John Cassidy writes:

If Barack Obama is victorious on November 4th, someone on his transition team should send inauguration tickets to Richard Fuld, the chairman and chief executive of Lehman Brothers.

This is meant to be ironic, I believe: Fuld was the straw that broke the camel’s back and brought down the house of cards that was the American banking system etc etc.

But this got me wondering . . . could Cassidy’s statement be literally true??

I remember from talking with Tom Ferguson that, while the superrich generally favor the Republican Party, the financial sector is one area that leans Democratic. So I looked up Richard Fuld and–hey–here he is:

Richard Fuld, Lehman Rothers – Chairman, CEO 1994-present
Total donations since 1978: $208,550
To Democrats: 63%
To Republicans: 16%
To Special Interests: 21%

In 07/08, he seems to have been covering his bets: $10K each to the Republican and Democratic Senatorial Committees, $4600 to Hillary Clinton, $2300 to Barack Obama, $4600 to Chris Dodd, $2300 to John McCain, $2000 to John Reed in Rhode Island, and $10K to the “Securities Industry and Financial Markets Association Political Action Committee.”

So maybe he’ll get an invite to the inaugural party no matter who wins.

P.S. I was kinda hoping Fuld had only contributed to Obama–that would make a more interesting story. (Or I suppose if he’d only contributed to Republicans all his life, then there’d be an even better story of Richard S. Fuld, Jr., as a sleeper agent for the Democratic Party.) Actually, though, he’s all over the map, basically giving to almost every big name in the tri-state area and then some, including Pete Dawkins, Pete Du Pont, John Glenn for President (remember that?), Brendan Byrne, Phil Gramm, Joe Lieberman, Bob Dole, Al D’Amato and several of his opponents, Joe Lieberman, Jon Corzine, etc etc.

Laura Wattenberg has a fascinating discussion of the one topic you think you’ve already heard enough about . . . Sarah Palin’s kids’ names. You really have to read the whole thing, but here’s the gist:

No naming event has ever filled my [Wattenberg's] inbox with as many reader queries as the unveiling of Sarah Palin–mom to Track, Bristol, Willow, Piper and Trig–as John McCain’s running mate. “Any comment?” “I’ve never heard Trig as a name for anything but a math class.” “Is this ‘an Alaska thing’?'”

In a way, yes, it is “an Alaska thing.” If you had nothing to go on but the baby names and had to guess about who the parents were, you’d guess that that they lived in an idiosyncratic, sparsely populated region of the country…and that they were conservative Republicans. . . .

For the past two decades, a core set of “cultural conservative” opinions has served as a theoretical dividing line between “red” (Republican/conservative) and “blue” (Democratic/liberal) America. These incude attitudes toward sex roles, the centrality of Christianity in culture, and a social traditionalism focused on patriotism and the family. If you were to translate that divide into baby names it might place a name like Peter—classic, Christian, masculine—on one side, staring down an androgynous pagan newcomer like Dakota on the other. In fact, that does describe the political baby name divide quite accurately. But it describes it backwards.

Characteristic blue state names: Angela, Catherine, Henry, Margaret, Mark, Patrick, Peter and Sophie.

Characteristic red state names: Addison, Ashlyn, Dakota, Gage, Peyton, Reagan, Rylee and Tanner. . . .

Why is it the blue parents who name with red values? Because in baby naming as in so many parts of life, style, not values, is the guiding light. . . .

The states won by the Democrats and Republicans in recent elections are almost the opposite of the result of the election of 1896:

In their article, “Activists and partisan realignment in the United States,” published in 2003 in the American Political Science Review, Gary Miller and Norman Schofield describe this as a complete reversal of the parties’ positions. In their story, in 1896 the parties competed on social (racial) issues, with the Republicans on the left and the Democrats on the right. Then the parties gradually moved around in the two dimensional social/economic issue space, until from the 1930s through the 1960s, the parties primarily competed on economic issues. Since then, in the Miller/Schofield story, the parties continued to move until now they compete primarily on social issues, but now with the Democrats on the left and the Republicans on the right.

It’s an interesting argument but I have some problems with it. First off, it was my impression that the 1896 election was all about economic issues, with the Democrats supporting cheap money and easy credit (W. J. Bryan’s “cross of gold” speech) and the Republicans representing big business. At least in that election, it was the Democrats on the left on economic issues and the Republicans on the right.

Getting to recent elections, the evidence from surveys and from roll call votes is that the Democrats and Republicans are pretty far apart on economic issues, again with the D’s on the left and the R’s on the right. So, from that perspective, it’s not the parties that have changed positions, it’s the states that have moved. The industrial northeastern and midwestern states have moved from supporting conservative economic policies to a more redistributionist stance. Which indeed is something of a mystery, and it’s related to attitudes on social issues, but I certainly wouldn’t say that economic issues don’t matter anymore. According to Ansolabehere, Rodden, and Snyder, social issues are more important now in voting than they were 20 years ago, but economic issues are still voters’ dominant concern.

1896 vs. 2000 by counties within each state

Here are some more pretty pictures. First, within 6 selected states, a scatterplot of Bush vote share in 2000 vs. McKinley vote share in 1896. There are completely different patterns in different states! Nothing like as clean a pattern as the statewide plot above.

And here’s another plot, this time showing each county as an ellipse, with the size of the ellipse proportional to the population of the county (more precisely, the voter turnout) in the two elections.

Nowadays the Democrats clearly do better in the big cities (in these graphs, the large-population counties). In 1896 the pattern wasn’t so clear.

The recent role of population density

I asked Jonathan Rodden what he thought of the above graphs, and he replied, “I would like to see when this relationship developed, in which states, etc. My hunch is that suburbanization, especially after the race riots, significantly reduced the heterogeneity of cities. The era of Democrats winning 80 percent of the presidential vote in big cities seems fairly recent.” He also sent along these graphs of voting by population density:

As Jonathan noted, the pattern of high-density areas voting strongly Democratic is relatively new. (But I don’t buy the way his lines curve up on the left; I suspect that’s an unfortunate artifact of using quadratic fits rather than something like lowess or spline.) Also there seems to be some weird discretization going on in the population densities for the early years in his data. But the main trends in the graphs are clear.

Jonathan added the following comment: “The relatively high values on the left side of graphs in early years is due to Southern Democrats and some mining districts. Graphs of the UK, Australia, and Canada look very similar during the same period, with left voting concentrated in urban and mining districts.”

Drew Linzer writes:

I read your paper with some interest, as within the last week or so I’ve started analyzing the state tracking polls available on pollster.com using a simple Bayesian mean model, and posting my results here.

The model updates the Obama share of the Obama-McCain vote as new polls come in, and then calculates the posterior probability that that proportion is greater than 0.5.

I’m doing this as more of a hobby than anything else…was frustrated with analyses I’ve seen that strike me as overly complex, unstable, totally opaque, and frankly, fairly unbelievable — there’s a real chance Obama could get EVs in the 400s? come on. The R code I use to generate my graphs and predictions are also posted if you click the Data tab.

My goal was to create a model that was very simple, but made reasonable predictions. So, for example, I don’t have any time component — the model assumes the true state level proportion for Obama is constant. Maybe this is a good assumption, probably not, but also probably the actual within-state support numbers are not actually fluctuating as much as some of the predictions out there make it seem. The first time I set up the model, I just used the posterior from one poll as the prior on the next. Problem was that the variance of the priors got so small after a while that there didn’t seem to be enough flexibility to capture trends when they did seem to arise. So then I added a multiplier to increase the variance of the prior in proportion to how many days old the last poll was. I tinkered around with it a bit and came up with this that seemed reasonable.

sd.prior.flex <- sd.prior.flex * (1+(0.05*log(dat$daysold[i]+1)))

Changing the 0.05 makes the trend line more or less sensitive to new polls. It's really just kind of acting as a smoother as the polls appear.

The other thing the model doesn't have is any sort of cross-state correlation structure built in. Every state is treated as its own independent entity. This probably isn't very realistic either, but in these battleground states there also seems to be enough state-level polling going on to get decent enough within state estimates. Where I would like to take account of cross-state correlation is when I simulate election results. Doesn't seem like that would be too hard to estimate in a second stage after the trendlines have been calculated (or simultaneously in a more complicated model), I just haven't gotten around to it.

Anyway, so that's basically it. the "predicted electoral vote" adds up the EVs for each candidate who my trend line has above 50%. And the simulation that produces the "probability of winning" and the histogram just draws from each state's most current posterior distribution 1 million times and adds up the number of Obama EVs. As I said, I don't know if the model is "good" but it is clean and transparent, relatively stable, and, to my mind, produces predictions that accord better with the available polling data.

My thoughts: First, I don’t think it’s impossible that Obama could get EV’s in the 400s, given the uncertainties in national forecasts. It’s not likely but it’s possible. Second, I think poll aggregation is fine (whether it be Drew’s method or Realclearpolitics or 538.com or whatever), but when it comes to forecasts, I think the best thing is a weighted average of polls and model-based predictions, with the model having two parts: (1) the national popular vote and (2) the states relative to each other.

Here.

I’ll be talking about Red State, Blue State on the Kathleen Dunn show on Wisconsin Public Radio tomorrow (Tues 23 Sept), from 10-11 Central Time (that’s 11-12 Eastern Time). For the second half of the show, you can call in with questions!

National elections are predictable from fundamentals (see, for example, the research of Steven Rosenstone, James Campbell, Robert Erikson, and Chris Wlezien, along with many others), but this doesn’t stop political scientists, let alone journalists, from obsessively tracking swings in the polls. The next level of sophistication–afforded us by the combination of ubiquitous telephone polling and internet dissemination of results–is to track the trends in state polls, a practice which was led in 2004 by Republican-leaning realclearpolitics.com and now in 2008 at fivethirtyeight.com, a website maintained by Democrat (and professional baseball statistician) Nate Silver.

Presidential elections are decided in swing states, and so it makes sense to look at state by state polls. On the other hand, the relative positions of the states are highly predictable from previous elections. So what is to be done? Is there a point of balance between the frenzy of daily or weekly polling on one hand, and the supine acceptance of forecasts on the other? The answer is Yes, a Bayesian analysis can do partial pooling between these extremes. We use historical election results by state and campaign-season polls from 2000 and 2004 to estimate the appropriate weighting to use when combining surveys and forecasts.

CLICK HERE for more on what we did (research article by Kari Lock and myself).

And here’s an illustration of the method, based on the February SurveyUSA polls of the Clinton vs. McCain and Obama vs. McCain matchups in each of the 50 states:

The short answer is that the polls in individual states–even those large Survey USA polls–have a lot less information than you might think. In some cases the polls are probably telling you something real–for example, in Arkansas, Clinton would do better against McCain than Obama would. But those maps people were making showing which states Clinton or Obama would win–those were drastic overinterpretations of transient poll data.

You can’t just take the state polls, slap on standard errors, and think you’re capturing the uncertainty about the election outcome.

The key idea is to separate the forecasting information at the national level from the information about the relative positions of the states. These are really two different things. The forecasts (and, to a lesser extent, the polls) tell you about Obama and McCain’s strength nationally, and about each candidate’s strength in Ohio (say) relative to his national strength. It’s not statistically efficient to look at Ohio, or any other state, in isolation.

I’ll be speaking on the book this Monday (22 Sept) at 4:30pm at the University of Pennsylvania. It’ll be at the Annenberg School for Communication, Room 109. The address is 3620 Walnut Street, Philadelphia, PA. This is your chance to ask questions and also to meet some interesting people: the talk is cosponsored by the departments of Statistics, Biostatistics, and Political Science as well as the Annenberg School.

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.

Jonah Lehrer, a neuroscientists blogging at The Frontal Cortex from withing ScienceBlogs, comments on new research on partisan bias in perceiving reality:

Yesterday, we looked at some new research that found that when conservatives were exposed to evidence demonstrating the falsity of a partisan belief – such as a report demonstrating that Iraq didn’t have WMD, or that lowering taxes doesn’t increase government revenue – they became more convinced than ever that those beliefs were actually true. The scientists call this “the backfire effect”.

The researchers argue that conservatives are particularly vulnerable to this cognitive flaw, as their beliefs tend to be more rigid and immutable. But I’m not so sure. As a liberal partisan hack, I’m very aware of how my political biases distort my processing of information. I fixate on news that jives with my beliefs and tend to ignore those inconvenient facts that contradict my inner talking points.

We discuss this in our book, in chapter eight: 

Polarization as a perceptual screen on reality appears ubiquitous. We can see an example of this in a recent survey on 9/11 conspiracy theories. One prominent conspiracy theory about the attacks centers around the claim that President Bush knew about the attacks in advance. This conspiracy comes in the form that Bush either planned the attacks himself or was too incompetent to do anything about them despite his knowledge of their imminence.

Respected commentators of all political stripes have categorically rejected this theory. But what about the public? Republicans in the survey rejected the idea that President Bush knew about the attacks in advance by a 7-1 margin. On the other hand, Democrats were close to evenly split on the question.

The country is divided geographically as well as by party. For example, Edward Glaeser and Bryce Ward note that in 2004, “twenty-three percent of respondents in Oregon, Washington and California thought that Saddam Hussein was personally involved in the September 11, 2001, attacks. Forty-seven percent of respondents in Texas, Oklahoma and Arkansas had that view.” Glaeser and Ward also report that “56 percent of Mississippi residents think that AIDS is God’s punishment for immoral sexual behavior. Only 16 percent of Rhode Island residents share that view.”

Looks like partisan filters are a generic feature of being human (one might describe them as especially strong priors). But do these filters have policy consequences? Perhaps Condorcet’s jury theorem can save us (if errors are independent), perhaps not (if they are not). Or perhaps the moderates that help decide elections are far less inclined to such mistakes than committed partisan. I’m not sure; I’d like to see some evidence on this score.