The poison pill one is not functionally identical at all, because the question is functionally changed every single time the setup is changed. That’s what I meant by my example earlier. “Is Poe’s The Raven seven words long?” is interchangeable with “Is Poe’s The Raven exactly seven words long?”. But we can’t derive that “adding the word exactly changes nothing”, because “Is this question seven words long?” has a very different answer from “Is this question exactly seven words long?”
If you set up the problem in a certain way, then you can expect everyone else to have the same setup, and expect them to expect others to expect others, etc. Every subtle change makes the coordination dynamic completely different.
A really important element is what this or that version presents as a “do nothing” default. One logical counterpart of your pill one is: everyone is offered an injection of antidote, and told that if and only if a majority take the injection, the whole set of people will be injected with the poison, against their will or no. If you say “Yes, of course I choose the injection”… I don’t know what to say. You could have just done nothing. That would have been the same as ordinary daily life.
For the pill one, you and 100 really smart people had to coordinate, then “Don’t take the pill” works great as coordination. But wait, you say! That’s an admission of red over blue! Yes, because “What if one person messes up” simply isn’t going to happen. Our physical instincts are part of the equation here. The opposite scenario, where everyone takes the pill followed by the antidote, requires a collective defiance of physical instincts, not merely button-pressing, which is 100% “neutral”. That’s what I’m getting at when I say: what if choosing red also entails taking a sip of urine, or something. Do you really intend to get dozens or hundreds of people to do that, unanimously, “just to be on the safe side because death was on the line.” That’s a situation where everyone Could Just Not.
Now, of course, you say “But if the pill version is applied to the human population, lots of toddlers and confused people might take it!” Yes, and that’s horrible. But even then, coordinating a majority to take the pill-and-then-antidote as well will be much, much harder then when it was merely pressing buttons. You all have to automatically trust the physics of the situation: that the antidote will work perfectly, you won’t be sick afterward, etc. I don’t know what, if anything, is a parallel to the trust problem in a pure-button version. That is to say, supposing everyone unanimously presses blue, what bad outcome do we fear remaining possible according to the human imagination? We’re not told how the death is applied at all. Maybe red-pressers just assume the blue buttons are electrified or something?
