No that’s not how this works. We are calculating the expected value of a vote. The expected value is more than just “best case—worst case”. You factor in all possibilities weighted by their probability.
As long as the probability you are voting for the correct candidate is higher than 50%, the expected value of a vote is positive. And obviously it’s impossible to get odds worse than that, for a binary decision. You can then multiply the probability you are voting for the correct candidate by the expected value of a correct vote, and it’s likely to still be worth your time to vote.
Robin Hanson is a bit more conservative and believes the expected value of a vote is only positive if you are more informed than the average voter, and otherwise you should abstain. That’s still not a very high bar to pass. The average voter is not terribly informed.
What this entire discussion has been about, is that even if you vote for the correct candidate, is the expected value of a vote really that high? OP demonstrated an upper limit for the expected value of a correct vote. I am simply arguing that even if his estimate is off by orders of magnitude, it’s still large.
This makes it worthwhile to 1) take the time to vote, if you thought it was a waste of time. And 2) do more research on the candidates and become a more informed voter, which increases your odds of voting for the correct candidate. And 3) spend effort trying to get other people to do the same.
There is a pervasive attitude at Lesswrong and related communities that all politics is a waste of time. I think this calculation, even if a bit naive and imperfect, demonstrates it might not be so.
That’s impossible. You can’t have less than 50% confidence on a binary decision. You can’t literally believe that a coin flip is more likely to select the correct option than you.
Huh? Of course you can. People consistently make worse-than-random choices all the time. Especially in an information-abusive environment such as casinos, advertising, or politics.
In fact, this entire post and concept is based on the idea that without you, the voting populace would make the wrong binary decision.
It is possible to have a less than 50% track-record regarding binary decisions. However, I am doubtful that anyone could reasonably say about any particular binary decision that he/she has a less than 50% confidence in his/her choice. If he/she really thought that, then the thing to to would be to make the opposite choice at which point he/she would have a greater than 50% confidence in that particular choice.
What do you mean you can’t have less than 50% confidence in a decision? The whole idea of expected value is that you can be less than 50% sure that something will have positive consequences, and do it anyway. In this very post the idea is that your vote is almost certainly worthless, but there is a very small chance of a very large effect, and therefore you should vote anyway. But you are much less than 50% sure it will have any positive effect at all. So likewise you can be much less than 50% sure your candidate is the right one.
If you really believe your candidate is less than 50% likely to be the “correct” candidate, you can just vote for the other one. Then you will necessarily have a >50% confidence you voted for the correct candidate. You can’t possibly do worse on a binary decision.
You could vote for the other one, but you might not want to, say e.g. that almost all your friends think that the person is the correct candidate.
Also, when you think of the sentence, “my candidate is less than 50% likely to be the correct candidate,” you are likely to dislike that assertion, and to start thinking of reasons for saying that they are more than 50% likely to be the correct candidate.
You are mistaken. My choices are not to vote for candidate A or to vote for candidate B. My choices are to vote for candidate A, for candidate B, to write in somebody (e.g. Cthulhu), and to not vote at all.
From whose point of view? From my own personal perspective there might well be a noticeable difference in utility between writing in Cthulhu and just avoiding the voting station.
In any case, since there are at least three alternatives, one of them does not necessarily have to have >50% confidence.
The fact that you count it as not voting does not mean it is in fact not voting, and it especially does not mean that the person is choosing not to vote (they are not choosing that unless they think they are not voting.)
Well, suppose I think the probability that Johnson would be the best president is 40%, the probability that Clinton would be is 30%, that Stein would be is 20%, and that Trump would be is 10%...
In a first past the post election third parties are irrelevant.
More specifically, the calculations above apply to a close election. 538 gives Johnson a less than 0.01% chance of winning. Obviously the probability of you being the tie breaking vote is many many orders of magnitude smaller than is worth calculating.
Third parties aren’t stable. They can appear, but they inevitably split the vote. They always hurt their cause more than help it. Unless they are so popular they can outright replace one of the parties.
There is a pervasive attitude at Lesswrong and related communities that all politics is a waste of time. I think this calculation, even if a bit naive and imperfect, demonstrates it might not be so.
I think the naivety and imperfections make it useless as a demonstration of this. Taking such ridiculous estimates of the difference between candidates and your level of knowledge about those differences (and especially the difference between you and the median voter you’re hoping to override) makes me doubt the seriousness of the calculation, and makes it impossible to make decisions based on.
Heck, the range of possibilities between “$hundreds of thousands to charity (not mentioned: and many millions to non-charity cronies of the winner)” and “worth your time to vote”, even if we discount the “negative value if you’re wrong” option (which is real, but probably only reduces EV for this group rather than making it net negative) is enough to show that people making monetary EV arguments are on the propaganda side rather than the truth side of the calculation.
Are you referring to OP or me? I don’t think my estimate of the difference between candidates is ridiculous. It’s pretty clear the president can have a massive impact on the world. So large that, even when multiplied by a 1 in 10 million probability, it’s still worth your time to vote.
Using dollar amounts might be a bit naive. Instead look at utility directly, perhaps some estimate like QALYs. I think something like health care reform alone has the potential to be worth tens of millions of QALYs. A major war or economic depression can easily cost similar amounts.
And again this is just the scenario where you are the tiebreaking vote. I think there is something to be said for the value of voting that goes beyond just the likelihood of being a tiebreaker. For instance, consider all the people that think similar to how you do. If you decide to not vote, they will also decide to not vote. So your decision to vote can still change the election, in a sort of acausal way.
“Even if the lower limit is 2 orders of magnitude lower,”
The lower limit is the negative of the upper limit, since your political opinions may be mistaken.
No that’s not how this works. We are calculating the expected value of a vote. The expected value is more than just “best case—worst case”. You factor in all possibilities weighted by their probability.
As long as the probability you are voting for the correct candidate is higher than 50%, the expected value of a vote is positive. And obviously it’s impossible to get odds worse than that, for a binary decision. You can then multiply the probability you are voting for the correct candidate by the expected value of a correct vote, and it’s likely to still be worth your time to vote.
Robin Hanson is a bit more conservative and believes the expected value of a vote is only positive if you are more informed than the average voter, and otherwise you should abstain. That’s still not a very high bar to pass. The average voter is not terribly informed.
What this entire discussion has been about, is that even if you vote for the correct candidate, is the expected value of a vote really that high? OP demonstrated an upper limit for the expected value of a correct vote. I am simply arguing that even if his estimate is off by orders of magnitude, it’s still large.
This makes it worthwhile to 1) take the time to vote, if you thought it was a waste of time. And 2) do more research on the candidates and become a more informed voter, which increases your odds of voting for the correct candidate. And 3) spend effort trying to get other people to do the same.
There is a pervasive attitude at Lesswrong and related communities that all politics is a waste of time. I think this calculation, even if a bit naive and imperfect, demonstrates it might not be so.
“As long as the probability you are voting for the correct candidate is higher than 50%,”
The probability may be lower than 50%, so my statement stands as it is.
That’s impossible. You can’t have less than 50% confidence on a binary decision. You can’t literally believe that a coin flip is more likely to select the correct option than you.
Huh? Of course you can. People consistently make worse-than-random choices all the time. Especially in an information-abusive environment such as casinos, advertising, or politics.
In fact, this entire post and concept is based on the idea that without you, the voting populace would make the wrong binary decision.
It is possible to have a less than 50% track-record regarding binary decisions. However, I am doubtful that anyone could reasonably say about any particular binary decision that he/she has a less than 50% confidence in his/her choice. If he/she really thought that, then the thing to to would be to make the opposite choice at which point he/she would have a greater than 50% confidence in that particular choice.
What do you mean you can’t have less than 50% confidence in a decision? The whole idea of expected value is that you can be less than 50% sure that something will have positive consequences, and do it anyway. In this very post the idea is that your vote is almost certainly worthless, but there is a very small chance of a very large effect, and therefore you should vote anyway. But you are much less than 50% sure it will have any positive effect at all. So likewise you can be much less than 50% sure your candidate is the right one.
If you really believe your candidate is less than 50% likely to be the “correct” candidate, you can just vote for the other one. Then you will necessarily have a >50% confidence you voted for the correct candidate. You can’t possibly do worse on a binary decision.
You could vote for the other one, but you might not want to, say e.g. that almost all your friends think that the person is the correct candidate.
Also, when you think of the sentence, “my candidate is less than 50% likely to be the correct candidate,” you are likely to dislike that assertion, and to start thinking of reasons for saying that they are more than 50% likely to be the correct candidate.
You are confusing “confidence” and “the probability you are voting for the correct candidate”. These are quite different things.
From your subjective view the expected value of a vote is always positive. That does not mean that it’s actually positive—see Cromwell.
Yes, from your subjective view your vote is always positive. Thus you should always vote.
You are mistaken. My choices are not to vote for candidate A or to vote for candidate B. My choices are to vote for candidate A, for candidate B, to write in somebody (e.g. Cthulhu), and to not vote at all.
No, the choice is to vote for your preferred candidate, or to not vote. Write ins count as “not voting”.
From whose point of view? From my own personal perspective there might well be a noticeable difference in utility between writing in Cthulhu and just avoiding the voting station.
In any case, since there are at least three alternatives, one of them does not necessarily have to have >50% confidence.
The fact that you count it as not voting does not mean it is in fact not voting, and it especially does not mean that the person is choosing not to vote (they are not choosing that unless they think they are not voting.)
Well, suppose I think the probability that Johnson would be the best president is 40%, the probability that Clinton would be is 30%, that Stein would be is 20%, and that Trump would be is 10%...
In a first past the post election third parties are irrelevant.
More specifically, the calculations above apply to a close election. 538 gives Johnson a less than 0.01% chance of winning. Obviously the probability of you being the tie breaking vote is many many orders of magnitude smaller than is worth calculating.
*Looks at the UK*
Are they, now?
Third parties aren’t stable. They can appear, but they inevitably split the vote. They always hurt their cause more than help it. Unless they are so popular they can outright replace one of the parties.
Huh? You mean for their cause it’s better to just curl up and die, but refusing to do so subverts their cause..?
Basically yes. First Past The Post does not satisfy the criteria Independence of Irrelevant Alternatives.
Looking at reality (as opposed to theoretical abstractions), this does not seem to be true.
I think the naivety and imperfections make it useless as a demonstration of this. Taking such ridiculous estimates of the difference between candidates and your level of knowledge about those differences (and especially the difference between you and the median voter you’re hoping to override) makes me doubt the seriousness of the calculation, and makes it impossible to make decisions based on.
Heck, the range of possibilities between “$hundreds of thousands to charity (not mentioned: and many millions to non-charity cronies of the winner)” and “worth your time to vote”, even if we discount the “negative value if you’re wrong” option (which is real, but probably only reduces EV for this group rather than making it net negative) is enough to show that people making monetary EV arguments are on the propaganda side rather than the truth side of the calculation.
Are you referring to OP or me? I don’t think my estimate of the difference between candidates is ridiculous. It’s pretty clear the president can have a massive impact on the world. So large that, even when multiplied by a 1 in 10 million probability, it’s still worth your time to vote.
Using dollar amounts might be a bit naive. Instead look at utility directly, perhaps some estimate like QALYs. I think something like health care reform alone has the potential to be worth tens of millions of QALYs. A major war or economic depression can easily cost similar amounts.
And again this is just the scenario where you are the tiebreaking vote. I think there is something to be said for the value of voting that goes beyond just the likelihood of being a tiebreaker. For instance, consider all the people that think similar to how you do. If you decide to not vote, they will also decide to not vote. So your decision to vote can still change the election, in a sort of acausal way.
Yes. This is quite an important point.