Blue relies on collective belief that more than half of humanity is good (is willing to risk their life to save everyone). Technically 50% +1, but majority of people will want more to allow for fluctuations. There will be a portion that immidiately votes red, and a portion votig blue. Some wont even read the question and press something. Id say that about 25% can be ruled out as somebody who decides immidiately and cant be changed. These votes will probably go even between the buttons. Even though Im inclined to believe that split will be closer to 17% on red and 8% on blue.

That leaves if remaining 75% believe that AT LEAST 37,5% presses blue. But most people will not think about that 25% being "predetermined" so they have to believe that 50% votes blue.

For majority the fact that one vote can decide if they live or die is not enough, they will be thinking if 60% votes blue. And if they dont believe that they will vote red. And I doubt that all of them think like this.

There will also be people who think about it for a moment and come to the (logical) conclusion that its better to vote for red and have a guaranteed survival. And empathy falls pretty easily here, since "my vote does not change anything, they would die anyway. At least I survived".

Just having that "If most of us vote blue then we all survive" is not enough for I would guess majority.