The first point is interesting. You could fork the question over this and have a few variants:

1.) The pure form where the button presses and restricted to legal agents (i.e. people with credible legal standing over their choices). 2.) The mixed form with the caveat listed here inclusive of all humans whether they are even physically capable of pushing a button. 3.) you could also go for a more expansive scenario that takes 2 to the extreme and includes animals as well.

1.) gets to the game theoretic form of the question. 2 muddies things, and 3 sets up a case for blue since the non agentic voters asymptote to 50-50 and a slim edge is morally preferable to killing half.

You don't even have to go that far from the original question. If instead of the entire world being a single game, if you have hundreds of millions of sub-games where 9 random people are placed within, what should you do?

Surely some of those groups are going to be filled with selfish red pickers. Should the kind coordinating players still go blue? All the red pickers are going to lie that blue is sensible. I suspect that more coordinators will die in this way than the always blue pickers if every coordinating player went red.

So now the full-world version only has the law of large numbers on their side, but they have no way of knowing just what percentage of the population is a selfish red picker. Going for team blue is the much riskier option that can yield catastrophe.

With 3, especially if the animals outnumber humans, you’d first want to do some research into animal psychology to see whether red or blue has an edge for animals.