As I write, the apologists for the Chavez “victory” have an explanation for the peculiar coincidences that critics have observed, to wit, the number of instances in which several voting machines at a particular voting center recorded identical numbers of “si” (anti-Chavez) votes. That oddity has fostered suspicions that a fair number of machines were programmed to record “si” votes as “no” after the former reached a pre-determined cap. Here is the response from Jimmy Carter’s election “watchdogs”, as reported in the Wall Street Journal [link probably for subscribers only]:
Carter Center officials said the pattern detected by the opposition, which showed up in groups of machines at about 700 voting tables out of a total of about 12,000 nationwide, appeared to be a naturally occurring effect that surfaced in tabulations of both pro- and anti-Chávezvotes. . . .
The Carter Center said it found a pattern of matching “yes” votes to oust Mr. Chávez at 402 voting tables, which each have one or more machines. It found a similar pattern affecting support for Mr. Chávez in machines at 311 tables.
“The most important thing is that it affects both sides,” said Jennifer McCoy, the director of the Carter Center’s mission to Venezuela. “It would appear to indicate a random mathematical effect.”
Experts seemed to agree. Aviel Rubin, a computer-science professor at Johns Hopkins University, said he calculated odds of roughly one in 17 that two of three computers at a voting table would have identical results. That compares to about one in 15 that so far have shown similar results in Venezuela’s referendum.
It is certainly true that some matches would be expected on the basis of chance, but this dismissal ignores a lot of salient facts.
First, some procedural background (with thanks to Venezuelan blogger Miguel Octavio for a more lucid explanation than I’ve seen in any of the major media): Each polling place had one to five mesas, each with one to three touch screen voting machines. A voter touched “si” or “no”, received a paper ballot recording his choice and deposited it in a ballot box. When the polls closed, the poll watchers noted the number of “si” and “no” votes recorded by each machine, certified the number in an acta and transmitted the actas to the national electoral commission (the “CNE”).
Discovering erroneous voting machine tallies should have been easy. One only needed to count the paper ballots immediately and compare them to the machine readouts. That step was not taken, because the pro-Chavez CNE majority refused to agree to it. The ballot boxes were simply placed in the custody of the pro-Chavez armed forces, which has held onto them ever since.
Anti-Chavez observers, sifting through those portions of the vote count to which they have access (the CNE hasn’t released full, mesa-by-mesa, machine-by-machine tallies), quickly found an odd pattern: In a surprisingly large proportion of mesas, two or three machines registered exactly the same number of “si” votes. An opposition politician in the state of Bolivar claims that this happened at 24 of the state’s 60 voting centers. Most of the coincidences involve two out of three machines. In every one of them, the third machine shows fewer “si” votes than the two with matching totals.
To get a concept of how reasonable it is to attribute this phenomenon to chance, let’s consider an analog. If one rolls three six-sided dice, what is the probability that two or three of the numbers will be the same? Readers can probably work out for themselves that there are 216 permutations (6 x 6 x 6), of which 6 have the same number on all three dice and 30 have two identical dice. Hence, there is are 36 chances out of 216, or 1 in 6, of pairs or triplets of the same number.
A mesa with three voting machines can be compared to three dice with many more than six sides each. Each of these “dice” has as many faces as there are numbers of “si” votes that it could record. Let’s suppose that a plausible range spans about 50 numbers, from, say, 110 to 160 votes. Usually, each machine will record a different number, but occasionally two, and more rarely all three, are bound to be the same. Assuming a random distribution, there is a six percent probability that two of the three will agree and a minuscule chance (1 in 2,500) of unanimity. (This back-of-the-envelope calculation is, I suspect, the one that Professor Rubin performed; if he was more sophisticated, he nonetheless arrived at the same result.)
Now we can see some of the flaws in the Carter Center’s bland reassurances:
The Center says that there were “about 12,000” mesas. So far as I can discover, that is an inflated figure. Sr. Octavio says that there were 8,142 (about ten percent of which used paper ballots rather than machines). Other sources give numbers of “about 8,300” and 8,465. One figure on which there is no disagreement is that the government purchased 20,000 Smartmatic machines, meaning that no more than 6,666 mesas could have had three machines. Since some had one or two, it appears that there were, at most, about 6,000 mesas where coincidences could be observed. By Professor Rubin’s estimate, one would expect about 360 instances, divided equally between “si” and “no”. Over 700, with a four-to-three ratio in favor of “si”, is hard to characterize as the product of innocent chance.
The Center doesn’t disclose how many of the coincidences were of the extremely rare three-machine variety. If the Bolivar authorities are to be believed, the number in their state alone was more than one would expect in the entire country.
Also not disclosed is whether, where two of three machine readouts matched, the third was invariably lower than the other two, as was reportedly the case in Bolivar. That pattern would be consistent with the hypothesis of a cap and is hard to account for otherwise.
It would also be interesting to know the geographical distribution of the coincidences. If the government employed this means to rig the vote, it didn’t have to fix all machines everywhere, only enough to be confident of the outcome.
In all of this confusion, one fact stands out with stunning clarity: The Carter Center endorsed the government’s version of the vote count almost as soon as it was announced and has since treated all questions as inconvenient annoyances, to be shunted aside with only superficial examination. Whether or not fraud really took place, Mr. Carter’s minions were no barrier to its commission. The former President should be ashamed of himself, though one doubts that a man who has praised so many tyrants is capable of feeling remorse at assisting another in consolidating power.
Note: I’ll be traveling this weekend and may lose track of developments. Those who are interested in keeping up (not much of the blogosphere, alas – isn’t the consolidation of a pro-terrorist dictatorship in a major oil producer at least as interesting as where John Kerry was on December 25, 1968?) should read Caracas Chronicles, Venezuela News and Views and The Devil’s Excrement.
Update: Here is a summary of the anti-Chavez front’s attempt to persuade Jimmy Carter to be more than just a yes-man for a budding dictator:
The Coordinadora Democrática just met with Gaviria and Jennifer McCoy. They are asking for a wider audit. The Coordinadora complained that the pre-agreed live audit was never carried out on Sunday. The CD says that the results do not agree with the exit polls, but were advanced to the international press agencies at midnight (three hours before they were reported). They criticized that before the OAS audit was completed, the Brazilian OAS representative wrote a report saying that things were normal and did not mention the problems reported with the machines. The CD reiterated there are more than 1800 cases of the coincidences among machines, therefore they think that this is so improbable that the OAS can not accept the results as they are being reported. They reminded the Carter Center that in the Florida case, Carter himself said that there should be no rush to judgement and that ALL the ballots should be counted. Why, the CD asked, is this case any different?
The CD gave OAS Secretary Cesar Gaviria, copies of each of the Actas with the numerical coincidences, corresponding to each of the machines. This is what I have been asking for all day. On the audit that was supposed to take place last Sunday, the agreement was that it would happen in all states. It was done in only 14. It had been agreed that it would be done in 199 locations, it was done in only 7 states with presence of CD representatives. In these cases, the Si [anti-Chavez] received 63%, the No received 37%
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