

What is the probability your vote will make a difference?  [pdf] - yarapavan
http://www.stat.columbia.edu/~cook/movabletype/mlm/probdecisive.pdf

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gjm11
This paper focuses specifically on US presidential elections, though the broad
principles are applicable to other elections.

One of the authors is Nate Silver (of fivethirtyeight.com), who has probably
spent as much time doing statistics on US presidential election results as
just about anyone else in the world. Another is Andrew Gelman, who's no slouch
either. Academically he's got way more depth than Nate Silver, but he isn't as
focused on elections. Authors Gelman and Edlin wrote a paper about why it
might be rational (in utility-maximizing terms) to vote that's famous enough
that I've read it (which isn't necessarily very famous).

One-sentence summary (though the whole thing is only 9 pages long and not
terribly scary): in a US election, your chance of deciding the election if you
vote ranges from about 1 in 10^7 in swing states to about 1 in 10^10 or less
in very one-sided states. The average vote, in some sense, has about one
chance in 60 million of being decisive.

~~~
diN0bot
the next statistic i want to see is the number of people effected by political
advertisements...or say this paper.

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mattmaroon
This fails to take into account margins of error. An election won by one vote
would result in suits over the count being within the margin of error. In some
states any result within a certain margin is decided by other means, including
runoffs or even coin flips (though I'm not sure how this would apply in the
case of a federal election).

The hubbub over Coleman vs. Franken showed its not as simple as guy wins by 1
vote, gets elected.

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lifeisstillgood
Voting is like innoculation.

I do not merely vote for a 'mainstream' candidate to ensure that my choice
gets in. I also vote so that 'extreme' candidates are excluded. A vote for a
mainstream candidate is an innoculation for society against extremist
diseases.

It is vanishingly unlikely that my vote will be at the exact tipping point, ie
a hanging chad county in Florida. It is also unlikely that my innoculation
against killer flu will be the one innocluation that stops the spread of the
virus. But from society's point of view it does not matter - the more who are
innoculated, the safer society is.

Similarly, the more people who vote the more candidates need to pander to the
mainstream opinion, not the extremist. In general we become safer.

This all breaks down if mainstream opinion is actually 'wrong'. But thats a
different issue.

PS

Here in the UK the fascist BNP have got two MEPs and will be controversially
appearing on a wellknown politics talk show. Innoculations need to be kept up.

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MarkPNeyer
The assumption they make is that the payoff for voting on a decision is
linearly proportional to the number of people the decision affects.

In my case, that's not true - i don't get utility from telling other people
what to do. Quite frankly, the assumption that people enjoy telling others
what to do scares me. I'd like to think it isn't true, but something tells me
that's just idealism.

~~~
camccann
It's not about _you_ telling other people what to do, it's about picking
_someone else_ who will be telling people what to do. Nothing you do will
change the fact that _somebody_ will be selected; all you can do is influence
the choice. Unless all candidates are (by your evaluation) of equal merit,
voting for the one you prefer is (disregarding any costs of participation)
pretty much by definition going to influence how much utility you get. And,
unless you assign nonlinear utility (or none at all) to the experiences of
other people, the number of people impacted is obviously going to be, in the
limit, linearly proportional to the utility payoff.

Gratuitous example: Political Candidate X runs on a platform that he will
indefinitely imprison and torture 0.1% of the population, but only people that
you personally have never (and will never meet). His opponent, Candidate Y,
runs on a platform of doing absolutely nothing in office. How does the utility
of voting for Candidate Y differ depending on whether the relevant population
is a thousand people, or ten million?

