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.