Robert Max Jackson

Curious doings.

Well we all know that the Presidential election process in Florida has aroused a furor over apparent flaws. In particular, the ballot used in Palm Beach County produced an extraordinary number of rejected ballots because voters accidentally voted twice for the same office. It also produced an exceptional number of votes for Buchanan, that have been attributed to a flawed ballot.

A number of scholars have been intrigued by the possibility of showing that the number of votes Buchanan received is implausible, given what we know about other voting during this or past elections. Below, I will point toward web sites where you can find much interesting information they have put together and analyses they have produced.
Here, I display a couple modest contributions to the effort. Let me acknowledge up front that I do not normally study voting behavior. But, this was too much fun to pass up, and I was asked by a couple people to make it available this way. So......

Some Initial Findings

The basic question is simple. It seems obvious on the surface that the Buchanan received a disproportionate number of votes in Palm Beach County (who would have thought that its voters would become the center of the 2000 Presidential election?). Can we go beneath the surface to show that this is true in a stronger way? The first efforts to do this used the votes received by other candidates in this Presidential election as the measure of what we should expect (see the sites listed below). It seemed to me that these efforts, although well aimed, were overstating the case a bit. They were predicting Buchanan's vote using only the votes for Bush. I thought that the prediction should use the votes for all the minor candidates, expecting that this would improve the quality of the prediction and thus the legitimacy of the findings. After all, I find it hard to believe that people who vote for fringe candidates are distributed randomly across the land in direct proportion to the population in each area. Also, I was concerned that in creating a regression equation to predict Buchanan's vote, Palm Beach was omitted for its estimation (because including it makes its supposedly mistaken votes influence the parameters to which it is supposed to be compared), but other counties were not treated in the same way. So, to shorten the story quickly, I did an analysis in which I used the votes for all other Presidential candidates to predict the Buchanan vote and I omitted each county while estimating the coefficients used to predict the Buchanan vote there. The results look like this (where each little box in the chart stands for one of Florida's counties):

Even after treating th data in a cautious, balanced way, the results in this analysis are consistent with the expectation that Palm Beach got far to many votes for Buchanan. (For this and the other charts, the variables were all adjusted with a natural log transformation before applying a simple linear regression, then the resulting predictions were adjusted back with an antilog transformation for clarity in the charts.) By themselves, still, they may not seem overwhelming. True, Palm Beach is shown with far more votes being cast for Buchanan that we would expect from voting patterns throughout the state. But, perhaps this result, however statistically compelling it may appear, still reflects some peculiarity of the data outside the Palm Beach Presidential ballots.

Some better findings.

A better way to do this, from an analytical point of view, is to use data that comes from someplace other than the election itself. A simple approach to this is to use past elections. The following chart follows the same prediction and comparison process as that above, but for predictor variables it uses the votes cast in the 1996 Presidential election and the 2000 Presidential primaries. These votes took place long before the recent election and therefore their use in a regression prediction equation has high legitimacy. Here is what we find.

Here again, we see pretty dramatic results. It turns out that the results from past elections are extremely good at predicting the Buchanan vote by county. For every county except Palm Beach. (For the statistically inclined: this analysis produces an adjusted R-squared of .90, using a regression that each county while estimating the coefficients for it.) The "point estimate" or prediction for Palm Beach county is for Buchanan to have received 583 votes in the 2000 Presidential election (compared to the tabulated count of 3407). Every other county is vastly closer to the predicted value than is Palm Beach. While we can give this difference a statistical meaning in terms of the improbability it would occur by chance--as you expect the probability is miniscule--realistically it seems obvious that it did not. And the strongest point is the comparison with the previous chart, based on different predictors.

Some more nice findings.

Another way of predicting the Buchanan Presidential vote by county that makes sense--because it is direct yet not based on the Presidential votes themselves--is to use the votes received by the Senate candidates in Florida. There were four party candidates for the Senate seat, with the Reform Party and the Natural Law Party (about which I admit total ignorance) joining the Democrats and Republicans with statewide candidates. Although splitting tickets is common in U.S. elections, we would reasonably anticipate that the distribution of votes for the Senate candidates would have a strong relationship with the distribution of votes for the Presidential candidates. The Palm Beach ballot design is suspect for causing people to err on their Presidential votes, not on their Senate votes (to the best of my knowledge). Here is what we find:

Obviously, this chart looks remarkably like the preceding one. Using the Senate votes here to predict the Presidential votes (following the same procedures as in the previous example) produces a "point estimate" prediction for the Palm Beach Buchanan vote of 681 (with an adjusted R-squared of .88), again similar as when predicting using the '96 Presidential votes and '00 Primary votes to do the predictions. Here, however, the basis of the prediction is not the prior voting behavior by county (commonly preferred for a causal analysis), but the coterminous votes for the Senate, which rely on the simultaneous voting behavior of the electorate. [For anyone wanting to check more specifically how these charts were created, I have attached for this one the full results, with a complete copy of the computer output and chart are here. This is supplied to conform with reasonable expectations that we meet high standards of scholarly methodology and to help those who suspect these results by giving them more in which they may sink their teeth.]

The implications of this are presumably self-evident. But, just in case it is not, to make the case clearer, let us see what we find if we reverse the logic. Instead of predicing the vote for Buchanan, the Reform Party Presidential candidate, from the Senate votes, let us predict the vote for the Reform Party Senate candidate from the Presidential votes (using all the '00 Presidential candidates, with the usual log transformations to avoid statistical distributional issues). How well does this work?

The comparison here is fairly straightforward again. The distribution of votes for the Reform Party's Senate candidate (which resembles the vote for Buchanan in size) is highly predictable from the Presidential votes in this same election, and Palm Beach is exactly where we would expect it to be. The contrast with the preceding charts speaks for itself.

For those interested, I have added a further analysis of the same problem, but using data from the entire nation. This attempts to show whether the Palm Beach results are anomalous when weighed against the much greater variation of all counties in the United States rather than just Florida. It is located here .

Some even better findings, hopefully.

Of course, as every scholar knows, the primary alternative possibility to the interpretation you offer is that you have made some grave error in your analysis. Fortunately, a number of people have been having fun with this. So, for more information, much more thorough on most of the important points, try the following (which will, in turn, lead you to more).

• Craig Fox of Duke has published a fine analysis of the vote and an exceptional review of everyone else's efforts, with an excellent list of links.
• Greg Adams of Carnegie Mellon shares thoughtful efforts, including the data (for which I thank him).
• Burt Monroe of Indiana has published a growing analysis including a comparison to predicting Perot in '96.
• Christopher Carroll of Johns Hopkins has published a careful statistical test of the improbability of the event.
• Matt Ruben of UC San Diego has a nice analysis and description of all aspects.
• Henry Brady of UC Berkeley for a really compulsively careful analysis at the precinct level.

Parting thoughts.

I think that these efforts are fun and a nice example of scholars trying to show how their techniques can allow us to see things more clearly in the world of politics. But, realistically, the voting problems in Palm Beach Florida seem obvious enough, that this effort cannot really reveal anything new. All in all, the more than nineteen thousand invalidated ballots is really a bigger story than the several thousand apparently wrongly goint to Buchanan. Showing that the Buchanan vote is implausible is really an indirect way of showing that this exceptional number of voided ballots is equally the result of an unfortunate ballot design. Errors in the electoral process are commonplace. Here, however, we have come face-to-face with a situation where the flaws in one locality have become magnified because they threaten the legitimacy of the national election process for the Presidency.

And we would be foolish to think that the political currents swirling about these events will respond to such analyses as provided by the researchers listed above. Still, I think this has been a fine effort by all concerned.