Hamilton’s Rule

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Hamiltons Rule


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 (19362000) 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 progressionfrom 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, ones willingness to sacrifice for otherswhether individuals, a group, or societycan be measured by the degree of kinship involved.

Hamiltons 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 Darwins 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 Hamiltons 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 todays 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 Hamiltons 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 occursand 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


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Lall Ramrattan

Michael Szenberg

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Hamilton’s Rule

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