# Proportional Giving

**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._

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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_](http://www.givingwhatwecan.org/about-us/the-pledge "Giving What We Can: the 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 says is that **a weighted-utilitarian should keep a fixed absolute amount _S_-_g_ of his or her income, and give all the rest away**. The fixed absolute amount will depend on the weight _w_ (hence, on exactly which people are benefited by the donations) and on the utility per dollar given _t_ (hence, on exactly what charities are serving them and how severe their need is), but not on the person's pre-donation income _S_.

(Here's a quick oversimplified example. Suppose that utility is proportional to log(income), that the people your donations will help have an income equivalent to $1k/year, that you care 100x more about your utility than about theirs, and that your donations are the equivalent of direct cash transfers to those people. Then _u_' = 1/income, so you should keep everything up to $100k/year and give the rest away. The generalization to other weighting factors and beneficiary incomes should be obvious.)

This argument seems reasonably watertight given its premises, but proportional giving is so well-established a phenomenon that we might reasonably trust our predisposition in its favour more than our arguments against. Can we salvage it somehow?

Here's one possibility. One effect of income is (supposedly) to incentivize work, and maybe (mumble [near mode](http://www.overcomingbias.com/2010/06/near-far-summary.html) mumble) this effect is governed entirely by anticipated personal utility and not by any benefit conferred on others. Then the policy derived above, which above the threshold makes personal utility independent of effort, would lead to minimum effort and hence maybe less net weighted utility than could be attained with a different policy. Does this lead to anything like proportional giving, at least for some semi-plausible assumptions about the relationship between effort and income?

At the moment, I don't know. I have a page full of scribbled attempts to derive something of the kind, but they didn't work out. And of course there might be some better way to get proportional giving out of plausible ethical principles. Anyone want to do better?