I think the probability of changing the election is generally underestimated.
The probability distribution of votes approximately follows a bell curve. If you’re ignorant of the election, it peaks at 50%. If there’s a uniform distribution, the expected value of your vote is also the average effect on one citizen if you do make a difference, multiplied by a constant to take into account that not everyone votes. If it peaks at 50%, then that’s a higher probability density than uniform distribution, so you’ll make a bigger difference.
If you’re less lazy, and you look into the expected results, it will get more refined. It might still peak at 50%, but with a much narrower peak, in which case your vote matters orders of magnitude more than before. The much more likely result is that it will peak somewhere else, and have a sharp decline. In this case, your vote matters orders of magnitude less.
As a result, it looks like it’s not worth voting in any given election, but unless you’ve actually done the research, it’s worth voting.
I’m pretty sure I don’t live in a battleground state, which means that I already know I have an extra low probability of making a difference. It still matters a little, since the politicians know they have to cater to the voters to keep winning. In this case, I figure I might as well vote for a third party, since that will make my position more clear. I can only give one bit of feedback if I vote for a major candidate, but I can give two or three by looking at the third parties.
I think the probability of changing the election is generally underestimated.
But the analysis that follows seems to suggest a different conclusion: (1) If you are ignorant, then your subjective probability of changing the outcome is more than people often think, (2) If you aren’t ignorant, then your subjective probability of changing the outcome is very small (but, I note, it is probably comparable to the probabilities estimated by Gelman in the study linked here), and (3) the high-probability case is a bit like that where someone goes into a casino thinking he has a winning system and (correctly, given that belief) estimates a substantial probability of coming out richer.
It seems to me that the “informed” probability is the relevant one here. I’m not sure how to tell whether this is generally overestimated or underestimated; among people who have followed Coscott’s link to Gelman’s paper, I’d guess it’s estimated reasonably well unless Gelman’s analysis is bad.
If you are uninformed, the informed probability is probably low, but it might be high. By conservation of expected evidence, the expected value is always equal to the uninformed probability.
I think the probability of changing the election is generally underestimated.
The probability distribution of votes approximately follows a bell curve. If you’re ignorant of the election, it peaks at 50%. If there’s a uniform distribution, the expected value of your vote is also the average effect on one citizen if you do make a difference, multiplied by a constant to take into account that not everyone votes. If it peaks at 50%, then that’s a higher probability density than uniform distribution, so you’ll make a bigger difference.
If you’re less lazy, and you look into the expected results, it will get more refined. It might still peak at 50%, but with a much narrower peak, in which case your vote matters orders of magnitude more than before. The much more likely result is that it will peak somewhere else, and have a sharp decline. In this case, your vote matters orders of magnitude less.
As a result, it looks like it’s not worth voting in any given election, but unless you’ve actually done the research, it’s worth voting.
I’m pretty sure I don’t live in a battleground state, which means that I already know I have an extra low probability of making a difference. It still matters a little, since the politicians know they have to cater to the voters to keep winning. In this case, I figure I might as well vote for a third party, since that will make my position more clear. I can only give one bit of feedback if I vote for a major candidate, but I can give two or three by looking at the third parties.
But the analysis that follows seems to suggest a different conclusion: (1) If you are ignorant, then your subjective probability of changing the outcome is more than people often think, (2) If you aren’t ignorant, then your subjective probability of changing the outcome is very small (but, I note, it is probably comparable to the probabilities estimated by Gelman in the study linked here), and (3) the high-probability case is a bit like that where someone goes into a casino thinking he has a winning system and (correctly, given that belief) estimates a substantial probability of coming out richer.
It seems to me that the “informed” probability is the relevant one here. I’m not sure how to tell whether this is generally overestimated or underestimated; among people who have followed Coscott’s link to Gelman’s paper, I’d guess it’s estimated reasonably well unless Gelman’s analysis is bad.
If you are uninformed, the informed probability is probably low, but it might be high. By conservation of expected evidence, the expected value is always equal to the uninformed probability.