What should we do about future generations? The impossibility of ...

Economics and Philosophy, 5, 1989, 235-253. Printed in the United States of America.

WHAT SHOULD WE DO ABOUT FUTURE GENERATIONS? Impossibility of Parfit's Theory X

YEW-KWANC N G

Monash University, Australia

Parfit's requirements for an ideal Theory X cannot be fully met since the Mere Addition Principle and Non-Antiegalitarianism imply the Repugnant Conclusion: Theory X does not exist. However, since the Repugnant Conclusion is really compelling, the Impersonal Total Principle should be adopted for impartial comparisons concerning future generations. Nevertheless, where our own interests are affected, we may yet choose to be partial, trading off our concern for future (or others') goodness with our self-interests. Theory X' (maximization of number-dampened total utility) meets all Parfit's requirements except the Mere Addition Principle in less compelling cases. Many of our present actions (such as resource usage, environmental protection, population policies, child-care centers, education, etc.) have significant effects on the well-being of future generations as well as their population sizes. The moral comparison of alternative situations (or worlds) of different population sizes is thus of direct importance to the moral foundation of our present policies. In a recent article and a recent book, Parfit (1982, 1984) raises interesting and agonizing problems and paradoxes concerning future generations. In the concluding chapter of his book, Parfit admits failure in his search for a Theory X that can answer all the problems he raises, but believes that if others tried, they could succeed. Section I outlines the problem and Parfit's requirements for an ideal Theory X. Section II argues that Theory X does not exist because some of Parfit's requirements (the Mere Addition Principle and

I am grateful to the editors, referees, and Derek Parfit for their comments. © 1989 Cambridge University Press 0266-2671/89 $5.00 + .00.

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Non-Antiegalitarianism) imply the rejection of another (the avoidance of the so-called Repugnant Conclusion). Two alternative escapes from this impossibility result are then discussed. First, Section III argues that the Repugnant Conclusion is not really repugnant, but is in fact compelling. Hence, the Impersonal Total Principle should be our moral criterion concerning future generations. Nevertheless, this does not imply that we must sacrifice our welfare to create a big population, since we may want to be partial to our own welfare. Secondly, Section IV shows that Theory X', which seems closest to Parfit's ideal, satisfies all his requirements except the Mere Addition Principle in less compelling cases. I. PARFIT'S REQUIREMENTS AND THEORY X

Consider two alternative policies toward resources called (reasonable) conservation and (rapid) depletion that may be pursued by the present generation and would have implications for people generations from now. The usual argument against depletion is that it would drastically reduce the welfare of future generations with a relatively small gain to the present generations. But Parfit argues that there is no person in the far future whose existence is independent of which policy is pursued. Conceptions at different times and even different marriages will be made, meaning different people will be born under each policy. Depletion would lower the quality of life in the far future, but the people who would then be living would not have been born if instead we had adopted conservation. Those who would be living would be another set of people. If these people's lives were still worth living, depletion would be better for them. Parfit concludes that depletion would be worse for no one while it makes the present generation better off. However, Parfit is not in favor of depletion. To solve what he calls the Non-Identity Problem illustrated above, he proposes the Same Number Quality Claim [Q]: "If in either of two outcomes the same number of people would ever live, it would be bad if those who live are worse off, or have a lower quality of life, than those who would have lived." (Parfit, 1984, p. 360) For cases where different numbers of people are involved, we need a more general theory than Q. Parfit calls this Theory X, which will solve the Non-Identity Problem as well as meeting some other reasonable requirements. Two well-known potential candidates for Theory X are the Impersonal Average Principle and the Impersonal Total Principle. Impersonal Average Principle: If other things are equal, the best outcome is the one in which people's lives go, on average, best. Impersonal Total Principle: If other things are equal, the best outcome is the one in which there would be the greatest quantity of whatever makes lives worth living. If we are utilitarians and ignore the welfare of other sentients, or hold it constant, we may drop the qualification "other things equal," and it http://journals.cambridge.org


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IMPOSSIBILITY OF PARFIT'S THEORY X

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is utility (which is happiness or welfare if we are hedonists) that makes lives worth living. For nonconsequentialists, we may have to hold unchanged not only other aspects of the outcomes, but also the procedures and some other possible relevant considerations. However, since all these are held constant for the relevant comparisons in this article, it does not matter. Put differently, the issue of the Impersonal Average Principle versus the Impersonal Total Principle and other similar issues in normative population theory are relevant among both consequentialists (including utilitarians) and nonconsequentialists. We shall thus abstract from objections to consequentialism and utilitarianism as such by holding unchanged other morally relevant factors or by assuming that we are all utilitarians. The Impersonal Average Principle has, as an implication, what I personally regard as one of the greatest sins of all time. If Outcome A involves 10 persons each with 100 utils (or other units of worthiness) and Outcome B involves 10,000,000,000 or more persons each with 99 utils, the Impersonal Average Principle prefers A to B. How could we morally justify a slightly higher utility for 10 persons if this choice involves denying billions of prospective happy lives of only slightly lower average utility? Some people argue that these billions of individuals will not be born under A and hence they have no moral claim. However, if we do not consider the possible welfare of the prospective people in the alternative possible outcome (B), then we can solve neither Parfit's Non-Identity Problem, nor the Extinction Paradox.1 Second, for questions concerning future generations, they are all unborn now, they are all prospective people; no one has more moral right than another.2 The Impersonal Average Principle also violates what I call the Mere Addition Principle. Mere Addition Principle: For any given outcome A, if an alternative outcome A+ contains all the individuals in A with exactly the 1. "Suppose that a chemical has been invented which if released into the air will clean up the atmosphere and make us healthy, able to enjoy life better and not get any older. But it will also make us all sterile (but sexually still active, if not more so) and die painlessly after one hundred years. Suppose also that everyone regards the better health, etc. as more than compensating for the inability to have any more children. So all existing persons will be made better off and no new person will be born. Should the chemical be released? The answer is yes if we ignore prospective persons. I hope that this extinction paradox will persuade readers that prospective persons should not be ignored" (Ng, 1983, p. 165). 2. It is true that one may make the subtle distinction between people who have not yet been born and people who will never exist. However, as convincingly argued by Parfit (1982), actual policy choice (such as conservation versus depletion of resources) affects not only the number but also the actual set of people to be born in the distant future. Thus, the 10 persons will be people who will never exist under a policy choice favoring more people, and the 10,000,000 persons will also be people who will never exist under a policy choice favoring fewer people. Thus, neither set of people should have more moral rights than the other.



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same utility profile as in A (the utility level is the same between A and A + for each and every individual, but different individuals may or may not have the same utility level) plus a number of additional individuals all with worthwhile lives (i.e., positive utility levels), then A + is better than or at least not worse than A. Consider the following specific alternative outcomes: C: Two persons, one with 120 utils and one with 80 utils. D: The same two persons, one with 120 utils and one with 80 utils, exactly as in C, plus another person with 99 utils. By assumption, the two persons enjoy the same amounts of utility in either alternative and hence are not adversely affected by the presence of the additional person who would be happy and would rather live than not be born at all. Usually, C is presented just as two persons each with 100 utils. This had led some people to worry about the unequal utility distribution in D. But as ably argued by Parfit (1984, pp. 422-25), we cannot appeal to inequality in rejecting D. Moreover, in the revised form of situations C versus D, D in fact has a more equal distribution of utility than C. Clearly, D should be regarded as better than C but the Impersonal Average Principle dictates the reverse. The moral unacceptability of the Average Principle (impersonal or otherwise) is obvious. (Cf. Bayles, 1980, esp. Appendix 1; Ng, 1983.) On the other hand, the Impersonal Total Principle has what Parfit and many others regard as a repugnant implication. Repugnant Conclusion: For any given outcome G with a given population size (e.g., 10 billion people), all with a very high quality of life (e.g., 1 billion utils each), there exists (hypothetically) another outcome G' with a much larger population (e.g., 100 billion billion people) whose members all have lives barely worth living (e.g., 1 util each). Yet the Impersonal Total Principle prefers G' to G as long as total utility is higher in G'. Parfit, as well as most other philosophers, believes that the ideal Theory X should satisfy the Mere Addition Principle, but should avoid the Repugnant Conclusion. In addition, I think everyone would agree that it should satisfy the following. Non-Antiegalitarianism: If alternative B has the same set of individuals as in alternative A, with all individuals in B enjoying the same level of utility as each other, and with a higher total utility than A, then, other things being equal, alternative B must be regarded as better than alternative A. It can be seen that Non-Antiegalitarianism is extremely reasonable. Total utility increases, average utility increases, the profile of utility distribution is more (and in fact perfectly) equal, and other things remain unchanged. There is simply no acceptable ground not to regard this as preferable. It might be argued, "What a dull world it must be if everyone has http://journals.cambridge.org


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the same level of utility!" This argument ignores the fact that average utility increases. If there is some dullness, its negative effects must have been more than offset by other favorable effects. Second, we are not having equal distribution of some objective things such as income or jobs. It is just that all people, on average, enjoy life better such as to have a higher and equal level of utility. Third, since we are comparing ultimate outcomes, arguments along the lines of favorable effects for the future due to incentives, the need for elitist activities, and so on are not applicable.3 Obviously, Non-Antiegalitarianism is extremely compelling and is implied by each of the Average and the Total Principle (personal or impersonal) and accepted by everyone in the discussion. In particular, it appears that Parfit (1984, Ch. 19) finds it compelling. Thus, though he does not explicitly define it, we may include it in the set of Parfit's requirements - solution of the Non-Identity Problem, avoidance of the Repugnant Conclusion, satisfaction of the Mere Addition Principle, and Non-Antiegalitarianism (see Figure I).4 3. Non-Antiegalitarianism implies the denial of perfectionism, which curiously still commands some adherence. However, this adherence is based on the fallacy of confusing nonultimate considerations with basic values (Ng, 1988). 4. Alternatively, if Parfit does not subscribe to Non-Antiegalitarianism, we cannot conclude that his Theory X does not exist. Instead, we conclude that Theory X violates Non-Antiegalitarianism, still not a palatable outcome. In response to an earlier draft of this article, Parfit indicates his nonacceptance of Non-Antiegalitarianism ("Ng also adds, to my list of criteria, 'Non-Anti-Egalitarianism'. It wasn't an oversight that led me to omit this from my list"). However, upon re-reading Parfit's Ch. 19, I am now more convinced that Non-Antiegalitarianism is there. Figure 1 is a reproduction of the figure on p. 419 in Parfit's book, where the width of a block indicates the number of population and the height indicates the utility of the people involved. Referring to this figure, Parfit argues convincingly that "B is as good as Divided B" and "Divided B is better than A + " (p. 426). Among others, Parfit writes: "In a change from A+ to Divided B, the worse-off half would gain more than the better-off half would lose. On our ordinary moral assumptions, this would be a change for the better. Since this is the Same Number [of population] Case, we can appeal to Maximin and to the Principle of Equality. Divided B is better than A+ according to both these principles. . . . It might be said that principles of equality apply only within some society, where there can be social injustice. If this is so, Divided B is still better than A + on any principle of beneficence. And this claim about equality is not plausible. . . . Most of us would believe that, if I help either, it would be better to help Poor rather than Rich. . . . [T] his would make the outcome better, both because Poor would gain more than Rich would lose, and because neither would be worse off than the other. Most of us would believe this even though Rich and Poor live in two societies" (p. 426). I personally subscribe 100 percent to Non-Antiegalitarianism but I am sure 1 am not as egalitarian as the belief contained in the above quoted passage. For one thing, I don't subscribe to Maximin, which is extremely egalitarian. Non-Antiegalitarianism only requires us not to favor a less equal distribution of welfare when the total welfare also decreases. In fact, if desired, we can drop my version of Non-Antiegalitarianism and replace it with Parfit's argument justifying the superiority of B over A+. If we like, we can call this the P-version of Non-Antiegalitarianism. Whenever NonAntiegalitarianism is used here, it could be replaced by the P-version, if desired. http://journals.cambridge.org


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The average "level in A +

B

A+ FIGURE

1.

Divided B

(From Parfit, 1984.)

II. THE NON-EXISTENCE OF THEORY X

While Theory X appears to be reasonable, it can be shown that it does not exist. This is established by showing that the Mere Addition Principle, with Non-Antiegalitarianism, implies the Repugnant Conclusion. If this is so, there cannot possibly exist a theory that satisfies both NonAntiegalitarianism, the Mere Addition Principle, and avoids the Repugnant Conclusion at the same time. Consider the following alternatives: A: 1 billion individuals with an average utility of 1 billion utils. A + : The same 1 billion individuals with exactly the same utility levels plus 1 billion trillion individuals each with 1 util (i.e., barely worth living). E: The same individuals as in A + with a somewhat higher total utility but equally shared by all (i.e., each with, say, 1.01 utils). Clearly, the Mere Addition Principle implies that A + is better than or at least no worse than A, and Non-Antiegalitarianism implies that E is better than A +. So E is better than or at least not worse than A. (Cf. Parfit, 1984, pp. 431-32.) Since a life with 1.01 utils (this positive figure can be made as small as we like by a suitable change in numbers in the earlier example) is still barely worth living, the necessity to say that E is better than or at least not worse than A must still be regarded as an instance of the Repugnant Conclusion. It is true that the superiority of A + over A here appears less compelling than the example taken by Parfit (where the smaller number of additional people have utility only somewhat lower than those in A, not as low as in the A+ here). However, the moral principles upon which A+ can be argued to be better than A are exactly the same in



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IMPOSSIBILITY

OF PARFIT'S THEORY X

FIGURE

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2. (From Parfit, 1984.)

both cases: no one is worse off, additional individuals have worthwhile lives, and it is a comparison of ultimate outcomes. It is as illogical not to accept the superiority of A+ here (in contrast to Parfit's case) as the Chinese communists are in disallowing (in theory rather than in practice these days) the private employment of more than five employees on the ground that private employer-employee relationship involves exploitation. Compare the argument: "If the Davises and Ehrlichs (who strongly oppose population growth) say that their lives are of value to themselves, and if the rest of us honour that claim and say that our lives are of value to us, then in the same manner the lives of additional people are of value to those people themselves. Why should we not honour their claim too?" (Simon, 1981, p. 10). Clearly, the superiority of A+ over A above is still very compelling. Parfit (1984, pp. 430-32) believes that the Mere Addition Principle and Non-Antiegalitarianism do not force us to the Repugnant Conclusion (see Figure 2). To sustain this belief, he takes the Mere Addition Principle to imply merely that A+ is not worse than (instead of "better than") A and argues that "not worse than" is not a transitive relation. But in the argument above, no appeal needs be made to the transitivity of "not worse than" (see Appendix, which also argues that Parfit's argument on the nontransitivity of "not worse than" is unconvincing since the "not worse than" here is "clearly not worse than," not merely "not clearly worse than"). Applying the Mere Addition Principle in the less (but still very) compelling case of the comparison of A and A + above, we can go to the repugnant result (E) in a single intermediate step. We conclude that a Theory X that satisfies both the Mere Addition Principle and Non-Antiegalitarianism, and avoids the Repugnant Conclusion, does not exist. One of these three requirements has to go; which one? Two alternative escapes from the above impossibility result are con-



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sidered in the rest of this essay. The first escape (considered in the next section) is to accept the Repugnant Conclusion. This is my favored alternative. In fact, I go so far as to argue that the Repugnant Conclusion is not only acceptable but compelling. The second escape (Section IV) is to reject the Mere Addition Principle in less (but still very) compelling cases. III. WHY IS THE REPUGNANT CONCLUSION COMPELLING?

Non-Antiegalitarianism is compelling. Total utility and average utility both increase, the profile of utility distribution is perfectly equal, and other things remain unchanged; it must be accepted as preferable. The Mere Addition Principle is also compelling. No one is adversely affected, some happy individuals are given a chance to live.5 Again, there is no valid reason not to prefer A+ to A. We are thus forced to accept the Repugnant Conclusion. If the Repugnant Conclusion is compelling, why do most people find it repugnant? This, I believe, could be due either to an inability to understand the implication of large numbers or to misplaced partiality. Consider the following alternative worlds: A: 1 single utility monster with 100 billion utils. B: 1 billion individuals each with 200 utils. C: 1 billion billion individuals each with 0.001 utils. Intuitively, most people prefer B to C and also prefer B to A. This is so because B looks similar to our present world and we are not prepared to sacrifice a decrease in average utility from 200 to 0.001 even if the increase in population size more than compensates (in terms of total utility) to this reduction. Also, we are not prepared to sacrifice numbers from 1 billion to 1, even if the gain in average utility overbalances this. But this is taking a partial view from our standpoint. From an impartial viewpoint or from the viewpoint of comparing two hypothetical, mutually exclusive alternatives, if B is better than A, then C is much better than B. The number of people in C (Nc) is exactly 1 billion times larger than NB, the same ratio as NB/NA. But UC/UB > L/B/UA, where Ux stands for the average utility in situation x. If we prefer B to A, we must logically prefer C to B. Alternatively, if we prefer B to C, we must prefer A to B, i.e., preferring one single utility monster, even if total utility decreases - in my view, a more repugnant result than the Repugnant Conclusion! Some people may find C inferior to B even from an impartial viewpoint because they fail to comprehend that the big difference in popu5. The avoidance of the Absurd Conclusion (note 10, p. 244) may also be added; see Section IV.



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lation size more than offsets the decrease in average utility. They may believe that, since a life of 0.001 util is barely worth living, the tremendous population size of 1 billion billion cannot mean much. However, though 0.01 cent is a sum of money barely worth having, if I obtain 0.01 cent from each of 1 billion billion individuals, my wealth will be worth many times the GNP of the whole world! As long as the average utility is positive, a larger population cannot fail to make the total utility significant. Secondly, if we consider a life of 0.001 util as barely worth living in comparison to a life of 200 utils, we ought also to admit that a life of 200 utils is barely worth living in comparison to a life of 100 billion utils. The fact that we have to admit that C is a better world than B does not, however, imply that, if our present world is B and if we can move to C if we choose to, we must do so. This second choice does not just involve two hypothetical alternatives but involves our actual present situation. We may then want to be partial.6 As two hypothetical alternative worlds, C is better than B. But if we are already living in world B, moving to C would involve all of us sacrificing 199.999 utils each. We can quite rationally refuse to accept such a big sacrifice even if the increase in total utility of the new people is even more. As an analogy, suppose that we all believe that for a society of a given set of individuals, other things being equal, a more equal distribution of the initial endowment of wealth is a morally better alternative. However, if we have already started with an unequal distribution, the rich may refuse to share their wealth equally, even abstracting from the complicating issues of incentive effects and the isolation paradox (see Sen, 1961). In other words, in our choice, we may be guided by our selfinterests, not just by ideal ethics. Nevertheless, for the issues of the effects of our present policies on future generations, we must take an impartial view. This is so because we are not future people, so we have no reason to be partial.7 Between two alternative policies to which we are indifferent, our self-interests are not at stake and we can choose purely on ideal ethics; we must then 6. If we believe in Parfit's (1984, Part 3) reductionist argument about personal identity, we should be less partial. 7. It may be argued that, since "we" refers to all currently existing human beings and alternative policies involve someone doing one thing rather than another, someone must be affected one way or another. This is quite true in practice but we may first confine comparisons to cases where the positive and negative effects on the present generation ("us") are offsetting to each other to yield neither net gain nor net loss to us as a whole. Second, where net gain or loss exist, we have to trade-off our gains/ losses with the losses/gains of the future generations in addition to the clarification of our moral position regarding alternative futures for the future generations themselves (which is the principal concern of this essay). It may also be noted that, if future people are not in the distant future but will grow up before the present people die, there may arise the problem of generationdependent morality (Dasgupta, 1988, p. 119 ff.).



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prefer a future population of higher total utility. For policies that do affect our own interests, we have to trade off our interests against our concern for future (or others') goodness. Unless this trade-off is infinite (highly immoral), the total utilities of future generations still have to be taken into account.8 In the next section, we present Theory X', which meets all Parfit's requirements except the Mere Addition Principle in less compelling cases. Thus, Theory X' may be considered for adoption by those who are not persuaded by my argument in this section in favor of the Repugnant Conclusion. For those persuaded, they may still use Theory X' where some sacrifice in our own utility is involved.9 IV. A COMPROMISE SOLUTION: THEORY X'

To avoid the Repugnant Conclusion, Parfit began his search for the ideal Theory X by first placing a limit on the significance of the quantity of utility. But since intense suffering should not have a limit in its negative implications, this asymmetry leads to the Absurd Conclusion (Parfit, 1984, Ch. 18).10 The adoption of a lexical ordering does not solve the problem either (Parfit, 1984, Ch. 18). 8. It might be argued that, while the argument of this last paragraph may be persuasive in high principle, in practice people care more about the future generations of their own family, nation, race, etc. This argument loses much of its force if we confine the "we" in the last paragraph in the text to the whole human race and confine "future generations" to those far into the future. Moreover, why shouldn't we use high principles (if compelling or at least reasonable) to influence what people believe or prefer in practice? Isn't this one of the main functions of applied philosophy? A commentator also questions the reasonableness of the Impersonal Total Principle for multiple agents when it need not be reasonable for the case of single agents. "I may rationally prefer to suffer 101 pains of - 1 util each rather than one -100 uril pain. (This assumes the utility scales are defined other than by the Von NeumannMorgenstern method.)" This is not rational, since I have shown elsewhere (Ng, 1984) that, assuming reasonable axioms no stronger than the Von Neumann-Morgenstern hypothesis and recognizing finite sensibility, the utility index or function derived by the Von Neumann-Morgenstern method is the same as the classical subjective utility function. 9. Parfit himself has a secondary argument ("The second version of the Paradox," discussed on pp. 433-38), which seems to argue that the Repugnant Conclusion cannot be avoided unless some elitist arguments are accepted. In Parfit (1986), he actually develops a perfectionist (an elitist-type) argument. However, Parfit's version of perfectionism is open to the same criticism (that it either involves the fallacy of confusing nonulrimate considerations with basic values or involves abhorent ethics) as Temkin's version criticized in Ng ( 1988). 10. The Absurd Conclusion: "In one possible outcome, there would exist during some future century both some population on the Earth that is like the Earth's present actual population, and an enormous number of other people, living on Earth-like planets that had become part of the Solar System. Nearly all of the people on these other planets would have a quality of life far above that enjoyed by most of the Earth's actual population. In each 10 billion of these other people, there would be 1 unfortunate



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In this section, I use Theory X' to show that Parfit need not have gone to the extremes of placing limits and adopting lexical orderings. I believe Theory X' is what Parfit is after, or something very close to Theory X. Theory X' solves the Non-Identity Problem, implies neither the Repugnant Conclusion nor the Absurd Conclusion, and satisfies Non-Antiegalitarianism and the Mere Addition Principle in all cases regarded by most as more compelling.11 If Parfit confines the Mere Addition Principle to the more compelling cases only, Theory X' meets all his requirements and thus in fact may be exactly the Theory X he is after. On the other hand, if Parfit refuses to restrict or revise the Mere Addition Principle, then his requirements are either internally inconsistent and Theory X does not exist, or it violates the compelling Non-Antiegalitarianism (Section II). The Average Principle maximizes U, average utility per head and the Total Principle maximizes NU where N is the number of individuals. The exclusive maximization of U leads to morally unacceptable results as discussed above, and equal emphasis of number (N) and quality (IZ) leads to the Repugnant Conclusion. Theory X' avoids this by subjecting N to a "dampening" process of transformation by a concave function /(N). Instead of maximizing NU, Theory X' maximizes/(N) • U. To ensure avoidance of the Repugnant Conclusion, the function / can be constructed so that it never reaches infinity, even if N goes to infinity. As illustrated in Figure 3, /(«) always increases with N and yet never exceeds / ; it approaches / asymptotically. An example of a concave function suitable for our purpose here is the following, where 1 > a > 0. The value of / when N = 1 is 1; when N = 2, / = 1 + a; when N = 3, / = 1 + a + a2. In general, / = 1 + a + a 2 + ••• + a N "'. When N approaches infinity, /approaches / = 1/(1 - a), which is of finite value. For example, for a = 0.99, / = 100, as illustrated in Table 1.

person, with a disease that makes him suffer, and have a life that is not worth living. "In a second possible outcome, there would be the same enormous number of extra future people, with the same high quality of life for all except the unfortunate 1 in each 10 billion. But this enormous number of extra future people would not all live in one future century. Each 10 billion of these people would live in each of very many future centuries. "In our view, the first outcome would be very bad, much worse than if there were none of these extra future people. The second outcome would be very good. The first would be very bad and the second very good even though, in both outcomes, there would be the very same number of extra future people, with the very same high quality of life for all except the unfortunate one in each 10 billion" (Parfit, 1984, pp. 410-11). 11. I first proposed the maximization of number-dampened total utility in Ng (1986) as a compromise solution in my comment on Blackorby and Donaldson (1984).



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FIGURE 3.

Table 1 N /(N) df/dN

0 0 1

1 1 0.99

2 1.99 0.9801

3 2.9701 0.9703

10 9.5618 0.9044

00

100 0

As shown in the last row of Table 1, the value attached to the first person (the value of df/dN as N increases from 0 to 1) is 1, the value attached to the second person is 0.99, and so on. As N becomes very big, this value becomes very small but always positive. Note that the value of a population of size N and with average utility U is the product of /(N) and U, not just/(N). A doubling of the average utility U doubles the values of Uf(N) at all values of N. It is only N that is subject to the dampening process of transformation by a concave function, not U.12 It may be noted that Theory X', as well as the Impersonal Average and Total Principles, solves the Non-Identity Problem and satisfies NonAntiegalitarianism since N is an impersonal number and since NonAntiegalitarianism involves comparison of the same N. Second, Theory X' avoids the great sin of the Average Principle since N is not ignored completely. Third, as /(N) always increases with N, and as Theory X' maximizes /(N) • U (instead of taking utility and disutility asymmetri12. See pp. 249-50 for discussion on Hurka's variable value view and its similarity and differences with Theory X'.



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cally, it takes either the average or the representative utility, as will be discussedj, it avoids the Absurd Conclusion.13 Fourth, since/(N) never exceeds / , the Repugnant Conclusion can also be avoided, as will be shown.14 The first Quadrant of Figure 4 is the same as Figure 3. Any given outcome G is represented in the fourth Quadrant by a point G indicating the number of individuals NG and the average utility or representative utility Uc. (The representative utility of a given situation is that level of utility that, if enjoyed by every individual in that situation, will make the situation equally desirable as the actual situation that may not have equal utility for all individuals. For example, a situation of two persons, one with 12 utils and another with 8 utils, will be deemed by utilitarians as having an average = representative utility of 10 utils, but will be deemed by utility-egalitarians, as distinct from income-egalitarians, as having a representative utility of less than 10 utils.)15The point G is then plotted into the point g in the second Quadrant by keeping UG unchanged (transformed through the identity 45° line in the third Quadrant) and by transforming N by a concave function/(N) through the first Quadrant. The pointg then forms a rectangle gU G0Y with the two axes. 13. I find the asymmetrical treatment of utility and disutility unconvincing. No matter how great is the disutility, it can always be compensated by a sufficiently big amount of utility. This is true for most of our personal choice and I see no reason for its rejection in social choice. If we take an alternative as encompassing all its implfcations for the whole future and consider all utilities and disutilities together, as I think we should, and then consider what the average or representative utility is, the Absurd Conclusion is avoided by Theory X'. 14. In his book, Parfit mentions view (5) which is close to if not exactly Theory X'. "On view (5), at any level of quality, the value in extra quantity asymptotically approaches zero. . . . The value of quantity can never be above certain upper limit" (Parfit, 1984, pp. 402-03). This seems to be very close to Theory X'. However, Parfit goes on, "The world's actual population now consists of several billion people. . . . Most of those who accept view (5) would agree that, in the world now, the value of extra quantity can be regarded as having reached its limit" (p. 402), making "views (5) to (7) agree" (p. 404). View (7) is that only quality has value. View (6) is that the "value of quantity has an upper limit, and in the world today this limit has been reached" (p. 403). From here, Parfit ignores view (5) and discusses view (6). Second, I do not know whether utility and disutility are treated symmetrically or asymmetrically in view (5). From Parfit's discussion, it seems that the latter is the case, making view (5) still conducive to the Absurd Conclusion. Thus, while view (5) is close to Theory X', I am not sure it is Theory X'. If Parfit is prepared to say that his view (5) is identical to Theory X', 1 am perfectly willing to acknowledge his priority over Theory X'. Then, my contribution in this Section I is limited to showing that Parfit's view (5), which he ignores after a brief mention, is in fact closest to his ideal. However, a referee noted several differences between Theory X' and view (5). 15. Utility-egalitarianism may be due to what I call "utility illusion," the double-discounting of income due to the diminishing marginal utility of income (Ng, 1975, Section 2). For more details on the use of representative utility, see Blackorby and Donaldson (1984).



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FIGURE 4.

(The rectangle is shaded in Figure 4.) Theory X' compares any two situations by comparing the areas of the respective rectangles thus formed. The outcome or situation with a larger area is preferred. From the point g, plot the point g' on the same horizontal line as / such that the rectangle formed by g' with the axes is equal in area to that formed by g. Then, there exists no situation C such that its average or representative utility is smaller than g'f and yet preferred by Theory X' to G. So the Repugnant Conclusion is avoided. This is so because the Repugnant Conclusion implies, in terms of Figure 4, that, by increasing N sufficiently, we can construct a rectangle in Quadrant 2 bigger than the shaded one in area and yet extremely thin (in width), as thin as we like. But the concave function / ensures that any rectangle in Quadrant 2 that is larger than the shaded one must be at least ofwidth larger than g'f since no rectangle can have a height larger than Of. This means that average utility cannot be diminished to a level smaller than g' f. So the Repugnant Conclusion is avoided. We may make the minimum utility level g'f as close to Uc as we like by making f(N) as concave as we like. In the limit, if we make /(N)



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coincide with 0/L, Theory X' collapses into the Impersonal Average Principle maximizing only U. At the opposite extreme, if we make /(N) a 45° straight line, Theory X' collapses into the Impersonal Total Principle maximizing NU. Thus, Theory X' can be seen to be a generalization with the two principles as possible polar cases. (One could go further by making / convex, but that is an ethic entertained by no one.) If the chosen function /(N) is not of extreme concavity, the Mere Addition Principle can be preserved for more compelling cases. By more compelling cases, I mean cases where the average utility of the added people is not very much lower than those of the preexisting people, and the number of the preexisting people has not become very large, so that most people find it very compelling to agree that the situation with the added people is better than the original situation. (Some people are content to say that, at least, the situation cannot be worse.) We have thus shown that, if we choose a /(N) that is moderately concave, we can simultaneously avoid the Repugnant Conclusion, satisfy Non-Antiegalitarianism and the Mere Addition Principle in more compelling cases, as well as solve the Non-Identity Problem and avoid the Absurd Conclusion - i.e., meet all Parfit's requirements for an ideal Theory X except the Mere Addition Principle in less (though still very) compelling cases. In these less compelling cases, either the additional persons would have utility levels well below those of existing individuals, or the existing population size is already very large. Many people doubt whether such an addition leads to a better outcome. Personally, I believe it to be better (assuming of course no side effects, as we are comparing ultimate outcomes). Parfit may believe likewise and does not want to compromise on the Mere Addition Principle even for the least compelling cases (where the added persons have lives barely worth living). In itself, this is perfectly defensible. However, as shown in Section II, it is inconsistent with either Non-Antiegalitarianism or the avoidance of the Repugnant Conclusion.16 A commentator noted the similarity of Theory X' and Hurka's variable value view. After reading Hurka (1983), I must admit the striking similarity. However, it appears that Hurka applies the concave transformation directly onNL/ with different functions as U differs, while Theory X' applies an unchanged concave transformation on N only and uses this same f(N) to multiply with any If. Second, Hurka justifies the 16. In his response to an earlier version of this paper, Parfit appears to have some doubts on the acceptability of the Mere Addition Principle for less compelling cases. However, upon rereading Parfit's (1984, Ch. 19) argument on the issue, it appears that the argument in favor of preferring A+ to A is compelling even for the less compelling cases. Specifically, the change from A to A + discussed in Section II satisfies Parfit's version of Mere Addition: "There is Mere Addition when, in one of two outcomes, there exist extra people (1) who have lives worth living, (2) who affect no one else, and (3) whose existence does not involve social injustice" (p. 420).



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relative higher value on N when N is small on "the urgency that would attach to population questions in the event of a nuclear holocaust" (p. 502) because one "of the principal duties of the handful of people who survived a nuclear holocaust would be to procreate" (p. 497). In my view, this may be misleading to readers, causing them to confuse the means with the ends due to insufficient attention to the fact that alternative outcomes for evaluation are mutually exclusive and ultimate outcomes. What is at issue is to compare two mutually exclusive alternatives one with a higher average utility and the other with a higher total utility (due to a larger population); both may involve the same time scale of existence. I perfectly agree that the handful of people who survived a nuclear holocaust should procreate (assuming that the resulting viable world involve happy people). But this is mainly because of the value of bringing more people about to ensure survival of the human race. Thus, it is the high value attached to the additional people and the additional generations that make the few survivals and their immediate offsprings of high (mainly instrumental) values. In contrast, Theory X' is to attach relatively higher ultimate values on N as such when N is small. Hurka's analogy that, "when the whooping crane population gets to be small enough, the value of an individual whooping crane life increases in our eyes" (p. 497, italics added) is open to the objection above plus the objection that happy human lives are valuable in themselves and not in the eyes of someone else. Additional whooping cranes have diminishing marginal utility to us just as additional income brings diminishing marginal utility to the person possessing the income. But human beings are not possessed by anyone. Our diminishing marginal valuation of additional whooping cranes cannot be used to justify the diminishing marginal value of additional persons. Partly because of this, I regard neither Theory X' nor Hurka's variable value view as ethically sustainable and I personally subscribe to the Impersonal Total Principle but propose Theory X' only as a compromise partly for those who still find the Repugnant Conclusion objectionable and partly as a possible trade-off between our self-interests and the right moral principle.

REFERENCES Bayles, M. D. 1980. Morality and Population Polio/. University of Alabama Press. Blackorby, C, and Donaldson, D. 1984. "Social Criteria for Evaluating Population Change." journal of Public Economics 25:13-33.

Dasgupta, P. 1988. "Lives and Well-being." Social Choice and Welfare 5:103-26. Hurka, T. 1983. "Value and Population Size." Ethics 93:496-507. Ng, Y-K. 1975. "Bentham or Bergson? Finite Sensibility, Utility Functions and Social Welfare Functions." Review of Economic Studies 42:545-70. . 1983. "Some Broader Issues of Social Choice." In Social Choice and Welfare, edited by P. K. Pattanaik and M. Salles. Amsterdam: North Holland.



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— . 1984. Expected Subjective Utility: Is the Neumann-Morgenstern Utility the Same as the Neoclassical^?" Social Choice and Welfare 1:177-86. — . 1986. "Social Criteria for Evaluating Population Change: An Alternative to the Blackorby-Donaldson Criterion." Journal of Public Economics 29:375-81. — . 1988. "Welfarism and Utilitarianism: A Rehabilitation." Monash Economics Seminar Paper No. 11/88. Parfit, D. 1982. "Future Generations: Further Problems." Philosophy and Public Affairs 11. . 1984. Reasons and Persons. Oxford: Clarendon Press. . 1986. "Overpopulation and the Quality of Life." In Applied Ethics, edited by Peter Singer. Oxford: Oxford University Press. Sen, A. K. 1961. "On Optimising the Rate of Saving." Economic journal 71:479-96.' Simon, J. L. 1981. The Ultimate Resource. Princeton: Princeton University Press.



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APPENDIX

To avoid the Repugnant Conclusion, Parfit takes the Mere Addition Principle to imply only that A + is not worse than (instead of "better than") A and argues that "not worse than" is not a transitive relation. "When there is only [intrinsic] rough comparability, not worse than is not a transitive relation" (1984, p. 431) and Parfit gives examples in the ranking of poets versus novelists. For this case, due to the difficulty of a precise comparison, we may say that A is not "clearly worse than" B, B is not "clearly worse than" C, . . . Z, without having to commit ourselves to saying that A is not "clearly worse than" Z. The relation "not clearly worse than" is not necessarily transitive. However, the same intrinsic "roughness" does not apply to the Mere Addition Principle. The argument that A + must be regarded as better than or at least not worse than or clearly not worse than A is precise and compelling (Parfit, Ch. 19). Thus the relation "at least not worse than" or "clearly not worse than" should be transitive. In other words, "not clearly worse than" and "clearly not worse than" are quite different. Parfit argues that "not worse than" does not imply "at least as good as." "Consider an outcome-which is like A + , except that the extra people have a somewhat higher quality of life. Call this Improved A +. This outcome is clearly better than A +. If we believe both that A + is not worse than A, and that Improved A + is better than A +, must we conclude that Improved A + is better than A? No. We can claim that, while Improved A+ is better than A + , both of these are merely not worse than A" (Parfit, 1984, pp. 430-31). However, the compelling arguments Parfit competently puts forward in favor of the Mere Addition Principle should convince most people that A + is not just "not clearly worse than" A but "clearly not worse than" if not actually better than A. Improved A+ is thus clearly better than A. (I personally regard both A+ and Improved A+ to be clearly better than A.) Second, even if we accept the questionable nontransitivity of "not worse than," our prior conclusion that E (or Parfit's B) is better than or at least not worse than A still holds. This is ably explained by Parfit: Suppose we believe both that B is better than A + and that A + is not worse than A. Because not worse than does not here imply at least as good as, we are not forced to conclude that B is better than A. We can only conclude that B is not worse than A. And we should check that, in reaching this conclusion, we have not assumed the transitivity of not worse than. We have not. We decided that A+ is not worse than A, but is worse than B. We concluded that B cannot be worse than A. This conclusion was justified. Assume the contrary. Assume that B is worse than A. Since A+ is worse than B, and B is worse than A, A+ must be worse than A. This argument is valid since, unlike not worse than, worse than is transitive. But we reject this argument's conclusion. We believe



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that A + is not worse than A. Since we also believe that A + is worse than B, we must reject this argument's other premise. We must conclude that B cannot be worse than A. (Parfit, 1984, pp. 431-32). Why then does Parfit still believe that he is not forced to accept the Repugnant Conclusion? This is so because Parfit believes that we need more than one intermediate step of comparison to get to the Repugnant Conclusion. As illustrated in Figure 2 (a reproduction of Parfit's figure on p. 388), we go from A to B via A + (A plus additional people of moderate utility levels), and from B to C via B +, and so on. Thus, if we either accept the "better than" part of the Mere Addition Principle (i.e., that A+ is not just "not worse than" but actually "better than" A) and/or agree that "clearly not worse than" is transitive, we only have to use the Mere Addition Principle for cases where the utility levels of the added people are not much lower than those of the preexisting people. After repeated steps, we still obtain the Repugnant Conclusion. Taking only the "not worse than" part of the Mere Addition Principle and maintaining that "not worse than" is not transitive, Parfit believes that he is not forced to the Repugnant Conclusion. Thus, immediately after the above quoted passage, Parfit adds: We can be forced to this conclusion [i.e., that B cannot be worse than A]. But we cannot be forced from here even to a weakened form of the Repugnant Conclusion. It is true that, by the same reasoning, C cannot be worse than B, D cannot be worse than C, and so on. But since not worse than is not transitive, we can claim that, while C is not worse than B, which is not worse than A, C is worse than A. (p. 432) However, since we have shown in the text that, applying the Mere Addition Principle in the less (but still very) compelling case, we can go to the repugnant result in a single intermediate step (our E above is equivalent to Parfit's Z). Parfit's argument resisting the Repugnant Conclusion on the ground of intransitivity fails.



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