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Giving Your AllThe math on the back of the envelope

By Steven E. Landsburg
Posted Saturday, Jan. 11, 1997, at 3:30 AM ET

CARE is a noble organization that fights starvation. It would like your support. The American Cancer Society is a noble organization that fights disease. It would like your support, too. Here's my advice: If you're feeling very charitable, give generously—but don't give to both of them.

Giving to either agency is a choice attached to a clear moral judgment. When you give $100 to CARE, you assert that CARE is worthier than the cancer society. Having made that judgment, you are morally bound to apply it to your next $100 donation. Giving $100 to the cancer society tomorrow means admitting that you were wrong to give $100 to CARE today.

You might protest that you diversify because you don't know enough to make a firm judgment about where your money will do the most good. But that argument won't fly. Your contribution to CARE says that in your best (though possibly flawed) judgment, and in view of the (admittedly incomplete) information at your disposal, CARE is worthier than the cancer society. If that's your best judgment when you shell out your first $100, it should be your best judgment when you shell out your second $100.

When it comes to managing your personal portfolio, economists will tell you to diversify. When it comes to handling the rest of your life, we give you exactly the same advice. It's a bad idea to spend all your leisure time playing golf; you'll probably be happier if you occasionally watch movies or go sailing or talk to your children.

So why is charity different? Here's the reason: An investment in Microsoft can make a serious dent in the problem of adding some high-tech stocks to your portfolio; now it's time to move on to other investment goals. Two hours on the golf course makes a serious dent in the problem of getting some exercise; maybe it's time to see what else in life is worthy of attention. But no matter how much you give to CARE, you will never make a serious dent in the problem of starving children. The problem is just too big; behind every starving child is another equally deserving child.

That is not to say that charity is futile. If you save one starving child, you have done a wonderful thing, regardless of how many starving children remain. It is precisely because charity is so effective that we should think seriously about where to target it, and then stay focused once the target is chosen.

People constantly ignore my good advice by contributing to the American Heart Association, the American Cancer Society, CARE, and public radio all in the same year--as if they were thinking, "OK, I think I've pretty much wrapped up the problem of heart disease; now let's see what I can do about cancer." But such delusions of grandeur can't be very common. So there has to be some other reason why people diversify their giving.

I think I know what that reason is. You give to charity because you care about the recipients, or you give to charity because it makes you feel good to give. If you care about the recipients, you'll pick the worthiest and "bullet" (concentrate) your efforts. But if you care about your own sense of satisfaction, you'll enjoy pointing to 10 different charities and saying, "I gave to all those!"

Here's a thought experiment for charitable diversifiers. Suppose you plan to give $100 to CARE today and $100 to the American Cancer Society tomorrow. Suppose I mention that I plan to give $100 to CARE today myself. Do you say, "Oh, then I can skip my CARE contribution and go directly on to the American Cancer Society?" I bet not.

But if my $100 contribution to CARE does not stop you from making CARE your first priority, then why should your $100 contribution to CARE (today) stop you from making CARE your first priority tomorrow? Apparently you believe that your $100 is somehow more effective or more important than my $100. That's either a delusion of grandeur or an elevation of your own desire for satisfaction above the recipients' need for food.

We have been told on reasonably high authority that true charity vaunteth not itself; it is not puffed up. You can puff yourself up with thank-you notes from a dozen organizations, or you can be truly charitable by concentrating your efforts where you believe they will do the most good.

Early in this century, the eminent economist Alfred Marshall offered this advice to his colleagues: When confronted with an economic problem, first translate into mathematics, then solve the problem, then translate back into English and burn the mathematics. I am a devotee of Marshall's and frequently follow his advice. But in this instance, I want to experiment with a slight deviation: Rather than burn the mathematics, I will make it available as a link.

I propose to establish the following proposition: If your charitable contributions are small relative to the size of the charities, and if you care only about the recipients (as opposed to caring, say, about how many accolades you receive), then you will bullet all your contributions on a single charity. That's basically a mathematical proposition, which I have translated into English in this column. If you want to see exactly what was gained or lost in translation (and if you remember enough of your freshman calculus to read the original), then click here.

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Steven E. Landsburg, author of The Armchair Economist: Economics and Everyday Life, is a professor of economics at the University of Rochester. You can e-mail the author at .
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