According to utilitarianism, we should always pick the blue button

In case you’re not familiar with the blue button and red button dilemma, here’s an alternative formulation that became popular on Reddit and I think best represents the situation:

The world is walking on a road that splits but then rejoins in 100m. Path 1 (red button) has no obstacles; Path 2 (blue button) has a locked gate that only opens if 50+% choose path 2, if not then all who chose path 2 die. Which path do you choose?

If all humans were rational beings capable of coordination, they would all choose red.

Because there is no sense in walking a path that has an obstacle that may lead to your death. And, if everyone chose the path without obstacles, there would be no deaths.

However, a portion of humanity will choose blue out of pure misunderstanding or stupidity.

Let’s suppose that 0.1% of humanity chooses blue (it would probably be more than that). And that the chance of blue winning is 0.1% (it would probably be more than that).

0.001 × 0.001 × 8,000,000,000 = 8,000

Therefore, even assuming a small portion of humanity choosing blue and a small chance of saving them as well, choosing blue has an expected value of saving 8,000 lives, in a mathematical calculation.

From a utilitarian perspective, a human being has a moral duty to sacrifice themselves whenever the expected value of their death is equal to or greater than that of 2 lives saved.

Therefore, it is clear and crystalline that there is a moral duty to choose the path with the gate (and, perhaps, sacrifice your life).

In fact, any thought experiment that gives one of two options the possibility, however minute, of saving a portion of the world population, will naturally lead to the conclusion that this is the correct choice, simply because the world population is very large. Even if this leads to the sacrifice of your life. Therefore, no matter how tiny the probability that these people would be saved, the mathematical calculation would lead this option to be chosen.