How to Lie With Statistics example number 12,498,122

November 12, 2012

(This article was originally published at Statistical Modeling, Causal Inference, and Social Science, and syndicated at StatsBlogs.)

This post is by Phil Price.

Bill Kristol notes that “Four presidents in the last century have won more than 51 percent of the vote twice: Roosevelt, Eisenhower, Reagan and Obama”. I’m not sure why Kristol, a conservative, is promoting the idea that Obama has a mandate, but that’s up to him. I’m more interested in the remarkable bit of cherry-picking that led to this “only four presidents” statistic.

There was one way in which Obama’s victory was large: he won the electoral college 332-206. That’s a thrashing. But if you want to claim that Obama has a “popular mandate” — which people seem to interpret as an overwhelming preference of The People such that the opposition is morally obligated to give way — you can’t make that argument based on the electoral college, you have to look at the popular vote. That presents you with a challenge for the 2012 election, since Obama’s 2.7-point margin in the popular vote was the 12th-smallest out of the 57 elections we’ve had. There’s a nice sortable table at Wikipedia if you would like to look at the numbers.

How do you make a narrow win in the popular vote look like a mandate? Time to get creative. You need to choose some metric by which Obama’s victory seems historically large rather than historically small. You need to cherry-pick. Start looking for cherries.

Well, let’s just look at re-elections instead of all elections; does that help? It’s quite a fair thing to do: there’s a good argument to be made that if people re-elect a president, that should provide more of an endorsement than electing him in the first place because in a re-election you have a lot more information about how the guy will act if he wins. So, how does Obama’s popular-vote margin compare to other re-elected presidents? W won re-election by only 2.5 points in the popular vote, so that’s a promising start. But Clinton won re-election by 8.5 points, Reagan by 18, Nixon by 23, Eisenhower by 15, FDR by 7.5 in his worst re-election and by 24 in his best (recall, back then presidents could serve more than two terms). In fact, Obama’s popular-vote margin was the second-smallest re-election in history, second only to W. Evidently one cannot base a case for Obama’s mandate on the size of his re-election margin.

Well, what about the percent of the vote? Thanks to third-party candidates, the popular vote margin of victory is not perfectly correlated with the percentage of the vote that a candidate receives. That’s how Clinton won by substantial margins with only 43 and 49% of the vote. Maybe if we just look at the percent of the popular vote in re-elections? Obama 50.6, W 50.7, Clinton 49.2, Reagan 58.8, Nixon 60.7, Eisenhower 57.3, Roosevelt 60.8  54.7  53.3, Wilson 49.2…OK, that didn’t work either, we’ve already gone back 100 years and Obama is ahead of only Clinton and Woodrow Wilson.  But hey, wait a second, what if we include the first term too? This really doesn’t make any sense, or at least not much, but it does some magic to our list: We can knock off W (who won with less than 50% thanks in part to a Nader candidacy), and Nixon (strong third-party challenge from Wallace).  Only 8 presidents in the past 100 years have been re-elected, counting Obama; applying a 50% filter on the second election knocks off Clinton and Wilson, and applying a 50% filter to the first one as well knocks off W and Nixon. We are down to four. Genius! We have found a way to make Obama’s victory seem like a historic mandate…kind of. If you don’t think about it. It’s a great example of how to lie with statistics.

[To try to anticipate the comments some people might otherwise make, I'll say here that I (Phil Price) greatly prefer Obama to Romney and that I overwhelmingly prefer the Democratic platform to the Republican platform. Obama won and, as W famously said, "elections have consequences." But that doesn't make this "only four presidents..." trivia any less laughable.]

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