if yea is the right choice for every decider, it's because "always yea" actually does better than "always nay.
It is the best choice for every decider who only cares about the kids in their Everett branches.
It's not the best choice for deciders (or non-deciders, though they don't get a say) who care equally about kids across all the branches. Their preferences are as before.
It's a really lousy choice for any non-deciders who only care about the kids in their Everett branches. Their expected outcome for "yea" just got worse by the same amount that first lot of deciders who only care about their kids got better. Unfortunately for them, their sole decider thinks he's probably in the Tails group, and that his kids will gain by saying "yea", as he is perfectly rational to think given the information he has at that time.
There is no contradiction.
I suppose I'll avoid repeating myself and try to say new things.
You seem to be saying that when you vote yea, it's right, but when other people vote yea, it's wrong. Hmm, I guess you could resolve it by allowing the validity of logic to vary depending on who used it. But that would be bad.
(Edited for clarity)
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.)