u/APersonNotToLive

There are two states where no one dies, the far left (everyone presses red) or the far right (50%+ press blue). No matter what state you're in, pressing the other option either increases the number or likelihood of deaths.

If you assume red is the default, anyone pressing blue makes more people die (shown by moving right on the chart and increasing the number of deaths). If you assume blue is the default, anyone pressing red makes it slightly more likely many people die (shown by moving left on the chart and bringing us closer to the death precipice). The optimal move depends on what option you assume everyone else is going with, and if you assume a default deviating from that becomes obviously wrong.

This shows how even if you ignore any selfish aspect (and so counting your death only as bad as any other death), it's still optimal to press red if you think everyone is pressing red. I think it's actually an interesting variation on the problem to highlight this: make it so that who dies is decoupled from what button you pressed. People now die at random proportionally to how many people press blue, unless blue gets >50% then no one dies. This removes the selfish/selfless aspects of it, and shows how even without that there's underlying game theory stuff at play.