Executive summary: The practice of giving a fixed fraction of one's income to charity is near-universal but possibly indefensible. I describe one approach that certainly doesn't defend it, speculate vaguely about a possible way of fixing it up, and invite better ideas from others.

Many of us give a certain fraction of our income to charitable causes. This sort of practice has a long history:

Deuteronomy 14:22 Thou shalt truly tithe all the increase of thy seed, that the field bringeth forth year by year.

(note that "tithe" here means "give one-tenth of") and is widely practised today:

GWWC Pledge: I recognise that I can use part of my income to do a significant amount of good in the developing world. Since I can live well enough on a smaller income, I pledge that from today until the day I retire, I shall give at least ten percent of what I earn to whichever organizations can most effectively use it to help people in developing countries. I make this pledge freely, openly, and without regret.

And of course it's roughly how typical taxation systems (which are kinda-sorta like charitable donation, if you squint) operate. But does it make sense? Is there some underlying principle from which a policy of giving away a certain fraction of one's income (not necessarily the traditional 10%, of course) follows?

The most obvious candidate for such a principle would be what we might call

Weighted Utilitarianism: Act so as to maximize a weighted sum of utility, where (e.g.) one's own utility may be weighted much higher than that of random far-away people.

But this can't produce anything remotely like a policy of proportional giving. Assuming you aren't giving away many millions per year (which is a fair assumption if you're thinking in terms of a fraction of your salary) then the level of utility-per-unit-money achievable by your giving is basically independent of what you give, and so is the weight you attach to the utility of the beneficiaries.

So suppose that when your income, after taking out donations, is $X, your utility (all else equal) is u(X), so that your utility per marginal dollar is u'(X); and suppose you attach weight 1 to your own utility and weight w to that of the people who'd benefit from your donations; and suppose their gain in utility per marginal dollar given is t. Then when your income is S you will set your giving g so that u'(S-g) = wt.

What this s...

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