u/Medical-Clerk6773

People like to appeal to game theory as proof that red is logical. It's true that red is the dominant strategy, which means it's always the best choice if your only goal is to maximize the chance of your survival (with no regard for the lives of others, and no concern for what world you'll have to inhabit afterwards). This does not mean that red is always the most rational in all circumstances, for all levels of human altruism.

Here is a more nuanced, principled way of determining what the logical choice is. Note that it still makes some simplifications, such as it doesn't factor in concerns like "what will the world even be like if I red wins and survive, and how much do I want to live there"? Those considerations could move your personal decisions more in favor of blue. If you actively support the "culling of idiots" or whatever, that might move your decision more in favor of red (hopefully there ain't a lot of those types here).

This chart shows which choice maximizes expected utility if you have a utility function that takes the form of "P(You survive) + x * E(number of others who survive)". So, that utility function is the sum of the probability that you survive plus a weighted term of the expected number of other survivors. By changing x, you can change how much you value other lives relative to yours (x = 1 is strict utilitarianism, "a stranger's life is worth exactly as much as my own").

The graph shows the optimal choice as a function of your priors, in this case, there are two parameters: expectation on how many people will vote blue, as well as your confidence interval.

The colored regions show when blue is worth it for a given threshold of valuing strangers (for example, the median altruism region is if you value your life at 3-10 stranger's lives). The dashed line shows the decision boundary for a strict utilitarian (all lives equal, including your own).

This is the closest thing to an objective answer that exists.

This image was flagrantly stolen from user azercoco from this post. They did all the mathematical calculations involved in creating this chart.
https://www.reddit.com/r/trolleyproblem/comments/1t3epel/comment/ojuqope/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

I think this is kind of a bistable perception phenomenon like "the dress" or laurel/yanny. People latch onto a frame of "this is the default button that does nothing and the other is the death button". When first presented with the problem, blue seemed overwhelmingly obvious and I had no doubt it would win if this situation actually happened. I thought "Why would anyone press a button that might kill millions to billions when you could just... not do that?".

However, after seeing that about 40% of people would vote for red, and assuming that real life or death stakes will skew the result more towards red, I feel that the risk of red winning is *very high*, so now I have to admit I would definitely vote for red.

This doesn't mean I actually started to "see it the red way" ("red button does nothing" / "blue button is suicide"), it's just that the red victory started to look probable so I adapted. As far as how I logically analyze the problem, I largely have abandoned the framing of both sides, and try to view it as impartially as possible. Neither side can avoid responsibility. There is no "do nothing button" and there is no "death button". Red is safer for yourself, but potentially harms others if your vote is pivotal. Blue voluntarily places yourself at risk, but potentially saves others if your vote is pivotal. (And yes, the scenario where your vote is pivotal actually matters, because the low likelihood and massive impact largely cancel out.)

However I also have to admit that despite voting red out of fear, my surface-level intuition still favors blue, and I'm still surprised a lot of people defaulted to red (I'm actually quite bummed about it).

The logical answer depends on your priors

I think blue makes more sense, but seeing the number of red-supporters made me choose red out of fear.