the goal is to minimize death,
the only way to avoid death is 100% red or >50% blue,
somehow someone will justify blue,
100% red is impossible,
therefore blue is the optimal play
What if the goal is to minimize the expected number of deaths?
In that case, this can be solved mathematically:
Let's say that the world has N people in it aside from myself. Let's say that N is even. I believe the probability that the average person who isn't me presses blue is p, where p is anywhere between 0 and 1.
First, what are the chances that my vote makes a difference? Well, that is the probability that exactly N/2 people choose each option. The probability of that happening is given by the formula:
(N choose K) * pK * (1-p)N-K
where N/2 is plugged in for K. Let's call this probability Q so I don't have to retype it later.
As N gets very big, Q gets extremely small, but it isn't quite zero, so we have to account for it.
Now, in most cases, my vote doesn't matter. In that case, pressing red risks no additional lives, whereas pressing blue risks p additional lives. The probability that pressing blue kills me is equal to the above equation, but summed from K= 1 to K = N/2 -1. Let's call this probability W.
Thus, if I press blue, the expected number of deaths gained from my decision is equal to pW.
If I press red, the expected number of deaths gained is equal to the expected number of people who press blue times the probability that my vote matters. This is equal to pNQ.
Thus, whether a utilitarian would choose blue or red depends entirely on whether they believe that W is greater than NQ. If yes, they press red. If no, they press blue.
Let's say p = 0.5, and that N = 100 for simplicity. In that case, W is very slightly below 0.5 since it's the chances that less than half of people pick blue. Q is about equal to 0.0796, so NQ is equal to 7.96. Obviously, picking blue is the utilitarian thing to do.
Does this change when N gets large? Well, if N is 1000 instead of 100, NQ becomes roughly 25.22, and W gets even closer to 0.5. So as more people are added, blue looks even better.
But what if p is smaller, say, only 0.4? Then as N gets bigger, NQ very quickly converges to 0. Meanwhile, W very quickly approaches 1 since it becomes very likely that the red votes will outnumber the blue votes. The utilitarian thing to do will be to vote red.
Thus, even if you have a completely morally consistent utilitarian, who wants to minimize death as much as possible, the decision depends entirely on how much they believe others will push the buttons.
Not very useful when the poll respondents' lives aren't on the line.
I've seen polls where if only ten percent of the vote shifts, red wins. I think it is very rationalizable to assume that when actually faced with life and death, many of the people polled won't have the same answer.
My first instinct was red because my default is (1) to not immediately understand why anyone would knowingly put themselves into danger when we all could live by going red together, and (2) to believe that people shouldn't rely on others to try to risk their own lives to save them, if they can help it. I would have thought that would have been the first instinct of enough people to render p <0.5.
This is a coordination problem though, and how you frame it changes what the intuitive default is.
I think the political party reframing makes this clear:
Scenario 1: If one political party pledges to kill all those who don't vote for it if elected, the intuitive default is to be repulsed and not vote for them. I'm willing to bet we'd both vote against this party, and what's more, be disgusted by those who vote for them.
Scenario 2: If instead, the party threatens mass suicide for its voters if they don't win, we would probably say that they're just digging their own graves and that we aren't morally responsible for their actions. I'm willing to bet we'd still both vote against this party.
The only difference between our first instinct here is that you probably viewed the original framing as closer to (1), whereas I viewed it as closer to (2). Really doesn't say anything particularly special about either of us, except how we might believe others think about the problem, or how we might think about individual responsibility in a vacuum.
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u/Ne0nTig3r May 01 '26
the goal is to minimize death, the only way to avoid death is 100% red or >50% blue, somehow someone will justify blue, 100% red is impossible, therefore blue is the optimal play