I don’t get the sentiment of “your vote only matters if it would be an exact tie otherwise.” By that logic, if the outcome of a US presidential election would either save 10,000 lives or not, then the altruistic thing to do is to get the vote as close 50⁄50 as possible, so that every voter can save 10,000 lives each for a total of 3 trillion lives saved, as opposed to the normal outcome, where no lives are saved at all.
Hmm, I see your point; but if each vote is independent, then given how all the other voters voted, my vote really does decide the election. E.g. if I go into the ballot box, what I write on my poll slip does not cause and is not caused by what’s written on all the other slips (as I don’t see them and they don’t see mine).
How about this thought experiment: I am the very last person in the country to vote. Unknown to anyone, all the votes made before mine constitute a tie, so my vote will be the deciding vote. Then it really is the case that if I vote one way, 10,000 lives are saved, and the other way, none are. And it is also the case that, given how I voted, if my neighbour had voted the other way, he would have changed the outcome too. (Incidentally it seems only people who vote the same way as me have the power to decide the outcome, given how I voted.)
I do sense the counterfactual complications. Is your argument that the 10,000 lives saved should be apportioned among all the voters in the case of a tie-break, and hence it still isn’t worth anyone’s while voting? What is the argument for apportioning?
[ADDED:]
Here’s a further hand-wavy argument:
You’re saying that in the case of a tie-break, everyone who voted for the winning party each gets to save 10,000 lives (overcounting the benefit). But in a normal outcome with no tie-break, none of them do, even though 10,000 lives are still saved (undercounting the benefit). If we account differently, with only the final voter getting the 10,000-life benefit in the tie-break case, and all voters for the winning party (or all after a majority was reached?) sharing the 10,000 in the normal case, so that in every winning scenario the benefit adds up to exactly 10,000 lives (more intuitively), doesn’t it all work out the same in terms of expected benefit per voter? (I wonder, without thinking/calculating further.)
Actually I was saying that if only tie breaks matter, then in the case of a tie-break, everyone who voted for the losing party also saves 10,000 lives each. Because if they didn’t vote against saving lives, then it wouldn’t be a tie break, and then no individual would save any lives at all.
Of course, I don’t actually believe that—I think voting matters even if it wouldn’t break a tie.
In the scenario where you vote last in the tie-break, it is true everything depends on you. But everything depended on everyone else too, even though they already voted. In terms of expected utility of your decision, you get to tell your utility function that you saved 10,000 lives. In terms of moral credit though, everyone who voted SAVE still gets a fraction of the credit, because without their vote you couldn’t have done it.
Let’s consider a smaller scale vote, like a supreme court decision. Even if you know exactly how other justices will vote, and you know it’s going to be 5-3 not including you, well your decision still matters, and not just for signalling reasons. 6-3 is different from 5-4 because in the former case, two of the five would have to flip in order for it to change and in the latter case, only one of the five would have to flip for it to change. Even if everyone knew how everyone else was going to vote ahead of time, still each justice’s preference for one ruling over another still matters.
Also, I don’t think it makes sense to say that one ballot matters more than another ballot, based solely on the order that they are counted. Votes are votes.
Yes I follow your argument, though I’m a bit doubtful about a result that produces a large difference between utility function and moral credit.
Re your Supreme Court example (and I agree this is a clearer way of thinking about it), I don’t quite follow the argument. It’s true that if the other justices had voted differently, more of them would have had to vote differently (‘flip’) had you done so, but as it’s a given that you knew how everyone else was going to vote, flipping is ruled out—their votes are set in stone.
And re ‘still each justice’s preference… matters’, I wasn’t clear if this is the same point or a separate point—i.e. a signalling or similar argument that the size of the majority matters, e.g. politically.
I don’t get the sentiment of “your vote only matters if it would be an exact tie otherwise.” By that logic, if the outcome of a US presidential election would either save 10,000 lives or not, then the altruistic thing to do is to get the vote as close 50⁄50 as possible, so that every voter can save 10,000 lives each for a total of 3 trillion lives saved, as opposed to the normal outcome, where no lives are saved at all.
Hmm, I see your point; but if each vote is independent, then given how all the other voters voted, my vote really does decide the election. E.g. if I go into the ballot box, what I write on my poll slip does not cause and is not caused by what’s written on all the other slips (as I don’t see them and they don’t see mine).
How about this thought experiment: I am the very last person in the country to vote. Unknown to anyone, all the votes made before mine constitute a tie, so my vote will be the deciding vote. Then it really is the case that if I vote one way, 10,000 lives are saved, and the other way, none are. And it is also the case that, given how I voted, if my neighbour had voted the other way, he would have changed the outcome too. (Incidentally it seems only people who vote the same way as me have the power to decide the outcome, given how I voted.)
I do sense the counterfactual complications. Is your argument that the 10,000 lives saved should be apportioned among all the voters in the case of a tie-break, and hence it still isn’t worth anyone’s while voting? What is the argument for apportioning?
[ADDED:]
Here’s a further hand-wavy argument:
You’re saying that in the case of a tie-break, everyone who voted for the winning party each gets to save 10,000 lives (overcounting the benefit). But in a normal outcome with no tie-break, none of them do, even though 10,000 lives are still saved (undercounting the benefit). If we account differently, with only the final voter getting the 10,000-life benefit in the tie-break case, and all voters for the winning party (or all after a majority was reached?) sharing the 10,000 in the normal case, so that in every winning scenario the benefit adds up to exactly 10,000 lives (more intuitively), doesn’t it all work out the same in terms of expected benefit per voter? (I wonder, without thinking/calculating further.)
Actually I was saying that if only tie breaks matter, then in the case of a tie-break, everyone who voted for the losing party also saves 10,000 lives each. Because if they didn’t vote against saving lives, then it wouldn’t be a tie break, and then no individual would save any lives at all.
Of course, I don’t actually believe that—I think voting matters even if it wouldn’t break a tie.
In the scenario where you vote last in the tie-break, it is true everything depends on you. But everything depended on everyone else too, even though they already voted. In terms of expected utility of your decision, you get to tell your utility function that you saved 10,000 lives. In terms of moral credit though, everyone who voted SAVE still gets a fraction of the credit, because without their vote you couldn’t have done it.
Let’s consider a smaller scale vote, like a supreme court decision. Even if you know exactly how other justices will vote, and you know it’s going to be 5-3 not including you, well your decision still matters, and not just for signalling reasons. 6-3 is different from 5-4 because in the former case, two of the five would have to flip in order for it to change and in the latter case, only one of the five would have to flip for it to change. Even if everyone knew how everyone else was going to vote ahead of time, still each justice’s preference for one ruling over another still matters.
Also, I don’t think it makes sense to say that one ballot matters more than another ballot, based solely on the order that they are counted. Votes are votes.
Yes I follow your argument, though I’m a bit doubtful about a result that produces a large difference between utility function and moral credit.
Re your Supreme Court example (and I agree this is a clearer way of thinking about it), I don’t quite follow the argument. It’s true that if the other justices had voted differently, more of them would have had to vote differently (‘flip’) had you done so, but as it’s a given that you knew how everyone else was going to vote, flipping is ruled out—their votes are set in stone.
And re ‘still each justice’s preference… matters’, I wasn’t clear if this is the same point or a separate point—i.e. a signalling or similar argument that the size of the majority matters, e.g. politically.
I think this EA forum post explaining Shapley Values encapsulates my current opinion better than my comments above.