The logic that you should donate only to a single top charity is very strong. But when faced with two ways of making the world better there's this urge deny the choice and do both. Is this urge irrational or is there something there?
At the low end splitting up your giving can definitely be a problem. If you give $5 here and $10 there it's depressing how much of your donations will be eaten up by processing costs:
The most extreme case I've seen, from my days working at a nonprofit, was an elderly man who sent $3 checks to 75 charities. Since it costs more than that to process a donation, this poor guy was spending $225 to take money from his favorite organizations.
By contrast, at the high end you definitely need to divide your giving. If a someone decided to give $1B to the AMF it would definitely do a lot of good. Because charities have limited room for more funding, however, after the first $20M or so there are probably other anti-malaria organizations that could do more with the money. And at some point we beat malaria and so other interventions start having a greater impact for your money.
Most of us, however, are giving enough that our donations are well above the processing-cost level but not enough to satisfy an organization's room for more funding. So what do you do?
But what about when you're not sure? Even after going through all the evidence you can find you just can't decide whether it's more effective to take the sure thing and help people now or support the extremely hard to evaluate but potentially crucial work of reducing the risk that our species wipes itself out. The strength of the economic argument for giving only to your top charity is proportional to the difference between it and your next choice. If the difference is small enough and you find it painful to pick only one it's just not worth it: give to both.
(It can also be worth it to give to multiple organizations because of what it indicates to other people. I help fund 80,000 Hours because I think spreading the idea of effective altruism is the most important thing I can do. But it looks kind of sketchy to only give to metacharities, so I divide my giving between them and GiveWell's top pick.)
I also posted this on my blog