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The more interesting question from an economics point of view is why does anyone bother voting. Since races almost never come down to one vote, your vote almos

The more interesting question from an economics point of view is why does anyone bother voting. Since races almost never come down to one vote, your vote almost certainly doesn't matter. Nevermind the fact that more people voted for democrats for the senate and the presidency and still lost both. The latest theory I've heard for why people vote is that being seen as a team player has social value. https://eml.berkeley.edu//~sdellavi/wp/turnout13-11-13.pdf https://eml.berkeley.edu//~sdellavi/wp/turnout13-11-13.pdf The Freakonomics guys bring this up every so often. https://www.nytimes.com/2005/11/06/magazine/why-vote.html https://www.nytimes.com/2005/11/06/magazine/why-vote.html Also I just wanted to let everyone know that I voted ;)

throwawaymath 8y ago
From a mathematical perspective it's pretty silly to claim your vote doesn't matter just because it's not the tie breaking vote. You should give this a read: https://www.skishore.me/voting.html https://www.skishore.me/voting.html. Frankly this viewpoint has always puzzled me. Your specific claim that a vote almost certainly doesn't matter because elections don't come down to a single vote seems...unsupported, to put it politely. It might be more intuitively attractive to say your vote doesn't matter if you're not in a swing election, but it's not rigorously defensible. It's incorrect. It's like saying 4 and 5 are the same thing because they're both significantly smaller than 100,000. No, they're materially different quantities. If more people accepted this straightforward and uncontroversial truth - and acted on it - then more change might actually be effected. Instead this becomes a self-fulfilling and self-defeating prophecy with no rational basis. It's lazy cynicism, to put it bluntly.
- matt-attack 8y ago
  Bit logically where was he wrong? It seems like a bit of a paradox to me. You keep say it’s wrong but can you point out exactly where his reasoning is wrong? My vote yesterday simply didn’t change any of the outcomes. That is a fact. None of the races were won by a single vote.
  - glastra 8y ago
    Or maybe it did, if you voted for the winning side. What if you ordered the winning votes and losing votes randomly, side by side, and eliminated pairs of opposing votes. You would be left with a set of winning votes, cast by individual people. You could attribute the victory to exactly those people. Now, to extrapolate this to all of the winning voters, simply "sample" reorderings, or average it, and you have a spread responsibility amongst all those people who voted for the winning candidate/party. In other words, votes cast for the winning side did decide the result, because of their collective behaviour. The effect of a single vote can be defined in statistical terms as being interdependent with the rest of the votes in the same direction. This means any winning vote cannot be said to lack all effect, meaning or power. If the vote is not without effect, then it must have some effect, albeit not absolute. Another way to look at this is that if the voting is won by a difference of exactly one vote, whose vote was it anyway? You would spread the responsibility of turning the election equally amongst all voters for that side. If we wanted to somehow quantify the "contribution" to winning that each vote has, we have to take into account how many votes were actually required to win. Let X be the number of votes in the winning side and Y in the losing side. Of all the X votes in the winning side, only Y+1 were actually necessary to win. So the contribution of each voter could be (Y + 1)/X, which is always <= 1 as Y + 1 <= X, measured in "decisive votes per person", or something along those lines. So if the voting is won by exactly one vote, all votes in the winning side are decisive: without any one of them, the voting would not be won. If, however, everyone voted for the same side, it would be 1/X, where you could remove all but one vote and still be short of removing a whole "decisive vote".
  - throwawaymath 8y ago
    I pointed out the error in reasoning. You are repeating the intuitive heuristic, which is that a single vote doesn't change outcomes. I'll try to explain my point more fully, but there isn't much more ground to cover here. glastra made a good sibling comment covering the basic probabilistic points, so I'll try a different direction. If your bar for voting to have meaning is that your individual vote will change outcomes, you'll find that not a single model of democracy (much less implementation) is satisfying. That's an impossible, nonsensical bar. You can't possibly hope to swing a state to your party if everyone on the underdog side stays home because it seems unlikely to happen. Your vote has meaning even if you weren't personally the arbiter of political change. Aggregates are defined by their constituent parts. You're acting as though voting is worthless if your cause doesn't receive enough votes to pass a cutoff point. It's true that it won't pass, but that doesn't mean the vote didn't matter. Apply this model of thinking elsewhere: if you made 2 points in a basketball game and your team lost, were those 2 points meaningless just because you didn't win? Should you recuse yourself from playing because it's unlikely your team can win? How about raising money for a Kickstarter - was it a waste of time just because you didn't raise the goal and won't receive the funds? Should you not try to raise money and find as many donors as you can, just because there's a minimum cutoff for payout? Since analogies are imperfect it might be instructive to consider whether or not you can come up with a point at which you think your vote matters. If your vote is one of five, is that meaningless because two are on your side and three are not? How about one of 100? One of 10,000? One of 1,000,000? Can you - in a way that isn't arbitrary - come up with a point at which it stops mattering? The fundamental problem is that if one vote doesn't matter, two cannot possibly matter either, and so on. Unless you disagree with very straightforward math, you can clearly see a single vote has some inarguable meaning. At that point you're just haggling on how much meaning it has as an individual, not on whether or not it has meaning. From there we can continue to have a discussion about why you should take this knowledge and vote with it, because regardless of your party affiliation the 2016 election was won with fewer than 100,000 votes. 1/n != 0. On the other hand if you disagree with the basic math I probably can't convince you. But I can at least just tell you you're wrong without as much handwringing. There is no real paradox here. The only problem is that we as humans slip into intuition more than rationality. There is no perspective from which it is irrational to vote. It costs you nothing and can only have upside for your party affiliation. If you disagree we're separated by an axiomatic impasse, not a logical one.
stephen_g 8y ago
This kind of thing pops up in all sorts of different areas in any large society. There are plenty of things that don't make much difference if a few people do them, but make all the difference if a lot of people do or don't. But in my area at least, votes do occasionally come down to a couple of dozen votes. I'm not in the US though and we don't really have gerrymandering, nor do we have anyone trying to disenfranchise on racial or class grounds - (in fact, here voting is compulsory!).

throwawaymath 8y ago

From a mathematical perspective it's pretty silly to claim your vote doesn't matter just because it's not the tie breaking vote. You should give this a read: https://www.skishore.me/voting.html https://www.skishore.me/voting.html. Frankly this viewpoint has always puzzled me. Your specific claim that a vote almost certainly doesn't matter because elections don't come down to a single vote seems...unsupported, to put it politely. It might be more intuitively attractive to say your vote doesn't matter if you're not in a swing election, but it's not rigorously defensible. It's incorrect. It's like saying 4 and 5 are the same thing because they're both significantly smaller than 100,000. No, they're materially different quantities. If more people accepted this straightforward and uncontroversial truth - and acted on it - then more change might actually be effected. Instead this becomes a self-fulfilling and self-defeating prophecy with no rational basis. It's lazy cynicism, to put it bluntly.

matt-attack 8y ago
Bit logically where was he wrong? It seems like a bit of a paradox to me. You keep say it’s wrong but can you point out exactly where his reasoning is wrong? My vote yesterday simply didn’t change any of the outcomes. That is a fact. None of the races were won by a single vote.
- glastra 8y ago
  Or maybe it did, if you voted for the winning side. What if you ordered the winning votes and losing votes randomly, side by side, and eliminated pairs of opposing votes. You would be left with a set of winning votes, cast by individual people. You could attribute the victory to exactly those people. Now, to extrapolate this to all of the winning voters, simply "sample" reorderings, or average it, and you have a spread responsibility amongst all those people who voted for the winning candidate/party. In other words, votes cast for the winning side did decide the result, because of their collective behaviour. The effect of a single vote can be defined in statistical terms as being interdependent with the rest of the votes in the same direction. This means any winning vote cannot be said to lack all effect, meaning or power. If the vote is not without effect, then it must have some effect, albeit not absolute. Another way to look at this is that if the voting is won by a difference of exactly one vote, whose vote was it anyway? You would spread the responsibility of turning the election equally amongst all voters for that side. If we wanted to somehow quantify the "contribution" to winning that each vote has, we have to take into account how many votes were actually required to win. Let X be the number of votes in the winning side and Y in the losing side. Of all the X votes in the winning side, only Y+1 were actually necessary to win. So the contribution of each voter could be (Y + 1)/X, which is always <= 1 as Y + 1 <= X, measured in "decisive votes per person", or something along those lines. So if the voting is won by exactly one vote, all votes in the winning side are decisive: without any one of them, the voting would not be won. If, however, everyone voted for the same side, it would be 1/X, where you could remove all but one vote and still be short of removing a whole "decisive vote".
- throwawaymath 8y ago
  I pointed out the error in reasoning. You are repeating the intuitive heuristic, which is that a single vote doesn't change outcomes. I'll try to explain my point more fully, but there isn't much more ground to cover here. glastra made a good sibling comment covering the basic probabilistic points, so I'll try a different direction. If your bar for voting to have meaning is that your individual vote will change outcomes, you'll find that not a single model of democracy (much less implementation) is satisfying. That's an impossible, nonsensical bar. You can't possibly hope to swing a state to your party if everyone on the underdog side stays home because it seems unlikely to happen. Your vote has meaning even if you weren't personally the arbiter of political change. Aggregates are defined by their constituent parts. You're acting as though voting is worthless if your cause doesn't receive enough votes to pass a cutoff point. It's true that it won't pass, but that doesn't mean the vote didn't matter. Apply this model of thinking elsewhere: if you made 2 points in a basketball game and your team lost, were those 2 points meaningless just because you didn't win? Should you recuse yourself from playing because it's unlikely your team can win? How about raising money for a Kickstarter - was it a waste of time just because you didn't raise the goal and won't receive the funds? Should you not try to raise money and find as many donors as you can, just because there's a minimum cutoff for payout? Since analogies are imperfect it might be instructive to consider whether or not you can come up with a point at which you think your vote matters. If your vote is one of five, is that meaningless because two are on your side and three are not? How about one of 100? One of 10,000? One of 1,000,000? Can you - in a way that isn't arbitrary - come up with a point at which it stops mattering? The fundamental problem is that if one vote doesn't matter, two cannot possibly matter either, and so on. Unless you disagree with very straightforward math, you can clearly see a single vote has some inarguable meaning. At that point you're just haggling on how much meaning it has as an individual, not on whether or not it has meaning. From there we can continue to have a discussion about why you should take this knowledge and vote with it, because regardless of your party affiliation the 2016 election was won with fewer than 100,000 votes. 1/n != 0. On the other hand if you disagree with the basic math I probably can't convince you. But I can at least just tell you you're wrong without as much handwringing. There is no real paradox here. The only problem is that we as humans slip into intuition more than rationality. There is no perspective from which it is irrational to vote. It costs you nothing and can only have upside for your party affiliation. If you disagree we're separated by an axiomatic impasse, not a logical one.

stephen_g 8y ago

This kind of thing pops up in all sorts of different areas in any large society. There are plenty of things that don't make much difference if a few people do them, but make all the difference if a lot of people do or don't. But in my area at least, votes do occasionally come down to a couple of dozen votes. I'm not in the US though and we don't really have gerrymandering, nor do we have anyone trying to disenfranchise on racial or class grounds - (in fact, here voting is compulsory!).