About 1 in 60 million for the average American voter on the last presidential election day. Was the total difference between your favorite candidate and the other one, divided by 60 million, worth your time and effort? Quite possibly. At the very least it seems absurd to say it definitely wasn’t worth your time.
If 1⁄6000000 seems like worth it to you, I would suggest spending much less time and effort buying lottery tickets and after winning (here in Brazil the odds are 1 to 52 million) invest your money in financing SIAI or whatever you think makes a difference....
You’ve also got to consider the size of the outcome. Winning a lottery gives you, what, a few hundred thousand to a few million dollars? The expected value of buying a lottery ticket is then around 2 cents- less than the price of a lottery ticket, and so buying is a terrible decision.
Elections have much larger impacts. The 2000 election is a classic example: it’s been argued that Gore would not have invaded Iraq, and that the Iraq invasion has cost around a trillion dollars; in that case, your vote has an expected value to the US of around 16,000 USD. (More if you live in a swing state, more if you believe Gore would have been better in other ways. Less otherwise.)
Not that I’m saying that this is a closed question- in fact, my point is that it isn’t.
Note that you also have to consider how certain it is that your preferred candidate really is better. And since the division of opinion is usually 50⁄50 or so, unless you are extremely overconfident, it is quite uncertain that your candidate is better. So you need do multiply the benefit not only by the probability that you will cause your candidate to win, but also by the probability that your candidate is better, and then you have to subtract the disutility in the case that your candidate turns out to be worse.
Note that the probability in general that an electoral system using something like the electoral college increases the chance for everyone that they will be the deciding vote assuming that no voting area is extremely in the direction of one candidate. To see this with a small example, consider the toy example of 9 people with three states each of three people with an election for two candidates.. If the election is by popular vote then the only way your vote matters is if exactly four of the people vote for one candidate and exactly four vote for the other. But, if you use the states then your vote breaks a tie whenever the other two states disagree and your state has a 1-1 for the other two voters. That’s a much larger set of circumstances. This applies in general although the math to show it becomes a bit uglier when one has many different states of different sizes.
Agree with your point. But notice that if we consider the case in which you actually win, which would be GuySrinivasan’s proposal, then those 4 millions you win in the lottery could be invested in things that will have much greater proportional impact, for you’d be investing in the curve’s tail....
Just a reminder. The post is NOT about politics and voting. It is about overdetermination and decision theory.
A probability of 1 in 10 million is tiny but, as discussed by Edlin, Gelman, and Kaplan (2007), can provide a rational reason for voting; in this perspective, a vote is like a lottery ticket with a 1 in 10 million chance of winning, but the payoff is the chance to change national policy and improve (one hopes) the lives of hundreds of millions, compared to the alternative if the other candidate were to win.
(it was 1 in 10 million in New Mexico, Virginia, New Hampshire, and Colorado)
If you want to make a post about overdetermination, I’d say don’t use the voting example, since here’s one person at the very least who thinks the example’s far from clear-cut. The movies thing is fine—the probability enough people go to ruin everyone’s experience times the experience ruined is still tiny, not plausibly large.
What is the probability your vote will make a difference?
About 1 in 60 million for the average American voter on the last presidential election day. Was the total difference between your favorite candidate and the other one, divided by 60 million, worth your time and effort? Quite possibly. At the very least it seems absurd to say it definitely wasn’t worth your time.
Tim Gowers has a blog post about the expected value of voting:
http://gowers.wordpress.com/2010/05/03/is-the-british-voting-system-fair/
If 1⁄6000000 seems like worth it to you, I would suggest spending much less time and effort buying lottery tickets and after winning (here in Brazil the odds are 1 to 52 million) invest your money in financing SIAI or whatever you think makes a difference....
You’ve also got to consider the size of the outcome. Winning a lottery gives you, what, a few hundred thousand to a few million dollars? The expected value of buying a lottery ticket is then around 2 cents- less than the price of a lottery ticket, and so buying is a terrible decision.
Elections have much larger impacts. The 2000 election is a classic example: it’s been argued that Gore would not have invaded Iraq, and that the Iraq invasion has cost around a trillion dollars; in that case, your vote has an expected value to the US of around 16,000 USD. (More if you live in a swing state, more if you believe Gore would have been better in other ways. Less otherwise.)
Not that I’m saying that this is a closed question- in fact, my point is that it isn’t.
Note that you also have to consider how certain it is that your preferred candidate really is better. And since the division of opinion is usually 50⁄50 or so, unless you are extremely overconfident, it is quite uncertain that your candidate is better. So you need do multiply the benefit not only by the probability that you will cause your candidate to win, but also by the probability that your candidate is better, and then you have to subtract the disutility in the case that your candidate turns out to be worse.
In other words, don’t vote.
Note that the probability in general that an electoral system using something like the electoral college increases the chance for everyone that they will be the deciding vote assuming that no voting area is extremely in the direction of one candidate. To see this with a small example, consider the toy example of 9 people with three states each of three people with an election for two candidates.. If the election is by popular vote then the only way your vote matters is if exactly four of the people vote for one candidate and exactly four vote for the other. But, if you use the states then your vote breaks a tie whenever the other two states disagree and your state has a 1-1 for the other two voters. That’s a much larger set of circumstances. This applies in general although the math to show it becomes a bit uglier when one has many different states of different sizes.
Agree with your point. But notice that if we consider the case in which you actually win, which would be GuySrinivasan’s proposal, then those 4 millions you win in the lottery could be invested in things that will have much greater proportional impact, for you’d be investing in the curve’s tail....
Just a reminder. The post is NOT about politics and voting. It is about overdetermination and decision theory.
A quote from the linked article:
(it was 1 in 10 million in New Mexico, Virginia, New Hampshire, and Colorado)
If you want to make a post about overdetermination, I’d say don’t use the voting example, since here’s one person at the very least who thinks the example’s far from clear-cut. The movies thing is fine—the probability enough people go to ruin everyone’s experience times the experience ruined is still tiny, not plausibly large.