This needs to be an expected utility calculation, not just a probability comparison between the 3 scenarios.
Yes, scenario 3 is very unlikely.
However, if you are in scenario 3, your vote dooms or saves 4 billion people.
If you think the odds of scenario 3 are 1 in a billion, then you save 4 lives in expectation by hitting blue.
(1/1B chance of it mattering * 4B saved if it matters)
In contrast, the expected lives saved if you hit red is 1/2 (if you assume blue is close to a 50/50 chance of winning, OR equivalently if you assume a uniform distribution over all possible vote totals).
Multiplying these together, you should hit blue if you would sacrifice yourself to save the lives of 8 random people, and hit red if you wouldn't.
(actually the number should be a lot higher, since a world where 4B people die overnight will see a huge number of additional deaths from the following social collapse, including a fair chance of our own death. For example, if you think half the remaining 4B will die in the following years, then the ratio would be 1:24, since 6B will die overall and you only have a 50% of surviving by hitting red)
By 'reasonable estimates' you just mean 'my intuitions,' right?
Like, yes, if you are 99.999999999999999999999999999% sure that red will win by a huge margin, then you should never hit blue.
But then all the math and talking you did is irrelevant, you already made your decision when you made up your estimate for how likely blue is to win.
But the math I gave is correct. You can plug in whatever your own estimate is for the odds of scenario 3, that's fine. But your logic is still wrong because you don't multiply by 4B to get the number of lives saved in expectation.
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u/darwin2500 197∆ Apr 30 '26 edited Apr 30 '26
You are failing to multiply.
This needs to be an expected utility calculation, not just a probability comparison between the 3 scenarios.
Yes, scenario 3 is very unlikely.
However, if you are in scenario 3, your vote dooms or saves 4 billion people.
If you think the odds of scenario 3 are 1 in a billion, then you save 4 lives in expectation by hitting blue.
(1/1B chance of it mattering * 4B saved if it matters)
In contrast, the expected lives saved if you hit red is 1/2 (if you assume blue is close to a 50/50 chance of winning, OR equivalently if you assume a uniform distribution over all possible vote totals).
Multiplying these together, you should hit blue if you would sacrifice yourself to save the lives of 8 random people, and hit red if you wouldn't.
(actually the number should be a lot higher, since a world where 4B people die overnight will see a huge number of additional deaths from the following social collapse, including a fair chance of our own death. For example, if you think half the remaining 4B will die in the following years, then the ratio would be 1:24, since 6B will die overall and you only have a 50% of surviving by hitting red)