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February 01, 2013 3:37 PM If you’re havin’ electoral problems I feel bad for you son, I got 538 problems but partisan bias ain’t one

By Andrew Gelman

As Andrew Thomas, Gary King, Jonathan Katz, and I discussed in our recently published article (see also discussion here), the electoral college has had little partisan bias in recent decades. By this we mean that, by our calculations (details below), the percentage of the two-party vote needed by the Republican or Democratic candidate to have a 50/50 chance of winning in the electoral college is close to 50%.

In the wake of the 2012 election there has been some talk of an electoral college lock for Obama (see, for example, this article by Nate Cohn), but after looking at the state-by-state results carefully, we retrospectively estimate that Romney needed about 50.5% of the national two-party vote to have had a 50/50 chance of winning in the electoral college.

This is a bias, for sure, but a small bias. Enough to have made a difference in 2000 (when Al Gore received 50.3% of the two-party vote) but not 2004 (when George W. Bush received 51.2%).

In contrast, the bias that would ensue if the electoral vote were conducted via congressional districts—-that would be huge.

And, again, there’s nothing particularly special about 2012. In most of the elections of the past several decades (only the blowouts of 1964 and 1984 excepted), the partisan bias of the electoral college has been small but the partisan bias of a CD-based system would’ve been huge.

This is not to say the electoral college is perfect—-like many others, I find the focus on “battleground states” to be distorting, and I’d prefer a national popular vote system—-but the problems of the electoral college aren’t really one of partisan bias. And we shouldn’t let the occasional and small partisan bias of the existing electoral college serve as any sort of excuse for instituting changes which would increase bias to a whole new level.

My quick calculation

I started by applying a uniform partisan swing to the state-by-state vote, increasing Romney’s share until he reached the magic 270 electoral votes. He would need 51.2% of the popular vote.

But that calculation’s not quite right. In a hypothetical replicated election, the state votes would not be swung exactly uniformly. You can see my 1994 paper with King for details, but the basic idea is to add noise at the state level.

To keep things simple, I redid the what-would-Romney-need-to-get-270 calculation using expected electoral votes, after adding independent randomly distributed noise with standard deviation sigma to the state-level vote totals. This isn’t quite right (again, see the 1994 paper for details) but it should be close enough.

With sigma = 1% or 2%, Romney would need 50.7% of the two-party vote to have a 50/50 chance of winning at least half the electoral votes.

With sigma = 3%, Romney would need 50.6% of the vote. With sigma = 4%, he’d need 50.5%. With sigma = 5%, he’d need 50.4%.

Overall, 50.5% seems to me a reasonable summary. Again, a bias of zero would be preferable, and, like Nate Cohn, I’d be happy for this to be used as an argument to move toward a national popular vote system, but it’s much smaller than the bias associated with the count-the-winners-of-the-congressional-districts system.

[Cross-posted at The Monkey Cage]

Andrew Gelman is a professor of statistics and political science and director of the Applied Statistics Center at Columbia University.