I'm assuming all deciders are coming to the same best decision so no worries about deciders disagreeing if you change your mind.
I'm going to be the odd-one-out here and say that both answers are correct at the time they are made… if you care far more (which I don't think you should) about African kids in your own Everett branch (or live in a hypothetical crazy universe where many worlds is false).
(Chapter 1 of Permutation City spoiler, please click here first if not read it yet, you'll be glad you did...): Jura lbh punatr lbhe zvaq nsgre orvat gbyq, lbh jvyy or yvxr Cnhy Qheunz, qvfnoyvat gur cnenpuhgr nsgre gur pbcl jnf znqr.
If you care about African kids in other branches equally, then the first decision is always correct, because although the second choice would make it more likely that kids in your branch will be better off, it will cost the kids in other branches more.
I think your reasoning here is correct and that it is as good an argument against the many worlds interpretation as any that I have seen.
The source is here. I'll restate the problem in simpler terms:
You are one of a group of 10 people who care about saving African kids. You will all be put in separate rooms, then I will flip a coin. If the coin comes up heads, a random one of you will be designated as the "decider". If it comes up tails, nine of you will be designated as "deciders". Next, I will tell everyone their status, without telling the status of others. Each decider will be asked to say "yea" or "nay". If the coin came up tails and all nine deciders say "yea", I donate $1000 to VillageReach. If the coin came up heads and the sole decider says "yea", I donate only $100. If all deciders say "nay", I donate $700 regardless of the result of the coin toss. If the deciders disagree, I don't donate anything.
First let's work out what joint strategy you should coordinate on beforehand. If everyone pledges to answer "yea" in case they end up as deciders, you get 0.5*1000 + 0.5*100 = 550 expected donation. Pledging to say "nay" gives 700 for sure, so it's the better strategy.
But consider what happens when you're already in your room, and I tell you that you're a decider, and you don't know how many other deciders there are. This gives you new information you didn't know before - no anthropic funny business, just your regular kind of information - so you should do a Bayesian update: the coin is 90% likely to have come up tails. So saying "yea" gives 0.9*1000 + 0.1*100 = 910 expected donation. This looks more attractive than the 700 for "nay", so you decide to go with "yea" after all.
Only one answer can be correct. Which is it and why?
(No points for saying that UDT or reflective consistency forces the first solution. If that's your answer, you must also find the error in the second one.)