Some reservations about Singer’s child-in-the-pond argument

Peter Singer is one of the most in­fluen­tial philoso­phers, and is a strong can­di­date for be­ing the per­son who has helped the effec­tive al­tru­ist com­mu­nity the most.

In the past, Peter Singer of­ten ar­gued that [the moral obli­ga­tion to rush into a shal­low pond to save a drown­ing child at the cost of ru­in­ing one’s shoes] is equiv­a­lent to [the moral obli­ga­tion to give to char­i­ties that re­duce ex­treme poverty]. For ex­am­ple, in this 2009 video he said:

Imag­ine that you’re walk­ing across a shal­low pond and you no­tice that a small child has fallen in, and is in dan­ger of drown­ing […] Of course, you think you must rush in to save the child. Then you re­mem­ber that you’re wear­ing your fa­vorite, quite ex­pen­sive, pair of shoes and they’ll get ru­ined if you rush into the pond. Is that a rea­son for not sav­ing the child? I’m sure you’ll say no it isn’t, you just can’t com­pare the life of a child to the cost of a pair of shoes, no mat­ter how ex­pen­sive. […] But think about how that re­lates to your situ­a­tion in the world to­day. There are chil­dren whose lives you can save […] Nearly 10 mil­lion chil­dren die ev­ery year from avoid­able, poverty re­lated causes. And it wouldn’t take a lot to save the lives of these chil­dren. We can do it. For the cost of a pair of shoes, per­haps, you could save the life of a child. […] There’s some lux­ury that you could do with­out. And with that money, you could give to an or­ga­ni­za­tion to re­duce ex­treme poverty in the world, and save lives of chil­dren. […] I think that this is what we ought to be do­ing.

Since Singer first posed the anal­ogy, new in­for­ma­tion and un­der­stand­ing has emerged, which cast doubt on the rele­vance of Singer’s anal­ogy. Singer used a differ­ent anal­ogy in his re­cent TED talk (in which he dis­cussed the death of Wang Yue), but whether ex­plic­itly or im­plic­itly, the “child in a pond” meme has caught on. In light of re­cent de­vel­op­ments, it’s im­por­tant to high­light the fact that the op­por­tu­ni­ties to donate to alle­vi­ate global in our pre­sent world are dis­analo­gous to the op­por­tu­nity in Singer’s “child in a pond” sce­nario.

The most ex­pen­sive pair of shoes that I own costs ~$120, and I would guess that the av­er­age Amer­i­can doesn’t own a pair of shoes that costs more than $200. With this in mind, Singer’s anal­ogy sug­gests that one can save a life of a child in the de­vel­op­ing world for less than $200. To de­ter­mine whether Peter Singer’s anal­ogy is a good one, we need to ex­am­ine the em­piri­cal data con­cern­ing the cost of sav­ing a child’s life.

GiveWell spent five years look­ing for out­stand­ing char­i­ties that alle­vi­ate poverty in the de­vel­op­ing world. GiveWell’s cur­rent top recom­mended char­ity, Against Malaria Foun­da­tion (AMF), dis­tributes long last­ing in­sec­ti­cide treated nets to guard re­cip­i­ents against malaria. GiveWell’s ex­plicit es­ti­mate of AMF’s cost per life saved is just un­der $2,300. The cost of bed nets has re­cently fallen, and this is ex­pected to de­crease AMF’s cost per life saved, but not by a large mar­gin.

GiveWell Co-Ex­ec­u­tive Direc­tor Holden Karnofsky has writ­ten about how ex­plicit ex­pected value es­ti­mates shouldn’t be taken liter­ally, and in par­tic­u­lar, that ex­plicit es­ti­mates of the value of philan­thropic op­por­tu­ni­ties should be ad­justed to ac­count for one’s Bayesian prior over the effec­tive­ness of all philan­thropic op­por­tu­ni­ties. In June 2012, GiveWell se­nior re­search an­a­lyst Alexan­der Berger wrote(speak­ing for him­self rather than for GiveWell)

I don’t think the ex­pected value of a $1600 dona­tion to AMF [an ear­lier cost-effec­tive­ness es­ti­mate for AMF’s cost per life saved] is ac­tu­ally any­where near one life saved. The rea­son for this has noth­ing to do with how AMF works and is more a fea­ture of its place in the to­tal dis­tri­bu­tion of char­ity cost-effec­tive­ness. I think there are a va­ri­ety of prac­tices in cost-effec­tive­ness es­ti­ma­tion that push in fa­vor of a difficult-to-es­ti­mate pos­i­tive bias (e.g. us­ing ev­i­dence from RCTs, which are gen­er­ally con­ducted in the most promis­ing cir­cum­stances), that the most ex­treme cost-effec­tive­ness es­ti­mates are more likely to be bi­ased, and that the benefit of a marginal con­tri­bu­tion is al­most always less than the benefit of an av­er­age con­tri­bu­tion. All of these con­spire to make me think that the es­ti­mate that GiveWell pro­vides for the “cost-per-life saved” for AMF is not the cor­rect num­ber for es­ti­mat­ing the ex­pected value of a con­tri­bu­tion to AMF.

In the sec­tion “Con­crete fac­tors that fur­ther re­duce the ex­pected value of donat­ing to AMF” of my blog post Ro­bust­ness of Cost-Effec­tive­ness Es­ti­mates and Philan­thropy, I listed eleven con­crete fac­tors that in­crease AMF’s ex­pected cost per life saved.

The rea­son why sav­ing the child drown­ing in a pond in Singer’s hy­po­thet­i­cal is ob­vi­ously the right thing to do is that the per­sonal cost as­so­ci­ated with do­ing so is neg­ligible rel­a­tive to the benefit to oth­ers. The cost of sav­ing a life in the de­vel­op­ing world by donat­ing to AMF is at least 10x greater than the cost in Singer’s “child in a pond” anal­ogy, and pos­si­bly much greater. This sub­stan­tially weak­ens Singer’s ar­gu­ment.

I raised this point in a re­cent com­ment thread on the GiveWell blog, and Doug S. con­curred, writing

Hon­estly, there re­ally is a big differ­ence to me if X is differ­ent by or­ders of mag­ni­tude. The U.S. fed­eral min­i­mum wage is cur­rently $7.25 an hour. Pay­roll taxes are 7.5%, so take-home pay be­comes $6.70 an hour. It takes 343 hours – two months, work­ing full time – work­ing a min­i­mum wage job to earn the $2300 it takes your #1 char­ity to save a life. There’s a big differ­ence be­tween $200 and $2000, be­tween one week of min­i­mum wage work and two months of min­i­mum wage work.

Holden re­sponded:

I think Jonah and Doug are both look­ing for more pre­ci­sion than is rea­son­able. Ro­bust facts about dis­par­i­ties in wealth – which you will also see qual­i­ta­tively if you travel to the de­vel­op­ing world – are suffi­cient to make the point that you have a great deal of power to help oth­ers a lot by giv­ing up a lit­tle. If you’re look­ing for any sort of pre­cise “dol­lar cost per quan­tity of good ac­com­plished” (over and above the kind of ro­bust com­par­i­sons I just de­scribed) such that a fac­tor of 5-10 is cru­cial to how much you de­cide to give, I think it is – and long know­ably has been – un­re­al­is­tic to get such a thing. I think nearly all tar­gets of Peter Singer’s ar­gu­ment have long im­plic­itly rec­og­nized this fact. Per­haps there are some ar­gu­ments for which such pre­ci­sion would be nec­es­sary, but if so they aren’t ar­gu­ments that I see as hav­ing much trac­tion. I don’t em­pathize with the view that such pre­ci­sion is nec­es­sary in or­der to make the broad ar­gu­ment that you ought to give gen­er­ously.

What Holden’s com­ment misses is that there’s a big differ­ence be­tween the fol­low­ing two state­ments:

(1) “A rough es­ti­mate for the cost of sav­ing a life is the cost of an ex­pen­sive pair of shoes, but it could be much higher or much lower”

(2) “A rough es­ti­mate for the cost of sav­ing a life is over 10x greater than the cost of an ex­pen­sive pair of shoes, but the cost is prob­a­bly higher, and pos­si­bly much higher, due to Bayesian re­gres­sion.”

The prob­lem with Singer’s “child in a pond” anal­ogy isn’t that real world cost-effec­tive­ness es­ti­mates aren’t pre­cise. The prob­lem with Singer’s “child in a pond” anal­ogy is that there’s a strong case for the cost-effec­tive­ness of donat­ing to AMF be­ing vastly lower than Singer’s anal­ogy sug­gests.

Peter Singer has been very suc­cess­ful in get­ting peo­ple in­ter­ested in donat­ing to alle­vi­ate global poverty. One could ar­gue that his “child in a pond” con­tributed to his suc­cess, and that con­tin­u­ing to use it is, for this rea­son, jus­tified. Nev­er­the­less, the anal­ogy is prob­le­matic.

Vipul Naik wrote (para­phrased):

There is a ten­sion be­tween the tac­ti­cally op­ti­mal ap­proach for con­vinc­ing a larger num­ber of peo­ple to donate more, and the ar­gu­ment that is most grounded in em­piri­cal re­al­ity. I think that rather than min­i­miz­ing the ten­sion, it’s more coura­geous and epistem­i­cally ad­mirable to openly and very ex­plic­itly ad­mit that Singer-style (im­plicit or ex­plicit) “you-can-save-a-life-for-the-price-of-a-pair-of-shoes” *if true*, would be far more com­pel­ling a rea­son to donate than the ar­gu­ment based on dis­par­i­ties in wealth.

See also this com­ment where Carl Shul­man writes: “I think it’s bad news for prob­a­bly mis­taken es­ti­mates to spread, and then dis­illu­sion the read­ers or make the writ­ers look bi­ased. If peo­ple in­ter­ested in effec­tive philan­thropy go around trum­pet­ing likely wrong (over-op­ti­mistic) figures and don’t cor­rect them, then the com­mu­nity’s cred­i­bil­ity will fall, and bad mod­els and epistemic prac­tices may be strength­ened.”

Singer’s ar­gu­ment is not the only ar­gu­ment for donat­ing to alle­vi­ate poverty in the de­vel­op­ing world. For ex­am­ple, in a re­cent blog post, Holden wrote:

To us, the strongest form of the challenge [to donate to alle­vi­ate poverty in the de­vel­op­ing world] is not “How much should I give when $X saves a life?” but “How much should I give, know­ing that I have mas­sive wealth com­pared to the global poor?” Per­haps the most vivid illus­tra­tion comes not from Against Malaria Foun­da­tion (our #1-rated char­ity) but from GiveDirectly (our #2). If you give $1000 to GiveDirectly, ~$900 will end up in the hands of peo­ple whose re­sources are a tiny frac­tion of yours. GiveDirectly’s es­ti­mate – which we be­lieve is less sen­si­tive to guess­work than “cost per life saved” figures – is that re­cip­i­ents live on ~65 cents per day, im­ply­ing that such a dona­tion could roughly dou­ble the an­nual con­sump­tion for a fam­ily of four, not count­ing any long term benefits.

As Vipul com­mented, this ar­gu­ment is much weaker than Singer’s “child in a pond” ar­gu­ment.

In Liv­ing High and Let­ting Die: Our Illu­sion of In­no­cence (pg. 135) Peter Unger gives a Singer-style anal­ogy that can be made more faith­ful to pre­sent day em­piri­cal re­al­ities than Singer’s “child in a pond” anal­ogy. The form of the ar­gu­ment (mod­ified for use in the pre­sent con­text) is this:

Imag­ine that you have a car that’s worth AMF’s ac­tual cost per life saved. You park your car on un­used train tracks and get out in or­der to walk around. You see a child play­ing in a tun­nel off in the dis­tance, and see a train headed to­ward the tun­nel. If the train pro­ceeds, the train will kill the child. You have ac­cess to a switch that can be used to di­vert the train to­ward the un­used train tracks where your car is parked. If you flip the switch, the train will de­mol­ish your car, but no­body will be kil­led. Do you flip the switch?

I think that most peo­ple would say that flip­ping the switch is the right thing to do. But I don’t think that they would say that the moral obli­ga­tion is as great as the moral obli­ga­tion in Singer’s “child in a pond” sce­nario.

Ac­knowl­edg­ments: Thanks to Vipul Naik, Nick Beck­stead and Luke Muehlhauser for helpful feed­back on an ear­lier ver­sion of this post.

Note: I formerly worked as a re­search an­a­lyst at GiveWell. All views are my own.