Dear All,
For those who like econometrics or statistics, here is a simple problem that is turning out to have significant political implications. It takes about 20 minutes to read and understand it. For those of you who teach econometrics or statistics, it makes an excellent problem for an introductory class -- an exciting real world example where the answer to a statistical question has real consequences.
Perhaps more importantly, it would be good if some of you would be willing to weigh in on it. As of now, a paper by two economists (Hausmann and Rigob�n, <http://ksghome.harvard.edu/~rhausma/new/blackswan03.pdf>http://ksghome.harvard.edu/~rhausma/new/blackswan03.pdf ) is being used to undermine the credibility of a very credible election result, by purporting to show econometric evidence of electronic fraud. Since this referendum was closely monitored and certified by the Carter Center and the Organization of American States, this paper has also called into question the credibility of the international monitoring process.
The election in question is a recall referendum that took place on August 15 in Venezuela, where the recall effort failed by a vote of 59 (NO) to 41 (YES) percent. The opposition put forth exit polls, conducted by opposition activists and supervised by the well-known American polling firm Penn, Schoen, Berland & Associates, that showed the opposite result: that President Ch�vez was recalled by a margin of 59 percent (YES) to 41 percent (NO). (These and other exit poll data were used by Hausmann and Rigob�n in their analysis).
The econometric model used by H & R is a bit complex (it is explained in the appendices to their paper), but the problem with their analysis is actually very simple. Here is a brief outline:
In this referendum voters expressed their preference (yes or no) with a touch screen voting machine. The machine then printed out a paper ballot with the voter's choice, which voters deposited in a ballot box.
Electronic fraud in this system is thus a difficult and risky enterprise: any rigging of the machines could be caught quite easily by comparison with the paper ballots at any polling center. In an audit after the vote, the National Electoral Council (CNE), together with the international observers from the Carter Center and OAS, drew a sample of 150 polling stations and compared the machine results to the paper ballots. The results matched almost perfectly -- with 0.1 percent difference -- a number that is statistically insignificant and easily explainable by the likelihood that some voters might have failed to deposit their paper ballots.
But Hausmann and Rigob�n came up with a theory of fraud that is consistent with a clean audit. To take their hypothetical example (p.28-30): suppose there are 3,000 voting centers where the machines are rigged, and the CNE randomly selects the remaining 1,580 centers to be clean. The electoral authorities then fix the program that randomly selects a sample of 150 centers for auditing, so that the sample is selected from only the 1,580 clean centers. The electronic results from these centers would then match the paper ballots, and the audited sample would show the election to be clean.
The problem with this theory is that under these assumptions, the audited sample is actually a random sample of the universe of (pre-vote, pre-fraud) polling stations. It therefore provides statistical evidence, which Hausmann and Rigob�n ignored, of the overall referendum result. And the sample came in very close to the official result: 41.6 of the audited sample voted YES, to recall the President. A relatively simple statistical test shows that:
-- The chances of getting an audited sample, under Hausmann and Rigob�n's assumptions of how it was selected, of 41.6 percent YES, if the true (non-fraudulent) vote were 59 percent YES, are less than one in 28 billion trillion.
-- Even if the true vote had the recall barely succeeding with only 50.1 percent YES, the chances of getting an audited sample of 41.6 percent YES are less than one in a million.
That should be the end of the story. However, after the Carter Center responded (see <http://www.cartercenter.org/documents/1834.pdf>http://www.cartercenter.org/documents/1834.pdf ) to Hausmann and Rigob�n, they responded with a new theory of the fraud (see <http://ksghome.harvard.edu/~rhausma/new/CarterResponse.pdf>http://ksghome.harvard.edu/~rhausma/new/CarterResponse.pdf pages 2-3), in which the audited sample might have been not randomly selected but deliberately selected to be non-representative. In other words, it could have been chosen to be very pro-government, so that the 41.6 percent YES vote in the sample would match the overall (fraudulent) result.
However, this would mean that a very pro-government sample was selected for the audit. But there is no evidence of this; and in fact, in our paper we looked at the election results from 2000 and found that the people in the audited areas voted the same as the rest of the country in the 2000 election. In that 2000 election, Ch�vez received 61.8 percent of the major-candidate vote in the areas audited for the 2004 referendum, as opposed to 61.4 percent for the country. This is well within the margin of sampling error.
So there is no evidence of electronic fraud and no more reason to question the results of this election than there is to question that Ronald Reagan beat Walter Mondale in 1984, by the same margin.
All of this is explained in our brief paper: <http://www.cepr.net/publications/fraud_venezu_conspiracy.pdf>http://www.cepr.net/publications/fraud_venezu_conspiracy.pdf .
I want to add that this is not a personal or political dispute with Hausmann and Rigob�n. In fact, Professor Rigob�n has responded to me by e-mail and our correspondence has been useful, interesting, and friendly. And we continue to take them at their word that they are not simply trying to undermine the credibility of the electoral process, but indeed believe that an electronic fraud may have taken place, and that their paper provides statistical evidence of such fraud. Nonetheless I am very sure that they are completely wrong.
The problem is that, since their paper is a bit complicated, almost no one has read it and understood it. (Although it has had considerable influence in the U.S., international, and Latin American press, and of course also in Venezuela). However it is not necessary to go through all of their derivations. Some of you may take the time to read it, as we have, and to figure out how they might have gotten their result in the absence of electronic fraud. However, their theory of the fraud -- outlined above -- is explained on page 28-30 (see <http://ksghome.harvard.edu/~rhausma/new/blackswan03.pdf>http://ksghome.harvard.edu/~rhausma/new/blackswan03.pdf ); that, combined with the statistical evidence noted above and presented in our paper, is sufficient to make an informed decision on whether these allegations of electronic fraud should be taken seriously. Anyone with a basic knowledge of statistics can easily understand everything here.
If anyone in interested in looking at this issue, please contact me by e-mail or at the numbers below. The Carter Center will probably be reviewing these allegations again, and the controversy will continue, so anyone who is willing to take a little time to understand the very basic statistical analysis here may be very helpful.
Please feel free to forward this to anyone you know who might be interested, especially statisticians.
Thanks in advance,
Mark
Name: Mark Weisbrot E-mail: <[EMAIL PROTECTED]> Co-Director Center for Economic and Policy Research 1621 Connecticut Ave NW, Suite 500 Washington, DC 20009-1052 Phone (202) 293-5380 x228 Fax (202) 588-1356 (202) 333-6141 (home) (202) 746-7264 (cell) www.cepr.net
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Michael Perelman Economics Department California State University michael at ecst.csuchico.edu Chico, CA 95929 530-898-5321 fax 530-898-5901
