Yes, the Electoral College favors voters in small states (slightly and, on average). Mostly it favors voters in swing states. It does not favor large states, despite what is sometimes said.

September 19th, 2008, by Andrew

It is well known that the Electoral College favors small states: every state, no matter how small, gets at least 3 electoral votes, and so small states have more electoral votes per voter. This “well known fact” is, in fact, true. It’s not a huge effect–it’s trivial compared to the small-state bias of the U.S. Senate–but it’s there.

Unfortunately, confusion arises every four years as a few scholars and journalists rediscover an obscure and irrelevant mathematical argument that purports to support the counterintuitive claim that the Electoral College actually benefits large states.

So I’m trying to get ahead of the curve this year by explaining, in detail, why the intuition is correct that the Electoral College favors voters in small states, on average. My discussion involves mathematical reasoning and also empirical election data.

Voting power and the probability of a decisive vote

If you are a voter in a particular state, then the probability that your vote is decisive in the Presidential election is equal to the probability that your vote is decisive within your state (that is, the probability that your state would be exactly tied without your vote), multiplied by the probability that your state’s electoral votes are decisive in the Electoral College (so that, if your state flips, it will change the electoral vote winner), if your state were tied. When people talk about voting power, or about the Electoral College giving some states more influence than others, this is the probability they’re talking about.

If your state has N voters and E electoral votes, it turns out that the probability that your state is tied is approximately proportional to 1/N, and the probability that your state’s electoral votes are necessary is approximately proportional to E. So the probability that your vote is decisive–your “voting power”–is roughly proportional to E/N, that is, the number of electoral votes per voter in your state.

A counterintuitive but wrong idea

The point has sometimes been obscured, unfortunately, by “voting power” calculations that purportedly show that, counterintuitively, voters in large states have more voting power (”One man, 3.312 votes,” in the oft-cited paper of Banzhaf, 1968). This claim of Banzhaf and others is counterintuitive and, in fact, false.

Why is the Banzhaf claim false? The claim is based on the same idea as we noted above: voting power equals the probability that your state is tied, times the probability that your state’s electoral votes are necessary for a national coalition. The hitch is that Banzhaf (and others) computed the probability of your state being tied as being proportional to 1/sqrt(N), where N is the number of voters in the state. This calculation is based (explicitly or implicitly) on a binomial distribution model, and it implies that elections in large states will be much closer (in proportion of the vote) than elections in small states.

Above is the result of the oversimplified model. In fact, elections in large states are only very slightly closer than elections in small states. As a result, the probability that your state’s election is tied is pretty much proportional to 1/N, not proportional to 1/sqrt(N). And as a result of that, your voting power is generally more in small states than in large states.

Realistically . . .

Realistically, voting power depends on a lot more than state size. The most important factor is the closeness of the state. Votes in so-called “swing states” (Florida, New Mexico, etc.) are more likely to make a difference than in not-so-close states such as New York.

Above is a plot of “voting power” (the probability that your vote is decisive) as a function of state size, based on the 2000 election. These probabilities are based on simulations, taking the 2000 election and adding random state, regional, and national variation to simulate the uncertainty in state-by-state outcomes.

And above is a plot showing voting power vs. state size for a bunch of previous elections. These probabilities are based on a state-by-state forecasting model applied retroactively (that is, for each year, the estimated probability of tie votes, given information available before the election itself). On average, voting power is slightly larger in small states. But the effect is small. The biggest advantage is to states whose voting power are near the national average.

The punch line: you have more voting power if you live in a swing state, and even more voting power if you live in a small swing state. And, if you’re lucky, your voting power is about 10^(-7), that is, a 1 in 10-million chance of casting a decisive vote.

References

Here’s the our article in the British Journal of Political Science (joint work with Jonathan Katz and Joe Bafumi), making this argument in more detail.

Go here for more details on the statistical models (joint work with Jonathan Katz and Francis Tuerlinckx)

Actually, though, it’s still rational for you to vote, at least in many of the states.

Whassup?

Counterintuitive can be appealing. For example, see Timothy Noah’s articles here and here from 2004, where he writes that the two states with the most voting power under the electoral college are California and Texas. Umm . . . no. Noah’s articile is excellent journalism–readable, compelling, surprising. He just made the mistake of talking to the wrong experts, and also the mistake of not stepping back and asking: Hey–does this actually make sense?

One of my own goals in presenting my research is to describe it clearly and transparently enough so that, ultimately, it does make sense and does not appear counterintuitive.

Similar Posts:

• Popular vote and electoral college
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Entry Filed under: Voting