The Devil's Excrement

Just for the record, the paper “Analysis of the 2004
Venezuela Referendum and the Relation between the Official Results and the
Signatures Requesting it on automated centers” by Gustavo Delfino and Guillermo
Salas has been accepted
for publication in the Journal “Statistical Science”. (You can download the
last version there)

Somebody sent me the link to this website devoted to the Venezuelan Electoral system. It is well done and there are over 20 presentations on the problems of our electoral system, including evidence of fraud, problems with the electoral registry and the like. A lot of the material complements or explains with voice and slides, some of the stuff found in my RR Models section. Unfortunately, it is only in Spanish.

In four earlier posts, I presented a description of the work of Delfino and Salas and the complementary work of Medina on the evidence for fraud in the recal referendum. I wrote four posts on the subject, which you can find here, here, here and here. In the second one of those posts I discussed the parameter “k” a measure of the proportion of fraction of Si or Yes votes to recall Hugo Chavez, divided by the number of people in the same center that signed the petition to recall Hugo Chavez:

      Yes(Si) Votes
k= ——————
      Signatures

As a function of another “normalized” parameter s

      Signatures
s= ——————
     Total Votes

In the latest version of the paper, now in English, Delfino and Salas have added a compelling graph of k seen here:

Fig. 1. k as a function of the total number of votes on equal scales at each center for manual (left) and automated (right) centers. (Open circles are centers abroad)

What this plot does is to show k as a function of the number of total votes for voting centers of equal sizes, so that no distortions are introduced by the absolute number of voters. What can be seen is that the manual centers show a lot of fluctuations or scatterat smaller centers, which is what you expect. as the number of voters becomes small. This is because k in some sense measures how good a predictor the signatures were of the actual Si vote to recall Chavez, but as centers become smaller, the accuracy will diminish because the statitistics are “worse” since the number of voters is smaller. That is why you see scatter for small number of votes on the manual centers.

The problem is, that since the size of these centers are the same, one should see the same whether the centers are automated or not. But this simply does not happen as seen on the plot on the right for automated centers. In fact, for smaller centers the automated case curiousl seems to show even less fluctuations, which is absolutely counterintuitive. This is further evidence that the automated vote was manipulated at the recall referendum.

Some people have argued that the problem is that manual centers tend to occurr in more rural or sparsely populated areas, so that the data above simply reflect  socioeconomic or socio cultural differences between the manual and automated centers.

What Delfino and Salas did the, is to select centers which are classified by the CNE as “Mixed Townships” and “hamlets” and plot the data for these two specifica cases separately. This is shown below in Fig. 2:

Fig. 2. k as a function of s (defined above) for manual centers (left) and automated centers (right) in “Mixed Townships” (top) and “hamlets” (bottom)

As can be seen, the “strange” absence of scatter or fluctuations, still occurs in the automated centers when these two types of population centers are considered, while the manual centers in both cases show the expected scatter or fluctuations. This is once again evidence that the automated results were somehow manipulated and the data from the recall petition was somehow used mathematically to generate the results, rather than the actual vote.

If you are not mathematically inclined, Delfino and Salas have posted a presentation called “The ABC of the Referendum” (In Spanish, soon in English), where they try to make it simple to understand. You can think of this as k being how good a predictor of the vote in the recall was. If in the automated center k is of the order of one, this means there were as many votes to recall as signatures in the petition to have the recall take place. As k increases, it means there were more and more votes than you would have thought just from the signatures.

Below is a Google maps image taken from the Delfno and Salas presentation. It represents a Parish of the municipality of Valencia, thus, nearby centers are similar in socioeconomic profile. But as you can see, while the automated centers (blue) have k near 1, the manual centers (green) have k’s as large as 4.3 in one case, despite the fact that that particular center is very close to automated centers where k barely moved above 1.This makes abslutely no sense unless the data was faked.

Could it be clearer than that?

Abstract from the Center for Information Technology Policy at Princeton University on breaking the security of a Diebold voting machine, should we make a collection and send them a Smartmatic machine? You can watch the video showing the hacking:. Who was it that said Venezuela had the safest voting system in the world? Ignorance is bliss indeed!

Security Analysis of the Diebold AccuVote-TS Voting Machine

Ariel J. Feldman, J. Alex Halderman, and Edward W. Felten

Abstract   This paper presents a fully independent
security study of a Diebold AccuVote-TS voting machine, including its
hardware and software. We obtained the machine from a private party.
Analysis of the machine, in light of real election procedures, shows
that it is vulnerable to extremely serious attacks. For example, an
attacker who gets physical access to a machine or its removable memory
card for as little as one minute could install malicious code;
malicious code on a machine could steal votes undetectably, modifying
all records, logs, and counters to be consistent with the fraudulent
vote count it creates. An attacker could also create malicious code
that spreads automatically and silently from machine to machine during
normal election activities — a voting-machine virus. We have
constructed working demonstrations of these attacks in our
lab. Mitigating these threats will require changes to the voting
machine’s hardware and software and the adoption of more rigorous
election procedures.

While it
does not deal with Venezuela, maybe some readers would be
interested in a paper on Benford’s Law and elections written by Prof.
Mebane of the Department of Government at Cornell University.

The paper looks
at Benford’s law in the context of elections and the detection of fraud. It
looks at the effects of manipulations of data on the results and shows that
various simulated manipulations can have a strong impact on the expected results
from Benford’s Law.

The author
then looks at data from the 2004 Florida
election and the recent Mexican election. He concludes that the second digit
Benford test worked well in Dade, Broward and Pascon counties, although there
were some exceptions where questionable results were obtained.

In
contrast, the results from the Mexican election imply that there are problems
in many Mexican states with the results although not in most of them. Prof. Mebane
suggests that a manual recount of the vote would clarify these discrepancies. And
based on a recount with sampling, one could decide whether to carry out or not
a complete recount.

By the
way, the Mexican election shows a lot of cynicism on the part of both the
Venezuelan Government and the opposition. The Venezuelan Government because
while suggesting that they thought there had been fraud in the election, they
never came out and said that there should be a recount. This would be exactly the opposite of their position in local elections. The opposition, because
their apparent sympathy towards Calderon or antipathy towards Lopez Obrador,
stopped them from calling for a full recount in Mexico, which would have been completely
consistent with their positions on the Venezuelan elections. Shame on both
groups!

Hats off to Mexican
scientists that in just a week
are producing data and short papers and posts on the analysis of the elections
in Mexico.
If Venezuelan scientists had responded with similar speed and flexibility maybe
some part of history may have been changed with the 2004 RR. Maybe the precedent
helped!

The paper
on Benford’s law by Mansilla finds some discrepancies with the 8^th.
and 9^th. digit, which may be statistically significant, but nothing like those
found in the No vote for the RR, it will be interesting to see in the future
further detailed statistical analysis like what was done in Venezuela and what it may
tell us.

There is also a long
analysis and discussion by Mochan on the
evolution of the reported vote on the night of the election and the recount. Lots
of data and comments, but I have not digested it sufficiently to understand
even the graphs he is showing, but it looks quite interesting.

I guess those Governments that
want to cheat in future elections in LA are going to have to hire scientists so
that whatever they do to change the outcome matches all of these tests for the adequacy of their
fudged results.

Maybe one day UNEFA will honor them?

I find the whole thing very cool!

This series of four posts on Delfino, Salas and Medina is dedicated to the upcoming visitor from the Carter Center, hoping someone there will read it and will try to get an honest academic opinion on them.

I will close my posting on the work of Delfino, Salas and Medina by showing how curious the results of the failed audit of the night of the referendum were. This is probably the least impacting of the four, but it certainly gives you food for thought.

The CNE had promised the country to audit 1% of the voting machines or 196 of them. Unfortunately only 26 of them were audited on the fateful night of the RR. Curiously, the Si (Yes) vote obtained 63.47% in these 26 machines, compared to the 40.9% that it obtained nationwide.

What Delfino and Salas did was to order the centers that were supposed to be audited according to the fraction of signatures to voters at each center f=Signatures/Voters as shown in Fig. 1, from low f to high f. The sample of centers generated by the CNE had an average value of f=0.37, that is 37% of the registered voters in these 196 centers had signed to have the recall vote against Hugo Chavez. In contrast, the average f for those centers that were eventually audited that evening was a much higher f=0.54 or 54% of the voters in those centers had signed to have a recall vote, as can be easily seen in the plot below of all of the centers and where those that were effectively audited that night fell on the curve.

Fig. 1 Plot of the value of f at each of the centers that were supposed to be audited on the night of the recall vote, ordered from low f to high f. The crosses indicate the 26 centers that were effectively audited.

(The cross point with the low f around 0.17 that was audited curiously corresponds to the military hospital in Caracas)

Now, one can ask a very simple question: What was the probability that you would choose the 26 centers with an average value of f above 0.54 or f>0.54. What Medina did was to calculate it theoretically and then to also simulate it numerically and the probability comes out to an extremely small 3x 10-8 as shown below in the probability curve for getting each value above a certain f:

Fig. 2 Probability plot of the value of f being above a certain value when you chose 26 centers at random from the 196 centers that were chosen on the night of the recall referendum to be audited.

1x 10-8 is extremely unlikely…as so many things related to the recall vote.

What is intriguing is that centers with high f concentrate only a small fraction of all the voters as can be seen in the following figure, where you can see that the largest number of voters is concentrated around f=0.3, precisely where audits were not performed.

Fig. 3 Distribution of the number of votes as a function of the value of f for all automatic and manual centers, showing where the largets concentarion of votes was..

Curious, no?

In contrast with parts I and II of this series, this part requires some knowledge of statistics. I will try to explain things as much as possible, but it does require a little knowledge. Sorry!

Based on the Delfino and Salas hypothesis, Medina asked himself: Is there anything in the pro-Chavez versus anti-Chavez votes from each election or the recall vote that can reveal that if there is any difference between them? The answer is yes, you can look at the symmetry of the distributions and they will tell you whether there is one ir two random variables.

Suppose you have to variables, let’s say the 1998 anti-Chavez vote and the 2000 anti-Chavez vote at each voting center. You plot one versus the other such as the automated 2000 anti-Chavez vote versus the 1998 automated anti-Chavez vote, you get a plot that looks like this:

Fig. 1 Plot of anti-Chavez votes in 2000 versus anti-Chavez votes in 1998 at automated centers.

You now will measure what is called the vertical and transversal deviations of a graph like this. Let me explain this a little better:

For the graph above you would have an “expected value” which comes from doing a least squares fit to the line y=ax that best fits the data. Now, for each point in the voting data you measure the “vertical” deviation, that is how far is the point vertically from the “expected” or mean line y=ax and the “transverse” deviation, that is how far is each point from the mean line in the direction perpendicular to the line. (See Figure 3)

You now plot these two deviations in a histogram, where as you go away from deviation “zero” you will have fewer points in both the positive and negative directions. For the graph above from the anti-Chavez in the automated centers in 2000 and 1998 you get something that looks like this:

Fig. 2 Distriburion of transverse deviations for the automated votes of the RR

Now, the interesting thing is that there is a mathematical test to determine whether the two variables are random or not. If the two variables were random, which is what you expect from two consecutive elections at the same automated centers, then you get schematically, asymmetric distribution from the fertical deviations and an assymetric one from the transverse deviations.

Fig3. Only one variable is random. The other depends on it.

But, if one only one of the variables is random, i.e. in our case, if the two elections are not “independent” of each other but one set of results was obtained from each other then you expect the opposite, an assymetric distribution from the vertical deviatiosn and a symmetrical one form the transverse:

Fig4. Both variables are random

Well what Medina did was to plot this distributions for the RR versus the signatures and also the manual and automated centers and what he finds is that EXCEPT for the case of the data from the automated centers of the RR versus the signatures, everything else follows what you expect from two random variables. That is, in all cases but the RR, the vertical deviations show a positive asymmetry, while the transverse deviations are symmetrical. This suggests that both variables were independently random.

In contrast, the data for he automated centers of the recall vote versus the signatures shows the opposite, the vertical deviations are symmetrical, while the transverse ones are asymmetrical.

Now, for those of you that are not too mathematical inclined, this means that there is a mathematical test that shows exactly the positive behavior between the two cases.

In fact, Medina performed three mathematical calculations that showed that in the following cases there was only single random variable:

–The total number of votes versus voters in the RR

–The total number of signatures versus voters in the RR

–The total number of automated votes versus the signatures in the R

While he performed four others that showed in othere cases there were two independent variables:

–Total votes at the RR versus signatures.

–Manual votes un 2000 versus manual votes in 1998R

–Automated votes 2000 versus 1998

–Manual Votes RR versus signatures.

Mathematically, there is no other conclusion that the SI votes at the automated centers of the RR were obtained from the number of people who signed the petition to recall Chavez using some form of equation with a distribution

How about that!

Sometimes in the next few hours, I will get the one millionth “page read”
according to the salon.com ranking system. Remarkable that what started
as a curiosity on my part in August 2002 has had so many visitors and
despite its somewhat restricted topic has managed to stay up there in
the salon.com rankings. To tell you the truth, its not only had many
more visitors than I expected, but I have made more posts than I ever
imagined. It certainly beats the school newspaper I started in high
school called “Se dice…” (People say…), a weekly rag which was
banned by the school authorities after only three weeks of very
succesful printing.

Obviously I thank you all for your attention and participation.

While it is not easy writing this regularly, I have to say that the satisfaction of having posted on topics like the Chascon (Chavez/Tascon) list/database and the referendum studies on a timely manner, has been sufficient compensation for my effort.

Perhaps the thrill of writing a blog like this can be best summarized by something that happened last night.Two nights ago I posted
part II of the recall studies by Delfino, Salas and Medina and was particularly
taken by the results of the regional election in October 2004. To me,
seeing that data was the strongest and most compelling proof that may be understood by
anyone that the results of the 2004 recall referendum were fabricated
by the CNE. Then, I began exchanging emails with a good friend on how
strange those results were and amieres in the comments pointed out a single case that was truly amazing. In his own words:

“How about this one example: Escuela Raul Leoni, Parroquia Santa
Apolonia, Municipio La Ceiba, Estado Trujillo. Signatures=762,
Referendum 2004=616/938 (40%/60%); Regionals 2004=1247/530 (70%/30%);
Presidentials 1998=689/318 (68%/32%); Presidentials 2000=597/466
(56%/44%) In this center they have been pro opposition in 1998(68%),
2000(56%) but amazingly in August 2004(40%) the completely flipped and
in Octber 2004(70%) they flipped again and became the most pro
opposition they have ever been!!!

Think
about it. At this voting machine the opposition has always had more
than 56% of the vote, but miracolously, in the recall vote, the
opposition only got 40% of the vote in the form of 616 Si (Yes) votes
and then, as abstentrion went up and the opposition was demolarized, twice as many people came out in the October 2004 regional elections to vote, given the opposition 70% of the vote in the form of 1247 votes for it!

I
asked the same reader if he could check in how many voting machines the
number of pro-opposition votes was larger than the Si (Yes) votes in
the referendum and he quickly answered:

“There are 2181 cases (out 8228 centers, a full 27%) where there were
more votes in the regionals for the opposition than SIs in the
referendum!!! And that considering that many people didn’t vote in the
regionals because of the disapointment because of the Referendum result.”

This
is by far the clearest and most convincing proof of the fraud that took
place at the recall referendum. It does not require mathematical
knowledge to understand how implausible it would be that a demoralized
opposition, with abstention increasing from 30% to 60%, would increase
the absolute number of votes in 27% of the voting machines. Take that
Carter Center and Jorge Rodriguez! Dare to explain it!Or even try!

I
did not require this to believe that there was fraud, the matehmatical
studies for me were convicing enough. But this information should be
useful in convincing many that still think there was no fraud on that
fateful August day.

In contrast to these fake numbers, and we don’t even know how many of those there were in the recall referendum, my visitors are all real and they seem to like coming here
searching for the truth and helping in finding the truth. That in
itslef is satisfaction enough for all of the work that goes into writing this.