Arithmetic errors or fraud?

Skjellifetti, a reader, posted the following — very interesting — question and comment:

If the ballots are in the care of the TRIFE, how does Obrador know that “the figures were completely out of whack with the ballots in the packages?” My understanding is that current Mexican election law does not require TRIFE to recount all of the ballots. That law was agreed to by all of the parties before the campaign began. The Europeans and other neutral observors seem to think that the election was fairly clean. By asking for a change in the recount rule now, Obrador looks more and more like a sore loser.

Having said that, a recount of such a close election is not an unreasonable request in a democracy. But it would also not surprise me if Obrador lost the recount, too. Sometimes things are done cleanly, there are no conspiracies, and you discover that there really are more of them than there are of you.

The answer to the question is straightforward. At the end of election day, each polling place was supposed to count the votes manually — in the presence of an IFE officer and representatives of all the parties in the election. The result had to be recorded in an “acta” or document stating the total number of ballots received (TB), the ballots left unused at the end of the day (BU), and the votes cast (VC). The votes cast are broken down into votes for each candidate (say: PRD, PAN, PRI, NA, ALT) and void votes (VV). Then, a copy of the “acta” was supposed to be given to the IFE officer and each party representative, one copy had to be displayed outside of the polling place, and another copy had to be included with the ballots in the packages that everyone there had to seal and send to their respective electoral district.

Clearly, a consistency condition that can be easily checked just by looking at the “actas” — without knowing what’s inside the ballot packages — is this:

TB = BU + VC


VC = PAN + PRI + PRD + NA + ALT + VV

It would have been nice if the IFE had reported in the PREP, not only PAN, PRI, PRD, NA, ALT, and VV, but also BU and BR. They didn’t, although they have that information in their database, which could be accessed by the parties. What they did was to include a rate of “citizen participation,” i.e. VC/registered voters. But then you need to do inference.

A second issue is the consistency between the capture of the information from polling-place “actas” into the IFE’s computer system (posted on the PREP). There’s an awful lot of inconsistencies between the figures input in the PREP and what the physical “actas” say. López Obrador is claiming to have physical evidence that at least 60 per cent of the “actas” have inconsistencies! (They are scanning them all and they’ll soon be available online for everyone to peruse.) The “actas” report 1.5 million votes that cannot have a physical support in actual ballots — that is, if the number of ballots reported in the actas themselves are correct.

López Obrador is not talking about “actas” that made it into the 11,000+ “actas” the IFE dumped in its folder of inconsistent “actas.” As of today, the IFE only deems inconsistent 1.55 per cent of the “actas” — all other “actas” are fine, says the IFE. (Note that this figure used to be larger, which led — in some cases, during the district count — to opening the ballot packages, only to find that in an overwhelming number of cases, López Obrador had had his count decreased and Calderón’s increased in the “actas.”)

Let’s take a step back. Aren’t arithmetic errors common in any election? Yes, but if they are true arithmetic errors, you’d expect them to have the statistical distribution typical of a random variable. Say (without accepting such result as final) that the final outcome is, as the IFE says, PAN 36.38 per cent, PRI 21.57 per cent, and PRD 35.34 per cent. Then, the arithmetic errors should match these proportions pretty closely. I mean, we’re talking large numbers here — the laws of statistics apply.

The problem with these “arithmetic errors” is that they’re strongly biased against López Obrador. My suspicious mind guesses that’s the reason why you see López Obrador demanding a full recount — vote by vote, polling place by polling place — whereas Calderón and his powerful backers resist such event tooth and nail. How do you dispel these doubts without opening the packages?

Yesterday, López Obrador (along with his assistants Claudia Sheinbaum and Octavio Romero Oropeza and computer wiz Esteban) returned to Carlos Loret de Mola’s radio show in W Radio (Televisa’s XEW). They brought 21 well-labeled boxes with documents — copies of “actas”. In paper about 30,000, out of the 50,000 “actas” with “arithmetic errors” that López Obrador’s team has so far been able to review. (They left a DVD with evidence of the 50,000.) Claudia Sheinbaum said there are still more “actas” that their team hasn’t been able to review yet.

They showed to the camera a few cases of discrepancy between the figures in the “actas” and the figures in the IFE report. I’ll list here only those I was able to capture. (The video is here: By the way, at a point, Loret de Mola wondered whether they were cherry picking only “actas” with discrepancies that affected López Obrador. In reply, Claudia Sheinbaum challenged Loret de Mola to pick any “acta” and find discrepancies that didn’t help Calderón or hurt Andrés Manuel.

A casilla in Gustavo A. Madero, Distrito Federal
PRD in the “acta” 295
PRD in the IFE database 195

A casilla in Guadalupe, Nuevo León
PAN in the “acta” 186
PAN in the IFE database 786
VC 965
TB 603

A casilla in Ciudad Valles, San Luis Potosí
PAN in the “acta” 166
PAN in the IFE database 766
VC 884
TB 412

A casilla in Chilapa, Guerrero
PAN in the “acta” 32
PAN in the IFE database 132

A casilla in Michoacán
PRD in the “acta” 159
PRD in the IFE database 59

Loret de Mola, echoing an argument that critics of López Obrador have voiced, asked the candidate of the left why his representatives in those polling places where the “actas” were altered didn’t complain or why they signed those “actas” if they were so irregular. Of course, Loret de Mola, as an interviewer can ask loaded questions that may or may not reflect his personal political views. But what calls my attention is the tendency of López Obrador’s critics to blame the victim.

A few days before the election, I denounced on a Mexican Internet forum that López Obrador’s web sites had been hacked. For some reason I don’t understand, López Obrador’s team didn’t denounce that attack publicly (they have denounced the latest hackery, but not that one.) A serious poster on that forum replied saying that the blame fell on López Obrador’s computer team, because they didn’t have the security expertise required to do their job right. The discussion in the forum was political, not technical. So I replied (with an analogy way over the top, but I’ll say in my excuse that I was trying to make a point in a forum with lots of noise) saying:

“If your young sister is raped by a thug, instead of condemning the rapist, would you take it against your sister because she didn’t carry a gun in her handbag or because she didn’t learn martial arts to defend herself?”

I got no reply.


4 Responses to “Arithmetic errors or fraud?”

  1. Charles Says:

    Thanks for your reportage.

    There’s an interesting story in Jornada saying Calderon faked his Harvard degree:

    While an Executive MBA– which is what I assume “The Mid-Career Program” represents– is no joke, it certainly looks bad. Most people who get an Executive MBA are proud, because it’s a tremendously intensive course of study. So, if he’s calling it a Master’s instead of an Executive MBA, it sounds like The Mid-Career Program might be a cut-rate version.

  2. Charles Says:

    Oh– another point. If I understood IFE correctly, they are claiming they overcounted the ballots for PAN and PRD in the 2873 casillas by about 25,000 ballots. Ballpark, that’s a 3% arithmetic error. In elections, that’s huge and statistically impossible. Now, PRD is claiming that Rodrigo Morales is lying in claiming to have examined these casillas (

    All in all, the tone got nastier today, and perhaps for good reason.

  3. panchovilla Says:

    Thanks, Charles. I did read that story, but couldn’t make sense of it. It wasn’t clear to me to what votes they were referring to — is it votes from the “inconsistencies folder” or were they reviewing “actas” that had already been reviewed and input in the database? Anyway, the IFE is going to have a hearing before the TRIFE and things will get clarified as we go.

  4. Charles Says:

    Yeah, a good sign that a story is disinformation is that it doesn’t quite add up. It’s part of creating deniability. My point was that even if you accept the claim, you are also forced to accept a 3% net error rate, a flaming red flag for probable fraud.

    I’ve added a clarification on the Jornada story on Calderon’s “maestria.” The KSG does offer a one year program called a Master’s in Public Administration. Also, the typical American MBA doesn’t require a thesis. This may be a tempest in the teapot. However, if the KSG program is analogous to the Executive MBA, it doesn’t include the full nine yards of hands-on field service and extensive writing. I have asked the author of the article whether the Mexican people would have been misled by the claim.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: