The Truth (Damned Truth) of Election Statistics

The year 2004. A multiple of four. That means at least three things. A leap year, the Summer Olympics, and the U.S. Presidential election.

As for leap year, though it certainly applies this year, it actually doesn’t happen every multiple of four — and it isn’t really that big a deal anyway, is it?

Once upon a time, we could have just said that the Olympics take place every four years. Now they hold the Winter Olympics two years after the Summer ones, because they like to spread out the advertising revenue. So instead of something very special every four years, we get something a bit less special every other year.

That leaves the Presidential election. Surely this grand institution isn’t compromised in importance? Surely it’s as meaningful and fateful as everyone think it is?

Benjamin Disraeli said, “There are three kinds of lies: lies, damned lies and statistics.” If statistics isn’t a lie or a damned lie, then maybe there’s some hope for them to occasionally tell some truth. To find out the truth about Presidential elections, let’s look at some numbers. The source is the InfoPlease section on U.S. Elections.

Popularity Contest

Here’s a graph that shows how the popular vote has been distributed in Presidential elections since 1872, the first year in which the popular vote was systematically recorded. The blue line shows what percentage went to the Democrats, the red line shows the Republicans, and the green line shows the combined popular vote for significant third-party candidates.

Popular Vote %s

Even if we didn’t know what we were looking at here, it’d be very easy to see that this graph describes a stable system — two figures cycling around each other, trading places, and staying within a very particular range of values, right around the middle of the graph. So it’s a basic feature of the U.S. Presidency that the Democratic and Republican parties simply trade off every few years. Further, the winner always wins by a fairly close margin, with no more than about 60% of the vote and often much less. Indeed, a near tie occurs probably more often than people may realize (2000, 1976, 1960 and several other years). Other political parties get much less of the popular vote, but occasionally they are able to gain a significant portion, indicating strong forces in the country that wish to play something other than the typical two-party game.

If Democrats and Republicans each got 50% of the vote every time, we would conclude that half the country was always committed to each major party. If the votes swung wildly across the whole graph, with wins ranging randomly from nearly all votes to only a bit more than half, then we would conclude that there was no party loyalty. With the figures kept tightly between 40% and 60%, then, the conclusion is that about 40% of voters always vote Democrat, and 40% always vote Republican, with the remaining 20% representing uncommitted voters who generate the fluctuations between 40% and 60%.

The two major party blocks — the voters most committed to a major party platform — are equal in size. They therefore cancel each other out in the voting results — none of these voters make a difference in election outcomes. Only the remaining voters, uncommitted to either major party, decide the Presidency. This uncommitted group can end up all voting for one major party, all for the other or anywhere in between. At most, then, a candidate must convince just 20% of voters to choose him in order to win. However, he can — and often does — cinch the election by convincing only 10% of voters. Of course, due to the vagaries of the Electoral College, a President can even win with less than half of the popular vote — and thus less than half of this uncommitted group of voters.

Read on: Mountains Out of Molehills

3 comments for “The Truth (Damned Truth) of Election Statistics

  1. November 29, 2004 at 12:00 pm

    For a fascinating look at how these ideas reveal the red/blue state notion to be totally misleading, see One State, Two State, Red State, Blue State by Giulianna Lamanna.

  2. July 2, 2009 at 2:17 pm

    “Anatole has been explaining to me the native system of government. He says the business of throwing pebbles into bowls with the most pebbles winning an election — that was Belgium’s idea of fair play, but to people here it was peculiar. To Congolese (including Anatole himself, he confessed) it seems odd that if one man gets fifty votes and the other gets forty-nine, the first one wins altogether and the second one plumb loses. That means almost half the people will be unhappy, and according to Anatole, in a village that’s left halfway unhappy you haven’t heard the end of it. There is sure to be trouble somewhere down the line.
    “The way it seems to work here is that you need one hundred percent. It takes a good while to get there. They talk and make deals and argue until they are pretty much all in agreement on what ought to be done, and then Tata Ndu makes sure it happens that way. If he does a good job, one of his sons will be chief after he dies.”
    —Barbara Kingsolver, The Poisonwood Bible

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