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 thi...
Cross Posted on my blog, By Way of Contradiction.
Anti-Trigger Warning: There is not really any politics in this post. I doubt it will kill your mind.
If your favorite candidate in an election is a third party candidate, should you vote for him?
This question has confused me. I have changed my mind many times, and I have recently changed my mind again. I would like to talk about some of the arguments in both directions and explain the reason for my most recent change.
Con 1) Voting for a third party is throwing your vote away.
We have all heard this argument before, and it is true. It is an unfortunate consequence of the plurality voting system. Plurality is horrible and there are all better alternatives, but it is what we are stuck with for now. If you vote for a third party, the same candidate would be elected as if you did not vote at all.
Pro 1) The probability that you vote changes the election is negligible. All your vote does is add one to the number of people who voted for a given candidate. Your vote for the third party candidate therefore matters more because it is changing a small number by relatively more.
This argument is actually an empirical claim, and I am not sure how well it holds up. It is easy to study the likelihood that you vote changes the election. One study finds that it roughly varies from 10^-7 to 10^-11 in America for presidential elections. However, it is not clear to me just how much your vote affects the strategies of political candidates and voters in the future.
Pro 2) The probability that your vote changes the election or future elections is negligible. The primary personal benefit for voting is the personal satisfaction of voting. This personal satisfaction is maximized by voting for the candidate you agree with the most.
I think that many people if given the choice between changing the next president between the two primary parties or being paid an amount of money equal to the product of the amount of gas they spent to drive to vote and 10^7 would take the money. I am not one of them but any of those people must agree that voting is a bad investment if you do not consider the personal satisfaction. However, I think I might get more satisfaction out of doing my best to change the election, rather than placing a vote that does not matter.
Con 2) Actually if you use a reflexive decision theory, you are much more likely to change the election, so you should vote like it matters.
Looking at the problem like a timeless decision agent, you see that your choice on voting is probably correlated with that of many other people. You voting for a primary party is logically linked with other people voting for a primary party, and those people whose votes are logically linked with yours are more likely to agree with you politically. This could bring the chance of changing the election out of the negligible zone, where you should be deciding based on political consequences.
Pro 3) Your morality should encourage you to vote honestly.
It is not clear to me that I should view a vote for my favorite candidate as an honest vote. If we used the anti-plurality system where the person with the least votes wins, then a vote for my favorite candidate would clearly not be considered an honest one. The "honest" vote should be the vote that you think will maximize your preferences which might be a vote for a primary party.
Pro 4) Strategic voting is like defecting in the prisoner's dilemma. If we all cooperate and vote honestly, we will get the favorite candidate of the largest number of people. If not, then we could end up with someone much worse.
The problem with this is that if we all vote honestly, we get the plurality winner, and the plurality winner is probably not all that great a choice. The obvious voting strategy is not the only problem with plurality. Plurality also discourages compromise, and the results of plurality are changed drastically by honest vote splitting. The plurality candidate is not a good enough goal that I think we should all cooperate to achieve it.
I have decided that in the next election, I will vote for a primary party candidate. I changed my mind almost a year ago after reading Stop Voting for Nincompoops, but after recent further reflection, I have changed my mind back. I believe that Con 1 is valid, Con 2 and the other criticisms above adequately respond to Pro 1 and Pro 2, and I believe that Pro 3 and Pro 4 are invalid for the reasons described above. I would love to hear any opinions on any of these arguments, and would love even more to hear arguments I have not thought of yet.