Bringing up the Coleman/Franken election reminds me of my particular pet peeve. When the margin of victory is less than the margin of error, it's impossible to know the will of the people. One hundredth of one percent is not within any reasonable margin of error.
Sure, and in scenarios like that, perhaps the best thing to do is to flip a coin.
Instead of going to all the expense of flipping a coin, though, you could just take the person who seemed to get the most votes (after you've counted them all really hard to make sure you're within the margin of error). Just an arbitrary rule, no biggie.
Or have a runoff election, or have instant-runoff voting. Having elections determined by real or statistical coin-flips undermines the (important) story of self-rule.
I'm confused by your reply. The grandparent comment was saying "You should never flip a coin", the person you replied to said (roughly) "It's impossible to avoid all situations where you can't measure the winner, you have to either flip a coin or just take the person who happened to come out ahead in the vote count".
Your link to a place where they used a coin flip isn't disagreeing with him (nor really the grandparent, who wasn't claiming that you can't use a coinflip, but rather that you shouldn't use a coinflip).
In the end, if one candidate got 100,000 votes and the other got 100,001 then to the extent that we randomly select between the two I'm not sure that it really makes a difference which one wins. In this case the will of the people is that the two candidates are equally good.
"The greatest value of free elections is in all of the out-of-equilibrium outcomes that, because of the regularity of free elections, never come close to happening."
In this case the will of the people is that the two candidates are equally good
That's a very positive way to look at it. The problem of reduced legitimacy persists, though. The disgruntled Coleman supporters will probably always have a sneaking suspicion that the election was stolen from them, which tends to poison actual discourse.
Yeah, we aren't willing to admit it, but every voting system has a margin of error. Even 1 in a thousand voters will have problems with completely unambiguous questions.
I applaud your statistical sensibility, but I have a question – you're specifically looking for the margin of victory to be bellow the margin of error – but the margin of error of what, exactly?
Are you expecting the vote to be a proxy for the entire population of the country/state/whatever? Perhaps the entire population of eligible voters? Or, do you view it as simply the preference of those who took the time to vote?
Personally, I see little harm in disregarding the intentions of those who could vote but choose to not vote.
Issues of systemic inequalities in access to voting aside, I have little problem with viewing an election the task of accurately counting the votes of those who actually made it to the poling place. If you accept that concept, then the margin of error is extremely low – especially with electronic voting systems.
You're right. But for 3,000,000 votes cast, the margin of error is about 6 hundredths of one percent. At the 99% confidence level, it's .074% variance.
The margin of error of a poll is the margin of error at the 95% confidence level (two sigma). The standard "margin of error" when you are talking about polls.
In reality, you should apply a finite population correction, which would make the "margin of error" a bit smaller if you get a substantial percentage of the population voting:
