Voting irregularities, proper registration and showing identification at the polls have been growing concerns in recent elections. But here's a case where astronauts at the International Space Station today were able to cast their votes long distance. It makes for absolutely no excuse for those of us here on Earth not to cast our votes today.
Courtesy Theresa Thompson
Winston Churchill once quipped, "democracy is the worst form of government, except for all the others." Though said tongue-in-cheek, a recent article in New Scientist shows that, mathematically at least, Winnie was on to something.
Every election has winners and losers. Different countries have different systems for determining the winners, and dealing with the losers. And, it turns out, each of those systems has mathematical quirks which prevent the results from perfectly matching the will of the people.
In 1963, American economist Kenneth Arrow considered all these quirks and tried to describe the perfect voting system. He then proved that it was mathematically impossible. (Of course, this assumes the system he described really is perfect--I'm not so sure.)
It seems to me, though, that the problem isn't with democracy, but rather with representative democracy. The people of Minnesota elect only one governor, only one senator (at a time). And there's no way one person is going to perfectly reflect public opinion--be 53% in favor of issue A and 61% opposed to issue B. And even if they were, they still have to make a series of yes-or-no decisions, and be either 100% for 100% against any given bill.
The only way to have a perfect democracy is to have everybody vote on every issue, a system that would be far too cumbersome to work. Churchill was right: democracy is messy, but it's the best thing we've got.
So, I open up my web browser this weekend to check the news, and I see the following three polls, all on the same page:
These can’t all be right, can they?
Actually, they can. Or, at least, they can all be properly conducted, and just lead to wildly different results.
The only way to get a perfect result is to interview everyone in the country. (In fact, that’s exactly what we do on Election Day.) But that takes so much time and money that no individual pollster can do it. Instead, they interview several hundred people, maybe a couple thousand, and from there extrapolate what the country as a whole will do.
Now, mathematically, you can do this. You just can’t be sure of your answer. Here are a few of the reasons why.
Margin of error
Most opinion polls will state the margin of error. For example, they may say that that Candidate X is ahead by, say, 5 points, with a margin of error of plus-or-minus 3 points. Meaning, the real answer could be as high as 8 points or as low as 2 points.
(Sometimes, the margin of error is actually larger than the result. The poll shows Candidate X leading by 2 points, but with a margin of error of 4 points. Meaning, he could be ahead by 6, or he could actually be behind by 2! This seems to have happened a lot this year.)
A range of a few percentage points, when applied to a country with over 100 million voters, can lead to some pretty huge differences.
In addition to reporting a margin of error, polls also report a confidence interval, usually 90% or 95%. This means that, according to the laws of mathematics, there is a 95% probability that the real result is the same as the poll result, within the margin of error.
But what about the other 5% or 10% of the time? Well, the folks reporting the numbers don’t like to tell you this, but, mathematically speaking, the poll can do everything right, and still be completely wrong, as much as 10% of the time.
There have been over 700 polls released this election season, and over 200 just in October. No doubt, many of the polls you have heard about fall into this category.
In most elections, more women vote than men. If you conduct a survey and talk to 100 men and 100 women, you are going to have to give the women’s answers more weight to accurately reflect the Election Day results.
How much more weight? That depends. Do you think this election will be pretty much the same as previous years? Is there something happening this year that will make a lot more women come out to vote? Or, perhaps, something that will attract a lot more men?
The fact is, nobody knows. Weighting is just educated guesswork. And this year, it is more complicated than usual:
The different weighting factors used by the different polls probably accounts for most of the variability we see in the results.
Let’s face it – humans are complicated and sometimes uncooperative beings. There are lots of ways they can foul up a perfectly good poll.
So, with all these problems, how can we figure out who is going to win the election? Well, never fear – there is one sure-fire way to find out the winner:
Read the newspaper Wednesday morning.
And don’t forget to vote!
On November 4, America will go to the polls and choose its next president. But we do not vote for the president directly. Rather, we vote for electors to represent our state in the Electoral College, and they ultimately choose the president.
By a strange quirk of math, voting in an indirect, divided election such as this actually gives vote4rs more power than if we voted in a direct election. The best way to explain is through an example:
So, your favorite candidate needs only about half as many votes to win a divided election as they would to win a direct election. Which means your vote has the potential to be worth almost twice as much!
But what if you don’t live in one of the ten biggest states? That’s OK—those states almost always split between the major candidates, so that voters in other states also become crucial to winning the election.
It is true that under the Electoral College system, there are years when your vote doesn’t matter at all. But in the years that it does matter, it matters so much that, on average, you still come out ahead.
We recently put together a web exhibit to demonstrate this phenomenon. It includes an interactive calculator that allows you to change the voting populations of states and see how this affects voting power.