Archive for May 12th, 2006

On Mathematical Models of the recall vote and fraud: Delfino, Salas and Medina part II: Making the inconsistencies in the results quite evident

May 12, 2006

While in part I of my presentation of the Delfino, Salas and Medina results, I emphasized the correlation between the signatures collected to call for the referendum to recall Hugo Chavez and the number of actual Si (Yes) votes to recall at the recall referendum, I only did that in order to use as simple a language as possible as an introduction to the topic.

What Delfino and Salas did was to plot the data in a different manner in order to bring the anomalies out better in the data.

What they actually plotted was a “normalized” parameter k equals to

      Yes(Si) Votes
k= ——————


As a function of another “normalized” parameter f

f= ——————
      Total Votes

The reason for plotting the data this way, is that it magnifies those voting centers in which the number of Yes (Si) votes is much larger than the number of signatures at that center. Think about it. First of all f is limited to be between zero and one, the maximum number of signatures at one center can only be at most the number of voters at the same center. On the other hand, given the difficulties, limitations and methods for obtaining the signatures as discussed in part I of these articles on Delfino, Salas and Medina, there should be a number of centers where with a low number of signatures, but a high number of Yes (Si) votes, where people did go out and vote but could not sign the petition. Additionally, this would be emphasized in those centers with low f, since f measures the number of signatures. In those centers with difficulties to gather the signatures, the number of people signing should be small, but you would expect the number of people voting Yes (Si) to vary significantly, to fluctuate!

Well, remarkably this does not happen in the automated centers as shown in Fig. 1 (left) but does in the manual centers shown in Fig. 1 (right):

                                   f                                                                                                     f

Fig. 1 (Left) k versus f for automated centers (Right) The same k versus f but for the manual centers separating the centers abroad from the data set, because there were special difficulties for gathering signatures for those living abroad.

What is most remarkable about Fig. 1 (Left) is that despite the difficulties in obtaining the signatures, the data for the automated centers is quite uniform and there are very few centers where the number of actual SI (Yes) votes exceeds significantly the number of signatures. Only in seven automated centers is k >2 which is remarkable given that there were forms for only 30% of the people to sign, while everyone could go and vote. In fact, only seven of the automated centers exceeds k=2 but none of them do it by much.

In contrast with the result for the automated centers, in the manual centers the number of pints falling above k> 2 is large and you can see points as high as k close to 10, as would be expected from a process that was so difficult as that of the signatures. This is what you would expect, as only 30% of the people could sign, while close to 70% of them actually voted in the recall referendum. This should generate the type of fluctuations you see in the manual centers but is absent in the automated centers. This is very strange and makes no sense!

If the result above is strange, in my own mind, it is its inconsistency with the next graph that proves the the fraud. The opposition came out of the recall vote absolutely demoralized, three months later in October tehre were regional elections. There was not only a campaign to promote abstention, but abstention more than doubled, going from 30% in the recall referendum to over 70% in the regional elections in October 2004. Despite this, take a look at what happened if we plot the pro-opposition votes as a function of the recall signatures below on the left, in the same centers that were automated for the recall vote:

                                           f                                                                                        f

Figure 2. Left: Opposition votes normalized to the number of signatures k, at each center as a function of f the fraction of signatures to voters at each center for the regional election in October 2004. Right: The automated centers once again just for direct one to one comparison.

To me this graph is absolutely compelling: There are more than three dozen points above k=2 in contrast to the seven at the recall vote. There are points as high as k=6, this despite the fact that abstention was double in the regional election what it was in the recall, that it was the opposition that mostly abstained in it and nevertheless the opposition actually increased the number of votes with respect to the signatures in dozens of voting centers, all at once! In fact, I repeat the same plot for the automated centers in the recall next to that regional election just so that you can see how different the two results are.

Personally, I would like to challenge the Carter Center or whomever they designate to even attempt to explain how the results of the regional elections could be what they were compared to the recall vote in Figure. 2 and what was the mysterious mechanism by which opposition voters in so many centers came out in larger number that October to give those results, despite the higher abstention and the demoralized opposition. Where were this people the day of the recall? Why didn’t they go vote and then all of them in synch showed up in October 2004? This simply has no other explanation that the Delfino Salas hypothesis, which I advanced in my conclusions of Part I on the correlations. :

The official results of the recall vote in the automated centers were forced to follow a linear relation with respect to the number of signatures obtained at each of those centers in the recall petition.

For the sake of completeness, I also include below the graphs of the votes against Chavze in the 1998 and 2000 elections, both at the peak of Chavez’ popularity. Despite this, values as high as k=4 or even above can be seen in both cases. These are magically and mysteriously missing from the automated centers in the recall vote:

                                       f                                                                                                f

Fig. 3 Results for the 1998 and 2000 opposition votes as a function of the signatures in the recall petition k, as a function of the number of signatures collected in each center normalized to the total number of voters at each center.

Next, part III: We get a little dense to show that the statistical characteristics of the result of the recall vote show mathematically that the data came from a single set of numbers and not two as expected, indicating the results were obtained from the signatures used to petition the recall.