More on Altruism

A Critique of Becker Altruism

Howard Margolis offered the following evidence that donors to charity do not behave as Becker altruism predicts.

You currently have an income of a hundred thousand dollars of which you donate ten thousand a year to the Red Cross. You are a Becker altruist; the reason for your donation is that the utility of each person served by the Red Cross is an item in your utility function. You are accordingly donating an amount such that the marginal utility to you of the increased utility to each beneficiary from the increased services of the Red Cross due to an extra dollar donated by you, summed over all beneficiaries, equals the value to you of a dollar spent on yourself.

You get a ten thousand dollar raise. If you spent all of it on yourself the value to you of a dollar of consumption would fall below the value to you of a dollar donated, so you increase your donation.

By how much? The Red Cross has, we may assume, ten thousand people it serves, so an extra thousand dollars donated gives each of them ten cents — for simplicity I am imagining that the Red Cross simply hands out money. Ten cents is a very small part of their income so would have almost no effect on the rate at which their utility increases with increased income and only a tiny effect on their utility. Since their utility changes by only a tiny amount so does the rate at which your utility increases with their utility. It follows that an additional thousand donated, divided among ten thousand people, will have almost no effect on the utility you get from each dollar donated.

After donating an additional thousand dollars you are still consuming nine thousand more than before so the utility you get from a dollar consumed is still lower than before, the utility from a dollar donated is almost the same as before, so you donate another thousand. And another. Only when you have donated almost all of the ten thousand will your value for a dollar of your own consumption be back up to what it used to be, hence equal to the almost unchanged value to you of the increased beneficiary utility due to a dollar donated.

It follows that any increase in your income will go almost entirely to the Red Cross and any decrease taken almost entirely as a decrease in the amount you donate to them. Real people who donate money to charities that divide it among large numbers of recipients do not act that way. That is evidence that Becker’s model does not describe all behavior that is regarded as due to altruism — but also evidence that his model has enough substance to be testable.¹

Some theories don’t.

I will leave it to the more ambitious of my more mathematically sophisticated readers to convert the verbal argument I have given to a more precise argument in a more suitable language.

Money, Beauty, and Folk Songs

The Brown Girl she has house and lands, fair Ellender she has none.

—No. 73 of The English and Scottish Popular Ballads collected by Francis James Child

The choice between economic and non-economic approaches to marriage is a common theme in folk songs. A young man must choose between two women, one beautiful and one rich. Almost invariably he chooses the rich one. The result is tragedy; at least two and often all three of the parties end up dead. The lesson is clear: Marry the beautiful woman.

It is clear in such songs that marrying a woman for her money is bad but marrying her for her beauty is fine. It is less clear why. True, the Brown Girl (dark complexioned, hence less attractive than "Fair" Ellender) has done nothing to deserve her wealth; one could argue that she therefore does not deserve to get Lord Thomas. But no more does Fair Ellender deserve her beauty. All either of them has done is to pick the right parents, the one for wealth and the other for looks. Why then is it good and noble for Lord Thomas to reject wealth for beauty and base and wicked for him to reject beauty for wealth?

One answer may be that the plot depends on something that I assumed away in my previous post. In the world of folk songs — and in many, perhaps most, human societies — the bride and groom are not the only ones whose interests are involved in their marriage, nor are they the only ones with some control over it. If Lord Thomas marries Fair Ellender he will be the only one to benefit by her beauty; if he marries the Brown Girl, his parents may reasonably hope to get their hands on some of her wealth. Perhaps they are counting on it to support them in their old age. It is Lord Thomas's mother who persuades him to marry the Brown Girl.

If that is what is going on, it is clear enough which side of the generation gap the singer is on. Or, at least, which side he believes his audience is on.

Fair Ellender and the Rotten Kid

It is widely believed that beauty is, and wealth is not, one of the things that makes men fall in love with women. Our analysis of altruism suggests that people will work together more easily if one of them is an altruist with regard to the other, since it is then in the interest of both altruist and beneficiary to maximize their joint welfare. Lord Thomas is in love with Fair Ellender and is not in love with the Brown Girl, as he informs her immediately after the wedding, with the result that the Brown Girl stabs Fair Ellender, Lord Thomas kills the Brown Girl, and Lord Thomas then commits suicide, ending the song and presumably teaching his parents a lesson. If we are willing to identify "being in love" with altruism, perhaps the moral of the song is correct. If you marry the beautiful woman, you get not only beauty but also the advantage of being part of an efficient household coordinated by your own altruism.

Of course, it only works in one direction; we have no reason to believe that Fair Ellender's beauty makes her any more likely to act altruistically toward Lord Thomas. But that is not an important objection to the argument; we know, from the Rotten Kid Theorem, that one altruist in a family is enough.

A more serious objection is that it is not clear how close the relationship is between "being in love" and altruism; Fair Ellender's response to being jilted by the man she was "in love" with was to dress up in her finest ("every village she came through, they thought she was some queen") and go spoil her ex-boyfriend's wedding. "Being in love" seems to describe a mix of emotions, some far from altruistic. To what extent elements in the mix associated with physical beauty involve altruism, and, if they do, whether they are likely to survive the first six months of marriage, is an open question.

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1. The late George Stigler taught me an important lesson when he rejected the original version of what was to become my first published journal article in economics. He told me that in order to be publishable, the article required not only a theory — in my case of the size and shape of nations — but also some way of testing that theory. In revising to meet that requirement I not only found evidence in support of my theory I also, and perhaps more important, was forced to think through more carefully and precisely what the theory said.