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.
. . .
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.)