Here’s a fun discussion (still developing, it’ll be going through Thursday, I think) on red and blue America, featuring pollster John Zogby, journalist Bill Bishop, consultant Valdis Krebs, and myself, moderated by Tom Nissley at Amazon.com.

My strategy is to make my points using graphs.

Amazon.com has this cool website showing which sorts of political books people are buying in which states:

What struck me was the similarity of this to the “voting patterns of the rich” map from our book:

I wonder what data from Wal-Mart from Wal-Mart would look like. Maybe like one of the lower of the two maps? I’m not sure, though, since, even at Wal-Mart, buyers of political books are more politically active and thus maybe more like “rich people” in their red-blue divisions.

Katy Gartside pointed me to this site. It’s fun to see the new states gradually being added as the years go on. Here was the exciting 1796 election. (At that time most people weren’t allowed to vote.)

And here’s the Twentieth Century Reversal. First, the McKinley-Bryan matchup of 1896:

Red states in the northeast, upper midwest, and west coast; blue in the south, plains, and mountain west. That sounds right . . . hey, wait a minute!

Let’s go to the Bush-Gore map from 2000. The red states have switched to blue and vice-versa:

See here for more on the Twentieth Century Reversal, including some scatterplots. It turns out that, at the local level, it was not a simple switching of red to blue or a simple switching of party positions.

P.S. The historical maps on the above-linked site are great, but don’t take the probabilities on the site seriously.

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.

If you live in NYC, you can hear me tomorrow (Fri 29 Aug) from 12.30-1 on the Leonard Lopate show on WNYC, 93.9 FM and AM 820. I’ll be talking about the book and probably about the 2008 election as well.

P.S. The interview is here.

Bryan Caplan, author of The Myth of the Rational Voter (formerly called The Logic of Collective Belief: The Political Economy of Voter Irrationality), wrote some nice things about our book and also posted a variant of this graph that I made by putting together a bunch of exit polls:

Bryan also comments that, to his eyes, the correlation between income and voting is pretty small. He writes, “As an economist, I [Caplan] was raised to expect virtually all poor people to be Democrats, and virtually all rich people to be Republicans. From this starting point, Gelman’s data show that income is practically irrelevant.” I agree that income matters less than one might think in the U.S., and it actually matters even less in most other countries for which we have data. As we discuss in the book, the correlation between income and economic ideology is low (and it varies quite a bit by state). On the other hand, it’s a difference of 20% between the high and low end, and that ain’t nothing. It’s the difference between voting like Massachusetts and voting like Texas. We’re always dancing around the magic 50% point, and so even small differences can be important. As Bryan says, a lot of how you interpret this depends on where you’re coming from.

I also agree with Bryan that we are not really shooting down the ideas of journalists and others, but rather looking at polls and elections in a different way. We did try to convey in the book that we respect the insights of the many journalists who’ve talked about the red-blue divide, and that we’re trying to go further by seeing how these divisions have changed over time and how they vary across different groups of the population.

From our forthcoming Red State, Blue State book, here are some data going back to 1968 (from the National Election Study) on the voting patterns of different religious groups:

Perhaps also of interest is how this relates to religious attendance. More frequent attenders are more likely to vote Republican, but the pattern varies by denomination. Here’s what was happening in 2004 (as estimated from the Annenberg pre-election survey):

The graph for 2000 looks similar except that the line for Jews was flat in that year (maybe just a small-sample thing, I don’t know that I’d take it too seriously).