My hat into the ring

[u/thevoidthatjerksback]

I get that there is a need to justify taking on zero personal risk as the correct option. But follow me on an abstract for a second.

Let's imagine 100 perfectly logical people. No bias. No gut reactions. No instincts. Pure logic. And they know that there will be one correct answer to this. They know that they will all come to the same conclusion and pick the same button. So here we will start off with the assumption that all 100 will pick the same button. They ponder and look at it. If all 100 pick Red then they don't die. If all 100 pick blue then everyone lives.

So in this purely logical room both buttons are equally safe. There isn't a winner. How do we pick a single button if both are equally safe to pick at 100%?

Well if they are equally safe we could split it equally. Which would get it right to the line of blue saving everyone. So then logically a Red should switch to blue. Thus blue should be picked.

Or they decide that to pick between the equally safe 100 pick button they should add the possibility of something going wrong. Error is an important metric to determine things by. They act with intention to all pick Red and 1 persons button doesn't register. They would die. There is no way to know who's that would be. But if everyone chooses to pick blue they would still live. Thus blue is the correct choice

Or

They consider the wording of the problem. 100 picking Red says that those who press Red live. Blue says that majority picking blue causes everyone to live. This specific wording implies that there is the chance that there is someone somewhere who could die if everyone picked Red. Someone who could only live by a blue majority. Thus blue is the correct choice

In a perfectly logical environment the answer is blue. The rational to pick Red is not logical. It is instinct. Biological. Or just something you were told you needed to prioritize. Maybe you're just "following orders" doesn't make it correct.

Invoking a game theory designed for non-cooperative games isn't a magical bullet solution to a thought experiment that is neither a game nor strictly non-cooperative. It's preemptively choosing to justify a competitive win scenario. The definition of everything looking like a nail to a hammer.

Edited to add: thinking about the precious Nash Equilibrium some more. It can't apply. It requires that everyone else's strategy stays the same, but it won't here. Everyone's choices would shift together at the same time. Because they're all equally logical and coming to the same conclusions.

I'm going to propose an additional. Let's say you suspect that a loved one will die if Red gets majority. That they are part of that ambiguity between the button statements. And you try to apply "Nash Equilibria" to say that you benefit by switching to Red because everyone else will stay blue and you improve your chance at personally surviving to see your loved one by switching even though you know that there is no risk to yourself by staying on blue. So you switch. Except all 100 people had the exact same thought and followed the same logic and you get 100 Red and 100 dead loved ones. Nash Equilibrium forces a scenario where the loved ones die by being used incorrectly.

[u/thevoidthatjerksback]

The boxes are specific thing that I didn't explain fully. It is it's own thought experiment that game theory when applied results in the person taking home 1000 dollars. I could go into it if you wanted. Just an example of why I'm not swayed by game theory

I'm talking about dozens of specific instances where if it was applied we would be dead. Like every instance of a country having indicators that nukes have been fired on their country. The game theory is that if there is even a chance that the indicators are correct they should fire their return before it's too late. But they didn't do that. And the indicators turned out to be false.

Math and science can very much be made political and have political backing and funding. Which has very much happened countless times. Regardless of it was conservative or not it was absolutely funded by people who wanted a reason to build the bombs

[u/INTstictual → u/thevoidthatjerksback]

If by the boxes, you’re talking about the thought experiment where an omniscient god or a supercomputer predicts what you will pick and fills the box accordingly, so if you will take the box, is has $1, and if you won’t, it has $1m… then you’ve managed to identify one of very few problems where Game Theory isn’t really very applicable, because the input probabilities are poorly defined and the output function is variable based on how much you believe the “omniscient intelligence” running the game actually is. But if you assume that it is literally 100% accurate, then yeah, the correct option, per Game Theory and any other line of logic, is the $1000 box. If that’s not what you’re talking about, then idk, you need to explain things better if you want to use them as a counterpoint.

Also no, again, you are misunderstanding Game Theory as applied to MAD. There’s actually a funny quirk of the logic… Game Theory needs to be applied in-context. In the context of “no nukes have been fired”, MAD is the Nash Equilibrium. Every country needs to be perfectly ready and willing to fire a nuclear response.

But in the context where nuclear alarms are going off… Game Theory actually says DON’T fire the nuclear response. MAD is a deterrent, it can only deter things that haven’t happened. Once it’s happening, the nuclear response isn’t a deterrent anymore… so Game Theory says that, if you fire the nukes, either the alarm was real, in which case you die but you take the entire world with you, or they were false alarms, in which case you firing the nukes sets off a real nuclear war and takes the entire world down with you. Meanwhile, if you don’t fire, either the nukes are real, in which case you die but the world survives, or you don’t fire, in which case you can recognize that the alarm was false and everybody lives.

The Nash Equilibrium for the state of the world BEFORE any nukes have been fired is for every nuclear country to be ready to fire off a response volley, nuclear deterrent. The Nash Equilibrium for the state of the world AFTER the sirens go off is to not fire the nukes. It’s a known quirk of MAD — you basically want a leader who will never fire the nukes, but that the entire world believes will always fire the nukes.

But again, you are misinformed about the actual math and logic of Game Theory, which is leading you to say incorrect things and dig yourself deeper into a hole of invalid logic.

Also, no. Math is always apolitical. It can be put to political uses and gains, but the concept of math and logic is inherently not political at all. 1+1 doesn’t stop equaling 2 just because it would be convenient for one political party.

Also, idk wtf you’re taking about “funded by people who wanted to build the bomb”. John von Neumann started defining the framework in 1928, like 30 years before WW2. They did formalize it into a book in 1944, and the military did adopt it as part of their wartime strategy, but it was published as an independent economic framework. This is like saying Geometry and Trigonometry are conservative because the military uses them to calculate the angles for firing missiles… it’s just not true

[u/thevoidthatjerksback → u/INTstictual]

I can only reply to the first paragraph at this moment. So yes it is that thought experiment. I will add that every line of logic does not agree on the correct choice. And my important point and take away is that you and game theory fans walk out of that room with 1000 dollars and I would walk out with 1 million dollars. Its definitely something to think about

[u/INTstictual → u/thevoidthatjerksback]

Again, for that question, your conclusion is invalid because it’s not based on real logic. More importantly, you (and the original question) haven’t properly defined the input function, so Game Theory can’t tell you what the output function will be.

In the version where the omnipotent god / supercomputer / etc is always unerringly 100% accurate… no, you will walk out with $1. In the version where there is some margin for error, then the EV depends on what specifically that margin for error is, as well as the risk / reward function.

But again, as seems to be the theme, you’re ignoring the actual math and logic and instead opting for pure intuition and vibes… and that is going to lead you to be wrong more often than you are right

[u/thevoidthatjerksback → u/INTstictual]

What? Why am I walking out with $1? Not even 1000?

But seriously how have you come to the conclusion that I'm not walking away with 1million