I usually try not to push people on this particular point unless I think they’re already very high-level; my default assumption is that people are very akrasic and fragile when it comes to charity.
However, I’m raising my estimate of Landsburg’s level based on this—I guess one mostly hears about the disputable points he got wrong, not the indisputable points he got right, of which this is one (and a rarely appreciated one at that).
Landsburg’s argument is sound, and I mostly follow it and occasionally try to sell others on it. But I can think of one exception, which is if the political power of an organization that you support depends on the number of members it has. So for example I pay membership dues to one organization that is not my main charity because I want them to be able to claim one more member.
And there is one place that I think Landsburg gets it plain wrong. He says*:
To please diverse stockholders, corporations tend to diversify their giving, often through the United Way. For individuals, by contrast, it really is quite impossible to justify that level of diversity. Surely among the hundreds of United Way recipients there are some you consider worthier than others. That means you can target your charity more effectively by bypassing the United Way.
But if you think that the United Way comes tolerably close to sharing your values, but you think that they have better information than you do about relative needs and competencies across different organizations, then it makes perfect sense to donate to them, doesn’t it?
I usually try not to push people on this particular point unless I think they’re already very high-level; my default assumption is that people are very akrasic and fragile when it comes to charity.
Fair enough.
However, I’m raising my estimate of Landsburg’s level based on this
Glad to hear it; I’ve been a fan of his for years, based mainly on his Slate column and his first two books.
When I try to view that page, it briefly shows the math, then blanks and sits there loading forever, so I can’t quite see what he’s saying. If you’re able to see it, could you cut and paste?
Here’s my attempt at copy-and-paste, for those who have difficulty viewing (will require edits to fix):
[ETA: All right, can’t get the LaTeX plugin to work, so I’ll just use something like the old Usenet conventions.]
Suppose that there are three charities (the same argument would work with any number other than three), that those charities currently have endowments of x, y, and z, and that you plan to make contributions of delta x, delta y, and delta z). A truly charitable person will care only about each charity’s final endowment, and so will seek to maximize some function
U(x + delta x, y + delta y, z + delta z)
subject to the constraint that delta x+ delta y + delta z = C, where C is the amount you’ve decided to give to charity.
But assuming that your contributions are small relative to the initial endowments, this quantity is well approximated by
U(x,y,z)+ (partial U/partial x) dot delta x + (partial U/partial y) dot delta y+ (partial U/partial z) dot delta z.
which is maximized by bulleting everything on the charity that corresponds to the largest of the partial derivatives.
(The linear approximation fails if your contributions are large relative to the initial endowments, or if you have sufficient delusions of grandeur to believe that your contributions are large relative to the initial endowments.)
Note that if you have any uncertainty about what the various charities will do with their endowments, the costs of that uncertainty can be built into the definition of the function U. Thus, such uncertainty in no way undermines the main argument.
On the other hand, if you care not about what the charitable organizations receive but about what you give to them (as would be the case, for example, if you give in order to enjoy being thanked), then you will want to maximize some function
U(x,y,z)
In this case, it’s unlikely that the solution would be to bullet.
I usually try not to push people on this particular point unless I think they’re already very high-level; my default assumption is that people are very akrasic and fragile when it comes to charity.
However, I’m raising my estimate of Landsburg’s level based on this—I guess one mostly hears about the disputable points he got wrong, not the indisputable points he got right, of which this is one (and a rarely appreciated one at that).
Landsburg’s argument is sound, and I mostly follow it and occasionally try to sell others on it. But I can think of one exception, which is if the political power of an organization that you support depends on the number of members it has. So for example I pay membership dues to one organization that is not my main charity because I want them to be able to claim one more member.
And there is one place that I think Landsburg gets it plain wrong. He says*:
But if you think that the United Way comes tolerably close to sharing your values, but you think that they have better information than you do about relative needs and competencies across different organizations, then it makes perfect sense to donate to them, doesn’t it?
*http://www.slate.com/id/77619/
I see ciphergoth already made my first point. Sorry about that.
Fair enough.
Glad to hear it; I’ve been a fan of his for years, based mainly on his Slate column and his first two books.
Um....you might want to have a look at Landsburg’s math and see if you notice anything wrong.
ETA: Actually, never mind. I overlooked something. Silly me.
Of course, it’s still a good exercise to check.
When I try to view that page, it briefly shows the math, then blanks and sits there loading forever, so I can’t quite see what he’s saying. If you’re able to see it, could you cut and paste?
Here’s my attempt at copy-and-paste, for those who have difficulty viewing (will require edits to fix):
[ETA: All right, can’t get the LaTeX plugin to work, so I’ll just use something like the old Usenet conventions.]
Damn, sorry, I deleted the comment asking for this when I managed to find a way to read it. Thanks for sorting it out!
Is the error that he says x where he means delta-x in a couple of places?
No, that was my copying mistake. Fixed.
Then I don’t see the error, help me out?