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Notes -
I disagree that simply persuading people to choose blue is unethical. Ultimately it’s their decision, and it’s not obviously wrong.
But
A way to lose in real life is to get worked up over a silly hypothetical.
An example to demonstrate my point: there is a cult leader who has spiked the Kool-Aid with lethal poison. He genuinely, 100% earnestly believes that everyone who he convinces to partake of this drink will go to heaven; after he's tended to his flock he intends to follow them. Is it unethical to convince people to join him? He is genuinely acting in what he believes is their best interest. I think this figure is tragic, delusional, and dangerous, but, if he's a true believer, one could argue that he isn't unethical, though he is, at the bare minimum, projecting his utility function onto others.
Now, let's change the parameters: the cult leader is no longer certain that everyone who drinks the poisoned Kool-Aid will go to heaven. He's actually only about 50% sure. Maybe drinkers will go to heaven or maybe they'll just die. Nevertheless, he continues trying to convince everyone to take this gamble -- and he knows it's a gamble. Can he ethically advocate for Kool-Aid drinking? I think this is a decision that everyone should make for themselves after being informed of the risks, and that persuading people to drink the Kool-Aid (by asserting that their family and friends are going to drink it, for instance) is dubious and paternalistic. The strongest argument I think he is ethically permitted to make is something like, "I personally believe there is a 50% chance that drinking the Kool-Aid will get you into heaven; I believe the reward outweighs the risk and encourage anyone who agrees to follow me voluntarily."
This is not quite isomorphic to the button problem as posed but there are strong parallels. It is pretty close to the button problem where the results are already determined -- that is, no matter how many people you convince, the outcome won't change, and it's worth noting that this is the most common case: your advocacy is unlikely to change enough votes & minds to swing the results one way or the other. "The votes have already been tallied and one side has won by a significant margin: you and your family are the last ones left. How do you vote, and how do you instruct your family members to vote?"
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I suspect people get worked up because they know that a person who presses red is also a person who is very likely to defect in other scenarios requiring everyone to work together for the good of the whole, and they want to get rid of those who would benefit at the expense of others. But as you said, it's a hypothetical and it's best not to get worked up about it.
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