"Of the total number of previously unread or incorrectly read votes in 67 of the 67 counties reported (3,583 votes), 1,063 favored Governor Bush and 2,520 favored Vice President Gore. Recall that with the coin you’d expect an equal number of heads and tails over a large number of coin tosses. Similarly, we’d expect that each candidate would gain an equal number of votes in a recount, or proportion of .50(a 50/50 percentage). Instead, as a proportion of the total vote what we found is a proportional gain of Bush of .297 and one for Gore of .703."

"Using a binomial statistic that assumes a .50 proportion of error per candidate the actual proportions for Bush and Gore significantly differ from chance. The probability of such a large difference favoring one candidate over another is incredibly small. In other words, the odds are less than 1 in a billion that the original vote was a fair count: that number would be a decimal with nine zeros followed by a 1 (.0000000001). In fact, imagine a decimal with 133 zeros followed by a 1: the actual probability that the Florida count was fair is, in fact, even less than that number. Even when the probability is .05 (one in 20), statisticians, by convention assume that the result was not due to chance alone."
From "Doubting Florida Voting Data" By Lynn Miller, Professor of Communications at the USC Annenberg School.

"...Lynn Miller, a professor of communications at the University of Southern California, wrote that statistical analysis and probability theory show both candidates should come out of the recount process with equal adjustments (for example, Democratic candidate Al Gore gains 40 votes, but so does Bush). Since that was not the case, she said probability theory dictates that the original count must have been biased in favor of Bush. However, she backs this up with a few faulty assumptions, debilitating her analysis.

"Miller compares voting to the flipping of a coin as if there were only two potential results. There are at least four outcomes in any given two-party election: Candidate A, Candidate B, Spoiled (none of the above) and Void (the voter has tried to vote, but failed)—or to mention the fact that the presidential ballot contained 11 options. Votes for Candidates A and B are more likely than spoiled and void, but not overwhelmingly so. Where the electoral system is more complicated (either in design—like the Single Transferable Vote system — or in machines—such as complicated punch ballot papers), void votes will be more common. Any statistical analysis has to bear these facts in mind. As a result) it would be an incorrect conclusion to say the initial count was unfair because the special count revealed more votes for one candidate than another."
From "Beware of dubious data dredging in Florida" by Howard Fienberg and Iain Murray, Research and Senior Analysts with the Statistical Assessment Service (STATS).

"...The claim that there was an unusually large number of Buchanan votes in the county had been accepted, and even promoted, uncritically. This claim was further amplified made by a dozen or more authors, all circulated on the internet, that a statistical evaluation of the data showed that the Palm Beach Buchanan vote was grossly disproportionate to the vote that would otherwise be expected. A number of authors went the next two or three steps, and made predictions that a certain share of these Buchanan votes were intended for Al Gore. Estimates of 1000 to 5000 "lost" Gore votes were made, based on statistical models and sweeping assumptions about voter behavior. This analysis began as an evaluation of the representation of the data, and has grown to an assessment of the "lost vote" theory as well."

"...When you look at the votes in the hundreds of thousands—which are the votes totals in the biggest counties for Gore and Bush—the impact of Nader and Buchanan seem small and almost irrelevant. Indeed, a fair look at the data reveal that Palm Beach county wasn’t even one of Buchanan’s best counties, and he lost to Ralph Nader in the county by a 60% margin."
From "Statistical Analysis of the Florida Presidential Vote" by Patrick L. Anderson, Managing Director of Anderson Economic Group and former Deputy Secretary of State for Michigan.

"Now, the fraction of the three candidate (Bush, Gore, Buchanan) vote that went to Buchanan in Palm Beach County is about .8%. This figure is about .5% to .6% higher than we would expect given the observed Bush vote and equation (8) above and assuming that the observed Bush vote in Palm Beach County is equal to the true Bush vote. The observed Gore vote was about 63% and the true vote can’t be much higher than that. Hence, if about 2.2% to 2.7% of the true Gore voters mistakenly voted for Buchanan we would expect to find about 1.4% to 1.7% more Buchanan voters than we observe. But we do not find quite this many, suggesting that this estimate might be high because of the use of ordinary least squares in an ecological regression which sometimes provides estimates that are higher than more refined methods."

...Using data from the 67 Florida counties along with the data from the precincts in Palm Beach County, I find that there is strong likelihood that over 2000 of the Buchanan voters in the Palm Beach County were cast by Gore supporters who mistakenly punched Buchanan’s name. There is no evidence for the proportion that the extra Buchanan voters were Bush supporters."
From "What Happened in Palm Beach County" by Henry E. Brady, Professor of Political Science and Public Policy at the University of California, Berkeley.

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