The argument against neutrality about the size of population David Pomerenke Supervised by Stefan Fischer Jacob Rosenthal A thesis presented for the degree of Bachelor of Arts Department of Philosophy University of Konstanz Germany December 2019 Contents Introduction 2 1 Exposition 4 1.1 Welfare Economics . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 The intuition of neutrality . . . . . . . . . . . . . . . . . . . . . . 6 1.3 The argument against neutrality . . . . . . . . . . . . . . . . . 9 2 Critical analysis 15 2.1 Aggregation and justice . . . . . . . . . . . . . . . . . . . . . 15 2.2 The neutral range . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Relativism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Conclusion 35 References 37 Many thanks to Ilija Funk for helpful comments! This work is licensed under a Creative Commons Attribution 4.0 International License. Source files and bibliography are publicly available on Github. 1 Introduction How should we as a society value changes in population size? The question may be crucial when evaluating global warming scenarios. I defend the intuition of neutrality, which answers a part of the question. It states that – other things being equal – it is ethically irrelevant whether or not additional people are added to a population. The argument against neutrality criticizes the intuition of neutrality as inconsistent. The contribution of this thesis is twofold: First, the framework of welfare economics, the intuition of neutrality, and the argument against neutrality are presented with formal rigour. Second, the formalizations will be used for a critical analysis of the argument against neutrality. Three ethical frameworks will be assumed – the difference principle, average utilitarianism, and contractarianism –, and their relation to the explicit and hidden premises of the argument against neutrality will be investigated. The result will be that all three frameworks are compatible with the intuition of neutrality (or slightly modified versions); so the argument against neutrality does not hold within them. The analysis is built on several controversial philosophical views and does not necessarily disprove the argument against neutrality. Rather, it undermines the authority of the argument by pointing out the weakness of several premises within the three frameworks. I begin by briefly introducing the framework of welfare economics, which this essay argues within. I then present in more detail the intuition 2 of neutrality and the formal argument brought forward against it. The main part is dedicated to the development of three lines of argumentation in opposition to the argument against neutrality (thus defending the intuition of neutrality). I conclude with a systematic summary of the three lines of argumentation. 3 Chapter 1 Exposition 1.1 Welfare Economics Welfare economics is the theory how individual well-being should be aggregated to general well-being (or welfare). General well-being drives decisions in the welfare state. The theory is relevant for the execution as well as the design of economic policies. As in democracies the citizens and their representatives take part in the design process, welfare economics is subject to societal discourse in these nations. Within this discourse, citizens and media often do not only claim their own interests. Instead they also refer to ethical principles which are to guide democratic policy decisions. This essay is set within this democratic discourse and aims to defend a supposedly widespread intuition whose consistency has been challenged from the academic side. The core of welfare economics is the welfare function (see Harsanyi, 1955, p. 309). It is an aggregation function: a function which takes in the individual levels of well-being of several individual persons, and delivers the level of welfare for the whole aggregated population comprising these individual persons. Well-being and welfare (which refers to aggregated well-being) are abstract terms. They are usually interpreted 4 as a representation derived from a person's preferences about different lives (cf. Crisp, 2017, ch. 4.2). But they can also be interpreted simply as hedonic levels of lifetime pleasure (Crisp, 2017, ch. 4.1), which will be sufficient for the purpose of this thesis. Well-being (or utility) of a person p is denoted by u(p); individual persons are denoted by pi – the subscript is just there to differentiate between different persons. In similar fashion, welfare of a population P = {p1, p2, . . . , pn} is denoted by u(P). Definition 1: Welfare Function w : R|P|+ → R+, {u(p1), u(p2), . . . , u(pn)} 7→ u({p1, p2, . . . , pn}) The content of the general welfare function is intentionally unspecified. The function is just a vehicle for discussion within welfare economics. Several specific welfare functions have been proposed and we will deal with two of them in later sections. For example, the classical utilitarian welfare function states that welfare is simply the sum u(p1) + u(p2) + . . . + u(pn) of all individual well-being. I introduce welfare functions because they are precise formalizations of competing ethical beliefs. In sections 2.1 and 2.2, I will make use of them in order to demonstrate that when we assume certain ethical intuitions, the argument against neutrality does not hold. I will present two widespread competing ethical belief systems – average utilitarianism, and the difference principle – and try to refute the argument against neutrality from each of these views. The idea is that many people will adhere to one of these principles so that they can agree with at least one of the refutations. (Section 2.3 is of a different kind because, rather than to specific welfare functions, it relates to their justification.) It should be briefly noted that welfare economics are blind – and so will be this discussion – in that they are consequentialist. This means that they only evaluate actions by their outcome and in this context specifically by their impact on general welfare or goodness. Other elements 5 of ethical evaluation, such as the procedural requirements of justice, will have to be considered separately (cf. Broome, 2005, p. 401; Broome, 2012, p. 99f). These separate considerations will often require consequentialist considerations as part of their theoretical foundation, so this discussion may be indirectly relevant for them. 1.2 The intuition of neutrality The intuition of neutrality is assumed to be a widespread ethical intuition among humans (Broome, 2012, p. 176f). The content of the intuition is called the principle of equal existence (Broome, 2004, p. 146), but usually (and also in this thesis) the term 'intuition' is used to refer both to the empirical intuition of neutrality and to the propositional content of the intuition of neutrality. The content of the intuition is defined as follows: Let us assume two hypothetical scenarios A and B. The same people exist in both scenarios, except that in scenario B there are some additional people which do not exist in scenario A. The intuition says: Which one of the scenarios is better depends entirely on the well-being of the people who exist in both scenarios, and not at all on the additional people who only exist in B – as long as all the additional people in B have a well-being within a certain neutral range. More specifically, as long as the additional people in B are within the neutral range, scenario A is better in terms of welfare if the people who exist in both populations have a higher welfare in scenario A, and scenario B is better in terms of welfare if the people who exist in both populations have a higher welfare in scenario B. We can formalize the scenarios as different welfare distributions represented by the welfare functions uA and uB (read: u under the circumstances of scenario A, and u under the circumstances of scenario B). Let P0 be a population of people who exist in both scenarios but need not 6 have the same levels of well-being in both scenarios. Let P+ be the population of people who exist only in scenario B. Let [u1, u2] be the neutral range of well-being for added people. Definition 2: The intuition of neutrality ∃u1, u2 : (∀x ∈ P+ : uB(x) ∈ [u1, u2])→ (uB(P0) > uA(P0)→ uB(P0 ∪ P+) > uA(P0)) ∧ (uB(P0) < uA(P0)→ uB(P0 ∪ P+) < uA(P0)) The formalization is to be interpreted in the following way: It does not matter in terms of welfare whether there exists an additional person in the population who lives at a moderate level of well-being. There are several moderate levels of well-beings, which form a range between a low moderate level of well-being u1 and a high moderate level of wellbeing u2. If however the additional person is at a very low level of wellbeing – below u1 – then the person might matter for the calculation of general well-being. (Arguably, the welfare would decrease because of the added person; though this is not specified by the intuition.) Similarly, if the additional person is at a very high level of well-being – above u2 – then the person might matter for the calculation of general well-being. (Arguably, the welfare would increase because of the added person.) There is a specification of the intuition of neutrality where the neutral range has no upper limit, i. e., u2 = ∞ (Broome, 2012, p. 113). This may be an accurate of common belief. Whether the upper limit of the range is finite or infinite is of minor concern for this thesis; it is more important to note that there is some neutral range. If the range is sufficiently large, this might simplify welfare calculations, as the following examples demonstrate: • An exemplary application of the intuition is the evaluation of road safety (Broome, 2004, p. 144f). In this context, the deaths of people 7 dying in accidents must be weighed against the costs of preventing them. Whilst this is an ethically difficult problem on its own, one important long-term effect is usually left aside: The well-being of the expected potential offspring of the potentially dying person is completely neglected. One possible justification is the intuition of neutrality: According to the intuition, if we can expect the offspring to live within the neutral range of well-being, it is neither positive nor negative whether they exist or not. • A second example is the evaluation of different scenarios of global warming (Broome, 2012, p. 170). Global warming is likely to kill many people and thereby to prevent their offspring from existing. On the other hand, global warming may increase poverty, which is associated with higher birth rates. Thanks to the intuition of neutrality we can simply leave both of these effects aside in many of our evaluations – which comes handy as predictions in these domains attend to an enormous amount of uncertainty. Broome, 2012, p. 120ff. sees massive problems if the intuition of neutrality cannot be assumed to apply. It is important to understand that the intuition of neutrality does not imply neutrality about the consequences on the existing population which are caused by the additional population. These consequences may be negative or positive, leading to contrary political reactions such as China's restrictive one-child-policy and Europe's reproduction-promoting policy (Broome, 2012, p. 169). The consequences on the existing population may well determine whether additional people are good or not. Only the well-being of the additional people themselves does not do so according to the intuition of neutrality. The question whether the intuition of neutrality is in fact a widespread intuition among humans appears not to have been investigated. It is not necessary for the argument against neutrality to assume such an 8 empirical fact. Neither is it necessary for the refutation of this argument to assume so. If however this refutation were successful and the integrity of the intuition thus restored, then it would be desirable to investigate the empirical prevalence of the intuition. 1.3 The argument against neutrality Theorem: The argument against neutrality The intuition of neutrality (Def. 2) is incorrect. The argument against (the intuition of) neutrality (described in Broome, 2012, p. 176f) concludes that the intuition of neutrality is inconsistent. The argument is a version of the mere addition paradox (Broome, 2004, p. 148) and a modification of the adoption problem (Broome, 2004, p. 161). The argument against neutrality takes the logical form of a reduction to the absurd: It assumes that the intuition of neutrality applies, deduces a contradiction, and thus concludes that the intuition is incorrect. This section summarizes and formalizes the argument as stated in ?, ?, Broome, 2012. Premise 1: Intuition of neutrality (P1) The intuition of neutrality is right (see Definition 2). The deduction of the contradiction is based on the following counterexample: 9 Counterexample: The situation in the argument against neutrality (A1) Let A, B, C be scenarios with corresponding distributions of well-being uA, uB , uC and populations PA = P0,PB = PC = P0 ∪ P+, and some person p ∈ P0 such that uA(P0 \ {p}) = uB(P0 \ {p}) = uC (P0 \ {p}). (A2) Let uB(p) > uA(p). (A3) Let uC (p) < uA(p). (A4) Let P+ = {q} with uB(q), uC (q) ∈ [u1, u2] (A5) Let uB(p) + uB(q) < uC (p) + uC (q). (A6) Let inequality gB(P0 ∪ P+) > gC (P0 ∪ P+) (see below). The well-being of the persons in scenarios A, B and C with corresponding utility functions ua, ub , uc . Person p is the right person in A and the second person from the right in B and C. Person q is the rightmost person in B and C. Copied from Broome, 2012, p. 177. There are three scenarios A, B and C. They share the same population, except that one additional person exists in both B and C. In both B and C the additional person has a level of well-being within the neutral range. The argument is structured into two major steps: First, scenario A is being compared to scenario B and to scenario C. 10 The additional person can be neglected in this step because the person is within the neutral range. There is one person who is a little bit better off in scenario B than in scenario A. As all other persons have exactly the same level of well-being, it is reasonable that there is a higher welfare in scenario B than in scenario A. Contrarily, there is one person who is a little bit worse off in scenario C than in scenario A. As all other persons have exactly the same level of well-being, it is reasonable that there is a higher welfare in scenario A than in scenario C. As a consequence of these two observations, scenario B has a higher welfare than scenario C. Technically, this conclusion requires transitivity of the betterness relation. Premise 2: Transitivity of betterness (P2) uX (P) > uY (Q) ∧ uY (Q) > uZ (R) → uX (P) > uZ (R) Second, scenario B is compared directly to scenario C. Both scenarios comprise the same people, so there is no additional person in either scenario who could be neglected. The person who is not present in scenario A and has therefore been neglected above is much better off in scenario C than in scenario B. This big difference clearly outweighs the difference of the other person's well-being in favour of scenario B. As there is moreover a lower inequality in scenario C, scenario C has a higher welfare than scenario B. This is in contradiction to the result of step one, so the counter-example refutes the intuition of neutrality, which has been its core assumption. Whilst the argument above is intuitively plausible, it has two other important premises (Broome, 2012, p. 177f): First, if in two scenarios all persons have the same level of well-being except for one person who is better off in the second scenario, then the welfare in the second scenario is higher than in the first. Technically, we can say that the second scenario Pareto dominates the first (Osborne, 1997). (I will come back 11 to this notion in section 2.1.) Premise 3: Pareto domination (P3) 1. ∃p ∈ P : uX (a) > uY (p) ∧ ∀q ∈ P \ {p} : uX (q) = uY (q)) → uX (P) > uY (P) 2. ∃p ∈ P : uX (a) < uY (p) ∧ ∀q ∈ P \ {p} : uX (q) = uY (q)) → uX (P) < uY (P) Second, if in two scenarios with the same population the sum of individual well-being is higher in the second scenario, and at the same time the inequality of the distribution of well-being is lower in the second scenario, then the second scenario is better in terms of welfare than the first. I call this the fair aggregation principle. Premise 4: Fair aggregation principle (P4) ∑ p∈P uX (p) > ∑ p∈P uY (p) ∧ gX (P) < gY (P) → uX (P) > uY (P) with suitable inequality function g (see below). There are various ways to measure inequality, and the details need not concern us here. An excellent survey of one-dimensional inequality measures – as applied in welfare economics – is given in Sen & Foster, 1997. The most prominent inequality measure is probably the Gini coefficient (see Ceriani & Verme, 2012). Both of these premises appear to be very plausible, and they are dubbed "hard-to-doubt assumptions" in Broome, 2012, p. 176. The following proof concisely sums up the argument presented above. 12 It makes use of the technical premises (P...) and the assumptions that make up the setting of the counter-example (A...). We can infer from the contradiction in (C8) that at least one of the premises and assumptions must be false. The assumptions merely describe the setting of the scenarios as depicted in the figure above. They are simply the assumptions making up the counter-example and there is no reason to doubt them within this proof. Moreover, premises (P2), (P3) and (P4) appear to be very plausible. As a consequence, the intuition of neutrality must be the false premise. Proof 1: The argument against neutrality (C1) (P3) ∧ (A1) ∧ (A2)⇒ uB(P0) > uA(P0) (C2) (P3) ∧ (A1) ∧ (A3)⇒ uC (P0) < uA(P0) (C3) (C1) ∧ (P1) ∧ (A4)⇒ uB(P0 ∪ P+) > uA(P0) (C4) (C2) ∧ (P1) ∧ (A4)⇒ uC (P0 ∪ P+) < uA(P0) (C5) (C3) ∧ (C4) ∧ (P2)⇒ uB(P0 ∪ P+) > uC (P0 ∪ P+) (C6) (A1) ∧ (A5)⇒ ∑ x∈P0 uB(x) < ∑ x∈P0 uC (x) (C7) (C6) ∧ (P4) ∧ (A6)⇒ uB(P0 ∪ P+) < uC (P0 ∪ P+) (C8) (C4)⇔ ¬(C7) (C9) (C8) ∧ (A1− A6) ∧ (P2) ∧ (P3) ∧ (P4)⇒ ¬(P1) There are two major implications if this argument holds and the intuition of neutrality is inconsistent (cf. Broome, 2005, p. 411: 1. We as a society would have to develop a different, consistent principle to replace the intuition. We do not even currently know whether population changes should be evaluated as positive or as negative, just that they cannot simply be evaluated as neutral. The 13 finding of a new principle with wide acceptance would certainly present a major societal task and require many years of discourse. 2. As soon as we had found a suitable principle, we would need to gain better knowledge of which actions lead to which consequences with respect to population changes. Only then would we probably be able to apply a principle which is not based on neutrality. This requires new scientific analysis and simulation because such predictions have often been omitted in the past (Broome, 2005, p. 402; Broome, 2012, p. 115f). Broome, 2004 develops five possible responses to the argument against neutrality (see the overview on p. 149). Accordingly, one of the following alternative propositions could be embraced: (a) intransitivity of the betterness relation (b) conditional goodness (c) relative goodness (d) indeterminacy or vagueness of the betterness relation (e) a single neutral level The transitivity of the betterness relation (P2) is plausibly defended in (a) – see Broome, 2004, p. 151f. (P3) and (P4) have not been discussed so far. This is what I will do in section 2.1. Section 2.2 will be very similar to what Broome, 2004 develops with regard to proposition (d), but it will also be compatible with proposition (e). I will pursue a somewhat related approach to (b) and (c) in section 2.3. 14 Chapter 2 Critical analysis 2.1 Aggregation and justice I will start by delivering some general criticism on Pareto domination and aggregation and then continue to examine their relation to justiceoriented welfare functions, specifically the Maximin and Leximin rule. When we say that a scenario Pareto dominates another scenario, we mean that at least one person is better off in this scenario than in the other while all other persons are at an equal level of well-being. The Pareto principle I have formulated as (P2) says that in such cases the first scenario has a higher welfare than the other one. This principle, as well as the extending requirement of Pareto efficiency (cf. Osborne, 1997), find their due place in economics where the objective is the efficient allocation of scarce resources (Samuelson & Nordhaus, 2010, p. 4; Lange, 2019). However I doubt that they are suitable as ethical principles. Pareto efficiency has been criticized because the liberal paradox suggests that it may be incompatible with procedural elements of liberalism (see Sen & Foster, 1997). But I believe that there is a more general problem with Pareto efficiency and even with Pareto domination: Consider a large population with one person whose well-being is much 15 higher than the well-being of the others. Is it ethically desirable – is there a higher welfare – if the welll-being of this person is increased even more, while the well-being of the other persons remains the same? This can be intuitively doubted, and below I show some mildly convincing reasoning in favour of this doubt. A similar criticism applies to what I have called the fair aggregation principle. The fair aggregation principle is a combination of what can be called the simple aggregation principle – that general welfare is the simple sum of all individual well-being – with the additional requirement that distributions need be more equal to have a higher welfare. The principle is non-exhaustive: it does not tell us anything about populations with a higher sum of well-being and a lower equality, and it does not tell us anything about populations with a lower sum of well-being and a higher equality. But that is not a problem, since such populations do not play a relevant role in the counter-example to the intuition of neutrality. The problem with the requirement of equality is that, analytically, equality is a global criterion, which means that it somehow takes into account the well-being of every single person. This implies that a small decrease ε in well-being of the person who already is worst off can always be compensated by some large increase of equality within the rest of the population. This follows because otherwise the well-being of the worst-off person would completely determine the equality – which is intuitively plausible, but not incorporated in the conception of inequality measures. Now imagine three scenarios, all with the same people: In scenario X there is some utility distribution with lots of inequality. The person who is worst off in scenario X is called p. In scenario Y, the well-being of the worst-off person from scenario X is decreased by some very small amount ε. Due to the globality of inequality, this can be compensated in terms of equality by improving the equality within all the other persons to a more or less drastical amount. Let us assume that such compensa16 tion has taken place, so that the overall equality in scenario Y is higher than in scenario X. With the usual inequality functions this will be possible without decreasing the sum of well-being (cf. Ceriani & Verme, 2012). Let us further assume that in a third scenario Z all people are at the same level of well-being as the people in scenario Y, plus ε2 . The general equality has not decreased in Z in comparison to Y. (Depending on the inequality function, it may even have increased, because the relative differences between the least well-off and the most well-off have decreased.) However the sum of well-being is increased in Z in comparison to X because the well-being of many persons has been increased by ε2 while the well-being of only one person has been decreased by ε2 . As a consequence, both the sum of individual well-being and the equality are better in Z than in X, so according to the fair aggregation principle there is a higher welfare in Z than in X. At the same time, the worst-off person in X is even worse off in Z. This seems intuitively implausible and I will now present a theory which explains this implausibility. For this objection I will use as a specific welfare function the difference principle. The difference principle is a concept which is inferred from an analysis of justice. Its justification as the second principle of justice is given and extensively discussed in (Rawls, 2005, pp. 3-183). Rivalling average utilitarianism, the difference principle is probably the most prominent and most widely accepted welfare function. In its core formula, the difference principle states that differences from socioeconomic equality are only permitted if they are to the benefit of the least advantaged (Rawls, 2005, p. 302). This implies that society should aim to optimize the status of the least advantaged. The difference principle is therefore usually represented as a welfare function where general welfare is determined only by the well-being of the group with the lowest level of well-being. (Such representation commits a major error in ignoring the difference between primary goods and well-being as I discuss in Pomerenke, 2017, p. 12f. – But this does not bear upon the reasoning 17 here, which is based solely on Pareto comparisons.) Whilst the difference principle refers to the least advantaged group – which makes sense in application – there is no mistake in referring to the least advantaged person for the sake of theory (cf. (Rawls, 2005, p. 98)). Because of its resemblance to the decision-theoretic rule of minimum maximization, this formulation of the principle has also been called the Maximin rule. (Although this labelling has been rightly criticized in Rawls & Kelly, 2001, p. 43..) Definition 3: Difference principle / "Maximin" w(P) = minp∈P u(p) According to the difference principle in its Maximin version, both Pareto domination and fair aggregation are false: Imagine that one person who is not the worst-off in either scenario is better off in the first scenario than in the second while all other persons are equally well off. Then Pareto domination requires that the first scenario has a higher welfare. The Maximin rule, however, states that both scenarios have the same welfare because the well-being of the worst-off person has not changed. And we have seen above that as a consequence of fair aggregation a scenario may be evaluated as having a higher welfare even if the worst-off person is even worse off – in strict contradiction to the difference principle. But the difference principle in its Maximin formulation has been designed as a simplification with the practical idea in mind that there will seldom or never be a comparison in which the least advantaged will have the exactly same level of well-being in both scenarios. Yet for the theoretical case of a such comparison a more elaborate rule than the Maximin rule has been developed (cf. Rawls, 2005, p. 83): It says that in the case that the least advantaged are at the same level in both scenarios, the second-least advantaged must be regarded. And if the 18 second-least advantaged are also at the same level, then the third-least advantaged must be regarded, and so on. Because it resembles a lexicographical sorting algorithm, the extended rule is called the Leximin rule. It is most clearly formulated as a recursive selection function which outputs the better population of two populations whose members are sorted in ascending order according to their well-being: Definition 4: Difference principle / "Leximin" selection function The set of the best population(s) of two populations S = s1, ..., sn and T = t1, ..., tn which are sorted in ascending by well-being, i. e., • u(s1) ≤ ... ≤ u(sn), • u(t1) ≤ ... ≤ u(tn), is given by lexiMin(S = s1...sn,T = t1...tn) =  {S ,T} for S = T = ∅ {S} for u(s1) > u(t1) {T} for u(s1) < u(t1) lexiMin ((s2, ..., sn), (t2, ..., tn)) for u(s1) = u(t1) We can easily observe that – unlike the Maximin rule – the Leximin rule is compatible with Pareto domination: If all persons are equal in two scenarios except one who is better off in the second scenario, then the Leximin algorithm will recursively call another instance of the Leximin algorithm (where the worst-off from the outer instance will be disregarded), until an instance is called where the two persons in questions are the worst-off persons in their respective scenarios. This process automatically ensures Pareto domination. So at a second glance at the 19 difference principle, it does not contradict but indeed rather support Pareto domination. This is in favour of the argument against neutrality. The same, however, cannot be said about the relation of the difference principle to the principle of fair aggregation. We have seen above that fair aggregation in some cases evaluates distributions as being better than a second distribution even though the worst-off person is better off in the second distribution. In such a case, the Leximin algorithm would stop in the first iteration, with a result equivalent to the result of the Maximin rule. The algorithm would not regard the improved well-being of all the other persons, because not only the Maximin rule but also the Leximin rule deem all general improvements irrelevant if they are to the disadvantage of the least advantaged. So for one major welfare function the "hard-to-doubt" premise of fair aggregation (P4) is false and the argument against neutrality cannot succeed. At the beginning of this section, two intuitive objections to the Pareto principle and the fair aggregation principle have been raised. The objection to the Pareto principle appeared to be supported by assuming the difference principle as a welfare function; however it turned out that the difference principle is only contradictory to the Pareto principle in its Maximin formulation, not in the more general and theoretically preferable formulation as the Leximin rule. The objection to the fair aggregation principle, however, was supported by both the Maximin and the Leximin formulation of the difference principle. As the fair aggregation principle is a necessary premise for the argument against neutrality, the argument therefore fails when the difference principle is assumed as a welfare function. 20 2.2 The neutral range Whilst section 2.1 has dealt with the implications of assuming the difference principle as a welfare function, this section deals with a second popular welfare function, that is average utilitarianism. I will start by explaining how the argument against neutrality requires the neutral range to be a proper range rather than a single level. Afterwards, I will try to make plausible why (assuming average utilitarianism) we should rather assume a single neutral level in theory and elucidate how, taking uncertainty into account, this single neutral level may approach a proper neutral range in practice. So far, the formalization of the intuition of neutrality involves a neutral range [u1, u2] without specifying u1 or u2. As per Definition 2, the neutral range could in fact just be a single number with u1 = u2; but the interpretation of the intuition of neutrality tells us that this range is in fact supposed to be a proper range and rather large. The argument against neutrality, however, could be misunderstood as an argument against any kind of neutral range. The superficial reader – understanding that the argument denies the possibility of a neutral range – may suppose that it denies the possibility of any neutral range. I want to ward off this potential misunderstanding: As demonstrated below, the argument against neutrality only denies the possibility of a proper real range, that is, it denies that the intuition of neutrality holds for u1 6= u2. A careful analysis of the argument against neutrality yields that it interprets the intuition of neutrality in a way that does not permit that the neutral range is just a single level of well-being: In order to neutralize and counter the positive difference in well-being for person p between scenarios B and C, the difference in well-being between scenarios B and C for person q must be negative. So the neutral range must allow for such a difference, because the well-being of both p and q is to be within the 21 neutral range: Corollary 1: Proper neutral range (C10) (A2) ∧ (A3)⇒ uB(p) > uC (p) (C11) (C10) ∧ (A5)⇒ uB(q) < uC (q) (C12) (C11) ∧ (A4)⇒ u1 < u2 Formally (C12), as an implication of the argument against neutrality, is a substantive specification of the intuition of neutrality. Contentwise (C12) is completely in line with the idea behind the intuition of neutrality (cf. Broome, 2004, p. 146): Added lives are neutral except if they are at a very low or very high level of well-being (Broome, 2012, p. 172), so the neutral range is not only a proper range but also a rather big range. The crucial message from the Corollary is that the argument against neutrality has a hidden premise, which has not been made explicit so far: u1 < u2. Even if the intuition of neutrality in this form empirically holds as a widespread intuition, it is theoretically problematic: • One of its implications is for example that we cannot say that a scenario with many added people at the highest well-being within the neutral range is better than a scenario with many added people at the lowest level of well-being. This implication - that well-being within the neutral range is incomparable - is at least controversial. And there are other pressing theoretical questions: • What values should u1 and u2 assume? Imagine someone proposed as a specification that u1 should be, say, at the level of wellbeing of the person at the top of the lowest 10% of the population in terms of well-being. How should we respond? – How should we know whether that is correct? 22 – What kind of arguments would we have to employ in order to plead for a higher or lower value? – What kind of ethical principle determines the range? These problems do not arise if we restrict the intuition of neutrality to a single level of neutral well-being: 1. Such a restriction would directly invalidate the argument against neutrality and circumvent the problem of the incomparability of people within the neutral range which I have just touched upon. 2. There exists an established ethical theory which justifies the existence of this level and explains what value it should take. The theory in (2.) is average utilitarianism and one kind of justification for it is found in Harsanyi, 1955. Average utilitarianism is a highly controversial theory, specifically but not only when it is understood as a complete moral theory rather than only a theory of goodness (cf. Broome, 2012, pp. 50-54; Arrhenius, Ryberg, & Tännsjö, 2017, sec 2.1.1; Rawls, 2005, pp. 167-175, 572f). But it is a popular and consistent ethical theory which is not only able to account for many other ethical intuitions but also to answer our quantitative and justificatory questions regarding the neutral level of well-being. The welfare function of average utilitarianism states that general welfare is the average of all individual well-being: Definition 5: Average utilitarianism u(P) = ∑ p∈P u(p) |P| This implies that in order to be neutral to existing welfare, the welfare of an added population must equal the welfare of the existing population. Not every single added person needs to be at this neutral level, but rather the average of all added persons needs to be at this level. 23 Definition 6: The neutral range in average utilitarianism [u1, u2] = u1 = u2 = u0 = w(P) So average utilitarianism provides a response to the argument against neutrality by modifying the intuition of neutrality and assuming a neutral level instead of a neutral range. As a result, the intuition is consistent, calculable, and maybe even justified (regarding the justification, cf. Rawls, 2005, pp. 161-175; and also Arrhenius et al., 2017). Average utilitarianism plays (in this case) a revisionist role, a theory of moral error (cf. Mackie, 1990, p. 35): It tells us to slightly adjust our intuition – to sharpen it – so that it is consistent in itself and in its relation to other moral judgments. This is an acceptable, maybe desirable intervention to the beliefs from our intuition. Furthermore, this theoretical sharpening would not even necessarily change our application of the intuition of neutrality. This is because in practice, uncertainties are attached to all quantities of well-being, specifically the neutral value. When I talk of 'uncertainty' here, then I refer to 'measurement uncertainty' as used in statistics and the quantitative sciences. (The uncertainty in question is quantifiable, so in it falls into the decision-theoretic category of risk and not into the decisiontheoretic category of uncertainty.) Measurement uncertainty is a welldeveloped theory (see, e. g., Runge, 2007). Unlike the approaches of introducing indeterminacy in the forms of incommensurateness or vagueness (cf. alternative (d) in section 1.3) – which are pursued and discarded as a solution to the argument against neutrality in Broome, 2004, pp. 164-183 – uncertainty does not suffer from difficult problems such as greediness (a problem discussed in Broome, 2004, p. 170ff). The neutral value is affected by two kinds of uncertainty: 1. The first kind of uncertainty arises from the definition of the neutral level. Sensitivity analysis (cf. Runge, 2007) of Definition 5 tells us that 24 the uncertainty of the neutral level is composed of the average uncertainty of the well-being of all existing people. 2. The level of well-being of any actual person that is considered to be at the neutral level or not is also subject to some uncertainty. In both cases, the uncertainty arises from the difficulty to quantify the personal well-being of existing or hypothetical persons (see Harsanyi, 1955, p. 317-319 for discussion). These uncertainties are not on a theoretical level. On the theoretical level it has been questioned that such quantifications are metaphysically and psychologically possible at all (cf. Harsanyi, 1955, pp. 317-319). – On the practical level, these quantifications are de facto happening, but there is a great level of uncertainty attached to them (Broome, 2004, ch. 9). We can then accept the theoretical notion of a neutral level while at the same time both maintaining the practical idea of the intuition of neutrality and avoiding the argument against neutrality. Is doing so just a sophisticated trick? No: The specific nature of the intuition of neutrality had not been analysed before. Rather, it may have been a bit rash to conclude from the rough idea of the intuition of neutrality that it has to be formalized as a proper range. This section has explained that there is at least no obvious possibility of justifying such a range, and that as a consequence we do not know how to quantify the range. Average utilitarianism presents a possible justification for a neutral level, and together with uncertainty it can justify something like a range. This formal interpretation may be even closer to the empirical intuition of neutrality than the interpretation as a real range is. If it is not, the problem of the incomparability within the neutral range and the problem of the quantifiability of the neutral range present compelling reasons why we should adjust our intuitions. 25 2.3 Relativism While sections 2.1 and 2.2 examine how two different welfare functions affect the result of the comparison of scenarios with a changing population, this section investigates which persons are to be regarded in such comparisons. We will see that the argument against neutrality makes some controversial implicit assumptions about which persons are to be regarded; a modification of these assumptions may therefore avoid the argument against neutrality, regardless of the chosen welfare function. The difference principle and average utilitarianism are probably the two most prominent welfare functions. In both of them the argument against neutrality does not hold for different reasons. Yet, although these frameworks are so well received, they both raise the question of how they should be justified. The specific justificatory problem which matters in our context is that the frameworks assume a universal moral domain. This means that they assume that in the first place every person should receive moral consideration. If the universal domain is rejected, the results of sections 2.1 and 2.2 will no longer matter. We will now see that the argument against neutrality fails if the universal domain is rejected, and afterwards we will discuss whether such a relativistic position is acceptable. In the context of this section, 'relativism' refers to the procedure of undertaking ethical evaluations with respect to a certain (temporally limited) population rather than with respect to all persons ever existing. In a relativistic interpretation, 'goodness' is to be understood as 'goodness for someone or some group', and in our context usually as 'goodness for the current (world) population'. This form of relativism is more precisely referred to as metaethical relativism (cf. Westacott, 2019, ch. 2e; Gowans, 2019, ch. 2). So far we have interpreted the intuition of neutrality as a principle which is applied only in a particular instance of comparisons between welfare in different scenarios: Whenever there are additional persons in 26 one scenario who do not exist in the other scenario, then we can apply the intuition of neutrality. This is reflected in the reasoning in Proof 1: In (C3) and (C4) we have used the intuition of neutrality because there is a different number of persons in scenario A than there is in scenarios B and C. But in (C7) we have been comparing scenarios B and C, and these scenarios have the same number of persons, so we had to take into account the well-being of all people: "B and C contain the very same five people, so in comparing their values all five count as existing people." (Broome, 2012, p. 177) A simple escape from the argument against neutrality would be to deny that in such cases all people count as existing people. If we regard person q (the person who exists in scenarios B and C only) as nonexistent, then we cannot derive that C is better than B by direct comparison (C7), and the argument fails: Proof 2: Failing modification of the argument against neutrality Assume (C1) – (C6) from proof 1. Assuming that q is disregarded in the comparison between B and C, we do not arrive at (C7), (C8), and consequently (C9); but rather at the different conclusions (C7') and (C8') from which the result of (C9) cannot be deduced. This means that the proof fails under the modified assumption. That q is disregarded from the comparison between B and C formally follows from (P5): 'A is the base scenario.' This additional premise will be introduced and discussed below. (C7') (A1) ∧ (A2) ∧ (A3) ∧ (P1) ∧ (P5) ⇒ uB(P0 ∪ P+) > uC (P0 ∪ P+) (C8') (C4)⇔ (C7′) If we want to disregard person q in the comparison between sce27 narios B and C, we need a revised version of the intuition of neutrality (Definition 2; Premise 1). The differences to the original formulation in Definition 2 are highlighted in yellow. Definition 7: The intuition of neutrality (revised) ∃u1, u2 : (∀x ∈ P+ : uB(x) ∈ [u1, u2])→ (uB(P0) > uA(P0)→ uB(P0 ∪ P+) > uA(P0 ∪P+ )) ∧ (uB(P0) < uA(P0)→ uB(P0 ∪ P+) < uA(P0 ∪P+ )) In the definition above, the intuition has been modified in a way such that it also applies to comparisons where the persons are the same in both scenarios (such as in the comparison between scenarios A and B). As shown in 2, this avoids the argument against neutrality. But while this solution may be compelling so far, it brings with it a formal problem. In the original definition of the intuition of neutrality (Definition 2), we have not really needed to specify P0 and P+: P0 has been the population which exists in both scenarios and P+ has been the population which exists only in scenario B. This is no longer implicit in Definition 7: P0 and P+ both exist in both scenarios; they are not distinguished by the definition. P+ are the people who are neutral with respect to general welfare if their well-being lies within the neutral range; and P+ are the same people in B and in C. But P+ could be any persons: P+ could be all persons, no persons, or an arbitrary selection of persons. So as they are not already formally specified we need to specify P+: Definition 8: Additional specification of the intuition of neutrality P0 are the existing people and P+ are the non-existing people. This definition is completely in the spirit of the original intuition of neutrality: The intuition is originally about existing and non-existing people. Unlike all the formal definitions above, this is a material definition, 28 which is not a problem. The problem is that it is also a time-relative definition. Which people are existing and which are not depends on the time of evaluation. Example: Time-relativity When we consider whether it is good or not that a baby is born, we arrive at different evaluations before and after the pregnancy of the baby's parent. Before the pregnancy, the baby's wellbeing has to be ignored because of the intuition of neutrality, but after the pregnancy, the baby's well-being has to be considered. Imagine that we want to know whether it is positive or negative for the general welfare whether the baby suffers from a chronic disease. Then before the pregnancy we will derive that the chronic disease is neutral with respect to general welfare and after the pregnancy we will derive that it would be better for general welfare if the baby did not suffer from the disease. The evaluation of welfare depends on what scenario we use as a base scenario based on which we judge which persons are existent and which are not. (This has been suggested by Stefan Fischer in a discussion.) Such a base scenario may be either of the scenarios which we compare, or a third scenario. In the case of the argument of neutrality, we need to choose scenario A as our base scenario so that we can arrive at the alternative conclusion (C8'). Premise 5: Base scenario (P5) A is the base scenario, with the corresponding distribution uA of well-being. The additional specification and the additional premise are a form of metaethical relativism: We have to choose a base scenario, for which the ethical evaluation is conducted. This scenario will usually be our 29 own, current scenario, because we are interested in persons which are added to our own, current population. P0 will thus be the current world population, and P+ will be some potential additional future population. If the question wil be discussed again in ten years, then the society existing in ten years will read P0 as the population then existing, and P+ as a potential additional future population that comes into being later than ten years from today. Moreover – and now things are getting complicated – when our society in ten years deliberates about the decisions taken today, they will have to employ their own standard from their own time: This means, they will count both the current population and all people coming into existence between now and ten years from now as P0 when they want to arrive at their own normative evaluations. Only if they want to evaluate the current decisions from the perspective of the current population (which is usually a question of minor interest), the future population will, just like us today, use P0 to refer to the current population. A similar approach to the described relativism is pursued in Broome, 2004, pp. 157-162. There it is discarded for two reasons: 1. Because of the incoherence which arises when switching the base scenario (pp. 68-76). 2. Because of the difficulty to ethically justify person-relativity or community-relativity (p. 161f). I will now address both issues. The problem of incoherence cannot be denied: If ethical evaluations of welfare depend on the choice of the base scenario and if every person chooses the person's own (current) situation as the base scenario, incoherence will arise. Principally, there are relativistic inconsistencies of several kinds. E. g., one person could contradict another person from the same population. As we are concerned with population ethics here, where persons will usually somehow consider the whole population for 30 their evaluation, this is not necessarily a problem. A necessary problem is the time-dependence of the evaluation, which is pointed out in Broome, 2004, p. 75: "You choose rightly, but it later turns out you chose wrongly. Indeed, it may turn out that you ought later to undo what you rightly did. Moreover, you might be able to foresee even as you choose [your action] that just this would happen. This is a most implausible sort of incoherence in your activity." This criticism of time-relativity sounds like a problem at first, but I will now try to plausibilize that it might be acceptable. One possible defence of time-relativity is in denying that incoherence between actions is a problem at all. Incoherent actions are sometimes criticized in everyday situations; for example, when two persons or one person act out two actions which appear to follow opposite intentions, we might say that the actions are incoherent (or inconsistent). But the conceptual basis for such ascriptions is rather fuzzy and the existing theory of rationality does not provide a criterion for directly identifying incoherent actions. What the theory of rationality does provide is a criterion for identifying incoherent beliefs: Beliefs are incoherent if their propositional contents are contradictory. The only philosophically developed theory for criticizing inconsistent actions is (to my knowledge) to criticize inconsistencies in the belief set motivating the action (cf. Wilson & Shpall, 2016, ch. 4). The underlying beliefs in a situation of alleged incoherence due to time-relativistic reasoning are complex: Before action A, we think that we should do A. And we think that as a causal effect of doing A, we will regret having done A. So we think that we should do A, and that we will regret it afterwards. After the action A, we think that we should not have done A. We also think that we have thought that we should do A. The point is that there is no apparent formal contradiction within this belief 31 set. – It may very well be rational to think A at the moment and to expect that oneself would think the opposite of A under different circumstances. As the enactment of A causes a change of circumstances, the complex belief set above may come about, and there is nothing wrong with it. Similarly, one may deny that it is irrational to undo an action (cf. Broome, 2004, p. 75). A is done within one set of circumstances and then within another set of circumstances it is undone. The two actions of 'doing A' and 'undoing A' can be differentiated by the fact that they have taken place within different contexts (one context without the causal effects of A and one context with the causal effects of A). There is no obvious reason to ignore the contexts of the actions and to strip them down to the notions of 'doing A' and 'undoing A', creating a possibly false dichotomy. The above argumentation – that the apparent incoherence due to temporal relativity is not irrational – will certainly be highly controversial. But it is much more plausible that it applies to group beliefs and group actions. And it is group actions towards which the criticism of population-relativity in Broome, 2004, pp. 157-162 is directed. 32 Example: Coherence of group actions As an illustration, imagine a direct democracy called Alphaland whose citizens consider – say, because of their liberal ideal – to invade and annex an autocratic country called Betaland with a population bigger than their own population. They consensually adopt a resolution: "Alphaland wants to annex Betaland. Alphaland expects Betaland to condemn the violence related to the annexation. As the current citizens of Betaland will be the majority in Alphaland after the annexation, we expect that Alphaland will officially regret the annexation afterwards. But we expect that most former Betaland citizens will nonetheless want to remain in Alphaland for pragmatic reasons (so the annexation would not be without effect)." It is plausible that rationality does not require present Alphaland to consider the interest of future Alphaland. After all, future Alphaland is made up of different citizens than present Alphaland. This example illustrates that there is no requirement for communities to be coherent with their beliefs and expected beliefs over time. One might object to the above example: "If Alphaland was a single person, we would criticize the annexation as irrational." But this objection is beyond the point: Groups, though they may be identified – analogous to single persons – by names, do not possess beliefs in the same sense that persons do. This becomes apparent in situations like voting, where, for example, the voting paradox leads to counterintuitive conclusions (cf. List, 2013, ch. 1.1). And group actions also belie one's expectations with respect to temporal coherence. Even if the rationality constraints of temporal coherence may apply for individual persons (which I have questioned above), they do not for groups. The previous paragraphs have been about the coherence of group 33 beliefs. One might object: Are we not concerned with general ethical belief, which one would assume to be independent from the practical belief of some community? The answer is that in metaethical relativism all ethical evaluations depend on the fact which scenario is the base scenario, and the choice of the base scenario depends on the own, current population. After I have defended the form of metaethical relativism which comes along with Definitions 7, 8 and Premise 5, I will end with some brief remarks regarding the justificatory status of metaethical relativism. Relativism is dropped in Broome, 2004, p. 160f, mainly because of (1) the alleged incoherence discussed above and (2) the lack of justification for the required form of metaethical relativism. Regarding (2), there are indeed good reasons why metaethical relativism is preferable to other preferable positions. I point towards the argument from queerness and the argument from relativity found in Mackie, 1990, part 1 and summarized in Joyce, 2016, supp. 2. The contractarian tradition within ethics is closely associated with metaethical relativism (including timerelativism). One sophisticated contemporary ethical framework based on metaethical relativism is presented in Stemmer, 2013. These references shall suffice to make clear that the justificatory status of metaethical relativism needs not be considered problematic, but to the contrary can be seen as very satisfactory. Even more than the arguments in sections 2.1 and 2.2, the argumentation in this section touches upon several philosophical controversies, notably whether metaethical time-relativism is coherent and whether it is justified. The result is that if both questions can be answered with yes, the argument against neutrality is undermined. This is because metaethical time-relativism allows us to modify the intuition of neutrality in a way that is consistent with its original intention and which avoids the argument against neutrality by relying on a base scenario. 34 Conclusion This thesis has formally presented the framework of welfare economics, the intuition of neutrality, and the argument against (the intuition of) neutrality. It has proceded by critically analyzing the impact of three (meta)ethical frameworks on the soundness of the argument against neutrality, with the following results: 1. The difference principle in its Leximin formulation is in contradiction to the principle of fair aggregation, which is a premise for the argument against neutrality. The argument against neutrality therefore does not hold when assuming the difference principle. 2. The argument against neutrality has the implicit premise that the neutral range within which persons can be added to a population is a proper range. Average utilitarianism suggests to slightly modify the intuition of neutrality so that it uses a neutral level rather than a proper neutral range. Because of the uncertainty involved, this is in practice somewhat similar to the original intuition of neutrality. The argument against neutrality therefore does not hold when assuming average utilitarianism and slightly adjusting the intuition of neutrality accordingly. 3. Assuming metaethical time-relativism (as is usually the case in contractarian theories), the intuition of neutrality can be modified by introducing a base scenario for comparisons. This modification is in 35 line with the spirit of the original intuition of neutrality. The argument against neutrality does not hold when assuming this modification. This means that in any of the three frameworks – difference principle, average utilitarianism, implementations of metaethical relativism such as moral contractarianism – the argument against neutrality does not hold. These frameworks do not present a complete partition of ethical beliefs, but they are major ethical frameworks. C o n tr a c ta ria n ism A ve ra g e U til ita ria n ism D iff e re n c e Pr in c ip le Note Example C o m p a tib le 3 3 5 Utilitarianism with contractarian justification Harsanyi, 1955 3 3 5 3 Difference principle with contractarian justification Rawls, 2005 3 3 5 5 Contractarianism with other or no welfare function Stemmer, 2000 3 5 3 5 Utilitarianism with other justification Mill, 2016 3 5 5 3 Difference principle with other justification cf. Pomerenke, 2017 3 5 5 5 Other moral framework ... ? Possible combinations of the three ethical frameworks of contractarianism (in a metaethically time-relative version), average utilitarianism, and the difference principle; along with a short characterization; one exemplary theoretical text; and the compatibility with the intuition of neutrality. (Mill, 2016 is classified as average utilitarian in Myrdal, 2017, p; 38.) As a result, the intuition of neutrality can be assumed in these frameworks. Whether the intuition of neutrality should be adopted is left open in this thesis. Assuming that ethics is a system which should be built up from people's ethical convictions (a controversial claim on its own), an investigation into the empirical prevalence of the intuition should be conducted. If the intuition of neutrality is considered correct, it might simplify calculations with regard to pressing problems such as global warming. 36 References Arrhenius, G., Ryberg, J., & Tännsjö, T. (2017). The Repugnant Conclusion. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Spring 2017 ed.). Metaphysics Research Lab, Stanford University. Retrieved 2019-08-30, from https://plato.stanford.edu/archives/ spr2017/entries/repugnant-conclusion/ Broome, J. (2004). Weighing lives. New York: Oxford University Press. Broome, J. (2005). Should we value population? 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