I hope this article from a famous mathematician satisfies the naysayers and trolls who have tried like hell (unsuccessfully, I might add) to debunk Professor Freeman's analysis - and my own.
Here is my latest probability posting for easy reference:
http://www.democraticunderground.com/discuss/duboard.php?az=view_all&address=203x86863And here is the article from Mr. Paulos:
http://www.math.temple.edu/~paulos/exit.htmlFinal Tallies Minus Exit Polls = A Statistical Mystery!
by John Allen Paulos
OpEd in the Philadelphia Inquirer, Nov. 24, 2004
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Why did the exit polls taken on election day in the battleground states differ so starkly from the final tallies in those states? As my crosstown colleague, Steven Freeman of the University of Pennsylvania has demonstrated in his paper, "The Unexplained Exit Poll Discrepancy," the pattern is unmistakable. In Ohio, Pennsylvania, and Florida, the differences between Bush's final tallies and his earlier exit poll percentages were, respectively, 6.7%, 6.5%, and 4.9%.
Similarly huge differences between the final tallies and the exit poll percentages occurred in 10 of the 11 battleground states, all of them in Bush's favor. If the people sampled in the exit polls were a random sample of voters, Freeman's standard statistical techniques show that these large discrepancies are way, way beyond the margins of error. Suffice it to say that the odds against them occuring by chance in just the three states mentioned above are almost a million to one.
Since exit polls historically have been quite accurate (there is no question about likely voters, for example) and the differences as likely to have been in one candidate's favor as the other's, we're confronted with the question of what caused them. Given the indefensible withholding of the full exit poll data by Edison Media Research, Mitofsky International, the Associated Press and various networks, we can only hazard guesses based on what was available election night. The obvious speculation, alluded to above, is that the exit samples were decidedly non-random.
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Absent any proof or compelling reasons for the differences between the final tallies and the exit polls in the swing states, I don't understand why these gross discrepancies are being so widely shrugged off. After all, the procuring of random samples is far more of a problem for ordinary telephone polls where the minority of people who cooperate with pollsters presumably differs in some way from the majority who don't. Still, these polls are not dismissed with the same impatient nonchalance as this year's exit polls.
Of course, what makes these discrepancies more than a technical problem in statistical methodology is that there is a much less likely, much more ominous explanation for them: massive fraud. Fraud is hard to believe for many reasons, one being the widespread nature, extending over different states and regions, of the shift to Bush. The difficulty of concealing a conspiracy grows very rapidly with the number of conspirators.
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Hard evidence? Definitely not. Nevertheless, the present system is such a creaky patchwork and angry suspicions are so prevalent that there is, despite the popular vote differential, a fear that the election was tainted and possibly stolen. (If 68,000 Ohio Bush supporters - only about a half dozen voters per precinct in the state - switched their votes, Kerry would be president-elect. Considerably fewer switches would be required if, as is likely, most provisional and spoiled ballots were good and went for Kerry.) A high-level commission should thoroughly examine the exit poll discrepancies and our electoral apparatus in general.
This is not a partisan issue. People differ about whom they want in the White House, but almost everybody wants whoever is there to be seen by all as having been rightfully elected.
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Professor of mathematics at Temple University and winner of the 2003 American Association for the Advancement of Science award for the promotion of public understanding of science, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Plays the Stock Market.
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