In a recent Monkey Cage post, Andrew Gelman makes a point about reading the polls that always bears repeating: Never place too much stock in the latest poll, and instead consider the average of many recent polls. If the latest poll is an outlier, subsequent polls will probably be closer to the recent poll average.
In the context of this advice, Gelman disagreed with an argument by 538’s Nate Silver. This isn’t about how to read the latest polls: Both agree that you shouldn’t put much stock in the latest poll.
Instead, the disagreement is about whether polls resemble something called a “random walk.” Silver had said yes. Gelman says no. Readers might be confused by this debate. What exactly is a “random walk”? And why would it matter to ordinary people following the campaign? Answering these questions produces two simple but important lessons for reading election polls.
A random walk means this: It is very hard to predict the future movement in some quantity from its present value. Economists often argue that prices follow a random walk: The fact that a T-shirt costs $10 today doesn’t tell you whether it will cost more or less tomorrow.
So how does this apply to presidential polls? In actuality, Gelman and Silver are describing different things. Gelman writes about the sequence of poll results, as if one were to connect the dots from one poll result to another over time. Silver is discussing the underlying true voter preferences, for which we need to average over many polls.
Individual polls do not follow a random walk, as Gelman notes. If a poll outlier is published today — say, a poll that has Donald Trump beating Hillary Clinton by 10 points — future polls will probably show a smaller margin between the candidates. This is to say, future polls will be closer to the average of the recent polls. The fancy term for this is “regression to the mean.”
For this reason, it’s better to assume that the “trend” implied by a single poll does not reflect a shift in actual opinions but instead the vagaries of sampling plus other sources of survey error.
This leads to the first lesson: ignore the individual polls and follow polling averages, such as those at Pollster or Real Clear Politics, as smart observers increasingly do. Polling averages cancel out much of the sampling and other survey errors to measuring the actual opinions of Americans.
And here is where Silver is right: Polling averages do approximate a random walk, although with some qualifications. As we show in our book The Timeline of Presidential Elections, people’s vote intentions change slowly as a series of bounces and bumps. The bounces are short-term responses to campaign events that rarely last to Election Day. The more important bumps are the long-lasting responses to campaign events that add up to what might be called a “moving equilibrium” of vote intentions. This moving equilibrium follows a random walk.
Here’s what this means: Shifts in the polling average are more meaningful, but you cannot predict future shifts in polling averages from the current average or the most recent change — just as you can’t know what today’s T-shirt will cost tomorrow.
We can show this using all the presidential polls from 1952 to 2008. The graph below shows the relationship between month-to-month change in the polling average in one month compared with the previous month. The correlation is exactly zero, perfectly consistent with a random walk. If one candidate gains a particular month, this does not help predict whether this candidate gains or loses the following month.
Graph by Robert Erikson and Christopher Wlezien.
We can apply this principle to recent polls of the Clinton-Trump match-up. The average of these polls suggests a decline in Clinton’s once-robust lead during the spring. This seems to be meaningful and not simply survey error. It probably reflects the consolidation of the Republican Party behind Trump. We would probably deem it a shift in the “moving equilibrium.”
<script src=”http://elections.huffingtonpost.com/pollster/2016-general-election-trump-vs-clinton/embed.js”></script>
Put all this together, and you have the second lesson: You can’t predict future trends from recent shifts in the polls. The fact that polling averages are a random walk means that we cannot know what will happen next.
Readers might think that they hold extra information to justify thinking that Clinton will regain lost ground or that Trump will surge to the lead. But there is nothing in the numbers to say that either will happen or which is more likely. Based solely on polls that are close, the best guess of the future is a close race.
Ultimately, both Silver and Gelman are correct. You should pay less attention to the last poll you read and consult instead the average of recent polls. By averaging, survey error tends to cancel out and you have a clearer reading. Then remember the random walk, and you won’t make the mistake of thinking you can predict future trends from today’s polling average.
Robert Erikson is professor of political science at Columbia University. Christopher Wlezien is Hogg Professor of Government the University of Texas.