Hamilton’s Rule

BIBLIOGRAPHY

The dominant paradigm in economics holds that individuals in society seek to maximize their own self-interest. As Adam Smith observed, however, even selfish individuals have something in their nature that makes them altruistic. The British evolutionary biologist William D. Hamilton (1936–2000) attempted to give this altruism a biological basis. Hamilton expressed a rule for the evolution of social behavior as rb – c > 0, where r is a measure of genetic relatedness between an actor and a recipient, b is benefits to a recipient, and c is the cost to the actor of altruistic behavior.

The degree of genetic relatedness among kin follows a declining progression—from mother and child, to mother and nephew or niece, and so on. The implication of the progression is that closely related kin have a higher measure of genetic relatedness. Indeed, the probability that two relatives possess the same rare gene is high, because of a phenomenon known as kin selection. According to Hamilton, one’s willingness to sacrifice for others—whether individuals, a group, or society—can be measured by the degree of kinship involved.

Hamilton’s rule has been used to study altruism, aggression, and selfishness in social interaction. Genes that have survived through Darwinian competition can be deemed selfish and are responsible for the selfish behavior in individuals known as individual selection. In Darwin’s view of natural selection, the fittest survive. However, individuals evolve to act for the good of the species or society, through a process known as group selection. The argument for group selection is that a person who sacrifices for a group is more likely to survive than one who sacrifices for selfish benefits.

Individual and group selections can be profitably analyzed using the tools of game theory. If a woman is able to select the sex of a child, she will choose the sex that will maximize the welfare of her grandchildren. Gaming enters the process because the outcome of her decision will depend on the sex ratio in the population, which is a consequence of what other females selected as the sex of their child. Building on Hamilton’s and others’ works, John Maynard Smith has derived an evolutionary stable strategy (ESS) for such games. An ESS can be achieved by each woman tossing a coin to make her selection, yielding a 50:50 chance of selecting a male or a female. With today’s technology, a person can know the sex of a child before birth, but if abortion or other changes relating to wars, customs, and politics occur, then no ESS is guaranteed.

Some applications of Hamilton’s rule to economics have been successful. In a 2005 study, Samuel Bowles and Dori Posel examined migrant workers who remit income to their families. If a migrant with wage w transfers an amount, t, to his or her family with pre-remittance income, y, then the marginal cost to the migrant is 1/(w –t ), and the marginal benefit to the recipient is r /(y + t /n ). Optimal transfer occurs when the marginal benefit equals the marginal cost.

Some aspects of the Hamilton rule appear anomalous. Hamilton assumes that parents invest equally in male and female children, whereas economists usually think of parents as investing up to the point where equality of marginal benefits and costs occurs—and thus generally investing more in male children. More generally, the idea that genetic selection guides economic behavior seems somewhat problematic: Genetic changes are slow, whereas changes in prices, advertising, and R&D have an immediate effect.

SEE ALSO Aggression; Darwin, Charles; Evolutionary Games; Game Theory; Kinship, Evolutionary Theory of; Maximization

BIBLIOGRAPHY

Axelrod, Robert, and William D. Hamilton. 1981. The Evolution of Cooperation. Science n.s., 211 (4489): 1390–1396.

Bowles, Samuel, and Dori Posel. 2005. Genetic Relatedness Predicts South African Migrant Workers’ Remittances to Their Families. Nature 434 (7031): 380–383.

Dawkins, Richard. 1989. The Selfish Gene. Oxford and New York: Oxford University Press.

Day, Troy, and Peter D. Taylor. 1997. Hamilton’s Rule Meets the Hamiltonian: Kin Selection on Dynamic Characters. Proceedings: Biological Sciences 264 (1382): 639–644.

Hamilton, William D. 1964. Altruism and Related Phenomena, Mainly in the Social Insects. Annual Review of Ecology and Systematics 3: 193–232.

Hamilton, William D. 1964. The Genetical Theory of Social Behavior, I, II. Journal of Theoretical Biology 7 (1): 1–52.

Lessard, Sabin. 2001. William D. Hamilton: A Tribute. Theoretical Population Biology 59 (1): 7–9.

Matessi, Carlo, and Samuel Karlin. 1984. On the Evolution of Altruism by Kin Selection. Proceedings of the National Academy of Sciences U.S.A. 81 (6): 1754–1758.

Samuelson, Paul A. 1985. Modes of Thought in Economics and Biology. American Economic Review 75 (2): 166–172.

Smith, Adam, 1976. The Theory of Moral Sentiments, eds. D. D. Raphael and A. L. Macfie. Oxford: Clarendon Press.

Smith, John Maynard. 1993. The Theory of Evolution. Canto Edition. Cambridge, U.K.: Cambridge University Press.

Lall Ramrattan

Michael Szenberg