One of the most striking things watching the evolution of the vote count in Mexico, both the preliminary and the definitive one, is the strange, linear tendencies of the totals.

When the final count was around 75% or 80% done, al of a sudden the PAN started closing the gap with the PRD. For a while El Universal had a graph up showing the percentage lead that AMLO had plotted against the percentage progress of the vote count. I saw it in the middle of the night 3 or 4 a.m., when I got up to get a glass of water and checked the results. By the next morning, the graphic was gone and Calderón had a significant lead.

Having covered many elections over the years, and especially having my responsibilities focused on the presentation and analysis of vote counts, exit polls, etc., the behavior of the numbers in the Mexican election count didn't "feel" at all right to me. But I couldn't figure out how to explain it apart from the late night El Universal chart and the assertion that the straight-line change late in the recount just felt wrong.

Now Jorge A. López, Chair and Shumaker professor, Physics Dept., University of Texas at El Paso, has trained the instruments of mathematical analysis on the Mexican election vote numbers, and made an important discovery about their behavior.

Specifically, that the PRD and PAN votes did not vary independently, but rather varied together over time, increasing in a definite proportion to each other.

In the case of the preliminary count, each increase of 1,000 votes in the PRD totals brought a 1,008 increase in the PAN totals over roughly the last half of the counting, maintaining a 1% PAN lead over a long period.

In the case of the recount, PAN totals increased by 1,094 for every 1,000 PRD votes.

There is a statistical measure for testing whether two variables, such as the vote totals of these two parties, are changing each on their own account or are tending to move lock-step with each other. The measure is called Pearson's Correlation Coefficient, and can range in value from -1 (the two variables move perfectly opposite each others) to 0 (there is no apparent relationship between the two variable) to 1 (the two variables move up and down lockstep together).

For the recount, the Pearson correlation coefficient was 0.997183, and for the preliminary count the correlation coefficient was 0.999974! In either case, as close to 1 as makes no difference.

To understand the significance of this, it is necessary to keep in mind that these two candidates had widely varying levels of support in different areas. Thus one would expect the results to be "lumpy," now with the PRD adding a disproportionate number of votes, then the PAN.

But what the mathematical analysis shows is that the vote totals for these two parties increased smoothly together, without any "lumpiness" at all, over the time periods analyzed.

A correlation coefficient of 1 indicates that two variables are perfectly aligned. In statistical testing of measurements of natural phenomena, .8 is considered a strong positive correlation. In the case of the Mexican vote, the degree of correlation is astonishing beyond belief.

Moreover, the marginally less perfect correlation in the case of the final recount is very easily explained by the limitations of the data available for the analysis. The figures available to professor Lopez were percentages out to two decimal places of the precincts counted and the votes for each candidate. Thus rounding errors were introduced.

In each case it was possible for Professor Lopez to derive simple linear equations describing the vote of one party as a function of the other party's vote for roughly the last half of each count: 

 Y=279926 + 1.008060294

  

Y=-1646507 + 1.094013

 

 

Y=PAN

 

X=PRD

Again, the important fact is that PAN and PRD had sharply varying amounts of support in different parts of the country. It is said that the PAN squeaked out a victory at the end of the recount because results from the pro-Calderón areas came in more slowly.

However, if that were the case, then we'd see significant discontinuities in the vote totals towards the end of the recount, with sudden *disproportionate* jumps for Calderón, rather than the straight-line accumulation of X number of votes per 1% of precincts counted, which is what is claimed to have happened.

What the mathematical results suggest is that the correlation was, in fact, 1.0 at the source of the data, and the slight deviation from a mathematically perfect one are due to rounding and human error.

The easiest, simplest and in fact, virtually only way to obtain a correlation of 1 is to derive the numbers from mathematical formulas, rather than counts of actual ballots. As professor López put it, "the data ... are artificial."

Professor López's two papers reached me from Prof. Nelson Valdés's "Socialanalysis" email list as PDF attachments. Both are in Spanish. Through a Google search, I was able to confirm that professor Lopez exists and holds the appointments Nelson Valdes's credited him with. However, I was unable to find a web posting of the two papers.

Previously unpublished. Received via Marxmail.