The electoral college favors voters in small states (on average), not large states

Jonathan Bernstein writes:

The big, urban states traditionally did very well in the electoral college. . . . New York used to be a major swing state; California also was very contested once it became large, and even Texas had a run as a competitive state with big cities for a while. For whatever reason, all of that has slipped some over the last twenty or thirty years . . . Still, all else equal, a presidential candidate would rather pander to a large state with lots of winner-take-all electoral votes than a small one, which should tend, over time, to balance out the small-state advantage in the Senate.

I think this is wrong and I suspect Bernstein’s claims are based on casual reflections rather than a systematic study of the data. My colleagues and I have published three papers on the electoral college:

[2009] What is the probability your vote will make a difference? {em Economic Inquiry}. (Andrew Gelman, Nate Silver, and Aaron Edlin)

[2004] Empirically evaluating the electoral college. In {em Rethinking the Vote: The Politics and Prospects of American Election Reform}, ed. A. N. Crigler, M. R. Just, and E. J. McCaffery, 75—88. Oxford University Press. (Andrew Gelman, Jonathan N. Katz, and Gary King)

[1998] Estimating the probability of events that have never occurred: When is your vote decisive? {em Journal of the American Statistical Association} {bf 93}, 1—9. (Andrew Gelman, Gary King, and John Boscardin)

We have consistently found three things:

1. In the ultimate election outcome, the electoral college generally matches the popular vote winner pretty closely: if a candidate wins 51% of the popular vote, he typically has about a 95% chance of winning the electoral college.

2. The electoral college benefits voters in certain swing states, which vary from election to election (for example, Vermont was a swing state in 1992 but is not a swing state now).

3. On average, the electoral college benefits voters in small states, in the sense that an individual voter in a randomly-selected small state is more likely to have a decisive vote, compared to an individual voter in a randomly-selected large state. With a national popular vote, of course, all votes are equally likely to be decisive.

Thus, compared to a national popular vote, under the electoral college a presidential candidate would rather pander to a small state, not a large state as Bernstein claims. But, again, this is on average. New Mexico and Utah are both small states but only one of them is going to be competitive in 2012.

P.S. Here are some graphs from the above papers (click for larger versions). Here’s 2008:

Here’s another look at the 50 states:

Here’s 1952-1988 (excluding 1968), averaging across states to get a look at how Pr(decisive) varies by state size:

The above are all showing Pr(decisive), which is from the voter’s perspective, but it’s the exact same story from the campaign’s perspective, it just gets directly translated into the probability that a campaign will change the election outcome by persuading one person to change his or her vote (or by persuading two supporters to turn out to vote), or 1/1000 the probability that a campaign will swing the election by persuading 1000 people to change their votes, etc.

P.S. More here.

9 Responses to The electoral college favors voters in small states (on average), not large states

  1. Gordon Danning July 29, 2012 at 11:05 am #

    I think this somewhat misconstrues Jonathon Bernstein’s point. He refers expressly to whom it is best to pander to — voters in small states versus voters in large states. Suppose California and Vermont are both swing states in 2032. Suppose also that the key issue in the campaign is whether the federal government should open the California coast to oil drilling. Suppose also that Vermonters generally support drilling, while Californians oppose it. Would’t electoral calculus lead the candidates to oppose drilling? Sure, if they know that they can change only one voter’s mind, they should pander to the Vermonter, because one Vermonter gives them more bang for their buck than one Californian, but that is not realistic. The real question is, do I want to change the votes of 10% of Vermonters, or 10% of Californians? Why isn’t the answer, “10 of Californians”?

    • Andrew Gelman July 29, 2012 at 11:16 am #

      Gordon:

      Bernstein is comparing the electoral college to national popular vote. Compared to national popular vote, under the electoral college there is relatively more incentive to campaign in small states.

  2. Seth July 29, 2012 at 11:51 pm #

    It still sounds to me like these are two separate things. You’re making a claim about where voters are more likely to be pivotal, and Bernstein is making a claim about where campaigns will devote their resources. It’s not obvious that both would lead to the same answer. Bernstein’s claim is empirically testable — did the campaigns in 2008 spend more per voter in small swing states like New Hampshire and New Mexico or in large swing states like Ohio and Florida? Maybe Sides has the data.

    • Andrew Gelman July 30, 2012 at 2:02 am #

      Seth:

      Again, I’m not simply comparing states to each other, I’m comparing states to each other under the electoral college, compared to comparing states to each other under the national popular vote. It’s a difference in differences, and such a comparisons is inherently theoretical (for the U.S.) because we don’t have national popular vote. As you can see by going back to Bernstein’s blog, he is comparing to national popular vote himself.

  3. Anonymous Coward July 30, 2012 at 9:45 am #

    I think your point is that under the EC we get lots of campaign activity in states that are close, and smaller.*

    But under a national popular vote, we’d get campaign activity where the voters are. So lots of Republican activity in LA and to a lesser extent NY, and a fair amount of Democratic activity in Dallas and Houston.

    …but your post didn’t make it clear that that was your point. You seemed to be arguing that campaigns must prefer to expend resources in smaller, EC-blessed states, even if empirically they don’t seem to.

    *But Seth’s point still has some bite here — candidates want to devote resources to the biggest, closest states, especially if pandering to Ohio is more cost-efficient than pandering to, say, Delaware.

    • Andrew Gelman July 30, 2012 at 10:07 am #

      Anonymous:

      Even if Seth’s point is valid (that candidates will find it more cost-efficient to campaign in big states), that would be even more so with the national popular vote. Thus, I disagree with Bernstein’s claim that the electoral college favors large states, in comparison to the national popular vote.

  4. AmbiValent July 31, 2012 at 3:26 am #

    Excuse me, but why is the data for the years after 1988 missing? You might exclude 1968 for Wallace, and 1992 (maybe also 1996) for Perot, but the elections 2000 to 2008 should definitely be there.

    • Andrew Gelman July 31, 2012 at 3:52 am #

      Ambi:

      The data in that series stop after 1988 because we computed the numbers in 1992 (and the paper was published in 1998, after I belatedly realized that these results might be of general interest).

      • Beauga December 21, 2012 at 6:45 am #

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