Doesn’t this imply that it makes sense to donate to more than one charity? Consider just the top three charities; there are 3! ways to rank them and associated probabilities of each of those rankings being accurate. Say there’s a 90% probability that the 1st ranked charity is actually the most efficient, a 9% probability that the 2nd ranked charity is the most efficient, and a ~1% probability that the 3rd ranked charity is the most efficient. To me it makes sense to send 0.9X to charity #1, 0.09X to charity #2, and 0.01X to charity #3, where X is the amount of money available for charitable donations.
Not even close. Imagine if, instead of charities, these are colored balls. And instead of altruistic benefit, you’re getting paid (or money gets sent to your charity of choice). Say I gave you $10, and you get a return of 200:1 on any money placed on the ball that comes out. How do you distribute your money? Any distribution other than all on the most likely loses out.
Alternatively, imagine colored cards in a deck. You guess what color comes next, and you get $10 for every correct guess. What do you guess, assuming cards are replaced every time? In a hundred guesses, do you change your guess 10 times? If you do you’ll lose out.
If you split the donations in this way, you are lowering the expected money donated to the most efficient charity: it’s 0.9X*0.9 + 0.09X*0.09 + 0.01X*0.01, for a total of 0.8182X. By donating X to the 1st ranked charity, you donate 0.9X to the most efficient charity in expectation.
Actually, the ranking of the charities is irrelevant, as is the question of which charity is the most efficient; it’s only the absolute efficiency of your donation that matters. But if you look at that metric instead, the same problem occurs.
To put it another way: it’s almost certain that the ranking of the top charity is inflated; and it may even be almost certain that some of the other charities are better. However, no single charity is more likely to be good than the top charity. For each dollar donated, the single best place to send it is the top-ranked charity, and if you split your donations, that means that some of your dollars are going to a charity where they’re less likely to do good.
The answer is no, for reasons that are hard to articulate succinctly. But the fact that the variance in “actual” expected value is lower than it initially appears makes “donating to learn” more attractive, and for this reason, among others, GiveWell recommended that donors split their donations between its top charities.
Doesn’t this imply that it makes sense to donate to more than one charity? Consider just the top three charities; there are 3! ways to rank them and associated probabilities of each of those rankings being accurate. Say there’s a 90% probability that the 1st ranked charity is actually the most efficient, a 9% probability that the 2nd ranked charity is the most efficient, and a ~1% probability that the 3rd ranked charity is the most efficient. To me it makes sense to send 0.9X to charity #1, 0.09X to charity #2, and 0.01X to charity #3, where X is the amount of money available for charitable donations.
Not even close. Imagine if, instead of charities, these are colored balls. And instead of altruistic benefit, you’re getting paid (or money gets sent to your charity of choice). Say I gave you $10, and you get a return of 200:1 on any money placed on the ball that comes out. How do you distribute your money? Any distribution other than all on the most likely loses out.
Alternatively, imagine colored cards in a deck. You guess what color comes next, and you get $10 for every correct guess. What do you guess, assuming cards are replaced every time? In a hundred guesses, do you change your guess 10 times? If you do you’ll lose out.
If you split the donations in this way, you are lowering the expected money donated to the most efficient charity: it’s 0.9X*0.9 + 0.09X*0.09 + 0.01X*0.01, for a total of 0.8182X. By donating X to the 1st ranked charity, you donate 0.9X to the most efficient charity in expectation.
Actually, the ranking of the charities is irrelevant, as is the question of which charity is the most efficient; it’s only the absolute efficiency of your donation that matters. But if you look at that metric instead, the same problem occurs.
To put it another way: it’s almost certain that the ranking of the top charity is inflated; and it may even be almost certain that some of the other charities are better. However, no single charity is more likely to be good than the top charity. For each dollar donated, the single best place to send it is the top-ranked charity, and if you split your donations, that means that some of your dollars are going to a charity where they’re less likely to do good.
The answer is no, for reasons that are hard to articulate succinctly. But the fact that the variance in “actual” expected value is lower than it initially appears makes “donating to learn” more attractive, and for this reason, among others, GiveWell recommended that donors split their donations between its top charities.