Late reply, you might not read this, I might not read any reply you make to me.
Original question: all red, all blue have the same outcome: no one dies. If it's an elected leader, do we really believe the red leader would have the same policies (if everyone votes for them) as the blue leader?
You can change the framing (one of my favorite: red button = cat picture, blue button = dog picture), but don't change the meaning of the outcomes.
shouldn’t EV favour pressing blue? if you’re perfectly altruistic & your credence in being the tie breaking vote is over 1 in 4 billion, the expected lives saved is slightly above 1. if you are more selfish though, it seems EV would favour red button pressing. I wonder how the math works out
The probability you assign to being the tie-breaking vote will depend a lot on your background expectations about others' dispositions. In a global Blender case, for example, the chances of anywhere near -- let alone *exactly* -- half the population "jumping in" is surely vastly lower than that. But yes, for the original Buttons case it's very plausible to me that impartial EV strongly favors blue.
I wonder how much of the difference is just people imagining different voting scenarios. I bet blue button pickers are more likely to be imagining a game in which people can attempt to convince each other.
Suppose that the probability distribution for votes, if you did it enough times, is a normal distribution centered on 50%.
Just keeping my own wrong thoughts:
SEEMS IRRELEVANT: [[ Normal distribution is very nearly flat near the center. But not quite flat, except at the exact midpoint. The true value, before you vote (and with everyone else's votes tallied before yours is revealed), is a point on the distribution. ]] Best way to analyze it is that your vote doesn't change the overall distribution or its mean; consider an alternative way of thinking about it, where 4 billion people always vote Red, 4 billion always vote Blue, two people flip a coin, and then there's you: in two out of four cases of the coin flips, you can save or condemn 4 billion people with your vote, so if you always vote blue, blue wins 75% of the time.
I was thinking that the slope of the distribution was important. But what if the distribution of outcomes was flat, or even curved up at the ends? While binomial distributions (coin flips) look like the normal distribution, there could be an intermediate transfer function. The only thing that should matter to you is the chance your vote causes the total to pass the threshold. And I think if the distribution of outcomes was flat, from 0 to 1, it would decrease the expected "number of lives saved".
So: imagine that the normal distribution gives a family of possible worlds. For each value of B on the distribution, we have a world where the number of people answering blue is B for many trials, leading to a normal distribution of outcomes centered around B.
The possible worlds don't need to have a normal distribution. But we're just arbitrarily assuming (like with 'unknown unknowns') that every value of B is world where the distribution of votes has the same standard deviation as the normal distribution that contains B. (In actuality, if B is "only 10% of people vote for B on average", it seems unlikely that the distribution would be just as wide: it would probably be narrower.)
This lets us say that the distributions are mirrored: if B is two SD's below the mean, then the 50% voting threshold is two SD's above the mean for the world created by B.
So if you integrate all B's, then on average, a value of B with, for example, 1% probability (left tail of distribution) has a 1% chance that your vote will be on the threshold. But this does not mean that you are saving 1 life on average with your vote. Your chance is 1 in 4 billion that you will save 4 billion people. But with all B's less than 50%, the average number of B voters is less than 4 billion, which means the number who will die if your vote is nowhere close to the threshold is also less. With B's above 50%, it's also true: the number of people who voted blue is above 4 billion. If, for example, 6 billion voted blue, and the rules were changed to require 6 billion + 1 and you didn't know the total votes, you would be saving 6 billion with a blue vote.
Again, to summarize: if you vote randomly, then multiplying the probability of your vote being the tiebreaker times the number of people saved gives an average of 1 life saved. But the average lives lost when your vote would change nothing gives a lower result: in (4 billion - 1) trials where your vote would not matter, less than 4 billion die, maybe a lot less. If the trial distribution for each world created for a value of B does not match the distribution which contains B, then the probability of being the tiebreaker could be even less than 1 in 4 billion.
Important point, from which math should not distract: even if you don't value your own life, others could value it. Logic that leads to voting blue for altruism makes others vote the same way, even if total blue is still less than the threshold for survival.
EDIT to make long post even longer:
If the mean for the percentage of people who answer blue is over 50%, I think it's reasonable that the chance of saving 4 billion people could be greater than 1 in 4 billion.
But, this is what I had originally been trying to get at: a graph of 'number of people expected to die'. When about half of the world votes blue, then expected deaths is 2 billion. Changes in votes, if they all have the same, consistent explanation, create the curve of this graph, and its derivative becomes the expected consequence of the change in an individual's action that moves the graph slightly to one side.
Standard deviation for votes could be very low. Suppose that we just say everyone votes randomly, and we vary the probability P of voting blue, from 0 to 1. In this case, expected deaths are 2 billion at P=0.5, but with N=8 billion voters, changing P to 0.49 gives very close to 3.92 billion deaths. Basically, blue voters always die, and the graph just linearly decreases to 0 as P approaches 0. Similarly, P=0.51 results in basically 0 expected deaths.
I actually don't know, as you asked, "how the math works out" here. If you take the slope of the graph at P=0.5 or close to it, does it lead to 'expected lives saved' greater than 1? I already gave an example, with just two coin-flipping swing voters and you, where 'expected lives saved' is greater than 1, but how does it change if you give them biased coins and alter the proportion of voters who never alter their votes, like by assigning more to blue? Each change leads to a different graph of 'expected deaths' for some independent variable, and 'number of lives saved' can be calculated from this graph. Maybe not as simple as taking the slope. But, for example, the number of coin flippers could be set constant, while the independent variable is 'converting red voters to blue voters'.
ANOTHER EDIT: Listen Data's Binomial Distribution Calculator shows that for N=8 billion, P=0.5, the standard deviation is 45k. So if 8 billion people flip a coin, then 500k people changing their vote moves the outcome by 10 standard deviations, essentially from 0 to 1. If just 90k people swing their votes, it's two standard deviations: if mean total votes are 45k below 4 billion, then 90k voters switching to blue moves the distribution so that the threshold is 1 SD below. This is 68% of the probability distribution. 68% chance that 4 billion will be saved by 90k changing their votes is ~45k*0.68 = 30k lives saved per swing voter. (The math includes square root, so not a coincidence this number is the standard deviation.)
If you're 'lucky' enough to get a distribution that close to the threshold. It also means 30k lives lost per person switching from blue to red.
I admire your brevity I just went on at great length about this.
The interesting thing about the blender example, is that in real life if there were a giant blender in an urban area we would probably at least put up like a token fence or something around it. We clearly would care about people who might fall into a ravine, off a bridge, into some weird industrial machine and expend effort to prevent it. So the argument that rational red button pushers would naturally not care at all about blue button pushers seems easily shown to be empty hyperbole by reference to the actual world.
Surely if there were a dependent majority who votes the way you do that would be a reason the way you vote would make a difference. If my theory of rational choices tells me to do something and its subscribed to by the majority of people surely I would do that and expect that everyone else who so subscribes would likewise. I'd think I could not change my vote without them changing theirs and so on. You could say then it's not my choice, this implies in order for something to be my choice I have to purposefully reject external principles (I have to deliberately be irrational for example), that just seems wrong.
If our population would be more resilient by including some minority that always acts randomly, that clarifies how red is selfish. The hard part is explaining the social value of the "gadflies" that the blue option protects, but the story of Socrates' death might serve that purpose. It justifies protection of "freedom of speech" even when most people do not feel Socrates' urge to violate the (red) option of sticking to a list of allowed utterances (or avoiding disallowed).
"Just think of the children" provides a pretty strong reason to try to co-ordinate on blue in the original Buttons version. But presumably not so many people would be tempted to climb into the Blender, and there wouldn't seem much hope of coordinating a majority to try to follow the few random lunatics in that case.
Are you trying to reinvent https://en.wikipedia.org/wiki/Nudge_theory ? We don't have time to go crawling into every Blender anyone can invent on twitter, but the Buttons supposedly require a selection, so red is no easier than blue. What I find interesting about these chestnuts is that a truly individualistic selfish person has no reason to consider the children. Might that motivate invention of a surprise Blender that is advertised as you described but actually kills everyone outside?
Simple; picking blue is retarded, and if people picking blue are unable to take a minute to think, or value more virtue signaling, I don't care about them, as never do for any stranger honestly.
> there’s a sense in which the “first” people to pick blue are being deeply irrational and creating a problem that a society of logically perfect beings would avoid. But one has to deal with humanity as it is, not as we’d wish it to be, and saving others from lethal “mistakes” is a good thing to do if you can manage it.
Picking blue for this reason (if you expect the result to be close) seems perfectly intelligent and reasonable?
I don't get your point. They're still strangers to me; I'm pretty serious about that (I think everyone pretending otherwise are just projecting self-deceptions on others or are directly hypocrites). The only ones obligated for those children are their parents.
And I couldn't be managing a thing here, I would just be putting myself at stupidly unnecessary risk for stupid strangers.
This is a great example of how outcomes don’t fail at the level of logic—they fail at the level of interpretation. Same decision structure, different framing, different human behavior. That gap becomes a real risk once these kinds of decisions show up in systems people actually rely on.
Well, while making the choice less risky. But I take the point - I was implicitly imagining a large enough portion of the population that it ended up making things more certain, but if there were like 5 blue pickers, that wouldn't be the case.
Worth noting that there are also framings that make Red look worse, e.g. Red = vote for a leader who will kill all non-voters iff elected.
Late reply, you might not read this, I might not read any reply you make to me.
Original question: all red, all blue have the same outcome: no one dies. If it's an elected leader, do we really believe the red leader would have the same policies (if everyone votes for them) as the blue leader?
You can change the framing (one of my favorite: red button = cat picture, blue button = dog picture), but don't change the meaning of the outcomes.
shouldn’t EV favour pressing blue? if you’re perfectly altruistic & your credence in being the tie breaking vote is over 1 in 4 billion, the expected lives saved is slightly above 1. if you are more selfish though, it seems EV would favour red button pressing. I wonder how the math works out
The probability you assign to being the tie-breaking vote will depend a lot on your background expectations about others' dispositions. In a global Blender case, for example, the chances of anywhere near -- let alone *exactly* -- half the population "jumping in" is surely vastly lower than that. But yes, for the original Buttons case it's very plausible to me that impartial EV strongly favors blue.
I wonder how much of the difference is just people imagining different voting scenarios. I bet blue button pickers are more likely to be imagining a game in which people can attempt to convince each other.
Suppose that the probability distribution for votes, if you did it enough times, is a normal distribution centered on 50%.
Just keeping my own wrong thoughts:
SEEMS IRRELEVANT: [[ Normal distribution is very nearly flat near the center. But not quite flat, except at the exact midpoint. The true value, before you vote (and with everyone else's votes tallied before yours is revealed), is a point on the distribution. ]] Best way to analyze it is that your vote doesn't change the overall distribution or its mean; consider an alternative way of thinking about it, where 4 billion people always vote Red, 4 billion always vote Blue, two people flip a coin, and then there's you: in two out of four cases of the coin flips, you can save or condemn 4 billion people with your vote, so if you always vote blue, blue wins 75% of the time.
I was thinking that the slope of the distribution was important. But what if the distribution of outcomes was flat, or even curved up at the ends? While binomial distributions (coin flips) look like the normal distribution, there could be an intermediate transfer function. The only thing that should matter to you is the chance your vote causes the total to pass the threshold. And I think if the distribution of outcomes was flat, from 0 to 1, it would decrease the expected "number of lives saved".
So: imagine that the normal distribution gives a family of possible worlds. For each value of B on the distribution, we have a world where the number of people answering blue is B for many trials, leading to a normal distribution of outcomes centered around B.
The possible worlds don't need to have a normal distribution. But we're just arbitrarily assuming (like with 'unknown unknowns') that every value of B is world where the distribution of votes has the same standard deviation as the normal distribution that contains B. (In actuality, if B is "only 10% of people vote for B on average", it seems unlikely that the distribution would be just as wide: it would probably be narrower.)
This lets us say that the distributions are mirrored: if B is two SD's below the mean, then the 50% voting threshold is two SD's above the mean for the world created by B.
So if you integrate all B's, then on average, a value of B with, for example, 1% probability (left tail of distribution) has a 1% chance that your vote will be on the threshold. But this does not mean that you are saving 1 life on average with your vote. Your chance is 1 in 4 billion that you will save 4 billion people. But with all B's less than 50%, the average number of B voters is less than 4 billion, which means the number who will die if your vote is nowhere close to the threshold is also less. With B's above 50%, it's also true: the number of people who voted blue is above 4 billion. If, for example, 6 billion voted blue, and the rules were changed to require 6 billion + 1 and you didn't know the total votes, you would be saving 6 billion with a blue vote.
Again, to summarize: if you vote randomly, then multiplying the probability of your vote being the tiebreaker times the number of people saved gives an average of 1 life saved. But the average lives lost when your vote would change nothing gives a lower result: in (4 billion - 1) trials where your vote would not matter, less than 4 billion die, maybe a lot less. If the trial distribution for each world created for a value of B does not match the distribution which contains B, then the probability of being the tiebreaker could be even less than 1 in 4 billion.
Important point, from which math should not distract: even if you don't value your own life, others could value it. Logic that leads to voting blue for altruism makes others vote the same way, even if total blue is still less than the threshold for survival.
EDIT to make long post even longer:
If the mean for the percentage of people who answer blue is over 50%, I think it's reasonable that the chance of saving 4 billion people could be greater than 1 in 4 billion.
But, this is what I had originally been trying to get at: a graph of 'number of people expected to die'. When about half of the world votes blue, then expected deaths is 2 billion. Changes in votes, if they all have the same, consistent explanation, create the curve of this graph, and its derivative becomes the expected consequence of the change in an individual's action that moves the graph slightly to one side.
Standard deviation for votes could be very low. Suppose that we just say everyone votes randomly, and we vary the probability P of voting blue, from 0 to 1. In this case, expected deaths are 2 billion at P=0.5, but with N=8 billion voters, changing P to 0.49 gives very close to 3.92 billion deaths. Basically, blue voters always die, and the graph just linearly decreases to 0 as P approaches 0. Similarly, P=0.51 results in basically 0 expected deaths.
I actually don't know, as you asked, "how the math works out" here. If you take the slope of the graph at P=0.5 or close to it, does it lead to 'expected lives saved' greater than 1? I already gave an example, with just two coin-flipping swing voters and you, where 'expected lives saved' is greater than 1, but how does it change if you give them biased coins and alter the proportion of voters who never alter their votes, like by assigning more to blue? Each change leads to a different graph of 'expected deaths' for some independent variable, and 'number of lives saved' can be calculated from this graph. Maybe not as simple as taking the slope. But, for example, the number of coin flippers could be set constant, while the independent variable is 'converting red voters to blue voters'.
ANOTHER EDIT: Listen Data's Binomial Distribution Calculator shows that for N=8 billion, P=0.5, the standard deviation is 45k. So if 8 billion people flip a coin, then 500k people changing their vote moves the outcome by 10 standard deviations, essentially from 0 to 1. If just 90k people swing their votes, it's two standard deviations: if mean total votes are 45k below 4 billion, then 90k voters switching to blue moves the distribution so that the threshold is 1 SD below. This is 68% of the probability distribution. 68% chance that 4 billion will be saved by 90k changing their votes is ~45k*0.68 = 30k lives saved per swing voter. (The math includes square root, so not a coincidence this number is the standard deviation.)
If you're 'lucky' enough to get a distribution that close to the threshold. It also means 30k lives lost per person switching from blue to red.
I admire your brevity I just went on at great length about this.
The interesting thing about the blender example, is that in real life if there were a giant blender in an urban area we would probably at least put up like a token fence or something around it. We clearly would care about people who might fall into a ravine, off a bridge, into some weird industrial machine and expend effort to prevent it. So the argument that rational red button pushers would naturally not care at all about blue button pushers seems easily shown to be empty hyperbole by reference to the actual world.
Surely if there were a dependent majority who votes the way you do that would be a reason the way you vote would make a difference. If my theory of rational choices tells me to do something and its subscribed to by the majority of people surely I would do that and expect that everyone else who so subscribes would likewise. I'd think I could not change my vote without them changing theirs and so on. You could say then it's not my choice, this implies in order for something to be my choice I have to purposefully reject external principles (I have to deliberately be irrational for example), that just seems wrong.
https://allanolley898224.substack.com/p/why-might-it-matter-how-things-are?r=27ibk6&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true
If our population would be more resilient by including some minority that always acts randomly, that clarifies how red is selfish. The hard part is explaining the social value of the "gadflies" that the blue option protects, but the story of Socrates' death might serve that purpose. It justifies protection of "freedom of speech" even when most people do not feel Socrates' urge to violate the (red) option of sticking to a list of allowed utterances (or avoiding disallowed).
"Just think of the children" provides a pretty strong reason to try to co-ordinate on blue in the original Buttons version. But presumably not so many people would be tempted to climb into the Blender, and there wouldn't seem much hope of coordinating a majority to try to follow the few random lunatics in that case.
Are you trying to reinvent https://en.wikipedia.org/wiki/Nudge_theory ? We don't have time to go crawling into every Blender anyone can invent on twitter, but the Buttons supposedly require a selection, so red is no easier than blue. What I find interesting about these chestnuts is that a truly individualistic selfish person has no reason to consider the children. Might that motivate invention of a surprise Blender that is advertised as you described but actually kills everyone outside?
Simple; picking blue is retarded, and if people picking blue are unable to take a minute to think, or value more virtue signaling, I don't care about them, as never do for any stranger honestly.
Including young children?
As I write in the OP:
> there’s a sense in which the “first” people to pick blue are being deeply irrational and creating a problem that a society of logically perfect beings would avoid. But one has to deal with humanity as it is, not as we’d wish it to be, and saving others from lethal “mistakes” is a good thing to do if you can manage it.
Picking blue for this reason (if you expect the result to be close) seems perfectly intelligent and reasonable?
I don't get your point. They're still strangers to me; I'm pretty serious about that (I think everyone pretending otherwise are just projecting self-deceptions on others or are directly hypocrites). The only ones obligated for those children are their parents.
And I couldn't be managing a thing here, I would just be putting myself at stupidly unnecessary risk for stupid strangers.
My position is even stronger: maximizing the number of deaths of blue-button-pushers is a moral good. Pick red!
I wouldn't say is an absolute good, but in this imperfect scenario where we would all be trapped, yes is morally superior, no doubt.
This is a great example of how outcomes don’t fail at the level of logic—they fail at the level of interpretation. Same decision structure, different framing, different human behavior. That gap becomes a real risk once these kinds of decisions show up in systems people actually rely on.
What's the problem that myopic blue-pickers create?
Opting in to dying unnecessarily unless a majority makes the same risky choice.
Well, while making the choice less risky. But I take the point - I was implicitly imagining a large enough portion of the population that it ended up making things more certain, but if there were like 5 blue pickers, that wouldn't be the case.