A Solution to the Mere Addition Paradox

B.Contestabile admin@socrethics.com First version 2014 Last version 2018

Table of Contents

1. Introduction

2. Indifference Curves

3. Incommensurability

4. Theory and Practice

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].

**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) and expansionists (person #2):

▪
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*

The term (positive)*
welfare* is used here as a synonym for *happiness* and *quality of
life*.

There are two
different strategies to increase the average welfare, which correspond to *different*
*kinds of happiness* [Contestabile 2010, 107] and accordingly different
types of perfectionists:

(1) Satisfy as many desires as possible

(2) Eliminate desires in order to avoid frustrations

These two strategies correspond to different axiologies:

(1) Hospital axiology or classical utilitarianism

(2) Perfectionist Buddhism or negative preference utilitarianism

For information on these axiologies see Negative Utilitarianism and Buddhist Intuition.

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 one of the two interests to some extent (but not completely).

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).

**Sympathy**

1. Utilitarian Indifference Curve:

No matter how unequal the distribution, an increase in the utility of person #2 always compensates the loss of utility of person #1 (and vice-versa). There is no sympathy between the two conflicting interests.

2. Intermediate Indifference Curve:

The opposite interest is partially considered. This is the
characteristics of a *moderate* degree of sympathy.

3. Max-Min Indifference Curve:

The definition of the vertex presupposes a high degree of readiness
to make concessions. The population size cannot be increased without at the
same time increasing the average welfare (and vice-versa). These are the
characteristics of a *high* degree of sympathy.

**Repugnant Conclusions**

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

▪ 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.

** **

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. The interest of the majority could be far from the interest of an empathic impartial observer.

** **

** **

How could the theory of chapter 3 be implemented in practice?

As long as there
is no consensus on the desirable *degree *of sympathy, we do not know
which indifference curve has to be applied.

Is there something like an “objective” criterion for the desirable degree of sympathy?

An objective manifestation of sympathy corresponds to the interest of an empathic impartial observer. Unfortunately, under these premises, we do not even know, if the sign of total welfare is positive or negative [Contestabile, 2016]. It makes therefore sense to disregard the population size and focus on the average welfare.

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

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