11 ms·

Your odds of swinging the election with your vote are 1 in 100 million This assumption doesn't make sense

three14 16y ago
For a presidential election, you think this estimate is too high?
ghurlman 16y ago
It makes sense... it's just wrong. The odds that your vote is the last one counted in a 100M vote election is 1 in 100 million. The odds that the election would be decided by a single vote have not been considered.
pradocchia 16y ago
The rational voter never votes. At best he spends his effort convincing other people to vote a certain way, persuading others that their vote does indeed count, all the while knowing his own vote doesn't. If he participates at all, he does so as demagogue and charlatan.
yummyfajitas 16y ago
There are 100 million votes, one of which decided the election (the N+1'th vote on the winning side, assuming N votes on the losing side). If you prefer, you can play with binomial distributions to calculate P(side X wins with N votes && side X wins with N-1 votes) [1]. Using the normal approximation and ignoring the normalization prefactor (an overestimate) exp[(n(p-0.5)^2 / 1(np(1-p))] odds of having your vote matter. For p=0.501 (i.e., voters are split 50.1%, 49.9%), that works out to about 10^{-87}. For p=0.51, double floats are incapable of representing a number that small. I stand by my statement. Your vote doesn't matter. [1] Conceptually, this is slightly different from computing the odds that you cast the deciding vote, but I realize it is more useful from a decision theoretic perspective.
- jpwagner 16y ago
  There's no point in putting it to "hard numbers" if you make terribly impractical guesstimates.
  - yummyfajitas 16y ago
    Please explain which of my approximations you believe changes my results significantly. (By "significantly", I mean "increases the odds of your vote mattering to a number greater than, say, 10^{-86}. )
    - jpwagner 16y ago
      I can't help you clean up the calculations because the entire premise that the probability of "your vote mattering" times your potential financial gain from one candidate over another gives any reasonable estimate of utility of a vote is absurd.
      - yummyfajitas 16y ago
        It doesn't have to be financial gain - it can be altruistic gain from policy choices. As I said in another post, if you personally would be willing to spend $50k to legalize gay marriage (for example), you can replace $50k of financial gain by $50k worth of utility derived from helping others.
- simonft1 16y ago
  It varies by state. [0][1] [0] http://redbluerichpoor.com/blog/2008/10/what-is-the-probability-your-vote-will-make-a-difference/ http://redbluerichpoor.com/blog/2008/10/what-is-the-probabil... [1] http://www.stat.columbia.edu/~gelman/research/published/probdecisive2.pdf(pdf) http://www.stat.columbia.edu/~gelman/research/published/prob...

For a presidential election, you think this estimate is too high?

It makes sense... it's just wrong. The odds that your vote is the last one counted in a 100M vote election is 1 in 100 million. The odds that the election would be decided by a single vote have not been considered.

pradocchia 16y ago

The rational voter never votes. At best he spends his effort convincing other people to vote a certain way, persuading others that their vote does indeed count, all the while knowing his own vote doesn't. If he participates at all, he does so as demagogue and charlatan.

yummyfajitas 16y ago

There are 100 million votes, one of which decided the election (the N+1'th vote on the winning side, assuming N votes on the losing side). If you prefer, you can play with binomial distributions to calculate P(side X wins with N votes && side X wins with N-1 votes) [1]. Using the normal approximation and ignoring the normalization prefactor (an overestimate) exp[(n(p-0.5)^2 / 1(np(1-p))] odds of having your vote matter. For p=0.501 (i.e., voters are split 50.1%, 49.9%), that works out to about 10^{-87}. For p=0.51, double floats are incapable of representing a number that small. I stand by my statement. Your vote doesn't matter. [1] Conceptually, this is slightly different from computing the odds that you cast the deciding vote, but I realize it is more useful from a decision theoretic perspective.

jpwagner 16y ago
There's no point in putting it to "hard numbers" if you make terribly impractical guesstimates.
- yummyfajitas 16y ago
  Please explain which of my approximations you believe changes my results significantly. (By "significantly", I mean "increases the odds of your vote mattering to a number greater than, say, 10^{-86}. )
  - jpwagner 16y ago
    I can't help you clean up the calculations because the entire premise that the probability of "your vote mattering" times your potential financial gain from one candidate over another gives any reasonable estimate of utility of a vote is absurd.
    - yummyfajitas 16y ago
      It doesn't have to be financial gain - it can be altruistic gain from policy choices. As I said in another post, if you personally would be willing to spend $50k to legalize gay marriage (for example), you can replace $50k of financial gain by $50k worth of utility derived from helping others.
simonft1 16y ago
It varies by state. [0][1] [0] http://redbluerichpoor.com/blog/2008/10/what-is-the-probability-your-vote-will-make-a-difference/ http://redbluerichpoor.com/blog/2008/10/what-is-the-probabil... [1] http://www.stat.columbia.edu/~gelman/research/published/probdecisive2.pdf(pdf) http://www.stat.columbia.edu/~gelman/research/published/prob...