¹ See Cowen, Tyler and Parfit, Derek, “Against the Social Discount Rate”, in Philosophy, Politics, and Society, Volume 6: Justice Between Age Groups and Generations, ed. Fishkin, James S. and Laslett, Peter (New Haven: Yale University Press, forthcoming).Google Scholar

² See Barro, Robert J., “Are Government Bonds Net Wealth?” Journal of Political Economy, vol. 74 (1974), pp. 1095–1117.CrossRefGoogle Scholar

³ See Becker, Gary S., “A Theory of Social Interactions”, Journal of Political Economy, vol. 82 (11/12 1974), pp. 1063–94CrossRefGoogle Scholar, and A Treatise on the Family (Cambridge: Harvard University Press, 1981).Google Scholar

⁴ See Becker, , A Treatise on the Family, p. 183.Google Scholar Parents (and children) may be suspicious of the theorem already.

⁵ The application of the Argument to discount rates is criticized by Cowen and Parfit, “Against the Social Discount Rate.” On the other applications, see Bernheim, B. Douglas, “On the Voluntary and Involuntary Provision of Public Goods”, American Economic Revieiv, vol. 76 (09 1986), pp. 789–93Google Scholar; and Warr, Peter D. and Wright, Brian G., “The Isolation Paradox and the Discount Rate for Benefit-Cost Analysis”, Quarterly Journal of Economics, vol. 95 (02 1981), pp. 129–45.CrossRefGoogle Scholar

⁶ See Hirschman, Albert O., Tlte Rhetoric of Reaction (Cambridge: Harvard University Press, 1991).Google Scholar

⁷ See Barro, Robert J., “Are Government Bonds Net Wealth?”Google Scholar An early version of the theorem has been attributed to classical economist David Ricardo. Many deficits, of course, are paid off within the lifetimes of those who incur them. In this case, deficits and taxes are equivalent even in the absence of offsetting transfers. An increase in the deficit simply induces more saving to pay future taxes.

⁸ See Bernheim, B. Douglas, Shleifer, Andrei, and Summers, Lawrence H., “The Strategic Bequest Motive”, Journal of Political Economy, vol. 93 (12 1985), pp. 1045–76.CrossRefGoogle Scholar These authors even present econometric evidence which demonstrates correlations between expected size of bequests and the number of letters written to parents, visits to nursing homes, etc. I have recently seen a bumper sticker which read “Get Even—Live Long Enough to Be A Burden to Your Children.”

⁹ See Andreoni, James, “Giving With Impure Altruism: Applications to Charity and Ricardian Equivalence,” Journal of Political Economy, vol. 97 (1989), pp. 1447–58.CrossRefGoogle Scholar

¹⁰ See Barro, Robert J., “A Ricardian Approach to Budget Deficits”, Journal of Economic Pcrspectives, vol. 3 (Spring 1989), p. 52.Google Scholar

¹¹ See, for instance, ibid. for a survey of the evidence, pro and con.

¹⁶ The structures behind the multi-link Argument and the prisoner's dilemma are not identical, however. In the Argument, one attempts to establish the correct course of action given expectations about the future, but one is not playing against an opponent. Furthermore, the Argument requires that a sequence of separate individuals reason according to backwards induction.

¹⁷ See, for instance, Axelrod, Robert, The Evolution of Cooperation (New York: Basic Books, 1984).Google Scholar

¹⁸ Similarly, consider religious tithing, which is usually based around a fixed percentage of one's income, and not the contributions of other church members.

¹⁹ This is not true, however, to the extent that different generations live and offer gifts at the same time. Who should be the first to buy the children additional Christmas presents, Mother or Grandmother?

²⁰ John C. Calhoun stresses the limits which imperfect information places upon altruistic behavior; see Tabarrok, Alexander and Cowen, Tyler, “The Public Choice Theory of John C. Calhoun”Google Scholar, forthcoming in Journal of Institutional and Theoretical Economics. Hayek's distinction between the extended order and traditional society also stresses the role of markets in substituting for the informational limitations of altruism. See Hayek, Friedrich A., The Fatal Conceit (Chicago: University of Chicago Press, 1989).Google Scholar

²¹ New Zealand author Janet Frame, in her novel Living in the Maniototo (New York: George Braziller, 1979), pp. 41–42Google Scholar, presents the character of Lance Halleton, who slept with two pocket calculators under his pillow so he could reckon accurately the national debt. Lance was extremely concerned with how high the debt was and who would pay it off. Appropriately, New Zealand has an astronomically high per-capita debt.

²² This is demonstrated formally by Barro, Robert J., “Are Government Bonds Net Wealth?”Google Scholar

²³ On the collective-action problem of altruism, see Kavka, Gregory N., “Two Solutions to the Paradox of Revolution”, Midwest Studies in Philosophy, vol. 7 (1982), pp. 455–72.CrossRefGoogle Scholar

²⁴ Overlapping friendships would reduce these numbers. Some of my friends have the same friends, who should not be counted twice.

²⁵ This point is made most clearly by Bergstrom, Theodore C., “A Fresh Look at the Rotten Kid Theorem—and Other Household Mysteries”, Journal of Political Economy, vol. 97 (1989), pp. 1138–59.CrossRefGoogle ScholarKlein, Daniel B., “The Microfoundations of Rules versus Discretion”, Constitutional Political Economy, Fall 1990, pp. 1–19Google Scholar, demonstrates the relation between the Rotten Kid Theorem and the literature on time consistency.

²⁶ In fact, the Argument may imply that Martha will give additional money to Tommy. Assume plausibly that the marginal utilities of education and money interact. A better educated individual receives more pleasure from money than an ignorant individual; Martha will now give more money to Tommy, the rotten kid.

²⁷ Similarly, if Martha can precommit to punishing Tommy with sufficient severity, Tommy will not cheat on the test in the first place. But this does not rescue the Argument, which requires that redistributions which actually occur can be offset.

²⁸ The desirability of precommitment requires that not all goods can be redistributed by the benefactor. In the case of the idle son, leisure is the additional good which cannot be transferred. See Lindbeck, Assar and Weibull, Jorges W., “Altruism and Time Consistency: The Economics of Fait Accompli”, Journal of Political Economy, vol. 85 (12 1988), pp. 1165–82.CrossRefGoogle Scholar

²⁹ Kimball, Miles S., “Making Sense of Two-Sided Altruism”, Joumal of Monetary Economics, vol. 20 (09 1987), pp. 301–26CrossRefGoogle Scholar, uses the phrase “Hall of Mirrors.” Estlund, David, “Mutual Benevolence and the Theory of Happiness”, Journal of Philosophy, vol. 87 (04 1990), pp. 187–204CrossRefGoogle Scholar, refers to “benevolence loops.”

³⁰ However, perhaps romantic love is precisely such a perpetual-happiness machine and should be included as a possible case in a theory of altruism.

³¹ For the relevant mathematical calculations, see Kimball, , “Making Sense of Two-Sided Altruism.”Google Scholar

³² We cannot rely upon the postulate of diminishing marginal utility to promote convergence. The value of additional goods diminishes at the margin, but the value of extra utility need not. The diminishing marginal utility of utility is a meaningful concept for an altruist only if the altruist's concern for the other's utility is inversely related to how happy the other individual is. I may weight your utility as 50 percent of mine if you are miserable, but 20 percent of mine if you are very happy. This kind of weighting promotes convergence, but this does not follow necessarily from the postulate of diminishing marginal utility. Diminishing marginal utility in the traditional sense means only that I attach less importance to subsequent units of wealth that you receive.

³³ The economic theory of revealed preference requires that preferences be defined across observable entities and thus requires goods evaluation. The theory of revealed preference, however, is itself open to question and does not furnish a decisive argument in favor of goods evaluation.