Rotten kids and altruism


Jason Collins


April 29, 2011

Gary Becker’s 1976 article Altruism, Egoism and Genetic Fitness: Economics and Sociobiology is an article that I cite often. Becker’s closing paragraph has one of the earliest statements of the benefits of combining economics and sociobiology. He wrote:

I have argued that both economics and sociobiology would gain from combining the analytical techniques of economists with the techniques in population genetics, entomology, and other biological foundations of sociobiology. The preferences taken as given by economists and vaguely attributed to “human nature” or something similar - the emphasis on self-interest, altruism toward kin, social distinction, and other enduring aspects of preferences - may be largely explained by the selection over time of traits having greater genetic fitness and survival value.

Despite my regular references to the article, I have not spent much time dwelling on the article’s substance, an analysis of altruism as an extension of Becker’s “rotten-kid” theorem. At the recent conference Social Decision Making: Bridging Economics and Biology, Alan Grafen addressed Becker’s paper in his plenary presentation. This triggered me to revisit the paper.

Becker’s “rotten-kid” theorem, first laid out in a 1974 paper, works on the following premise. Suppose there is a parent who cares about the welfare of their children and will give them wealth and other gifts. Suppose further that one of the kids is rotten and he would like to harm his fellow siblings. Becker argued that if the parent redirected money to the hurt sibling when the rotten kid acted on his impulses, the rotten kid would have an incentive not to harm his siblings as it would cost him in the form of lost transfers from his parent. This induces to rotten child to act benevolently.

In his 1976 article, Becker extended this argument to general altruistic behaviour. Suppose there is a single altruist in a large group that cares about the welfare of all the members of the group. They are willing to transfer resources to other group members to increase their welfare. Becker argued that any egoist in the group would refrain from harming the altruist or others in the group to the extent that the harm would cut transfers to them from the altruist. This altruism exists through interaction, not kinship, so does not need the altruists or egoists to be related.

As well as analysing from the perspective of consumption, Becker examines the fitness of the altruist and egoist and shows that a similar result holds. The only added element that a consideration of fitness requires is that transfers may contribute to the fitness of the altruists and egoists at different rates.

Becker provides an example where there is a single egoist and altruist and the egoist could increase his income by $800 at the cost of $5,000 to the altruist. As the altruist cares about both his own and the egoists welfare, the net result of the egoist’s action is that the egoist will receive a lower transfer from the altruist and on net, will suffer a loss due to his egoism. As the egoist will not take the selfish action, the altruist’s altruism could be said to have saved him $5,000 in income.

This example, while providing a useful illustration, indicates the weakness in the model. The egoist will only be restrained to the extent that the transfer lost would be more than the gain from acting selfishly. If we reversed the above the numbers, the egoist would unequivocally take the action. The equation becomes even less tenable as a group becomes large. Suppose there is one altruist in a group of 10. The size of the transfer any egoist would receive from the altruist would be expected to be very small, and unlikely to be of a comparable size to any gain from cheating. This is particularly the case if the gain for the egoist approaches the size of the loss to the altruist (the technical term for these types of situation is a corner solution).

One of the interesting points Becker makes is the distinction between actual and simulated altruism. In his model, altruists are actual altruists because they care about the welfare or fitness of others. Egoists are simulated altruists because it is in their own personal interest to act altruistic, despite their egoist underpinnings. From an evolutionary point of view, I am not sure this distinction exists.

I should note, finally, that there is no shortage of other literature that addresses the “rotten-kid” theorem and this paper, and shows the restrictive assumptions that need to be applied to the model for it to work (such as by Bergstrom).