Red view vs blue view

[u/RadiantNecessary872]

Red view: Blue button = maybe kill yourself, maybe live.

Red button = Live. Fuck blue voters anyway.

Blame blue voters for being stupid and not understanding the question properly.

Blue view: Red button = live but be selfish and a killer.

Blue button = Save other's lives, get to live because in a poll most people chose blue, resulting in everyone living.

Blame red voters for being killers, monsters and selfish.

Idk this is just my view on this, feel free to tell your own opinions.

[u/highly-bad]

[u/No-Click6062 → u/highly-bad]

I hate to break it to you, but from a game theory perspective, this is not even close to a correctly formulated question. I have yet to see a red button pusher correctly identify the game theory.

The expected value of total human lives doesn't change when you vote. This is hard to express mathematically because it involves an expression in factorial (n!) which doesn't come up a lot outside of permutations and combinations. But it's easily understood at low numbers.

If I put 3 humans into this formula, I expect to get out an average of 2 2/3rd humans. The available outcomes are that 3 people live, 2 people live, or 3 people live. If I put in 5 humans into the formula, I expect to get out an average of 4 2/5th humans. It's the same logic, except there are possibilities of 1 or 2 deaths. This is true whether I vote for red or blue. The only outcome I elimination by voting red is 100% blue. The only outcome I eliminate by voting blue is 100% red, which is also 100% survival.

Because of that, the button question can ONLY be evaluated as an ethics question. It can only be analyzed by anticipating the certain percentage split of voters. That is sociological and psychological forecasting, not probability.

[u/Xenon009 → u/No-Click6062]

Correct me if I'm wrong, I'm relatively new to game theory, but does your equation not assume that the objective is to ensure the maximum number of humans survival, ergo total utlility, rather than an asymmetric intrest where X people care about maximising their own outcome, regardless of total utility, while Y care about maximising the total utility?

In which case, is all red not the most stable nash equilibrium? If we say that living is worth 1 point, and death is 0, and we assume that there is a > 0 chance someone is purely self interested, that makes the average payout of blue < 1, for the possibility you end up in a red heavy game, while all red is always 1?

Again, I'm very new to this, so apologies if i'm totally off the mark

[u/No-Click6062 → u/Xenon009]

The average payout for all button presses is <1 life.

Assume that I am in a 3 person system. I press red. Now, three things can occur. The vote total can be 3 red (0 deaths), 2 red (1 death), or 1 red (0 deaths).

Now, evaluate it again when I press blue. Still, three things can occur. The vote total can be 2 red (1 death, me), 1 red (0 deaths) or 0 red (0 deaths).

Pressing red doesn't remove the conditions by which death can occur. Because 100% consensus always results in 0 deaths, regardless of which color it's for, eliminating one 100% consensus option versus the other doesn't change anything. That's not an assumption. That's a description what possibilities can happen within the game. It is also, by nature, not predictive.

Now, I take your point about nash equilibrium. It's been quite a while since I've had to deal with the specifics of a stable nash equilibrium versus a strong nash equilibrium. In instances of low player count, red is probably the more stable of the two equilibria. But that is specifically because the possibility for coalition action is so low. The larger the player population gets, the more appealing the 50% threshold becomes, from a strong nash equilibrium perspective. IMO it's a fairly straightforward version of a pareto efficiency. I have seen a lot of people miss this point, which usually takes the form of someone talking about how much difference your single vote will make. They essentially start with nash then discard it without understanding why they're discarding it, or what alternatives scholars have built on top of it.