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Opinion and Analysis: Politics

The Statistical Fraud of Venezuela’s Opposition

The opposition’s claim of massive fraud, one which no international observer or any other disinterested third party can detect, has boiled down to two principal claims now. First, they say that exit polls they conducted showed that a 59% majority was in favor of recalling Chavez. Thus, according to them, a 59% win for Chavez must be wrong. Second, they say that numerous voting centers show that machines at the same voting center have the same number of “yes” votes, in favor of recalling Chavez, which, according to them, is a statistical near impossibility and must therefore constitute proof that the machines were rigged to limit the number of “yes” votes. Let us examine these two claims in detail.

Exit polls on the quick and easy

First, with regard to the exit polls, apparently the opposition had organized about five exit polls. Perhaps the most authoritative of these polls was one that was supposedly conducted by Penn, Schoen and Berland, a market research company. According to their press release, they conducted the poll in 267 voting centers and surveyed 20,382 voters immediately after they cast their vote on August 15. Their exit poll indicated that 59% of those surveyed voted “Si” or “yes,” in favor of recalling Chavez, and 41% voted “no,” against recalling Chavez. The margin of error was +/- 1%.

When the actual results turned out to be exactly the opposite, the opposition said that based on its exit polls (not on the basis of anyone else’s), the vote must have been a massive fraud, in effect stealing about 2 million “si” votes and turning them into “no” votes – no doubt one of the largest electoral frauds in world history of otherwise free elections.

Such a comparison of exit poll results with voting results should beg the question of which is a more reliable measure of voter will: an untransparent exit poll, conducted by an interested party, or an extremely closely monitored vote, with disinterested international observers and rules that both sides agreed upon? Nonetheless, Venezuela’s opposition insists that the exit polls are the valid measure, enough so to call the vote a fraud.

Perhaps instead of focusing on how a fraud could have been possible (for which they have no clue), the opposition would be better advised to carefully examine its own exit polls. Several possible (charitable) explanations exist.[1] Jesse Chacon, the Minister of Communication and Information, suggested that the reason for the false results had to do with the selection of the people who conducted the polls, who were provided by Sumate, the US-funded organization that provided much of the opposition’s logistical support for bringing the referendum about. That is, by choosing volunteers who are sympathizers of the opposition, the polls would inevitably present a bias towards the opposition, especially given the clear class difference in Venezuelan voting patterns and people’s general preference to approach people who are more likely to think, dress, and act like them. Another reason Chacon mentioned for the erroneous exit polling data was that Sumate urged Venezuelans to give their voting information to the exit pollsters. This, of course, immediately would brand the exit poll as an opposition operation and encouraged opposition sympathizers to reveal their vote, but probably acted as a disincentive for Chavez supporters.

A professional exit poll operation, however, should know to avoid such errors. Another explanation for wrong exit poll results would have to do with the selection of voting centers. Generally, these should be selected at random from all available centers. However, considering that the Sumate volunteers who conducted the poll for Penn et al. tend to come from the middle class, it is doubtful that they had enough volunteers from the barrios to staff the barrio exit polls. What this means is that they would have had to send middle class volunteers into the barrios, a proposition most average Venezuelans find quite unimaginable. To most middle class Venezuelans, the barrios are dangerous territory that is to be avoided at all costs, much like most whites avoid Harlem in New York City. It seems extremely unlikely that Sumate was able to properly cover the barrio voting centers. This inability to cover the barrios distorts the exit poll result disproportionately because, on average, barrio voting centers are much larger than the ones in middle class neighborhoods.

Finally, the +/- 1% margin of error that Penn et al. cite is very misleading. This margin of error refers to the accuracy of the poll with respect to the vote at the polled voting centers (a sample of 20,000 out of about 500,000 population at these centers, results in a +/- 1% margin of error). However, one must also consider the margin of error when sampling the voting centers themselves. That is, a sample of 264 polled centers out of a total population of 4,766 automated voting centers results in a margin of error of +/- 5.83%.[2] If the selection of representative voting centers ends up being off by only a few percent, the polls at those centers, especially given the biases already mentioned (such as partisan poll takers), the error would be magnified even more. That is, just a small error in the selection of voting centers in favor of anti-Chavez centers, could end up with an amplified distortion in favor of the “yes” vote, since voting in many centers tended to be very polarized (some centers disproportionately in favor of Chavez—the barrios—and some disproportionately against Chavez).

The “Yes” limit – the statistical fraud

The second “proof” of fraud involves the supposed existence of a “ceiling” on the “yes” vote. That is, the opposition has identified hundreds of instances where the number of “yes” votes, in favor of recalling Chavez, are oddly similar to each other, from one voting machine to the next. The first example that appeared of this came from Bolivar state, where the following numbers were presented for a voting center with three voting machines: 383 no – 133 yes; 345 no – 133 yes; 369 no – 133 yes.

The opposition has made a big deal of these “ceilings” claiming that it is statistically impossible for these numbers to repeat themselves so often. Some opposition leaders have compared this to a lottery, where it would be very rare to get the same three numbers in a row, as one would with a slot machine’s jackpot. They have even marshaled statisticians to explain that the odds are in the millions to one, especially if one considers that this pattern repeats itself in over 1,000 voting centers throughout the country. The opposition’s argument is these patterns prove that there was a massive fraud, that the machines were programmed in such a way as to limit the number of “yes” votes and to turn them into “no” votes once that limit had been exceeded.

It would seem, though, that no one in the opposition has ever taken statistics 101 in college. If they had, they would know that the comparison to a lottery is completely false. What most people do not realize (which could explain why some statisticians seem to agree with the opposition), the voting machines randomly sampled up to 650 voters of any given voting center. That is, each voter was assigned to a specific voting machine, based on the last two digits of their identification document. In other words, the votes in each machine represented a systematic random sample of the “yes” and “no” votes of any given center. As anyone who has studied statistics knows, if you randomly sample a population (the voting center) several times, then each sample should have more or less the same result. Thus, it should come as no surprise that three machines at the same voting center display the same result. As a matter of fact, it would be much more suspicious if each random sample (each machine) displayed very different results. That in some cases the number of “yes” votes should be identical should come as no surprise, given that there already is a tendency for each machine to approximate the other. If one were to look, one would almost definitely find a similar number of “no” votes that are repeated from one machine to the next in several different voting centers.

Perhaps an analogy would help. If we have a box with 1,000 balls, 400 of which are white and 600 of which are red and you randomly take 100 balls out of this box, the chance of selecting 40 white balls and 60 red balls is extremely high. 40-60 might not be the exact number that comes up every time, but if you take enough consecutive random samples, say 100, then the number 40-60 should come up quite frequently (a statistician could tell you with a fair degree of accuracy about how many times).

A lottery or a slot machine selection does not represent a random sample of a white/red or a yes/no population, but of a population that is much, much more complex. Rather, each number or symbol is represented only once. Thus, the odds of getting the same number from three successive samples is extremely small, about 1 in 10,000 for a population of 100 (with unique numbers ranging from 1 to 100) – the parallel that the opposition keeps making thus makes no sense whatsoever.

Cognitive dissonance

It would appear that a vast sector of Venezuela’s opposition is suffering from what psychologists call “cognitive dissonance.” That is, a situation in which you are confronted with a fact that completely goes against your most deeply held beliefs. Generally, such a situation provokes severe psychic distress for the person and will tend to lead them to believe just about any other explanation than the one that is presented to them.

In this case, most opposition supporters were completely and totally convinced that they would win the referendum; that their side represents a majority. Any other result can thus only be explained by the existence of fraud. It is a complete impossibility to them that Chavez won the vote fair and square. As a matter of fact, if one reads opposition websites and discussion fora, one can see that many are even convinced that no matter what anyone else says, no matter how many audits are conducted, Chavez lost and the opposition won.

The following academic description of cognitive dissonance is instructive:

Cognitive dissonance was first investigated by Leon Festinger and associates, arising out of a participant observation study of a cult which believed that the earth was going to be destroyed by a flood, and what happened to its members — particularly the really committed ones who had given up their homes and jobs to work for the cult — when the flood did not happen. While fringe members were more inclined to recognize that they had made fools of themselves and to "put it down to experience", committed members were more likely to re-interpret the evidence to show that they were right all along (the earth was not destroyed because of the faithfulness of the cult members). (James Atherton)

This is a very dangerous situation because it could easily lead those who are prone to violence to use the referendum as an excuse for engaging in terrorist activity against the government, with the argument that this is the only way to fight an illegitimate government (or “regime,” as many opposition supporters call it). Surely many opposition leaders are also caught up in this cognitive dissonance. However, there probably are many who know that the voting machines were secure, that the exit polls were faulty, and that the statistical arguments about “yes” vote limits are baseless. Opposition leaders who nonetheless continue to claim that there was fraud, in the hope of scoring political points, are being recklessly irresponsible because they are leading their followers off a cliff, much like a fanatical cult leader can lead his believers into collective suicide. Except, the repercussions, if they end in violence, will have consequences far beyond the group of followers, but will affect all of Venezuelan society.


[1] There are some uncharitable explanations, which I will not explore, but which say that the pollsters were paid to provide phony results, so as to influence and intentionally prejudice the official result. This is an explanation that is not all that far-fetched if one considers that the pollsters deliberately broke Venezuelan law by releasing the results at least twelve hours before the voting centers closed.

[2] Based on a margin of error calculator: http://www.americanresearchgroup.com/moe.html