There are two globally optimal solutions to this problem: > 50% pick blue (saving everybody), and 100% of the people pick red (saving everybody).

There is only one Nash equilibrium, which is for everybody to pick red. This is also strictly dominant for each player (if they choose red, they have a 100% chance of surviving, while if they choose blue, they only survive if > 50% of other people also choose blue). Knowing this, every participant has an incentive to choose red.

Only irrational people will pick blue. Let's say that's ~3% of the population. Trying to get another 47% of the population to pick blue risks losing all of them as well. That's not ethical.

People's "by default" behavior will never define what is rational. You don't do polling to choose rationality.

If there is a game in which you choose between two buttons, you know everyone will get this same choice, and one button says that you definitely live and the other button says that there's a chance that you will die, adding more rules to the "maybe death button" can not make it a more rational choice.

This is actually an experiment that I would get behind doing in real life. I will pick the red button. We could do it every morning.

There are enough collective action problems with real and obvious benefits leading to catastrophe without the need to create more unnecessarily, or to have any confidence in in a world full of strangers' collective ability to solve them. Campaigning for blue is actually murder; you've encouraged a situation that may result in the deaths of 49% of the population.

> There is no consequence for choosing blue

there are consequences in both cases.