A Solution to the Mere Addition Paradox

by Socrethics First version 2014 Last version 2018

Table of Contents

1. Introduction

2. Incommensurability

3. Indifference Curves

4. Sympathy

5. Population Ethics under Uncertainty

The Mere Addition Paradox was identified by Derek Parfit [Parfit 1984, Chapter 19].

For a description and analysis see On the Buddhist Truths and the Paradoxes in Population Ethics.

Above article ends with the following conclusion:

▪ 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* *[Contestabile 2010, 111].

** **

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 (average 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 Arrowian 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 Arrowian 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.

Besides the promotion of democracy there is no normative claim in this approach. Democracy, however, does not solve the Mere Addition Paradox, because it cannot prevent the Repugnant Conclusion. In democratic polls a majority can decide to indefinitely expand the population at the cost of the average welfare. In such a case the expansionist majority completely overrules the quality-conscious minority. A solution, which is based on sympathy, has to protect minorities. In the following we phrase this demand in the language of indifference curves:

**Distributive
justice**

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 __Fig.1__:

__Fig.1__

Picture from Welfare Economics, Wikipedia

The Mere
Addition Paradox can be seen as a conflict of interest between perfectionists
(person #1 in __Fig.1__) and expansionists (person #2 in __Fig.1__):

▪
For the expansionists utility is defined by the *population
size, *as long as there remains a minimally positive average welfare.

▪
For the perfectionists utility is defined by the
*average welfare, *as long as there remains a minimal population size

The term *welfare*
stands for *economic *welfare in this paper, because in practice the focus
of population ethics is on economic welfare. But the analysis is also valid for
*happiness*, *quality of life* and *life satisfaction, *as far
as these terms correlate with economic welfare.

In our context indifference curves define the distributive (in)justice between perfectionists and expansionists.

It is assumed that the available resources can be distributed in such a way that the result is

▪
either a *large population* *with low average
welfare *(the preference of the expansionists)

▪
or a *small population with high average welfare
*(the preference of the perfectionists)

▪ or a compromise.

- With the Utilitarian Indifference Curve there is no distributive justice, i.e. one of the two interests can completely dominate the other (in practice classical utilitarianism favors expansionists because it is easier to increase the population size than the average welfare)

- The Max-Min Indifference Curve is egalitarian, i.e. the two interests have the same weight.

- The Intermediate Indifference Curve is prioritarian, i.e. it prioritizes the expansionist interest or the perfectionist interest, depending on the segment of the curve.

The following description is adapted from Welfare economics, Wikipedia:

**Utilitarian Indifference
Curves**

The *Utilitarian
Indifference Curves* on the left hand side of __Fig.1__ correspond to different
levels of total utility, where

total utility = utility of person #1 + utility of person #2. Since a Utilitarian Indifference Curve confines an isosceles triangle, each total (represented by a point on the curve) results in the same value.

**Max-Min Indifference
Curves**

The *Max-Min
(respectively Maximin) Indifference Curves* in the middle of __Fig.1__ correspond
to different levels of total utility, where total utility is measured by the
utility of the worst-off. The total utility of a Max-Min Indifference Curve is
depicted by the vertex of the curve. The vertex is defined by an average welfare
and a population size, which have the *same utility* for both person #1 and person #2. *Solely* increasing the utility of person 1 (no matter how much) doesn’t increase the
total, because the total is measured by the utility of the worst-off (in this
case the utility of person #2). Analogously the total
cannot be increased by *solely* increasing the utility of person #2.

**Intermediate Indifference Curves**

The *Intermediate Indifference Curves* on the right hand side of
__Fig.1__ can be interpreted as showing that – with increasing inequality –
a larger increase in the utility of person #2 (i.e. a larger expansion of the population size) is needed to
compensate the loss of utility of person #1 (and vice-versa). The Intermediate Indifference Curve can be
constructed in such a way, that – at a certain point – it becomes virtually
impossible to increase the total by an increase in the population size, i.e.
the curve turns into a vertical line (as in the Max-Min Curve).

**Repugnant conclusions**

The Mere Addition Paradox is characterized by

- the Repugnant Conclusion, which says that it is repugnant to minimize the average welfare in order to maximize the population size.

- its reversal, which says that it is repugnant to minimize the population size in order to maximize the average welfare.

If these repugnant conclusions disappear, the paradox is solved.

The Stanford Encyclopedia lists eight different ways of dealing with the Repugnant Conclusion [Stanford], but none of them is based on indifference curves:

▪
The *Utilitarian Indifference Curve* allows
completely overruling the opposite interest, i.e. it is vulnerable to both the Repugnant Conclusion and its
reversal.

▪
The *Max-Min Indifference Curve* does not
allow overruling the opposite interest and is therefore immune to both kinds of
repugnant conclusions.

▪
The *Intermediate Indifference Curve*
allows approximating the *Min-Max Indifference Curve* for high average
welfare and for large populations, so that the repugnant conclusions can be
avoided as well.

Distributive justice is the result of sympathy, law of reciprocity or – as Kant called it – the categorical imperative.

** **

** **

**Degrees of sympathy**

The indifference curves can be assigned to degrees of sympathy as follows:

*1.
**Utilitarian Indifference Curve: *

There is no sympathy between the two conflicting interests.

*2.
**Max-Min Indifference Curve: *

Perfect sympathy, both interests are *equally*
considered.

*3.
**Intermediate Indifference Curve: *

Moderate sympathy, the interests are *unequally* considered,
but it is impossible to completely overrule the opposing interest.

* *

Since the targeted solution emphasizes sympathy, we exclude the *Utilitarian
Indifference Curve *and declare the *Max-Min Indifference Curve* to be
the ethical ideal. This has the following consequences:

▪
If resources are at disposition then the
expansionists – which like to have plenty of children – would use them for
expanding the population, whereas the perfectionists would use them for
increasing the average welfare. The *Min-Max Indifference Curve* says that
only a population policy which considers both interests *equally*,
improves the state of affairs.

▪
If, in contrast, if there is a lack of resources
then the expansionists would rather decrease the average welfare than having
less children, whereas the perfectionists would rather stop having children
than decreasing the average welfare. The *Min-Max Indifference Curve* says
that population size and average welfare have to be *equally* reduced.

**Ordering by degree of sympathy**

What makes a population better in a diagram with the parameters average welfare and population size?

The crucial point consists in *measuring* the equal weight,
given to the conflicting interests. In order to quantify *equality* we
have to define (under the side-constraint of pre-defined available resources)

- the maximal population size that can be realized with a minimal average welfare (expansionist interest)

- the maximal average welfare that can be realized with a minimal population size (perfectionist interest)

If we consider now any population, which satisfies the side-constraint, then we can assign

- a percentage for serving the expansionist interest (actual relative to maximal population size)

- a percentage for serving the perfectionist interest (actual relative to maximal average welfare)

A population
which serves both interests with the *same percentage* corresponds to
perfect sympathy. All other populations can be ordered according to their
degree of sympathy (deviation from equality).

**Population
ethics with negative welfare**

Indifference
curves can also be applied to population ethics with* negative total welfare*.
In this case there is a conflict between

- the interest to reduce the number of suffering people

- the interest to reduce the average level of suffering.

The solution is analogous to the one sketched above for population ethics with positive total welfare.

5. Population Ethics under Uncertainty

A different
normative approach consists in looking at the situation from the perspective of
an impartial empathic observer (see Ideal Observer
Theory). The solution of
the Mere Addition Paradox, which is described in chapter 4, is a solution of
the conflict between quantity and quality. From the perspective of an impartial
empathic observer, however, the major theoretical problem is not *quantity
versus quality*, but *positive versus negative total welfare*. We do
not know with certainty, if total (national, global) welfare is positive or
negative [Contestabile 2016]. Given this uncertainty, it makes sense to
disregard the population size and focus on average welfare.

In theory average utilitarianism is counter-intuitive, because

▪ a single person with a certain welfare (e.g. 6 points on a 10 point scale) is morally better than

▪ a huge population with a minimally lesser average welfare (e.g. 5.9 points)

[Arrhenius, 54]

In the comparison of nations, however, this argument does not apply.

There are additional theoretical deficiencies [Arrhenius, 54-57], but despite of that average utilitarianism is the most popular axiology among welfare economists [Arrhenius, 53]. It allows comparing the welfare of nations and is easy to understand for politicians and voters. A change in the population size

- is morally good, if the average increases

- is morally bad, if the average decreases

The crucial point remains the metric, which is used to compare happiness with suffering. As long as the sign of total welfare is uncertain, we should actually construct the hedonistic scale in such a way that total welfare becomes zero. From then on we can observe, in which direction the average moves – but not more. The uncertainty remains.

One could argue that – as long as the task is only to observe changes – one could as well operate with current indices like the OECD Better Life Index or the Satisfaction with Life Index. But the difference is a psychological one. The current indices suggest that the traumatic suffering of a minority can easily be compensated by the happiness of the majority. An average which circles around zero, however, suggests that it could also make sense to deny the world “as it is”.

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

6. Stanford Encyclopedia of Philosophy (2016), The Repugnant Conclusion

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