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.
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.