Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Proportional Giving

10 Post author: gjm 02 March 2014 09:09PM

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 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 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?

Comments (86)

Comment author: benkuhn 02 March 2014 11:55:44PM *  14 points [-]

Proportional giving was designed for people who didn't even necessarily want to be intrinsically motivated to give money (e.g. paying taxes or perhaps tithing to a church). If you want to raise money from such people, proportional donation aligns the incentives much better than threshold.

That said, there are a couple reasons why it's still useful for effective altruists:

  • The thing you mentioned about near mode.

  • As you get older, you gain more ability to buy utility at good prices: for instance, kids become increasingly expensive as they age.

  • It sets a norm that's easier for people to follow. For instance, fewer people would join Giving What We Can if the pledge were "give everything above $X" instead of "give 10% of your income".

  • It's more inclusive. Not everyone can give away everything above (e.g.) US$36k. A lot more people can give away 10% of income.

Nevertheless, many effective altruists (e.g. Toby Ord) do practice the fixed-income approach.

Comment author: Antisuji 04 March 2014 04:39:51AM 1 point [-]

As you get older, you gain more ability to buy utility at good prices: for instance, kids become increasingly expensive as they age.

Perhaps because my economic intuition isn't that sharp, I'm having trouble connecting the dots on this statement. I'm not seeing how the example implies the assertion, and I'm having trouble coming up with another example. Can you expand on this?

Comment author: someonewrongonthenet 04 March 2014 11:27:20PM *  0 points [-]

As kids grow older, they become more expensive because they increasingly demand more money.

The reason they demand more money is because money becomes more valuable to them as they age.

The reason money becomes more valuable to them as they age is because they can buy more utility per dollar.

(I don't know if this is true, I'm just explaining the argument).

Analogous to: People who like chocolate more eat more chocolate, people will spend more money when the store has a special sales deal, etc. Lower prices//higher benefits drive up demand.

Comment author: benkuhn 04 March 2014 05:39:02AM 0 points [-]

Suppose that I weight my own utility such that I'm willing to buy utility at 10 utils per dollar. As gjm noted, this exchange rate should stay constant unless my utility weightings change. But suppose that there are a number of things that provide utility at this rate:

  • playing video games
  • drinking alcohol
  • renting fancy cars
  • owning a house
  • having children

These things become available increasingly late in life, so my consumption would increase even though I spent money rationally (well, rationally_{weighted utilitarianism}) throughout.

Comment author: ESRogs 04 March 2014 08:48:03PM 1 point [-]

I'm still confused about how kids becoming more expensive is an example of becoming an increasingly good utility deal. Doesn't it sound like the opposite? Or do you assume that the utility from parenting goes up faster as the children age than the cost does?

Comment author: benkuhn 05 March 2014 04:54:16AM 0 points [-]

It doesn't matter how the utility is distributed, just that it averages out to 10 utils per dollar (such that having the kid is a good buy overall), while the costs rise.

Comment author: Lumifer 04 March 2014 09:04:51PM *  0 points [-]

I am fairly confused as well, but the parent post might mean opportunity costs.

If when you are young you can buy 10 utilons per dollar and when you are older you can get 20 utilons per dollar then spending the same amount of dollars on your kids represents a greater "loss" of utilons at the later age.

Comment author: gjm 03 March 2014 10:23:11AM 1 point [-]

Toby Ord

Damn, I meant to mention him and then forgot. (Is it really many effective altruists? He's the only example I know of, but I haven't gone looking very hard.)

Comment author: peter_hurford 03 March 2014 03:00:58PM 3 points [-]

It's the basis for Giving What We Can's Further Pledge. I know of a few other people who have taken it, either implicitly or explicitly.

Comment author: gjm 03 March 2014 03:17:16PM 0 points [-]

Gotcha. Thanks.

Comment author: benkuhn 04 March 2014 05:20:46AM 1 point [-]

Will MacAskill does, and I think many other CEA employees. I think Jeff Kaufman and Julia Wise do an ad-hoc thing but similar in that they mostly don't treat the percentage donated as relevant--they set their personal allowance based on making their best effort without taking into account how much they're currently earning. (I'm not 100% sure this is accurate though.) I don't know the giving habits of many other EtGers but I wouldn't be surprised if they used a broadly similar method to Jeff and Julia.

Comment author: jkaufman 05 March 2014 10:25:31PM 2 points [-]

Julia and I handle our donations differently:

  • Everything Julia earns is donated, after taxes.
  • I pick a percentage of my income at the beginning of the year to be donated.

Last year I went for 30%, this year I'm going for 33%.

Comment author: ThrustVectoring 03 March 2014 01:37:38AM 9 points [-]

There's a difference between what the best course of action for you personally is, and the best recommendation to push towards society at large. The best recommendation to push for has different priorities: short message lengths are easier to communicate, putting different burdens on different people feels unfair and turns people off, and more onerous demands are less likely to be met.

"Give at least 10% of what you make" is low enough to get people on board, conveniently occupies a very nice Schelling point, short enough to communicate effectively, and high enough to get a lot out of the targets it hits. Furthermore, if you want to give more, you're still following the rule, so you can ask people to do the same without hypocrisy.

In short, it's a good social policy to push for and reward those who follow it. Personally, you should follow some kind of weighted utilitarianism, since if you get the utility function good enough then small errors in how you distribute your spending don't make much difference.

As an aside, an altruism-maximizer with a higher income may spend more money on themselves than one with a lower income - usually in the form of buying goods and services that make their income-generating ability better. Say, eating nourishing meals rather than the cheapest available one, so that their work performance goes up.

Comment author: scrafty 03 March 2014 04:34:02AM 6 points [-]

A compromise that I find appealing and might implement for myself is giving a fixed percentage over a fixed amount, with that fixed percentage being relatively high (well above ten percent). You could also have multiple "donation brackets" with an increased marginal donation rate as your income increases.

Comment author: gjm 03 March 2014 10:02:35AM 2 points [-]

Yes, I like this approach too.

Comment author: peter_hurford 03 March 2014 03:02:02PM 1 point [-]
Comment author: Tedav 04 March 2014 03:31:10AM -2 points [-]

I like this approach.

It makes sense, and it mostly dodges the problem that other "simple" formulae for charity have - namely that most simple systems tend to be essentially voluntary regressive taxation.

This is why the 10% rule has always bugged me - it is a culturally accepted voluntary regressive tax, and as such it exacerbates social inequality.

[Also, one of my friends likes to joke that our culture holds that you give 10% of your income to charity, but capital gains are exempt...]

I'm always on the lookout for things that seem innocuous or even beneficial that actually are ways of enforcing the social structure and preventing upwards mobility, like our strange insistence on prescriptive rules of language, and upon the necessity of "sounding intelligent".

Language are evolved social constructs, and "correct grammar" is determined by native speakers. However, we impose additional rules that stray from the natural form of the language, and develop a notion that certain ways of speaking/writing are proper, and that other ways are ignorant. To learn how to speak in a way that sounds intelligent requires additional investment of time and effort, and those that cannot afford to do so (can't afford to spend as much time reading, or comes from an area with worse schools) will grow up speaking a completely intelligible version of the language, but one that is generally recognized as sounding like a marker of ignorance, and thus limits possibilities for advancement.

Ok, I really got off topic there, but my point was that our cultural construct that people should give a fixed percentage of their income to charity might very well not be a force for good, but rather a force opposing good.

It is a regressive taxation system, but one that is culturally supported. Further, because so many people feel like everyone is already voluntarily consenting to give to charity (especially through religious organizations) that actual taxation is an unnecessary imposition.

If we didn't have a culturally accepted obligation for charity, we wouldn't give as much money to inefficient charities and religious institutions, and might be more willing to consent to a higher progressive tax.

Comment author: gjm 04 March 2014 09:28:48AM 2 points [-]

voluntary regressive tax

How is it regressive? (I suppose if A has a policy of giving 10% of what you get after tax and B looks at A's giving as a fraction of income before tax then it'll look like a regressive policy. But you could equally say that if A gives 10% of income before tax, and B looks at giving as a fraction of income after tax, then proportional giving looks like a progressive policy.)

Many advocates of proportional giving would say that if you're poor then you shouldn't be feeling obliged to give at all, which would make the policy progressive overall.

but capital gains are exempt

I don't think it's fair to blame this on the idea of proportional giving.

If we didn't have a culturally accepted obligation for charity, we [...] might be more willing to consent to a higher progressive tax.

I suppose that's possible in theory. I gravely doubt it would actually happen in practice. (Perhaps if we were forbidden to give to charities privately, but that seems like an obviously really terrible idea.)

Comment author: Dias 05 March 2014 03:00:12AM 1 point [-]

If we didn't have a culturally accepted obligation for charity, we wouldn't give as much money to inefficient charities and religious institutions, and might be more willing to consent to a higher progressive tax.

And if people didn't naturally want to have sex, we might be more willing to consent to government-assigned reproduction!

Comment author: Tedav 05 March 2014 08:35:32PM 0 points [-]

Yes, that is true as well.

My point was that since our cultural instinct is to give, but in practice this is done inefficiently, [charities are wasteful, people don't give to charities to optimize utility but rather to charities that they think they like, and a flat percentage is probably worse than a progressive tax], and therefore it would probably be better for society if we didn't expect charity from people - this seemingly beneficial cultural obligation can be argued to be harmful.

Comment author: TsviBT 02 March 2014 09:27:34PM 6 points [-]

One factor you didn't mention is that significantly harder working people might need to spend more income to maintain their productivity. E.g. traders working 80-hour weeks might spend more on food because they don't have time to cook, more on clothes because their job requires signaling, more on airplane tickets because they have short-notice time-sensitive tasks requiring travel, etc. But there's still no reason this should work out to anything like proportional giving, so your point stands.

Comment author: army1987 03 March 2014 04:34:14PM 1 point [-]

If you only add this effect while keeping the rest of the reasoning the same, the amount you should give is your discretionary income minus a constant, rather than your total income minus a constant.

Comment author: Punoxysm 04 March 2014 08:17:41AM 4 points [-]

A pro of proportional giving is that it's dead simple to budget and keep in mind.

It can also get people to give a certain amount continually and keep them emotionally invested in charitable effort, while allowing them plenty of savings for contingencies and perhaps an eventual larger lump sum donation.

And even if it's not optimal, "indefensible" is a pretty strong claim.

Comment author: gjm 04 March 2014 09:18:24AM 1 point [-]

"indefensible" is a pretty strong claim.

That would be why I put "possibly" in front of it.

For the avoidance of doubt, I agree that it's simple and works pretty well in practice. That's why I'm curious whether there's a good theoretical justification for something like it.

Comment author: Punoxysm 04 March 2014 04:56:43PM 0 points [-]

I think you won't find anything without a lot of assumptions and caveats; Any concave utility function will simply never lead to proportional giving.

But certainly, many people will scale up their own expectations of lifestyle along with their income until a pretty high point: that is, they'll try to tell you or at least behave as if they don't have a concave utility function, until they're well into the six figures (sometimes more). Since income changes are slow and tend to co-occur with many other life changes, this, along with psychological biases, complicate any earnest attempt to sit down and say "I'll be best off giving X portion of my income this year".

Comment author: lincolnquirk 02 March 2014 11:57:18PM *  3 points [-]

I try to apply the hybrid philosophy of: "work hard, make money, give what you can afford to give today, give yourself a near-mode incentive to make more money, and create savings for the future".

The savings one is a big one you didn't mention. I feel like my future self has a high chance to smack me if I commit too much money now. It seems like the places I would give today can benefit more now from my donation than in the future, but I may find better places to spend the money or give it away in the future. Hence the hybrid.

Comment author: DanielLC 02 March 2014 11:13:40PM 2 points [-]

If you're an egoist, giving a fixed portion of your income has a fixed cost (since the marginally utility of money is approximately inversely proportional to what you have) and gives you a fixed amount of prestige, or signalling or whatever. That sort of thinking is useful for maximizing inclusive genetic fitness, so it's no surprise that we think that way.

Comment author: gjm 03 March 2014 01:16:07AM 2 points [-]

Does it give a fixed amount of prestige/signalling/whatever? Firstly, it only does so if you're telling the world about your giving (which, e.g., at least one of the ancient traditions featuring "tithing" strongly discourages); secondly, whether reasonably or not, I think you get more prestige from giving away 10% of what you have if you are either very poor (so that doing so really hurts) or very rich (so that it's an impressive-sounding sum that seems like it can do a lot of good).

However, the fact that a fixed fraction of income is kinda like a fixed sacrifice of utility does seem like it might be an important piece of the picture. Somehow.

Comment author: Nisan 05 March 2014 03:22:35PM 1 point [-]

An additional consideration is that a parliament of agents that cannot bind themselves to a contract would probably agree to split their resources in a way that reflects their political power. So if you model yourself as a parliament of agents, some egoist and some altruist, donating a fixed portion of your wealth and income can be "rational" in the sense that it is the result of your subagents behaving rationally in the context of politics. I think this is actually a reason people give a fixed portion of their income.

Comment author: drethelin 04 March 2014 02:58:09AM 1 point [-]

proportional giving is good because it's a kind of giving that you can get a lot of people to do. Not for weird math reasons. I agree with what you're saying given utilitarian calculations but I don't think you're doing the right calculation.

Comment author: gjm 04 March 2014 09:20:55AM 1 point [-]

This is Less Wrong. We tend to be all about the weird math reasons! Seriously, I was doing utilitarian calculations not because I think they're necessarily right but because they're an example of something that might have given something like the desired result, while also being a kinda-plausible way of weighing one's own interests against those of others.

Comment author: jsalvatier 06 March 2014 07:58:53PM 0 points [-]

Can you expand on that? What do you think would be closer to the right calculation?

Comment author: drethelin 06 March 2014 09:05:49PM *  2 points [-]

I think when proposing charitable giving strategies there are a few things that need to be considered that are usually forgotten. First, and something that a lot of people in this thread have said, is the probability of adoption and persistence of a given method. I think trying to get 10 percent of people to give 50 percent of their money is less likely to work than trying to get 50 percent to give 10 percent. a popular and relatively easy charitable giving strategy can give you a lot of friends who also do it, whereas a very costly and difficult one will make you poorer than everyone you know. In terms of social incentives, I think being unable to go to as many fun activities or have as good houses as people you know could easily counteract the bonus of "I give more to charity than anyone I know" since those facts are salient and come up a lot.

Second: I really like capitalism. I think capitalism is an extraordinarily powerful force that collates and acts on huge amounts of distributed information about what people want and can do, and is better at allocating resources than anything else we've tried so far. I don't think capitalism is perfect. Indeed, it's somewhat like fire. It lets us do things we never could without it but also can punish us in ways that nothing else can. One of the ways capitalism can act is to foster long-term technological growth, and historically, a lot of technological growth seems to be incentivized by the very wealthy. I don't know that there's a good way to measure this phenomenon, but there are examples such as automobiles, cellphones, televisions, computers, etc. which seem like, without attracting the money of the wealthy, they never would've become as useful or ubiquitous. And I think condemning people for spending their wealth on "themselves" can have chilling effects on this sort of slow, costly innovation.

Third, or kind of a subset of the second, is that encouraging huge donations instead of huge investments might be anti-utilitarian in the longterm, since fundamentally selfish profit seeking investment is how we develop a lot of our infrastructure and gather a lot of our resources. EDIT- as an elaboration: capitalism is better at skin in the game and feedback than charity, such that big capitalist efforts more reliably give many people what is wanted than big charity efforts. giving a 100 people food for a month might keep them alive but what does that buy us compared to a hundred people getting hammers? unknown.

I don't know and haven't really tried to figure out proper ratios, but I don't think "if you're wealthy, you should give everything above what you need to live to charity" is either going to be very widespread or necessarily good.

Comment author: gjm 06 March 2014 11:41:55PM 0 points [-]

Just in case I failed to make it clear, it is not my opinion that the calculation I described means that we should all give everything beyond what we need to charity, or that we should all give everything beyond some fixed threshold, or anything of that kind. I don't think weighted utilitarianism is necessarily a good system, nor do I think it's clear that (e.g.) motivational effects don't make a big enough difference to invalidate that naive calculation completely.

Comment author: jsalvatier 05 March 2014 01:24:55AM 1 point [-]

This seems obviously correct to me. In my experience this is not obvious to everyone and many people find it a bit distasteful to talk about. I'm glad you bring it up.

I haven't really tried hard, but I think I would find it pretty difficult to get myself to behave this way.

The way I "resolve" this dissonance is by thinking in terms of a parliamentary model of me. Parts of me want to be altruistic and part of me is selfish and they sort of "vote" over the use of resources.

Comment author: Gunnar_Zarncke 03 March 2014 08:01:27AM *  1 point [-]

Given that there are competing incentives (altruism vs. egoism and others) it is clear that some trade-off is needed. An optimum solution might be too complex to be understood and accepted as fair by everyone. Thus we have to look for simple approximations.

The simplest are

1 give nothing: g(x)=0

2 give a fixed amount: g(x)=c

3 give a fixed fraction: g(x)=fx

4 give everything above a treshold: g(x)=x>c?x-c:0

5 give a fixed fraction above a treshold: g(x)=x>c?f(x-c):0

6 give a by second order polynomial: g(x)=ax^2+bx+c

7 give a by second order polynomial with treshold: g(x)=x>c?ax^2+bx+d:0

Actually 4) is more complicated than

  • give/receive above a treshold: g(x)=x-c

which implies that I should take if I have less than the treshold.

What other simple functions are there and what do they imply?

Comment author: army1987 03 March 2014 04:42:23PM 0 points [-]

One effect of income is (supposedly) to incentivize work,

A way of modelling this is replacing u(x) with a u(X, L), where L is the number of non-work hours in a week, and replacing S with (168 - L)W, where 168 is the total number of hours in a week and W is your hourly wage. Then you maximize u((168 - L)W - g, L) + wtg with respect to L and g.