Are Elections Decided by Chance?

Are Elections Decided by Chance?

By Sean Trende - August 13, 2013

The first of three parts

Over the past nine months, the Republican Party has been consumed by a debate over how it should respond to Mitt Romney's loss in 2012. Should it reach out to Hispanics? Should it move to the center? Should it try to differentiate itself from the Democratic Party by moving more to the right? Or perhaps it should attempt to redefine what "left" and “right” mean, possibly by embracing a more populist approach?

Let me step a bit outside of the proverbial box here, and ask a more foundational question: What if the GOP doesn’t need to change all that much? This grows out of an article I wrote in the immediate aftermath of the last election, showing that the state of the party wasn’t nearly as dire as many had made it out to be. It is nowhere near as weak as it was in the 1930s, and hasn’t begun to plumb the depths it reached in the 1970s. In fact, at the sub-presidential level, it is in pretty solid shape. Even at the presidential level, over the course of the past six elections, the GOP has lost the popular vote by, on average, 3.9 percentage points. Democrats, by contrast, lost by 9.9 points on average from 1968 to 1988.

Let’s flesh this idea out by asking ourselves seven interrelated questions, each of which casts some cold water on the idea that a rebranding would be overwhelmingly helpful:

1) What if elections are simply random?

2) What if it really is just the economy, stupid?

3) What if Republicans actually aren’t that out of step ideologically?

4) What if party makeovers don’t work?

5) What if the American people just automatically self-correct?

6) What if this period of introspection is just what out-of-power parties do?

7) What if it makes no sense for a party to think more than 10 years out?

Naturally this takes a bit of space to work through, so we’ll split this discussion into three parts. We’ll tackle the first two questions today, Nos. 3 and 4 tomorrow, and Nos. 5-7 the next day, also offering some concluding thoughts at that time.

Before we begin, though, I need to make an important point. We have to make a distinction between how we’d like to see the Republican Party go about winning elections, and what it needs to do in order to win elections: a sort of psephologist’s analogy to the philosopher’s “is/ought problem.” There are many things I’d like to change about the Republican Party (and the Democratic Party, for that matter), and I think a lot of those changes would make it electorally stronger.

But that’s somewhat distinct from the question of how much it needs to change to win presidential elections, and likewise somewhat distinct from the question of how much benefit it will gain from such a change. As we’ll see, the gains are probably limited to a few points, at best.

1) What if elections are simply random?

Humans try to find patterns in chaos; it is part of our nature. And so when we see a statistic like the oft-recited observation that Republicans have lost the popular vote in five of the last six elections, we automatically try to attach some significance to it. I think this is because, in part, most people internally draw analogies to sports dynasties. For example, the Los Angeles Lakers won the NBA title five times during the 1980s. They are usually cited as the dominant team of the decade.

Winning an NBA championship five times in 10 seasons really does tell us something about the dominance of a team; it is not just luck. The probability of winning five championships in 10 seasons through chance alone from a field of 22 teams is 0.00387 percent. In other words, it should occur once every 25,840 seasons. It would be unusual to see that run even once over the course of 66 seasons (since the first NBA championship in 1947), if NBA championships were due to chance.

But in fact, we see it occur multiple times, with the Celtics and Bulls contributing similar runs. So we can say that there almost certainly was something about those teams that caused them to win that can’t be ascribed to chance (of course, you’d know that if you ever watched those teams play, but this is the theoretical explanation).

But winning five of six presidential elections when there are only two major parties competing is another beast altogether. I’m borrowing this very important point liberally from the great David Mayhew, but elections really do behave, over the long term, like coin flips, regardless of how the political parties might have positioned themselves in the interim.

“But,” you might say, “we’ve just seen Republicans go 1-for 6, immediately after Democrats going 1-for-6” -- although again, the respective margins for the parties during those “runs” are different – “that doesn’t sound random to me.” First, beware the arbitrary cutoff: The parties have each won six of the past 12 elections. Second, the initial description might not sound random, but randomness doesn’t imply that Republicans and Democrats should alternate winning elections. In fact, it implies the opposite (no, really).

If you toss an evenly weighted coin (I have no idea why statisticians traditionally feel the need to clarify that the coin is evenly weighted, but there you have it) six times, the probability of hitting five heads is not zero. In fact, that precise run should be relatively common: If you do 100 sets of six coin tosses, you should get five heads or five tails 18 times. You should get that run about once every five tries.

Getting back to presidential elections, there have been 34 of them since Reconstruction ended.* Suppose we had opted to decide those elections by coin toss. We’d expect to see five instances of one party or the other winning the popular vote in five of six elections.** In fact, we see four (Democrats from 1928-1948, 1932-1952, and 1992-2012; Republicans from 1968-1988).

Taking a broader look at probability, our elections during this time period look an awful lot like we’d expect them to look if they were decided by chance alone. Examine the following table. The second column shows how many times we would expect a variety of runs for one party or the other to occur between 1880 and 2012 (the list appears incomplete, but every time a party wins “1 of 3” elections, the other party necessarily wins “2 of 3”). The third column shows how many of each type of run we actually see from 1880 to 2012, and the final column is the difference between the number of runs we’d expect to see and the number we actually observe.

Things look an awful lot like they would if we decided elections by coin flip. To better visualize this, consider the following chart, which depicts the projected number of runs vs. the actual number of runs.

Now it’s not a perfect match, but with only 34 total attempts (and as few as 25 attempts for the runs of 10), we actually shouldn’t be that surprised by some deviations from a perfect binomial distribution. But the truth is, all of our errors are within two standard deviations of the mean.

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Sean Trende is senior elections analyst for RealClearPolitics. He is a co-author of the 2014 Almanac of American Politics and author of The Lost Majority. He can be reached at Follow him on Twitter @SeanTrende.

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