
Knockout Tournament?
The entire population is divided into a knockout tournament, initial pairings are decided completely at random. You can't communicate.
If you and whoever you paired up with press the same color, one vote for that color moves up in the bracket.
On a tie, both colors move up in the bracket. This will continue until the tie is broken.
If there is a tie in the finale, the winner is whoever had the majority of initial votes.
If blue wins this tournament, everyone survives. If red wins, everyone who pressed blue dies.
Does your choice become more or less important in this scenario? Does the impact of an individual's vote change at all? Does it feel like it changes? Do you change your answer in this scenario?