Compare two scenarios: in the first, the vote is on whether every one of the 3^^^3 people are dust-specked or not. In the second, only those who vote in favour are dust-specked, and then only if there’s a majority. But these are kind of the same scenario: what’s at stake in the second scenario is at least half of 3^^^3 dust-specks, which is about the same as 3^^^3 dust-specks. So the question “would you vote in favour of 3^^^3 people, including yourself, being dust-specked?” is the same as “would you be willing to pay one dust-speck in your eye to save a person from 50 years of torture, conditional on about 3^^^3 other people also being willing?”
Let me try and get this straight, you are presenting me with a number of moral dilemmas and asking me what I would do in them.
1) Me and 3^^^^3 − 1 other people all vote on whether we get dust specks in the eye or some other person gets tortured.
I vote for torture. It is astonishingly unlikely that my vote will decide, but if it doesn’t then it doesn’t matter what I vote, so the decision is just the same as if it was all up to me.
2) Me and 3^^^^3 − 1 other people all vote on whether everyone who voted for this option gets a dust speck in the eye or some other person gets tortured.
This is a different dilemma, since I have to weigh up three things instead of two, the chance that my vote will save about 3^^^^3 people from being dust-specked if I vote for torture, the chance that my vote will save on person from being tortured if I vote for dust specks and the (much higher) chance that my vote will save me and only me from being dust-specked if I vote for torture.
I remember reading somewhere that the chance of my vote being decisive in such a situation is roughly proportional to the square root of the number of people (please correct me if this is wrong). Assuming this is the case then I still vote for torture, since the term for saving everyone else from dust specks still dwarfs the other two.
3) I have to choose whether I will receive a dust speck or whether someone else will be tortured, but my decision doesn’t matter unless at least half of 3^^^^3 − 1 other people would be willing to choose the dust speck.
Once again the dilemma has changed, this time I have lost my ability to save other people from dust specks and the probability of me successfully saving someone from torture has massively increased. I can safely ignore the case where the majority of others choose torture, since my decision doesn’t matter then. Given that the others choose dust specks, I am not so selfish as to save myself from a dust speck rather than someone else from torture.
You try to make it look like scenarios 2 and 3 are the same, but they are actually very, very different.
The bottom line is that no amount of clever wrangling you do with votes or conditionals can turn 3^^^^3 people into one person. If it could, I would be very worried, since it would imply that the number of people you harm doesn’t matter, only the amount of harm you do. In other words, if I’m offered the choice between one person dying and ten people dying, then it doesn’t matter which I pick.
Assuming a roughly 50-50 split the inverse square-root rule is right. Now my issue is why you incorporate that factor in scenario 2, but not scenario 3. I honestly thought I was just rephrasing the problem, but you seem to see it differently? I should clarify that this isn’t you unconditionally receiving a speck if you’re willing to, but only if half the remainder are also so willing.
The point of voting, for me, is not an attempt to induce scope insensitivity by personalizing the decision, but to incorporate the preferences of the vast majority (3^^^^3 out of 3^^^^3 + 1) of participants about the situation they find themselves in, into your calculation of what to do. The Torture vs. Specks problem in its standard form asks for you to decide on behalf of 3^^^^3 people what should happen to them; voting is a procedure by which they can decide.
[Edit: On second thought, I retract my assertion that scenario 1) and 2) have roughly the same stakes. That in scenario 1) huge numbers of people who prefer not to be dust-specked can get dust-specked, and in scenario 2) no one who prefers not to be dust-specked is dust-specked, makes much more of a difference than a simple doubling of the number of specks.]
By the way, the problem as stated involves 3^^^3, not 3^^^^3, people, but this can’t possibly matter so nevermind.
There are actually two differences between 2 and 3. The first is that in 2 my chance of affecting the torture is negligible, whereas in 3 it is quite high. The second difference is that in 2 I have the power to save huge numbers of others from dust specks, and it is this difference which is important to me, since when I have that power it dwarfs the other factors so much as to be the only deciding factor in my decision. In your ‘rephrasing’ of it you conveniently ignore the fact that I can still do this, so I assumed I no longer could, which made the two scenarios very different.
I think also, as a general principle, any argument of the type you are formulating which does not pay attention to the specific utilities of torture and dust-specks, instead just playing around with who makes the decision, can also be used to justify killing 3^^^^3 people to save one person from being killed in a slightly more painful manner.
Compare two scenarios: in the first, the vote is on whether every one of the 3^^^3 people are dust-specked or not. In the second, only those who vote in favour are dust-specked, and then only if there’s a majority. But these are kind of the same scenario: what’s at stake in the second scenario is at least half of 3^^^3 dust-specks, which is about the same as 3^^^3 dust-specks. So the question “would you vote in favour of 3^^^3 people, including yourself, being dust-specked?” is the same as “would you be willing to pay one dust-speck in your eye to save a person from 50 years of torture, conditional on about 3^^^3 other people also being willing?”
Let me try and get this straight, you are presenting me with a number of moral dilemmas and asking me what I would do in them.
1) Me and 3^^^^3 − 1 other people all vote on whether we get dust specks in the eye or some other person gets tortured.
I vote for torture. It is astonishingly unlikely that my vote will decide, but if it doesn’t then it doesn’t matter what I vote, so the decision is just the same as if it was all up to me.
2) Me and 3^^^^3 − 1 other people all vote on whether everyone who voted for this option gets a dust speck in the eye or some other person gets tortured.
This is a different dilemma, since I have to weigh up three things instead of two, the chance that my vote will save about 3^^^^3 people from being dust-specked if I vote for torture, the chance that my vote will save on person from being tortured if I vote for dust specks and the (much higher) chance that my vote will save me and only me from being dust-specked if I vote for torture.
I remember reading somewhere that the chance of my vote being decisive in such a situation is roughly proportional to the square root of the number of people (please correct me if this is wrong). Assuming this is the case then I still vote for torture, since the term for saving everyone else from dust specks still dwarfs the other two.
3) I have to choose whether I will receive a dust speck or whether someone else will be tortured, but my decision doesn’t matter unless at least half of 3^^^^3 − 1 other people would be willing to choose the dust speck.
Once again the dilemma has changed, this time I have lost my ability to save other people from dust specks and the probability of me successfully saving someone from torture has massively increased. I can safely ignore the case where the majority of others choose torture, since my decision doesn’t matter then. Given that the others choose dust specks, I am not so selfish as to save myself from a dust speck rather than someone else from torture.
You try to make it look like scenarios 2 and 3 are the same, but they are actually very, very different.
The bottom line is that no amount of clever wrangling you do with votes or conditionals can turn 3^^^^3 people into one person. If it could, I would be very worried, since it would imply that the number of people you harm doesn’t matter, only the amount of harm you do. In other words, if I’m offered the choice between one person dying and ten people dying, then it doesn’t matter which I pick.
Assuming a roughly 50-50 split the inverse square-root rule is right. Now my issue is why you incorporate that factor in scenario 2, but not scenario 3. I honestly thought I was just rephrasing the problem, but you seem to see it differently? I should clarify that this isn’t you unconditionally receiving a speck if you’re willing to, but only if half the remainder are also so willing.
The point of voting, for me, is not an attempt to induce scope insensitivity by personalizing the decision, but to incorporate the preferences of the vast majority (3^^^^3 out of 3^^^^3 + 1) of participants about the situation they find themselves in, into your calculation of what to do. The Torture vs. Specks problem in its standard form asks for you to decide on behalf of 3^^^^3 people what should happen to them; voting is a procedure by which they can decide.
[Edit: On second thought, I retract my assertion that scenario 1) and 2) have roughly the same stakes. That in scenario 1) huge numbers of people who prefer not to be dust-specked can get dust-specked, and in scenario 2) no one who prefers not to be dust-specked is dust-specked, makes much more of a difference than a simple doubling of the number of specks.]
By the way, the problem as stated involves 3^^^3, not 3^^^^3, people, but this can’t possibly matter so nevermind.
There are actually two differences between 2 and 3. The first is that in 2 my chance of affecting the torture is negligible, whereas in 3 it is quite high. The second difference is that in 2 I have the power to save huge numbers of others from dust specks, and it is this difference which is important to me, since when I have that power it dwarfs the other factors so much as to be the only deciding factor in my decision. In your ‘rephrasing’ of it you conveniently ignore the fact that I can still do this, so I assumed I no longer could, which made the two scenarios very different.
I think also, as a general principle, any argument of the type you are formulating which does not pay attention to the specific utilities of torture and dust-specks, instead just playing around with who makes the decision, can also be used to justify killing 3^^^^3 people to save one person from being killed in a slightly more painful manner.