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?
If one option is much better than another then you really do need to make the choice. The best ones are enough better than the average ones that you need to buckle down and pick the best.
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
It does seem like there are significant side effects to donating to multiple charities, In that, if you've never donated before, I think a charity would generally prefer that you have donated at least once.
(I.E, if after processing costs, a charity had a choice between raising 1000 dollars after processing costs from one new donor, or 1000 dollars after processing costs from 100 new donors, I think most charities would choose the second for several potential reasons: Larger donor list, more publicity, etc, more potential warm call targets, more people that can be referred to allied charities, more people that can be asked to volunteer, a more reliable source of funding in general (single donors provide sporadic funding, whereas a large number of donors can provide a more regular stream of income. [I think this is why Charities also like people who have promised monthly donations.])
However, if you are absolutely certain you were NEVER going to give to those charities again, or that you gave money to charity based solely on calculations and were utterly immune to charity advertising, then you don't want to add yourself to the lists, because the charity will waste time and money effort trying to contact you for additional donations that are not forthcoming. In that case, it might actually be net beneficial to give anonymously or to give to as few charities as possible.
This leads me to what feels like a somewhat unusual conclusion: If you're sure that donating money all to one charity is beneficial, then it is. If you aren't sure, and are sort of thinking "Well, maybe I should and maybe I shouldn't, they're all good..." Then you are probably more likely to be susceptible to advertising from both and would likely donate more money net by getting exposure to as much charity advertising as possible, so you should probably do that . If you simply feel you don't know enough about the charities work to make a firm decision, then spreading your donations out is also an easy way to get charities happily sending you more information about themselves.