It can also be worth it to give to multiple organizations because of what it indicates to other people.
Here it is. Signalling has effects on the real world, and if I make other people contribute to charities, the total effect can be much higher than my personal contribution could do. Optimizing for the total effect is better than merely optimizing the effect of my money.
Let's assume there are two important charities, X and Y. I have two friends, A and B. The friend A would be willing to donate to charity X, assuming that someone else in his social sphere does too. But he would never donate to Y. On the other hand, the friend B would be willing to donate to charity Y, assuming that someone else in her social sphere does too; but she would never donate to X.
If I donate to both charities and give the relevant part of information to each of my friends, I can make A donate to X, and B donate to Y, which could be more useful than if both me and A donate all our money to X, but B does not donate anything.
Mathematically speaking, assume that me, A and B are willing to donate $100 each; charity X creates 2 utilons per dollar, charity Y creates 1 utilon per dollar. If I donate all $100 to X, my personal contribution to the world is 200 utilons, and together with A we create 200+200= 400 utilons. If I donate $50 to X and $50 to Y, my personal contribution to the world is 150 utilons, and together with A and B we create 150+200+100= 450 utilons. With these specific numbers, the second option is better.
But even if the difference among the charities is greater, I can improve the result by donating more to X and less to Y. Ideally, I should donate to Y only as much as B needs to be socially convinced to donate too.
Or you could donate in secret and lie to your friends, for 200+200+100 = 500 utilons, assuming you have no negative effects from lying.
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:
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