Archive for May 23rd, 2006

On Mathematical Models of the recall Referendum and Fraud: Delfino, Salas and Medina part IV: The curious statistics of the audit that never was

May 23, 2006

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?

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