In Mexico, the math does not add up

[eridani]

Anyone who can take on the physicist's article in Spanish, please go for it.

http://commentisfree.guardian.co.uk/james_k_galbraith/2006/07/the_mexican_standoff.html

To begin with, a simple matter. According to an article by Roberto González Amador in La Jornada, the vote totals don't match the percentages reported. Given the just over 15m votes Calderón was said to have earned, the percentage reported for him, 35.89%, could only be obtained by including invalid ballots in the total reported. If, on the other hand, one takes the overall vote total and the percentage reported for Calderón as correct, then his total vote must have been substantially less than was reported.

The same is true for AMLO and the other candidates, and there is a total shortfall of over a million votes between what can be justified by the official percentages of the valid votes, and the sum of votes reported. The discrepancy proves nothing, but even if it is only a simple error, it certainly seems to cast doubt over the competence of the count.

Let's turn to the harder stuff. An analysis by the physicist Luis Mochán of UNAM based on the realtime evolution of the vote count and the distribution of vote totals by polling place can be found here, and in greater detail in Spanish, here. It's not easy reading, but is immensely worthwhile. It's possible that Mochán's work inaugurates a new era in realtime checking for vote fraud, made possible by the simplicity of Mexico's first-past-the-post direct vote and the rich electoral data sets that can be made instantly available. Call it the age of transparency, in collision with an oligarchy of thugs.

Mochán's work calls attention to at least four important anomalies in the count.

1. Calderón's percentage lead in the count started at around seven percentage points, and diminished steadily in percentage terms through the first part of the count. This corresponded to a remarkably constant absolute differential between Calderón and AMLO as the count progressed. Is this normal? The count depended on the arrival of the boxes; if this were absolutely random then the proportions should have held roughly constant while absolute differentials widened, as actually happened to the differential between Calderón and the third major candidate, Madrazo of the PRI, for most of the evening. Why did the Calderón-AMLO differential follow a different rule?

2. The PREP results went on view only after the first 10,000 boxes had been processed. If those first 10,000 boxes resembled what came later, then extrapolating backward should produce a line intersecting the origin - each candidate should have started with zero votes. For Calderón this is the case, but for AMLO it is not: the AMLO intercept is actually at minus 126,000 votes. Thus, the first 10,000 boxes were markedly different from those that followed. How?

3. There are gross anomalies in the number of votes counted per five-minute interval as the count finishes. Over the course of the evening, the pattern of vote counts set a normal range for this variable. As the last boxes came in, however, it was radically violated, with many more votes piled in, per interval, than was normal before. Moreover, toward the very end, PREP reset the box count, which regressed from 127,936 at 13.17 on July 3 to 127,713 at 13.50, meaning that records for 223 boxes disappeared. 33 minutes had by then passed with no updates. When they resumed, there were updates with absurd results: more than 6000 votes per box at 13:57, and then updates with large negative votes per box at 13:57 and 14:03.

4. From a statistical point of view, the distribution across boxes of votes earned by each candidate should be smooth. For Madrazo it is. But for Calderón and AMLO it isn't. In Calderón's case, the distribution appears to be shifted out, with the shift localized among the last 40,000 boxes counted. In the case of AMLO, the distribution tails off abruptly from its peak. It is in the difference between the slightly fat distribution for Calderón and the shaved distribution for AMLO that the difference in the final outcome is to be found. A graph of the differences in Calderón and AMLO's votes per box, which ought to follow a normal curve, does not. Over a certain range, Calderón's margins appear abnormally large.

[fasttense]

1. Thanks for posting this again.

I read this about a week ago but it did not get much of a response. Those pesky numbers are hard to hide. Perhaps Fox has a reason for calling for a new election.