The Counterfactual Validity of Donation Matching

A foun­da­tion finds an or­ga­ni­za­tion do­ing good work with a fund­ing gap of about $5M. They could just give the or­ga­ni­za­tion $5M, but in­stead they de­cide to try and help the or­ga­ni­za­tion find some small donors to spread its reach. The foun­da­tion offers to match dona­tions up to $2.5M. This is a real match: they will give $1 for ev­ery $1 any­one else gives, up to their limit. When the match is over, how­ever, if the fund­ing gap still hasn’t been met they plan to make up the differ­ence.

Let’s con­sider some pos­si­blities:

Amount Raised Match Given Makeup Con­tri­bu­tion To­tal Re­ceived
$0 $0 $5M $5M
$100K $100K $4.8M $5M
$200K $200K $4.6M $5M
$1M $1M $3M $5M
$2M $2M $1M $5M
$2.5M $2.5M $0 $5M
$3M $2.5M $0 $5.5M
$4M $2.5M $0 $6.5M
If the or­ga­ni­za­tion raises less than $2.5M from small donors they end up with a to­tal of $5M re­gard­less of the amount the small donors give. This is de­scribed as a 1:1 match, but be­cause their “makeup con­tri­bu­tion” acts as a 1:-2 match the over­all effect on the char­ity is ac­tu­ally a 1:-1 match: for ev­ery dol­lar you give they’ll give one fewer! By donat­ing to the or­ga­ni­za­tion you’re effec­tively donat­ing to the foun­da­tion, by leav­ing them with more money to do other things. [1]

Most dona­tion match­ing isn’t this ex­treme, but this ex­am­ple shows the main con­sid­er­a­tion in dona­tion match­ing: how is the world differ­ent if you do donate ver­sus if you don’t? This is coun­ter­fac­tual rea­son­ing, and in the case of dona­tion match­ing it’s speci­fi­cally a ques­tion of coun­ter­fac­tual trust. You trust them to match your dona­tion if you give one, but do you trust that your dona­tion is nec­es­sary to prompt them to give?

Ben Kuhn re­cently ran a sur­vey to try to un­der­stand what peo­ple ex­pect when they donate to a match­ing cam­paign. His ques­tions looked like:

Good Ven­tures to­day an­nounced $5M in match­ing funds for dona­tions made to GiveDirectly from 2013-12-03 through 2014-01-31. All dona­tions to GiveDirectly dur­ing the pe­riod, up to $100,000 per donor, will be counted to­ward the match.

Sup­pose that, over the time pe­riod the match was ac­tive, GiveDirectly raised $4.5M. If you had donated $10 to GiveDirectly at that time, how much more money would they have re­ceived than if you had not donated any­thing?

This is ask­ing us how much we trust GiveDirectly’s match to be coun­ter­fac­tu­ally valid. If we think they would have just gone ahead and donated the $5M re­gard­less then we’d an­swer $10, while if we think they’ll would only donate in re­sponse to our dona­tion we’d an­swer $20. If we weren’t sure how much to trust the match we might say some­thing be­tween $10 and $20.

Ben writes that $20 seems to have been ac­cu­rate here:

In­ter­est­ingly, for both the Good Ven­tures and HCEA matches, we can check peo­ple’s be­liefs against re­al­ity. For Good Ven­tures, we can look at GiveWell’s blog post on the match:
If the full amount of the match is reached, we be­lieve Good Ven­tures will be giv­ing more in to­tal to our top char­i­ties this year than they would have been had a match not been a pos­si­bil­ity.
The word­ing “If the full amount… is reached” sug­gests that Good Ven­tures was in fact plan­ning to donate only the amount matched, so at least on the mar­gin the match was fully coun­ter­fac­tual.

Un­for­tu­nately “fully coun­ter­fac­tual” is too strong. Good Ven­tures has a bunch of money that they in­tend to give to the most effec­tive char­i­ties they can, and this is great! But their plan to use the money as close to op­ti­mally as pos­si­ble means this money can’t ac­tu­ally be swayed very much. Say I give $10 to Give Directly and Good Ven­tures matches my dona­tion with $10 they wouldn’t oth­er­wise donate this year. If I hadn’t donated, how­ever, they would have kept that $10 to spend in a later year on an op­por­tu­nity they con­sider ap­prox­i­mately as valuable.

Why do I say “ap­prox­i­mately as valuable”? Good Ven­tures is run by clear think­ing peo­ple who want to have as big a pos­i­tive im­pact on the world as they can. If they thought that Give Directly rep­re­sented a bet­ter op­por­tu­nity for giv­ing than they were likely to see in the fu­ture they would donate more to it un­til that was no longer the case, and vice versa. The only rea­son they’re will­ing to offer a match is that they don’t have a pre­cise tar­get for Give Directly in mind and they think the benefit of bring­ing in more donors out­weighs the benefit of be­ing slightly more de­liber­ate about which dona­tions hap­pen in one year vs an­other.

There’s one lit­tle gap here, how­ever, which we can get a good bit of mileage out of. What I de­scribe only holds if you and the matcher have ap­prox­i­mately the same val­ues. If you, say, think cur­rent peo­ple mat­ter far more than fu­ture peo­ple, how­ever, then tak­ing Good Ven­tures up on their match is great, be­cause it gets them to spend money now in­stead of de­lay­ing and spend­ing it on oth­ers later. This situ­a­tion is most ap­par­ent with “gen­eral” dona­tion matches, like an em­ployer offer­ing to match dona­tions to any 501(c)3 or­ga­ni­za­tion. If the size of the em­ployer pool is not fixed or you plan to give to a char­ity you think is much more effec­tive than the 501(c)3s the money would oth­er­wise go to, the coun­ter­fac­tual effect of your dona­tion re­ally is dou­bled.

There’s a spec­trum here, from “fun­der negates your match” through “fun­der ig­nores your match” through “fun­der acts on your match but would oth­er­wise fund some­thing about as valuable (to you)” up to “fun­der acts on your match and would oth­er­wise fund some­thing much less valuable (to you)”. A good guideline is to re­spect a match only when the match is un­tar­geted, when the fun­der is will­ing to match dona­tions to any char­ity: this matches up al­most ex­actly with when matches are fully coun­ter­fac­tu­ally valid. [2]

(Similarly you shouldn’t offer a fully gen­eral match, be­cause char­i­ties vary dra­mat­i­cally in their effec­tive­ness. [3] If you would like some­thing with the so­cial proof benefits of match­ing but with­out the dishon­esty of mis­lead­ing peo­ple about the effects of their dona­tion, con­sider mak­ing a dona­tion and then challeng­ing oth­ers to do the same.)

I also posted this on my blog.

[1] In­tent mat­ters a lot here in figur­ing dishon­esty. If the fun­der planned from the be­gin­ning to hit a tar­get re­gard­less of other peo­ple’s ac­tions that’s bad, but if in­stead af­ter failing to hit a tar­get they de­cide to be gen­er­ous and gill the gap that sounds good. Yet both are the same from a coun­ter­fac­tual rea­son­ing per­spec­tive: they give one dol­lar fewer for ev­ery dol­lar you give.

[2] This is the only situ­a­tion in which I’ll list a match on our dona­tions page. I still don’t count it to­ward my goal of 50% for the year, but I think count­ing it that way would be defen­si­ble.)

[3] To­masik claims to dis­agree, but this is a mat­ter of de­gree. While he re­jects claims 1000x claims of var­i­ance he does “sus­pect many char­i­ties differ by at most ~10 to ~100 times, and within a given field, the mul­ti­pli­ers are prob­a­bly less than a fac­tor of ~5” which is strong enough to ar­gue against fully gen­eral matches, and prob­a­bly field-re­stricted matches as well.