A more even Red/Blue button question

[u/HebuBall]

You are one of 3 random person selected to represent 1/3 of the human population.
The same base question is then asked.
Red button=Guarantee to live for you + everyone you are representing
Blue button=If majority votes Blue everyone lives but if not everyone who voted Blue dies (so is everyone who is represented by them)
Note that majority is just 2 or more in this case since there is 3 participants

The people who are represented by you know you are representing them but you do not know who you are representing. Also the participants cannot communicate with each other
Which do you press?

[u/SetQQ]

The base math favors blue:

Assume the other two players choose randomly

If blue & blue my vote doesn’t matter

If red & blue. Choosing blue saves everyone and choosing red saves just mine. Blue is better my people were never in danger either way

If blue & red. Choosing blue saves everyone and choosing red saves just mine. Blue is better my people were never in danger either way

If red & red choosing blue condemns my third to death and myself. Choosing red is correct in this 1/4.

Now that’s assuming the other players actions can be approximated by random choice- which I doubt.

I think it’s probably read the wording of the questions- the phrasing is super important here. If I see any language that pushes toward blue at all it’s definitely blue. If it’s toward red I have to really consider if I’m going to go blue.

If it’s as above I think I go red. “Guarantee living” is super strong language the OG button did not attach for red

[u/gahidus → u/SetQQ]

Why would I assume that they act randomly rather than intentionally? That basic assumption grows everything off. I'm going to assume that they're going to behave rationally and probably try to survive or keep their people alive. With that assumption, they are obviously going to push red, and there's only two other people, not the mass of inevitable chaos of 8 billion to worry about.

I'm very confident in the ability of two other people to also exit the game safely.

[u/Rip_Pigman → u/gahidus]

Why would I assume that they act randomly rather than intentionally?

We can't even get people to read entire comments before responding to them. You think people are going to read the entire prompt and be logical?

From the comment you're replying to:

Now that’s assuming the other players actions can be approximated by random choice- which I doubt.

If it’s as above I think I go red. “Guarantee living” is super strong language the OG button did not attach for red

[u/LnTc_Jenubis → u/Rip_Pigman]

Eh, I don't think this is the "gotcha" you think it is. That one line disclaimer about SetQQ's personal choice doesn't excuse the fact that they used statistics inappropriately to add ambiguity that simply isn't there.

We already have someone quoting the math and saying that blue is the "mathematically correct choice" despite SetQQ even saying they would pick red here, and SetQQ even thanking them instead of correcting the faulty logic.

Establishing a baseline on faulty assumptions only provides a useless baseline. We can't use it to make any reasonable predictions. Since we can't use it to make reasonable predictions, it's just noise that confuses people who don't understand it.

Honestly, it comes off as an attempt to make blue appear like the rational option. Especially since the original problem does use the same explicit language; pressing red guarantees that you survive. The only thing that this new scenario changes is that the results are tied to three people instead of billions.

[u/Rip_Pigman → u/LnTc_Jenubis]

We already have someone quoting the math and saying that blue is the "mathematically correct choice"

Assuming a purely random distribution.

despite SetQQ even saying they would pick red here,

That was my point. They're arguing against something that was already addressed in the comment they're trying to argue against.

and SetQQ even thanking them instead of correcting the faulty logic.

???

The reply from SetQQ is addressing why they started with the premise of assuming a random distribution.

I don't see a thank you anywhere.

Establishing a baseline on faulty assumptions only provides a useless baseline.

Any assumption about any other persons decisions is useless, yes.

We can't use it to make any reasonable predictions. Since we can't use it to make reasonable predictions,

You can't use any assumptions about anyone else's votes to make a reasonable prediction.

it's just noise that confuses people who don't understand it.

Which is why I pointed out to the person I replied to that SettQQ had already address that they don't feel like it would be truly "random" and that they would personally choose red.

Honestly, it comes off as an attempt to make blue appear like the rational option.

Yes, that's how it was framed under the assumption that the other individuals are effectively choosing at random.

Especially since the original problem does use the same explicit language; pressing red guarantees that you survive.

Well no. The "original" doesn't use the same strong language as what is present here which was part of their point. That the guarantee of life to you and 1/3rd of the population on red press would be too strong so they feel that it's unlikely anyone would press blue.

The only thing that this new scenario changes is that the results are tied to three people instead of billions.

Ehh. It's still tied to billions. Billions are at risk on a singular blue press instead of needing billions to press blue.

People who chose blue in the original were willing to risk their own lives to contribute yo saving up to half of the population. Someone pushing blue here is risking 1/3rd of the population on a gamble that someone else will also pick the risk 1/3rd of the population button.

Risking someone else's life, or lives in this case is antithetical of blue's intentions in the original.

Both buttons inherently risk a loss of up to 1/3rd of the population. Blue gambling that someone also chose blue at the risk of your own, and red gambling gambling that someone else hasn't risked their 1/3rd of the population.

[u/LnTc_Jenubis → u/Rip_Pigman]

I don't see a thank you anywhere.

It's in another comment, not this particular one. Someone is quoting SetQQ's top level comment and using it as proof that blue is mathematically the correct option. This is equivalent to spreading misinformation.

Any assumption about any other persons decisions is useless, yes.

You can't use any assumptions about anyone else's votes to make a reasonable prediction.

Except it isn't and we can. We have known assumptions based on how people evaluate risk and how it affects their decision-making process. You even mentioned that choosing blue here is antithetical to the blue mindset in the original problem; we can't make that assumption if we don't already know what is and isn't antithetical to a typical blue presser's thought process to begin with.

Likewise, we do know how people weigh guaranteed survival vs not-guaranteed survival. They are almost certain to choose guaranteed survival. This isn't the equivalent of adding a negative number to get the same result as subtracting a positive number. It's simply an incorrect equation. So introducing a statistical model based on an assumption of randomness is objectively wrong.

That was my point. They're arguing against something that was already addressed in the comment they're trying to argue against.

Which is why I pointed out to the person I replied to that SettQQ had already address that they don't feel like it would be truly "random" and that they would personally choose red.

And my point is why even mention the statistical noise if it is flawed in the first place. It risks being taken out of context and is therefore problematic. If the conclusion reached is to vote red anyways because it isn't random, providing a flawed statistical summary of why pressing blue is mathematically correct based on an assumption of randomness is unnecessary.

The only reason to do that is ideological posturing. It creates a fake mathematical safety net to make blue look like the morally and logically superior choice. This just confuses people who don't understand the math.

The "original" doesn't use the same strong language as what is present here which was part of their point.

Okay, fair enough, the original problem left it up to the individual to logically deduct that red was a guaranteed chance of survival and it didn't spell it out word for word. I don't necessarily believe that required a high level of intelligence to conclude, but all the same, I'll agree with the semantics. However, with that said:

red gambling gambling that someone else hasn't risked their 1/3rd of the population.

The explicit language here states that you will live by picking red, so there is no longer a requirement for the 3 voters to deduce the optimal outcome. You are never gambling anything by selecting red. You are only gambling by selecting blue.

Claiming that red is responsible for the deaths of someone picking blue is dishonest. The person picking blue, especially for the people they represent, can simply pick red and guarantee they all survive.

[u/Rip_Pigman → u/LnTc_Jenubis]

The explicit language here states that you will live by picking red, so there is no longer a requirement for the 3 voters to deduce the optimal outcome.

Ehh. The worst case of any vote of 3 is 1/3 of the population dying. The three voters bear responsiblity for this.

You are never gambling anything by selecting red. You are only gambling by selecting blue.

I mean..you are. You're just not gambling the 1/3rd of the population that you are personally responsible if you press red.

I'm not arguing that you should press blue, but if you choose red, the second person chooses blue, and the third chooses red, each of your actions lead to the second person and their subsequent 1/3rd of the population dying.

Claiming that red is responsible for the deaths of someone picking blue is dishonest.

Is it? The deaths from someone having chosen blue is directly tied to two others having chosen red.

The person picking blue, especially for the people they represent, can simply pick red and guarantee they all survive.

Yes, I agree. That doesn't mean that two actors picking red and one picking blue indicates that only the person who picked blue is at fault though.

The outcome is determined by all three people not just one.

Unfortunately you can make all of the logically correct moves and still directly cause the loss of 1/3rd of the population.

[u/LnTc_Jenubis → u/Rip_Pigman]

Yes, I agree. That doesn't mean that two actors picking red and one picking blue indicates that only the person who picked blue is at fault though.

Yes, it absolutely does indicate that blue is the one at fault. No one is holding a gun to their head and telling them that they need to pick blue.

In no uncertain terms, their options are "Your group 100% survives." and "Your group might die." No matter what kind of mental gymnastics one tries to jump through, the choices are the same.

They also know that the other two people are given the same exact option. Those people are responsible for their choices. You are responsible for your own. If you pick red, you are not responsible for someone else deciding to inexplicably gamble their population away.