Skip to content

Fraud in the recent Mexican election?

Jorge Lopez sent me the following report analyzing results from the recent Mexican election. He looked at the vote totals as they emerged through the election night, and saw patterns that led him to conclude that there was fraud in the vote counting. His report begins:

Many of us took advantage of the latest technology and followed last Sunday’s elections in Mexico through a novel method: web postings of the votes through the Program of Preliminary Results, or PREP by its Spanish initials. What Mexico’s Federal Electoral Institute (IFE) did not take into account is that the postings were not only informing, they were providing valuable data that can be –and was- examined to check its “health”. The bottom line is that the data presented is ill, so ill that it appears to have been given artificial life by a computer algorithm.

What the web surfers saw is that after an initial strong showing, which began at Sunday noon with a Calderon advantage of more than 4% over López Obrador (“AMLO”), the lead began to decrease in percentages. The diminishing trend continued and, around midnight, many of us went to bed forecasting a tie by 3:00 AM Monday, and an AMLO advantage of about 1% by wake up time on Monday. The morning surprise was that the trend had changed overnight and Calderon appeared with a slim but invariant advantage of about 1%; this sent many of us to what we, physics professors, do for a living: data analysis.

. . .

Here’s the full report.

I looked at the report, and I don’t think it represents convincing evidence of data manipulation. There are three reasons why I say this:

1. The report doesn’t have information on where the election returns came from. Thus, the changes in the votes (going one way, then reversing, etc, as shown on page 4) could arise from votes coming from different places.

2. It’s not such a surprise that the vote total will become more stable over time, because the vote total at time t+1 mostly comes from the vote total at time t. So I don’t see the correlation of .9999 as necessarily being meaningful.

3. In the picture on page 3, there’s no particular reason to expect a normal distribution. You will see differences of close to zero in percent as the counts go on over time.

The data being analyzed remind me of an analysis I did a few years ago of a local election in New York City; see this paper ,which appeared in Chance (and also will appear in Chapter 2 in our forthcoming book).

As I told Jorge, although I disagree with his conclusions, it’s good to air these things and let people make their own judgments, hence this blog posting. Jorge also send me this document from Eduardo Trejo which has some of the preliminary vote counts. Jorge also asked that if anyone has any comments, they can post them on this blog and also can send him email.

(For some more background on allegations of fraud in the Mexican election, see this Boingboing entry by Xeni Jardin, which has link to more stuff.)


  1. J Bravo says:

    Indeed, what you allude to on 1, i.e. "changes in the votes (going one way, then reversing, etc, as shown on page 4) could arise from votes coming from different places" is what actually happened. Once you look at WHERE the votes were coming the observed patterns seem wholly plausible for anyone with some substantive knowledge on Mexican politics at the sub-national level.

  2. web designer says:

    I think Jorge is on the right track to investigate the results. I think some of his conclusions are flawed in some respects. However, what he has done will certainly not hurt anything.

  3. Bruce McCullough says:

    If Professor Lopez bothered to read the newspapers,
    e.g., Financial Times (probably 7 July cover story — I subscribe to the print version but can't link
    to the electronic version), he would know that
    the late vote pattern was part of an intentional
    effort by Obrador's party.

    In heavily PAN states, the Obrador watchers refused
    to certify the boxes until several hours after
    the ballots were counted. This was a deliberate
    attempt to make Obrador's lead disappear during
    the night.

    Professor Lopez's failure to report this
    easily obtainable evidence does not reflect
    well on him.

  4. Jorge Lopez says:

    First of all, thanks for taking the time to read my exercise. I want to add three things:

    1) How the deviations were calculated. Letting X(n) and Y(n) be the total number of votes the two top candidates had at update n, to avoid problems with large numbers, the ratio R(n)=X(n)/Y(n) was constructed and its average <R> was calculated along with its standard deviation σ. The frequency chart (fig. 3) shows the differences R(n)-<R&gt binned in steps of σ/5.

    2) Data available and a more complete study. Mexico's UNAM professor Dr. Luis Mochan did a thorough study available at…, also, he has the data available for public access.

    3) Workshop in Mexico City. A discussion session to analyze the election data will be organized in Mexico City, those interested in participating please contact Dr. Gerardo Contreras-Puente (