Blue or red / Hebrew
A couple of weeks ago @lisatomic5 conducted an interesting survey among her Twitter subscribers:
Everyone who took part in this survey had to choose between the blue pill and the red pill.
– If more than half choose the blue pill, then everyone will survive.
– If not, those who chose the red pill will live, and those who chose the blue pill will die.
According to the results of the survey, 65% of the 68,000 respondents chose the blue pill.
The survey was repeated by other twitter users with minor changes:
A small difference in the wording of the questions or a difference in the mentality of the Russianspeaking and Englishspeaking twitter audience played a role here, but now only 55% voted for blue.
From the point of view of game theory, the results of the polls are very paradoxical. Indeed:

The best strategy for everyone is to choose red – this guarantees their personal salvation.

The Nash equilibrium of this game is simultaneously optimal for this game – if everyone bets on red, everyone is saved.

Thus, game theory supposedly predicts a result of >95% red – given that there will be a few nonconformists protesting the vote or simply getting the color mixed up.
Instead of this obvious result, we see an overwhelming majority of blue. Somehow, the collective subconscious of those who took part in the survey understands that there will be some number of people in the survey who chose the color blue – moreover, there will be many people who want to protect those who chose the color blue by sharing the risk with them, and what’s more, this set will be large enough for everyone to win. And although, in truth, those who vote on twitter are probably not risking their lives or anything else, in the blue majority, looking at the results of the poll, a kind of pride is formed in their heads:
We took a risk, we were together – and we won.
A friend of mine rightly remarked: 50% is a figure that seems achievable. If the death threshold for blue was set at 80%, blue would be guaranteed to lose. If they managed to get even 40%, let alone 65 or 80 – everyone would think that the case looks hopeless, and as a result the result of the vote would be something like >95% red majority against <5% nonconformists  exactly with theories of
But where is this threshold of achievement?
Let’s make a small mathematical estimate. Let the probable percentage of those who voted for blue (in a certain society with a certain wording of the question) be P(x) where x – Threshold value that blues need to reach for trust.
It can be assumed that P continuous and monotonically decreasing – the greater the risk, the less people want to risk. This means that the marginal win threshold for blue is somewhere between 50% and 65%. That is, there exists 0.5 < x < 0.65 such that P(x) = x.
It can be assumed that somewhere beyond the limit threshold the function will win P sharply drops to small values. The collective unconscious is surprisingly good at playing games related to the common good, so the fall can be expected on the outskirts of x. For example, 2/3 (66.6%) seems intuitively to be the threshold at which the Reds will receive the majority of the vote. But this is not accurate and needs to be checked.
This task seems to say something important about how society thinks.
Many compare this task with the prisoner’s dilemma. However, in the dilemma, the Nash equilibrium (when both bandits betray their comrade, acting to their advantage) is not equal to the social optimum (the best outcome for everyone). Something eludes us.
It seems that the victory when everyone chose red and the victory of the blue majority are ideologically different victories. In the first case, everyone survived, but turned out to be riskaverse cowards. In the second, the blue majority feels like the heroes of this story, thus winning more. In my imagination, the blues are not risking their lives for nothing – they are fighting for some common good that can be achieved if the majority votes in favor.
I think it will be easy for you to imagine several specific examples of such good.
Let’s conduct a poll according to slightly different rules:
WARNING!
There are two buttons: Blue and Red.
If less than 66.6% of people click blue, everyone who clicked blue will die.
If you press red, you will survive.
If more than 66.6% of people click blue, then everyone will survive and receive a reward.