1 In this section, we ignore the question what individual utilities stand for. In particular, whether they refer to individual preferences or individual happiness (discussed in section II); whether non-human sentients like animals are included in the relevant set of individuals. See Ng Y. K., ‘Some Broader Issues in Social Welfare’, in Pattanaik P. K. and Salles M. eds., Social Choice and Welfare, Amsterdam, 1983.
2 I use ‘welfarism’ as a synonym for ‘general utilitarianism’, see Sen A. K., ‘Personal Utilities and Public Judgements’, Economic Journal, lxxxix (1979), 537–58. However, some readers may prefer to use welfarism as w = w(w1, w2, …, w2) where w1 = welfare or happiness of individual 1. To be precise, w = w(u1, u2, …, un) is preference welfarism, w = w(w1, w2, …, wn) is welfare welfarism.
3 Radford C., ‘Utilitarianism and the Noble Art’, Philosophy, lxiii (1988), 63–81.
4 However, perception and affective feelings evolved simultaneously. As I hope to argue elsewhere, perception without affective feelings also serves no evolutionary purposes. Here, perception is defined as involving subjective consciousness, not just in the wider sense ‘reception and interpretation of signals from the environment’, regarded as evidenced in the bacterium E. coli, see Delbruik M., Mind from Matter? An Essay on Evolutionary Epistemology, Oxford, 1986.
5 Harsanyi J. C., ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility’, Journal of Political Economy, lxviii (1955), 309–21.
6 Ng Y. K., ‘Bentham or Bergson? Finite Sensibility, Utility Functions, and Social Welfare Functions’, Review of Economic Studies, xlii (1975), 545–70.
7 d'Aspremont C. and Gevers L., ‘Equity and the Informational Basis of Collective Choice’, Review of Economic Studies, xliv (1977), 199–209.
8 Fleming's result is also positive but he established only separability, i.e., w = f2 (u2) + …, +fn (un), but using very reasonable axioms. Fleming M., ‘A Cardinal Concept of Welfare’, Quarterly Journal of Economics, lxvi (1952), 366–84.
9 See Lyons D., ‘Human Rights and the General Welfare’, Philosophy and Public Affairs, vi (1976), 113–29; Hardin R., ‘The Utilitarian Logic of Liberalism’, Ethics, xcvii (1986), 47–74; and Kuflik A., ‘The Utilitarian Logic of Inalienable Rights’, Ethics, xcvii (1986), 75–87 on the consistency of utilitarianism with certain inalienable rights. However, the preference for certain counter-efficiency rights may be based on the ignorance of economics; see Ng Y. K., ‘Economic Efficiency versus Egalitarian Rights’, Kyklos, xli (1988), 215–37.
10 For some more realistic circumstances where the exercise of rights leads to disastrous outcomes, see Sen A. K., ‘The Moral Standing of the Market’, in Paul E. F. et al. eds., Ethics and Economics, Oxford, 1985, p. 6.
11 Gibbard A., ‘Inchoately Utilitarian Common Sense’, in Miller H. B. and Williams W. H. eds., The Limits of Utilitarianism, Minnesota, 1982, p. 83.
12 Ng Y. K., ‘Individual Irrationality and Social Welfare’, Social Choice and Welfare, vi (1989), 87–102.
13 Rawls J., A Theory of Justice, Oxford, 1972, pp. 150–61.
14 It is true that Rawls would argue that freedom to rape is not a basic liberty while the right to non-violation of the body is. However, how do we determine what are basic liberties? Either it is based on the utilitarian principle or it is open to the objection of the last subsection on the unacceptability of rights-based ethics.
15 Temkin L. S., ‘Inequality’, Philosophy and Public Affairs, xv (1986), p. 109.
16 Allais M. and Hagen O., The Expected Utility Hypothesis and the Allais Paradox, Dordrecht, 1979. See also Harsanyi J., Essays on Ethics, Social Behaviour and Scientific Explanation, Dordrecht, 1976, and Ng Y. K., ‘Expected Subjective Utility: Is the Neumann-Morganstern Utility Index the same as the Neoclassical's?’, Social Choice and Welfare, i (1984), 177–86.
17 For example, Locke's asymetric utilitarian solution to Parfit's population problem is open to the same objection; see Locke D., ‘The Parfit Population Problem’, Philosophy, lxii (1987), 131–57.
18 Temkin L. S., ‘Intransitivity and the Mere Addition Paradox’, Philosophy and Public Affairs, xi (1987), 172.
22 The preference for equality in Welfare as such may well be due to ‘utility illusion’, the double discounting of the incomes of the well-off; see Ng Y. K., ‘Bentham or Bergson?’, pp. 545–70.
23 Dworkin R., ‘What is Equality?’, Philosophy and Public Affairs, x (1981), 201–4.
24 Alexander L. and Schwartzchild M., ‘Liberalism, Neutrality, and Equality of Welfare vs. Equality of Resources’, Philosophy and Public Affairs, xvi (1987), 90.
25 Some people may take the (I think naive) position that a right or principle is either fully observed or not at all. In that case, the degree of observance assumes a value of either one or zero.
26 For simplicity, the possible dependence 0t Ot on variables at times other than t is ignored.
27 If the individual concerned does not like this sum-ranking method, we may just define vi = vi (w1, w2, …, wi–1, wi+1 …, wn) which is whatever function he uses for the welfares of other individuals.
28 Narveson J., ‘Moral Problems of Population’, The Monist, lvii (1973), 80.
29 Parfit D., Reasons and Persons, Oxford, 1984.
31 For the argument that, in this perspective, the Repugnant Conclusion is not repugnant at all and that Parfit's ideal theory X either does not exist or violates the compelling Non-Antiegalitarianism, see Ng Y. K., ‘What Should we do About Future Generations?’, Economics and Philosophy, v (1989), 235–53.
32 Ng , ‘What Should we do About Future Generations?’
33 See Harsanyi J. C., ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility’, Smart J. J. C. and Williams B., Utilitarianism: For and Against, Cambridge, 1973; Hare R. M., ‘Ethical Theory and Utilitarianism’, in H. D. Lewis, Contemporary British Philosophy, London 1976; and Riley J., Liberal Utilitarianism: Social Choice Theory and J. S. Mill's Philosophy, Cambridge, 1988.