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.
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.