Once EA is a popular enough movement that this begins to become an issue, I expect communication and coordination will be a better answer than treating this like a one-shot problem. Maybe we'll end up with meta-charities as the equivalent of index funds, that diversify altruism to worthy causes without saturating any given one. Maybe the equivalent of GiveWell.org at the time will include estimated funding gaps for their recommended charities, and track the progress, automatically sorting based on which has the largest funding gap and the greatest benefit.
I doubt that at any point it will make sense for individuals should be personally choosing, ranking, and donating their own money to charities as if they're choosing the ratios for everyone TDT-style, not least because of the unnecessary redundancy.
EDIT: Upvoted because it is a valid concern. The AMF reached saturation relatively quickly, and may have exceeded the funding it needed. I just disagree with the efficiency of this particular solution to the problem.
Here are some tentative thoughts that I haven't run by anyone to check for soundness. They're not genuinely original to me – they've been floating around the effective altruism community in some form or other for a while – I just hadn't thought them through in sufficient detail to take them to their logical conclusion. I'd appreciate any feedback.
Suppose that the expected number of lives saved per additional dollar donated to charity A is x and the expected value of lives saved per additional dollar donated to charity B is y, where x and y are constants, and x > y. Then if you're trying to maximize the expected number of lives saved (c.f. The "Intuitions" Behind "Utilitarianism"), you should make all of your charitable contributions to charity A.
In practice, x and y will not be constant, because of room for more funding issues. So splitting one's donations can maximize number of lives saved, if x is sometimes smaller than y.
But suppose that you're donating $d, where increasing the charities' budgets by $d would leave the condition x > y unaltered. A common view is that one should then donate all $d to charity A.
However, this doesn't take into account timeless decision theory. If all donors to charities A and B were identical to you, then your decision to donate $d to charity A would be equivalent to a decision for all donors' funds to go to charity A rather than charity B, effectively constituting a decision for charity A to get a little bit more money in exchange for charity B existing altogether. If x > y doesn't always hold, this is not expected value maximizing. The other donors aren't identical to you, but their decisions are still correlated with yours on account of the psychological unity of humankind, and shared cultural backgrounds.
Suppose that x > y is not always true. For simplicity, suppose that the total amount that donors will donate to charities A and B is fixed and known to you. If there were no correlation between your decision making and that of other donors, then it would be that you should give all of your money to charity A. If the correlation between your decision making and that of the other donors was perfect, then your ratio of donations to charity A to charity B should be the same as the ratio of the total amount of funding that you think charity A should get to the total amount of funding that you think charity B should get. This raises the possibility that your actual split of donations should be somewhere between these two extremes, and in particular, that you should split donations.
In practice it won't always make sense to split donations: it might be that for any given charity A, there are many charities B with the property that x > y is not always true, such that it would be a logistical hassle to split one's donations between all of them. But when one has a small handful of charities that one is considering donating to, it may make sense to split one's donations, even when one is a small donor.
Moreover, charities are closer in cost-effectiveness than might initially meet the eye, so that the condition that x > y is not always true holds more often than might initially meet the eye. So the case is for splitting donations is stronger than might initially meet the eye, and the split should be more even than might initially meet the eye.