A Solution to the Mere Addition Paradox

 

B.Contestabile       admin@socrethics.com       Dez 2016

 

 

 

 

Table of Contents

 

Abstract

 

1.  Introduction

2.  The Mere Addition Paradox

3.  Intuition and Interest

4.  Indifference Curves

5.  Incommensurability

6.  Conclusion

 

References 

 

 

 

 

 

Abstract

 

 

Starting point

Gustav Arrhenius – after having systematically investigated the most important axiologies and intuitions of population ethics – came to the conclusion that there is no normative theory which coheres with “our” moral beliefs. This result is immediately plausible on the basis of the following consideration:

-  Population ethics using a two-parameter model (welfare and population size) can be characterized by a conflict of interest.

-  Conflicting interests shape conflicting intuitions.

-  Conflicting intuitions make it impossible to find a coherent normative theory.

In order to find a coherent theory one would have to find a universal interest and a corresponding universal intuition. The obvious candidate to meet this request is sympathy. But since there is no universal consensus on the desirable degree of sympathy, the normative force of such an approach is limited.

Breaking out of the two-parameter model and accepting the incommensurability of certain qualities threatens the normative claim of population ethics [Contestabile 2010, 112].

 

 

Type of problem

The best known and most discussed example shattering our intuitions is Parfit’s Mere Addition Paradox.

How would an axiology look like, which is based on sympathy and solves the paradox?

 

 

Result

The Mere Addition Paradox can be solved by an axiology on the basis of sympathy between

-  people who prefer to increase (exclusively) the quality of life (e.g. perfectionist Buddhists).

-  people who prefer to increase (exclusively) the population size (expansionists).

 

A sympathetic population axiology has the following characteristic:

As the inequality in preference-satisfaction between Buddhists and expansionists increases

-  a larger improvement in the preference-satisfaction of the advantaged is needed

-  to compensate for the loss in preference-satisfaction of the disadvantaged.

 

Example:

Let us assume that the population is expanded at the cost of the quality of life, so that the preferences of the expansionists are satisfied at the cost of the Buddhists. As the inequality in preference-satisfaction increases

-  a larger improvement in the preference-satisfaction of the expansionists (population size) is needed

-  to compensate for the loss in preference-satisfaction (quality of life) of the Buddhists.

 

A sympathetic population axiology corresponds to an Intermediate Social Indifference Curve, where

“Intermediate” means “between Classical Utilitarian and Maximin”.

 

 

 

 

 

1.  Introduction

 

 

Starting point

Gustav Arrhenius – after having systematically investigated the most important axiologies and intuitions of population ethics – came to the conclusion that there is no normative theory which coheres with “our” moral beliefs. This result is immediately plausible on the basis of the following consideration:

         Population ethics using a two-parameter model (welfare and population size) can be characterized by a conflict of interest.

         Conflicting interests shape conflicting intuitions.

         Conflicting intuitions make it impossible to find a coherent normative theory.

In order to find a coherent theory one would have to find a universal interest and a corresponding universal intuition. The obvious candidate to meet this request is sympathy. But since there is no universal consensus on the desirable degree of sympathy, the normative force of such an approach is limited.

Breaking out of the two-parameter model and accepting the incommensurability of certain qualities threatens the normative claim of population ethics [Contestabile 2010, 112].

 

 

Type of problem

The best known and most discussed example shattering our intuitions is Parfit’s Mere Addition Paradox.

How would an axiology look like, which is based on sympathy and solves the paradox?

 

 

 

2.  The Mere Addition Paradox

 

(The following section is taken from the paper On the Buddhist Truths and the Paradoxes in Population Ethics, pp.104-105)

 

The Mere Addition Paradox was identified by Derek Parfit [Parfit 1984, Chapter 19]. In this paper the paradox is introduced in a two-step procedure. Each of the two steps seems to be intuitively right, but the consequence is a statement, which is intuitively wrong. The following diagram Fig.1 shows different populations, with population size represented by column width, and the population’s happiness (in percent) represented by column height.

 

Fig.1

 

                         A                        A

 

For each population represented, everyone within the population has exactly the same level of happiness. Population A, in contrast to B and C, is 100% happy; all their preferences are satisfied. It is assumed that population A and C in state 2 live on different planets so that there is no exchange of information between A and C [Parfit 2004, 11].

In classical utilitarianism, the only criterion which is used to valuate populations is the accumulated happiness:

 

         Intuition 1:

A+C is better than A, as long as all lives in C are worth living.

The happiness of the additional people C is added to the one of A.

 

         Intuition 2:

Let’s assume that state 2 and 3 contain the same number of people. Then

B is better than A+C, as long as the accumulated happiness in B is higher than in A+C.

The critical assumption is that two populations are commensurable, although they contain different levels of happiness. We will refer to this assumption later in the paper.

 

If B is better than A+C, then it is also better than A. This however leads to the following Repugnant Conclusion:

 

“A population Z, consisting of 500 billion individuals, each with a life that is barely worth living, is better than a population A consisting of 1 billion individuals, each having lives that are of extremely high quality – as long as the sum of happiness (welfare) is greater in Z than in A”.

 

 

 

3.  Intuition and Interest

 

(The following section is taken from the webpage http://www.socrethics.com/Folder2/Paradoxes.htm)

 

 

Buddhism

The Repugnant Conclusion can be avoided by assuming that additional lives do not improve the state of affairs:

         However, the higher the quality of the additional lives is thought to be, the more this assumption becomes counter-intuitive, a consequence which is called Reversed Repugnant Conclusion.

         The Reversed Repugnant Conclusion loses its counter-intuitivity, if non-existence is seen as a perfect state (instead of a neutral state). According to the Buddhist Truths perfection can only be reached by eliminating desires and finally dissolving the ego. The closeness of perfection and non-existence (of the ego) is the key to escape the Reversed Repugnant Conclusion.

 

 

Source of the paradox

The comparison of classical utilitarian and Buddhist intuitions demonstrates the close tie between intuitions and interests. The perplexing Buddhist intuition about non-existence contrasts sharply with the vital interest to procreate. Following a brief description of the basic (conflicting) interests and corresponding intuitions:

         The vital interest to expand life – which may originate in the biological utility function – favors the intuition that the size of the population is more important than the quality of life.

         The Buddhist truths – which discourage from expanding desires – favor the intuition that the size of the population is less important than the quality of life.

Only a minority supports a blind biological expansionism and only a minority adopts the Buddhist notion of non-existence. As a consequence, if one of the two interests is radically devaluated at the cost of the other, the combination becomes counter-intuitive for the majority:

         Many people would not mind to slightly decrease the average quality of life in favour of a larger population (with a higher total amount of welfare). But when this devaluation results in lives with minimal quality, it becomes counter-intuitive for the majority (Repugnant Conclusion)

         Similarly many people would not mind to slightly decrease the size of a population (and the total amount of welfare) in favour of a higher average quality of life. But when this devaluation results in a “near zero” population, it becomes counter-intuitive for the majority (Reverse Repugnant Conclusion)

Obviously, at some point, the repetition of a plausible procedure yields a counter-intuitive result. The accumulation of tolerable differences results in an intolerable difference, an experience which is perceived as a paradox.

 

 

 

4.  Indifference Curves

 

Let us resume the initial question: How would an axiology look like, which is based on sympathy and which solves the Mere Addition Paradox?

The guiding idea for the sought-after axiology can be found in the following picture:

 

 

File:Social indifference curves small.png

 

 

This picture was taken from the internet (author unknown)

 

 

Utility

In our context utility corresponds to the preference-satisfaction which is achieved by a certain quality of life or population size:

         For person # 1 utility is defined by the quality of life

         For person # 2 utility is defined by the population size

In other words:

         Person # 1 is a representative of the perfectionist Buddhist axiology, who thinks that additional people do not increase the state of affairs.

         Person # 2 is a representative of the biological utility function, who thinks that the population should be expanded at any cost.

The description of the following three axiologies is adapted from Welfare economics, Wikipedia:

 

 

Utilitarian Social Indifference Curves

The Utilitarian Social Indifference Curves on the left hand side correspond to different levels of social welfare. Since a utilitarian social indifference curve confines an isosceles triangle, each total of individual utilities represented by a point on the curve, results in the same value. No matter how unequal the distribution is, an improvement of utility of the expansionists always compensates the loss in utility of the Buddhists. The (classical) utilitarian axiology allows expanding the population at the cost of the quality of life (see chapter 2).

 

 

Max-Min Social Indifference Curves

 The Max-Min (respectively Maximin) Social Indifference Curves in the middle correspond to different levels of social welfare in a society, which measures welfare by the utility of the worst-off. The social welfare of a Maximin social indifference curve is the sum of two equal utilities and is depicted by the vertex of the curve. The vertex is defined by

         a quality of life, which has a certain utility for a Buddhist

         a population size, which has the same utility for an expansionist.

Increasing the utility of only one person (no matter how much) doesn’t increase social welfare:

1.      Increasing the population size does not increase the welfare of a Buddhist.

2.      Increasing the quality of life does not increase the welfare of an expansionist.

 

 

Intermediate Social Indifference Curves

The Intermediate Social Indifference Curves on the right hand side can be interpreted as showing that – with increasing inequality – a larger improvement in the utility of Buddhists is needed to compensate for the loss in utility of the expansionists (and vice-versa). Intermediate social indifference curves express sympathy of the Buddhists for the expansionists (and vice-versa).

The Intermediate Social Indifference Curve can be constructed in such a way, that – at a certain point – it becomes virtually impossible to compensate quality of life by population size (and vice-versa). The axiology is therefore neither vulnerable to the Repugnant Conclusion nor vulnerable to the Reversed Repugnant Conclusion. The more the size of a population is expanded at the cost of the quality of life (or vice-versa) the more these two preferences become incommensurable.

 

 

 

5.  Incommensurability

 

An ideal manifestation of sympathy corresponds to the interest of a perfectly empathic impartial observer [Contestabile 2016]. However, since there is no consensus on the impact of perfect empathy, the normative force of such an approach is limited. In democracies an Intermediate Social Indifference Curve (e.g. a progressive tax system) has to be implemented by majority decision.

 

The aggregation of incommensurable preferences is the most general approach to solve conflicts of interest. The “repugnancy” of a population can be considered to be a matter of individual preference. A majority-definition of “repugnancy” is then derived by aggregating the individual preferences for each combination of population-size and welfare. If the individuals are well informed about the consequences of a certain population policy and if they can freely express their attitude towards risk, the aggregation of their preferences delivers an intersubjective criterion to decide between policies. The focus shifts to forecasting and educational advertising.

 

There is a theoretical hurdle in the process of aggregation. Incommensurable preferences lead to Arrovian impossibility theorems [Arrhenius 2000, 264]. No voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a certain set of reasonable criteria [Arrow]. In practice this theoretical obstacle can be bypassed. The arrovian impossibility theorem only becomes effective if three or more options are at stake and not if the voters have to confirm or decline a specific population policy.

 

A more disturbing problem is the protection of minorities. Under certain circumstances the aggregation of preferences allows exterminating a minority by majority decision [Hare, 121-122]. Theories of justice [Rawls] prevent the worst cases of abuse, but in less evident cases the problem reappears. The majority decides what kinds of suffering are tolerable. This leads to the question, if the suffering of the minority can be compensated by the happiness of the majority. An ideal manifestation of sympathy may come to the conclusion that the sign of global welfare is negative [Contestabile 2016]. In this case any normative claim which asks for expansionist policies is out of the question; see Population Ethics with Negative Welfare.

 

 

 

6.  Conclusion

 

The Mere Addition Paradox can be solved by an axiology on the basis of sympathy between

         people who prefer to increase (exclusively) the quality of life (e.g. Buddhists).

         people who prefer to increase (exclusively) the population size (expansionists).

 

A sympathetic population axiology has the following characteristic:

As the inequality in preference-satisfaction between Buddhists and expansionists increases

         a larger improvement in the preference-satisfaction of the advantaged is needed

         to compensate for the loss in preference-satisfaction of the disadvantaged.

 

Example:

Let us assume that the population is expanded at the cost of the quality of life, so that the preferences of the expansionists are satisfied at the cost of the Buddhists. As the inequality in preference-satisfaction increases

         a larger improvement in the preference-satisfaction of expansionists (population size) is needed

         to compensate for the loss in preference-satisfaction (quality of life) of the Buddhists.

 

A sympathetic population axiology corresponds to an Intermediate Social Indifference Curve, where

“Intermediate” means “between Classical Utilitarian and Maximin”.

 

 

 

References

 

1.      Arrhenius Gustav (2000), Future Generations, A Challenge for Moral Theory, FD-Diss., Uppsala University, Dept. of Philosopy, Uppsala: University Printers

2.      Arrow Kenneth J. (1966), Social Choice and Individual Values, Wiley, New York

3.      Contestabile Bruno (2010), On the Buddhist Truths and the Paradoxes in Population Ethics, Contemporary Buddhism Vol.11, No.1, 103-113, Routledge, London

4.      Contestabile, Bruno (2016), The Denial of the World from an Impartial View, Contemporary Buddhism Vol.17, No.1, 49-61, Routledge, London

5.      Hare Richard Mervyn (1976), Ethical Theory and Utilitarianism, Contemporary British Philosophy, H.D. Lewis Ed.

6.      Parfit Derek (1984), Reasons and Persons, Clarendon Press, Oxford

7.      Parfit Derek (2004), Overpopulation and the Quality of Life, in The Repugnant Conclusion, Essays on Population Ethics, Kluwer Academic Publishers

8.      Rawls John (1971), A Theory of Justice, Belknap Publishers, Cambridge