## Archive for August 26th, 2004

### On Mathematical Studies of the recall vote part II: Exit Polls

August 26, 2004

The present study was performed by two Venezuelans who are Professors in the Department of Applied Mathematics and Statistics at the University of California at Santa Cruz, Bruno Sanso and Raquel Prado. You can find their full study here in postscript format or here in acrobat (Thanks Alfredo and Ed). I will try to summarize it as well as I can, hopefully the authors will read what I write and correct any imprecisions in my summary, which follows what they wrote.

What they have done is to look at the exit polls of Sumate and Primero Justicia and compare them to the actual results for the vote at the same voting centers where the exit polls were made. They had 527 exit polls with 36,629 interviews, 269 from Sumate and 258 from Primero Justicia. They eliminated the exit polls with less than 20 people and worked in the end with 475 centers after excluding the also those centers in which the count was manual, because the CNE data was incomplete.

The first figure below shows the histogram of Si voters according to the CNE in the top panel and in the bottom panel the same histogram for the Si votes according to the exit poll data: Top Figure: Proportion according to the results of the CNE (Actas) Bottom Figure: Proportions according to the exit polls

Note the difference between the two not only in where the main frequency is, but they seems to have different symmetries and the detail f the distributions are different.

To study this further, they did the following study: Suppose that the sample obtained in a single voting center corresponds to a population of binary experiments. The probability of obtaining a SI is taken to be the same as the proportion calculated from the final results (Actas) of each center according to the CNE. They then calculate the probability that under such a probabilistic model, they could observe the same number of SI votes that were obtained in the exit poll.

This result is shown in the next figure.  As can be seen, the range is of probabilities is between zero and 0.23 with roughly 40% of them ranging between zero and 0.02. This implies that the probability of obtaining the results of the exit polls based on the results of the CNE is extremely low. To check these discrepancies further, the authors looked instead at each voting center. For each center the simulated 5,000 runs of the same size as that obtained in the exit poll. They then calculated the proportions of Si in each sample and took the values that were above 2.5% and 97.5% respectively. In this way they obtain the interval in which 95% of their simulations. They conclude that there are significant differences between the results for the CNE and the exit polls for each specific center  if the proportion obtained in the exit poll is not contained in that interval.

From the above, they calculate the results state by state.  The bleu points are the proportions of the exit polls that fall outside the interval. The black points fall within the interval. Below I show only the results for the Capital District and Zulia state, the rest of the states are in the presentation.

Capital 55% discrepancies                                           Zulia 66% discrepancies  This is not a global analysis; it is center by center analysis so that the design of the sample for the exit poll is not relevant.

The discrepancies between the estimated Si votes in exit polls and those from the results are quite significant in at leas 60% of the centers. This difference is present in ALL states. (Also in the centers with manual votes not included in the results). The differences can not be explained by randomness. The only possible conclusion is that either the exit polls had a bias towards the SI or the CNE final results had a biased in favor of the NO

Someone could argue that the difference could be due to people not answering. In a center with a sample of 60 voters with a proportion of Si to NO of 60/40, the number of people not answering required to turn the results around completely would have to be 50 people ALL IN FAVOR OF THE NO. This would have had to occur in many centers simultaneously.

Another possibility is that since the exit polls were only carried out until 4PM a massive number of people would have voted NO after that time. In a center with 2,000 voters in which 600 had voted SI by 4 PM and 400 NO by 4 PM, this would require that of say 1,000 voters after 4 PM only 20% voted for the SI and 80% for the NO. This would have had to happen all over the country.

### On Mathematical Studies of the recall vote part II: Exit Polls

August 26, 2004

The present study was performed by two Venezuelans who are Professors in the Department of Applied Mathematics and Statistics at the University of California at Santa Cruz, Bruno Sanso and Raquel Prado. You can find their full study here in postscript format or here in acrobat (Thanks Alfredo and Ed). I will try to summarize it as well as I can, hopefully the authors will read what I write and correct any imprecisions in my summary, which follows what they wrote.

What they have done is to look at the exit polls of Sumate and Primero Justicia and compare them to the actual results for the vote at the same voting centers where the exit polls were made. They had 527 exit polls with 36,629 interviews, 269 from Sumate and 258 from Primero Justicia. They eliminated the exit polls with less than 20 people and worked in the end with 475 centers after excluding the also those centers in which the count was manual, because the CNE data was incomplete.

The first figure below shows the histogram of Si voters according to the CNE in the top panel and in the bottom panel the same histogram for the Si votes according to the exit poll data: Top Figure: Proportion according to the results of the CNE (Actas) Bottom Figure: Proportions according to the exit polls

Note the difference between the two not only in where the main frequency is, but they seems to have different symmetries and the detail f the distributions are different.

To study this further, they did the following study: Suppose that the sample obtained in a single voting center corresponds to a population of binary experiments. The probability of obtaining a SI is taken to be the same as the proportion calculated from the final results (Actas) of each center according to the CNE. They then calculate the probability that under such a probabilistic model, they could observe the same number of SI votes that were obtained in the exit poll.

This result is shown in the next figure.  As can be seen, the range is of probabilities is between zero and 0.23 with roughly 40% of them ranging between zero and 0.02. This implies that the probability of obtaining the results of the exit polls based on the results of the CNE is extremely low. To check these discrepancies further, the authors looked instead at each voting center. For each center the simulated 5,000 runs of the same size as that obtained in the exit poll. They then calculated the proportions of Si in each sample and took the values that were above 2.5% and 97.5% respectively. In this way they obtain the interval in which 95% of their simulations. They conclude that there are significant differences between the results for the CNE and the exit polls for each specific center  if the proportion obtained in the exit poll is not contained in that interval.

From the above, they calculate the results state by state.  The bleu points are the proportions of the exit polls that fall outside the interval. The black points fall within the interval. Below I show only the results for the Capital District and Zulia state, the rest of the states are in the presentation.

Capital 55% discrepancies                                           Zulia 66% discrepancies  This is not a global analysis; it is center by center analysis so that the design of the sample for the exit poll is not relevant.

The discrepancies between the estimated Si votes in exit polls and those from the results are quite significant in at leas 60% of the centers. This difference is present in ALL states. (Also in the centers with manual votes not included in the results). The differences can not be explained by randomness. The only possible conclusion is that either the exit polls had a bias towards the SI or the CNE final results had a biased in favor of the NO

Someone could argue that the difference could be due to people not answering. In a center with a sample of 60 voters with a proportion of Si to NO of 60/40, the number of people not answering required to turn the results around completely would have to be 50 people ALL IN FAVOR OF THE NO. This would have had to occur in many centers simultaneously.

Another possibility is that since the exit polls were only carried out until 4PM a massive number of people would have voted NO after that time. In a center with 2,000 voters in which 600 had voted SI by 4 PM and 400 NO by 4 PM, this would require that of say 1,000 voters after 4 PM only 20% voted for the SI and 80% for the NO. This would have had to happen all over the country.

### On Mathematical Studies of the recall vote part II: Exit Polls

August 26, 2004

The present study was performed by two Venezuelans who are Professors in the Department of Applied Mathematics and Statistics at the University of California at Santa Cruz, Bruno Sanso and Raquel Prado. You can find their full study here in postscript format or here in acrobat (Thanks Alfredo and Ed). I will try to summarize it as well as I can, hopefully the authors will read what I write and correct any imprecisions in my summary, which follows what they wrote.

What they have done is to look at the exit polls of Sumate and Primero Justicia and compare them to the actual results for the vote at the same voting centers where the exit polls were made. They had 527 exit polls with 36,629 interviews, 269 from Sumate and 258 from Primero Justicia. They eliminated the exit polls with less than 20 people and worked in the end with 475 centers after excluding the also those centers in which the count was manual, because the CNE data was incomplete.

The first figure below shows the histogram of Si voters according to the CNE in the top panel and in the bottom panel the same histogram for the Si votes according to the exit poll data: Top Figure: Proportion according to the results of the CNE (Actas) Bottom Figure: Proportions according to the exit polls

Note the difference between the two not only in where the main frequency is, but they seems to have different symmetries and the detail f the distributions are different.

To study this further, they did the following study: Suppose that the sample obtained in a single voting center corresponds to a population of binary experiments. The probability of obtaining a SI is taken to be the same as the proportion calculated from the final results (Actas) of each center according to the CNE. They then calculate the probability that under such a probabilistic model, they could observe the same number of SI votes that were obtained in the exit poll.

This result is shown in the next figure.  As can be seen, the range is of probabilities is between zero and 0.23 with roughly 40% of them ranging between zero and 0.02. This implies that the probability of obtaining the results of the exit polls based on the results of the CNE is extremely low. To check these discrepancies further, the authors looked instead at each voting center. For each center the simulated 5,000 runs of the same size as that obtained in the exit poll. They then calculated the proportions of Si in each sample and took the values that were above 2.5% and 97.5% respectively. In this way they obtain the interval in which 95% of their simulations. They conclude that there are significant differences between the results for the CNE and the exit polls for each specific center  if the proportion obtained in the exit poll is not contained in that interval.

From the above, they calculate the results state by state.  The bleu points are the proportions of the exit polls that fall outside the interval. The black points fall within the interval. Below I show only the results for the Capital District and Zulia state, the rest of the states are in the presentation.

Capital 55% discrepancies                                           Zulia 66% discrepancies  This is not a global analysis; it is center by center analysis so that the design of the sample for the exit poll is not relevant.

The discrepancies between the estimated Si votes in exit polls and those from the results are quite significant in at leas 60% of the centers. This difference is present in ALL states. (Also in the centers with manual votes not included in the results). The differences can not be explained by randomness. The only possible conclusion is that either the exit polls had a bias towards the SI or the CNE final results had a biased in favor of the NO

Someone could argue that the difference could be due to people not answering. In a center with a sample of 60 voters with a proportion of Si to NO of 60/40, the number of people not answering required to turn the results around completely would have to be 50 people ALL IN FAVOR OF THE NO. This would have had to occur in many centers simultaneously.

Another possibility is that since the exit polls were only carried out until 4PM a massive number of people would have voted NO after that time. In a center with 2,000 voters in which 600 had voted SI by 4 PM and 400 NO by 4 PM, this would require that of say 1,000 voters after 4 PM only 20% voted for the SI and 80% for the NO. This would have had to happen all over the country.