The randomized experiment you did is so cool! I love experiments like this -- like the Allais Paradox -- that reveal biases and irrationalities.
But in this case, as a game theorist, I aver that the switchers are correct. This is a classic application of Schelling points. If we all have the altruistic utility function "minimize death" then there are two Nash equilibria: (1) Everyone take the pill, and (2) no one take the pill. If the question is framed such that everyone taking the pill (like when it's just pressing one of two buttons) is focal, that's the equilibrium you expect and the one you rationally adopt yourself. When it's framed the other way, you expect the other equilibrium and rationally don't take the pill.
PS: I just realized that this is also the exact problem you called out in encouraging us to get set up on kbin for comments. The two equilibria are "no one else is going to set up an account so I won't bother to either" and "that's the new Schelling point for Dynomight comments so of course I want to be there too!"
PPS: Taking you up on your self-promotion encouragement, I predict that Dynomight readers will like the Beeminder blog, maybe especially the posts tagged "rationality". (Also I'm excited to see some of you at Less Online!)
Absolutely, no swallowing seems the superior equilibrium here. But what if we adjust that 50% threshold so that we all survive as long as at least two of us take the pill? If one person dies you're gonna feel pretty rotten, right? You could've single-handedly saved them! And they only took the pill out of exactly that fear.
Or what if we all get a nice prize if enough people take the pill? Now we might want to shout down the otherwise reasonable "don't screw around with voluntarily swallowing explosives" argument.
I've been posing this to friends/family and am getting that reaction a lot. How about this variant:
Take the red pill, labeled "look out for number one" with a picture of Voldemort on it, and be guaranteed to be one of the survivors.
Take the blue pill, labeled "zero deaths via cooperation" with a picture of Mr Rogers on it, and survive if and only if enough other people also take the blue pill.
Does that make the all-blue equilibrium focal enough?
Or what if the threshold is 100%, where literally everyone has to take the blue pill for everyone to be saved? And suppose you like this group of people. Taking the red pill might singled-handedly cause everyone else to die.
I guess the point of all of these is just that you really, really want to do the same thing everyone else is doing.
This is pretty central to such rationality fare as Meditations on Moloch and Inadequate Equilibria.
Fighting me and other survey results (dynomight.net)
Do extroverts have more martial confidence?