More on the study of Florida voting by UC Berkeley sociology professor Michael Hout and three graduate students (also see the post immediately preceding this one).

The study has now been reported in a few mainstream outlets. briefly describes the study. So does (entry for 11/18)., the website of the San Francisco Chronicle, reports "Several faculty members reviewed the analysis and could not find major flaws." However, the report also discusses possible flaws in the study. And it mentions two critics: Bruce Cain, a Berkeley political science professor, says the study is "incomplete" and Jack Pitney, an associate professor of government at Claremont-McKenna, "questioned the results of Hout's study." has a lengthy report. It quotes Professor Hout stating at a press conference, ""For the sake of all future elections involving e-voting systems, someone must investigate and explain the statistical anomaly we found in Florida."

O.K., I'll do it.

Professor Hout and the graduate students are to be greatly commended for posting their paper and their data on the Net. That makes investigating their results easier and more efficient. Here's what I discovered.

1. They estimate a regression model. The dependent variable is "Change in % Voting for Bush from 2000 to 2004". The observations in the analysis are all 67 counties in Florida . There are four independent, explanatory variables in their basic model: % Voting for Bush in 2000; % Voting for Bush in 2000, squared; total number of votes cast for Kerry and Bush in 2004; and--the variable of interest--a binary variable indicating whether the county used electronic voting in 2004. (15 of the 67 counties did so.)

The results from estimating the model using just these four explanatory variables do not support the hypothesis that Bush received an excess number of votes in counties using electronic voting. The coefficient on the electronic-voting variable is not positive--which would mean electronic voting raised Bush's total beyond what would be expected--but the opposite, negative (albeit with a t-ratio of just -0.66).

2. To obtain their reported results, they have to add two other explanatory variables: % Voting for Bush in 2000 times the electronic-voting binary variable and % Voting for Bush in 2000, squared, times the electronic-voting binary variable. These variables reflect the additional claim that problems with electronic voting occurred " . . . proportional to the Democratic support in the county, i.e., it was especially large in Broward, Palm Beach, and Miami-Dade [counties]." (Page 1 of the Hout., et. al. paper.)

But they have absolutely no theory for why electronic voting problems that spuriously created votes for Bush should affect counties in proportion to their Democratic votes!

However, let's set that aside for one moment. If the expanded model, with the two interaction variables included, is estimated, I obtain exactly the results they report in their paper. And those results indicate that Bush received about 150,000 "excess" votes in Palm Beach, Broward, and Miami-Dade counties, combined.

3. But the model is judging these votes "excess" based almost exclusively on Bush's vote in 2000. Anything that significantly altered voters' preferences between 2000 and 2004 is not captured by the model. I propose there is a logical, even obvious, candidate for such a factor: these three counties have an exceptionally high number of Jewish residents, and President Bush's policy toward Israel and his leadership of the war in Iraq convinced a number of these normally reliable Democratic voters to vote Republican for president in 2004. For example, an article in the Fort Lauderdale Sun-Sentinel stated (the link is to a secondary source as the article is now available only for a fee):

"Jewish Democratic Party leaders in Palm Beach County are worried. They are increasingly concerned that Republicans and the Bush administration have done such a good job of marketing themselves to Jewish voters that the once-reliable bloc of Democratic votes could go in a big way toward the president's re-election.

"With 22 days until Election Day, Democrats are scrambling to undo gains Republicans have made among Jews. "It's a very big problem," said Sylvia Wolfe-Herman, a vice president of the United South County Democratic Club. "We no longer have the bloc vote."

4. This hypothesis can be tested by adding to the Hout, et. al. model a variable that measures the number of Jewish residents in each Florida county. I obtained such data from The data are for 2000 and are less than ideal, but seem to be the best data readily available.

After adding the variable, the Hout, et. al. results become statistically weaker. The t-ratios for the electronic-voting binary variable falls from 3.26 to 1.68; the interaction variables have t-ratios of -1.42 and 1.10. But the authors could claim, with some justification, that their results are qualitatively the same after this addition.

5. But why shouldn't we treat the number of Jewish voters in the model similar to the way electronic voting is treated? That is, why not claim that it is not Jewish voters, per se, that matter, but Jewish voters only in heavily Democratic counties? There are at least two potential ways to justify this. First, the Bush-Cheney campaign seems to have focused time and money on these three counties. For instance, Cheney spoke in Palm Beach and former New York City mayor Ed Koch made at least two appearances on behalf of Bush-Cheney in Palm Beach County. Second, anecdotally at least, a lot of Jewish residents of South Florida are retirees who moved from the Northeast, particularly greater New York City. Former New York City residents might well be particularly sensitive to terrorism and 9/11.

Given this thinking, I reestimated the model adding two more variables: the number of Jewish voters times the % Voting for Bush in 2000 and the number of Jewish voters times the % Voting for Bush in 2000, squared. (That is, two interaction variables of the same form as the interaction variables involving electronic voting.)

This changes the Hout, et. al. results dramatically. The coefficients of the three electronic voting variables all become indistinguishable from zero (t-ratios of 0.52, -0.38, and 0.21; an F-test that the three coefficients are all zero yields a value of 2.06 with 3 and 57 d.f., which is not significant at the .10 level).

In plain English, the claim that there was something fishy about electronic voting in Palm Beach, Broward, and Miami-Dade counties can't be distinguished statistically from the claim that Jewish voters in those three counties voted in unusually high numbers for Bush. And given that there is a much more appealing reason to believe the second hypothesis than the first, I think the Haut, et. al. conclusion is severely questionable.