when the population is relatively small, judgments relating to the maximization of utility are largely based on the total sum of utility. However, as the populations’ increases, the importance placed on the total sum of utility, in maximizing utility, is reallocated to average utility. This is because, although Number Dampened Utilitarianism follows the Impersonal Total Principle, it adds the constraint that there is a limit on the total utility in a world, meaning total utility becomes less relevant as the population increases. As a result, Number Dampened Utilitarianism allows us to avoid the Repugnant Conclusion, as, in the most simplistic sense, the Repugnant Conclusion represents the problems that arise when quantity can trump quality under simple maximizing utilitarianism, but the effect of quantity here has been ‘dampened’.

A more detailed analysis of Number Dampened Utilitarianism shows that the solution, and the limit, are predicated on the idea that the total amount of utility in the world is a diminishing function of the population of that world. Thus, it allows us to avoid the Repugnant Conclusion as the diminishing marginal increase in the value of utility, as a result of increases to population, means the total utility of the world will reach a limit.

Number Dampened Utilitarianism, is based upon the mathematics of a sum of an infinite series that tends towards a limit, i.e. the simple sequence 1 + 1/2 + 1/4 + 1/16…. will tend to 2 (Flim = 2). In the context of which the Repugnant Conclusion was explained earlier, no matter the population of World ‘Z’, there will be some limit to the total happiness in the world (Zlim). Therefore, as long as World ‘A’ has a total utility greater than Zlim, it will be better than World ‘Z’, no matter the scale of the population increase.

Philosophers have developed various models based on Number Dampened Utilitarianism, however, Ng’s formulation of the Number Dampened Utilitarianism model is arguably the most well-known. Ng’s model applies an increasing concave function to the size of the population and in doing so, Ng’s maximization of Number Dampened Total Utility is not only able to avoid the Repugnant Conclusion, but solve the non-identity problem, whilst not implying counter-intuitive rankings. However, in less compelling cases it fails to satisfy the Mere-Additions principle, eluding to what will be a reoccurring problem with Number Dampened Utilitarianism: it fails to satisfy all the principles of Theory X at once.

However, Number Dampened Utilitarianism faces quite a few serious pitfalls. One such problem is that it violates Weakened Pareto. The problem can be seen in the example outlined below:

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Imagine a World ‘X’, in which there are 1 million very very happy people, leading fulfilling lives. Now we increase the population, say, by increments of 500,000 people who are equivalently very very happy and also leading fulfilling lives, and doing so in no way impinges on the happiness of the current population of ‘X’. If we use Number Dampened Utilitarianism, then the total goodness in ‘X’ will approach a limit. When we reach this limit, or get insignificantly far from it, each time we add 500,000 more people, the value that their happiness will add to the total welfare of ‘X’ will be negligible. However, this is an obvious violation of Weakened Pareto and therefore the problem at present can be set out as:

Number Dampened Utilitarianism violates Weakened Pareto

Weekend Pareto is true

(i , ii) Number Dampened Utilitarianism is false.

The same observation can made with regards to Weakened Negative Pareto. For example, imagine a world where the entire population live very very tortured lives, in which they are constantly suffering. Now we start to increase the population, by adding people whose lives are equally tortured and thus have a negative utility. As per the Number Dampened Utilitarian view, as we increase the population, the total suffering in the world will approach a limit. As before, when we reach this limit or get insignificantly far from it, each time we increase the population, the disvalue each additional person brings to the world will be negligible. This violates Weakened Negative Pareto and therefore the problem can be set out as:

Number Dampened Utilitarianism violates weakened negative Pareto

Weakened Negative Pareto is true.

(i , ii) Number Dampened Utilitarianism is false.

Whilst one may be able to concede that the value of adding extra lives with a positive utility may decrease asymptomatically, tending to a limit, the analogous assumption about lives with negative utility, as shown above, is arguably more repugnant than the Repugnant Conclusion itself.

Moreover, whilst Number Dampened Utilitarianism may be able to logically avoid the Repugnant Conclusion, it ultimately suffers the same pitfalls as the Average Utility Principle, most notably that it allows for situations in which it can be better, with respect to maximising welfare, to add people with negative utility to a world rather than creating a larger number of people with positive utility. This is widely referred to as the ‘Sadistic Conclusion’. Thus, in a sense, Number Dampened Utilitarianism’s greatest strength is ultimately its greatness weakness, in that it ultimately suffers the pitfalls of both forms of utilitarianism it is derived from, arguably making it a lesser alternative to either one of the individual principles.

Furthermore, whilst one can acknowledge the foundational logic of Number Dampened Utilitarianism in its avoidance of the Repugnant Conclusion, the analogous assumption with respect to negative utility individuals, as well as is allowance of the Sadistic conclusion, are both unattractive and unavoidable, presenting a large problem for Number Dampened Utilitarianism as a credible method of satisfactorily avoiding the Repugnant Conclusion.

On top of that, attempts to rectify the problems posed to Number Dampened Utilitarianism, by its original assumption with respect to negative utility individuals, through the alteration of models and amendment of assumptions, have resulted in different, but nonetheless intolerable consequences. For example, amending Number Dampened Utilitarianism’s view that the negative disutility each person contributes to a possible world, is a decreasing function of the total population of said world, in order to satisfy Weakened Negative Pareto, will ultimately engender the ‘Absurd Conclusion’ . The Absurd Conclusion is the notion that the proportionate expansion of a world which contains people of both positive and negative utility, will result in that world becoming a worse place as the population expands. This can be seen by an example:

Imagine a world in which there are 99 incredibly happy people with positive utilities and 1 terribly miserable person with a negative utility. If we proportionately expand the population, maintaining a ratio of 99:1 (positive utility individuals: negative utility individuals), the world will ultimately become a disproportionately worse place, as we tend towards the limit of positive welfare. In summation, as the addition of individuals with positive utility will have a diminishing marginal impact, whereas the addition of individuals with negative utility does not decrease relative to the size of the population, the amended Number Dampened Utilitarianism models will mean that proportionate increases in the population of a world will make it a disproportionately worse place. This heavily undermines the legitimacy of Number Dampened Utilitarianism as a method of satisfactorily avoiding the Repugnant Conclusion, as when it has a limit on negative welfare, Number Dampened Utilitarianism violates Negative Weakened Pareto, but when it is amended, the asymmetry between the logic of the positive and negative welfare leads to The Absurd Conclusion.

Another factor of Number Dampened Utilitarianism that should be subjected to scrutiny is its reasoning behind happy people being of diminishing marginal value. Whilst the suppositions of the various philosophers who maintain that happy individuals are of diminishing marginal value aren’t obviously false, there is as much reason to suggest that their reasoning is false than there is suggesting that it is true . One such reason revolves around the logic behind the fact that instrumental goods inherently posses diminishing marginal value. If one maintains that this is because they contribute less intrinsic value, as one increases the number of goods consumed, then it can be argued that this shouldn’t be applicable to ‘happy individuals’.

A good illustration of diminishing marginal returns can be done by imagining a person who is holding their breath underwater. When the person comes up for air, the utility they receive from that first gasp of air that they were desperate for, will be much greater than the 100th breath of air they take, 2 minutes after they are done holding their breath. It can be argued that instrumental goods such as food, wealth, conversation or oxygen, in our example, are only subject to the principle of diminishing marginal utility, because they make diminishing marginal contributions to a person’s utility. But surely, one can’t justify utility having diminishing marginal returns by the same reasoning, for how could one plausibly argue that utility makes diminishing marginal contributions to utility (in our specific population model).

Whilst, Huemer’s suspicion about the diminishing marginal values of worthwhile lives doesn’t prove that they don’t have a diminishing marginal value, it would be seemingly incoherent and ‘ad hoc’ to ascribe worthwhile lives properties such as we would with instrumental goods, without grounding such reasoning in strong ethical foundations.

In assessing the degree to which Number Dampened Utilitarianism satisfactorily avoids the Repugnant conclusion, one can reasonably state that it offers a logical, methodical, and coherent solution to avoiding the Repugnant Conclusion. However, one must remember that Number Dampened Utilitarianism is not a theory devised solely to avoid the Repugnant Conclusion. Therefore, as Number Dampened Utilitarianism’s avoidance of the Repugnant Conclusion will inevitably violate one or more of the principles relating to Theory X (anonymity, Pareto, continuity, etc.), or, worse, engender the Sadistic Conclusion, one can conclude that the degree to which it does so ‘satisfactorily’ is minimal.

In the years following Parfit’s introduction of Theory X, the Repugnant Conclusion and the Mere-addition Paradox to the world of modern philosophical debate, there have been various attempts to develop a concept of beneficence, that can solve the non-identity problem whilst avoiding the problems outlined by Parfit. However, there is yet to be a conclusive notion of Theory X. Attempts to avoid the Repugnant Conclusion whilst satisfying Theory X have yielded limited success. Similarly, challenges to Parfit’s reasoning, and even arguments that our intuition is misguided and we should thus, accept the Repugnant Conclusion, have been unproductive.

Perhaps there is no situation in which the Mere-addition principle and non-anti-egalitarian principle can combine to avoid the Repugnant Conclusion as well as other intolerable conclusions.

Given the inconclusive nature of the debate surrounding Theory X, one should acknowledge that whilst Number Dampened Utilitarianism doesn’t satisfactorily avoid the Repugnant Conclusion, the likelihood to which any theory could is negligible.

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Number Dampening Utilitarianism and Avoidance of the Repugnant Conclusion: Opinion Essay. (2022, March 17). Edubirdie. Retrieved December 4, 2022, from
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