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There are two issues here.
One is tracking of individual contributions. When a charity says "A $5000 donation saves one life" they do not mean that your particular $5000 will save one specific life. Instead they divide their budget of $Z by their estimate of Y lives saved and produce a dollars/life number. This is an average and doesn't have much to do with you personally other than that you were one data point in the set from which this average was calculated.
"I contributed to the common effort which resulted in preventing Y deaths from malaria" is a more precise formulation which, of course, doesn't sound as good as "I saved X lives".
Two is the length of the causal chain. If you, with your own hands, pull a drowning kid out of the water, that's one life saved with the causal chain of length 1. If you give money to an organization which finances another organization which provides certain goods for the third organization to distribute with the help of a bunch of other organizations, the causal chain is long and the longer it goes, the fuzzier it gets.
As always, look at incentives.Charity fundraising is effectively advertising with greater social latitude to use emotional manipulation. One strand in that manipulation is to make the donor feel an direct emotional connection with "direct" being the key word. That's why you have "Your donation saves lives!" copy next to a photo of an undernourished black or brown kid (preferably a girl) looking at the camera with puppy eyes.
If someone is saying "I saved 10 lives" because they gave $500 to a charity that advertises a cost per life saved of $50, then yes, that's very different from actually saving lives. But the problem is that charities' reports of their cost effectiveness are ridiculously exaggerated, and you just shouldn't trust anything they say.
What we want are marginal costs, not average costs, and these are what organizations... (read more)