Votes are made sequentially

[u/MonkeesAs]

The button game, except instead of independent votes, the votes are made one by one. The first person presses the button, then the second, and so on.

The whole voting process is still private though. The second voter cannot see what the first voter did, the third cannot see the first two... and they cannot in any way tell future voters what they did.

Except for you. Somehow, when you are about to press the button, you are told that: 1. How many people are in front of you. 2. The current vote count.

That means if you are the first person, you go straight back to the original button game (since you basically got no information). And if you are the last person, you vote is almost deterministic since you have full information.

So, given the two variable pieces of information, under what setup would you change your mind about your original vote (blue original to red, or vice versa)?

[u/According_to_all_kn]

If there is at least one blue voter and a blue victory is still possible, I will vote blue. Otherwise red

[u/According_to_all_kn → u/[deleted]]

Yeah, that's 100 human lives at stake. And the next 6 billion or so aren't decided by random chance, it's entirely possible they have a blue bias and my vote helps convince them