2004 Venezuelan Presidential Recall Referendum (2004 PRR): A Statistical Analysis from the Point of View of Electronic Voting Data Transmissions

2004 Venezuelan Presidential Recall Referendum (2004 PRR): A Statistical Analysis from the Point of View of Electronic Voting Data Transmissions

[ [ Universidad Simon Bolivar Isbelia Martín is Professor, Department of Physics, Universidad Simon Bolivar, Caracas 1083, Venezuela \printeade1.

Statistical comparisons of electoral variables are made between groups of electronic voting machines and voting centers classified by types of transmissions according to the volume of traffic in incoming and outgoing data of machines from and toward the National Electoral Council (CNE) totalizing servers. One unexpectedly finds two types of behavior in wire telephony data transmissions and only one type where cellular telephony is employed, contravening any reasonable electoral normative. Differentiation in data transmissions arise when comparing number of incoming and outgoing data bytes per machine against total number of votes per machine reported officially by the CNE. The respective distributions of electoral variables for each type of transmission show that the groups classified by it do not correspond to random sets of the electoral universe. In particular, the distributions for the NO percentage of votes per machine differ statistically across groups. The presidential elections of 1998, 2000 and the 2004 Presidential Recall Referendum (2004 PRR) are compared according to the type of transmissions in 2004 PRR. Statistically, the difference between the empirical distributions of the 2004 PRR NO results and the 2000 Chavez votes results by voting centers is not significant.


26 \issue4 2011 \firstpage528 \lastpage542 \doi10.1214/10-STS350


2004 Venezuelan Presidential Recall Referendum (2004 PRR)


a]\fnmsIsbelia \snmMartín\correflabel=e1]isbeliam@usb.ve

Electronic voting \kwdelectoral data transmission \kwdrecall referendum \kwdVenezuelan elections.

1 Introduction

During the Venezuelan Presidential Recall Referendum (PRR) held on August 15 of 2004, voters used electronic voting machines to cast their votes. A NO or YES vote meant a pro-government or anti-government vote respectively. In order to investigate the trustworthiness of the electoral results, we carry out a forensic analysis of the government official National Electoral Council (CNE) electoral results transmitted by machines nationwide and of data contained in Remote Authentication Dial-In User Service (RADIUS) logs of transmissions produced by authentication, authorization and accounting (AAA) servers used in wire and cellular transmissions between voting machines and totalizing servers 2 (), 3 (), 4 ().

While in this paper we only explore transmission data collected during the Venezuelan PRR of 2004, some of the methods presented here can be applied in different contexts. In particular, the discussion in the manuscript can inform governments and other international organizations who wish to plan electoral audits in the future, in Venezuela or elsewhere. Given the increasing popularity of electronic voting machines world-wide, the development of monitoring and auditing methods to guarantee the reliability of electronic voting processes is critically important.

Transmission data correspond only to communications through wire and cellular (mobile) telephony but cover 98.05% of the universe of electronic voting machines used in the electoral event. Four independent sources of information as far as transmissions through wire and cellular telephony were used: Two of the sources correspond to RADIUS logs, for wire and cellular transmissions respectively, containing information on several technological variables for individual voting machines, among them: amount of octets (bytes) of incoming and outgoing data to CNE totalizing servers, start and stop connection times to CNE totalizing servers, amount of packets of incoming and outgoing data, identification of users, hosts and routers, etc. The third and fourth sources are based on a report draft made by the wire telephone company to the CNE and the actual automated tallies printed by machines respectively. These reports served to cross-check information with the RADIUS logs to offer validity to the same logs as reliable sources of information as far as volume of transmitted data, connection times and duration of sessions by machine.

In the present article the forensic analysis consists first in studying the behavior of machines according to volume of data transmitted and received, and relating it to the vote totals counted electronically and transmitted by each voting machine. Second, a complementary statistical study is performed that puts emphasis only on the heterogeneity of the behavior of groups of machines found in the first analysis that allowed a classification according to transmissions to CNE totalizing servers. Directionality of data transmission is not relevant in this part since the statistical analysis is not affected by it.

According to electoral norms, all machines had to transmit vote totals scrutinized by the same machine. Also, the information transmitted must include polling station code numbers, poll’s closing time, number of registered voters, number of votes and vote totals results. This information had to be contained also in paper reports produced by the machine. Furthermore, the amount of bytes needed to transmit the data should have been exactly the same for all machines in the country, regardless of geographical location and any other differences such as polling center’s codes or voting volume at the center. Also, the software for recording votes, counting and transmitting results should be the same for all machines employed. The electronic information on tallies had a fixed length in bytes. Thus, any disparity in volume of data transmitted, not accounted for ordinary transmission errors as eventual lost packets of data, is unexpected given the electoral standards. Even more surprising is to find a linear dependence of transmitted data bytes on individual ballots for a high percentage of machines. This fact will be our concern. Furthermore, given the electoral normative, when a call session is established between the totalizing server and a machine at the closure of polls, only data relating to authentication, authorization and acknowledgment of reception of data should be sent to the machine. This amounts to a fixed volume of data, smaller in size than the one related to vote results sent by the machine. But the findings contradict these expectations.

In this analysis, the electronic voting machines were classified according to the amount of data units in bytes that were sent from machines to CNE totalizing servers (Outgoing Data) and according to the amount of data received by voting machines from totalizing servers CNE (Incoming Data). For this study only the data transmissions of the last successful connection between machines and CNE totalizing servers were taken into account. We suppose a priori that when several calls were made from the same machine it was due to defective transmissions, that is the reason why the last connection is presumed to be the successful one and that the amount of data transmitted in both directions in that occasion was the expected information according to the programmed procedure. Machines communicating more than once amounted to less than 15% of the total.

We find that the electronic voting machines fall into three groups: High Traffic (A) for wire transmission machines if the number of outgoing bytes added to incoming bytes surpasses 23 thousand bytes, Low Traffic (B) for wire transmission machines with total data traffic lower than 7.5 thousand bytes and machines communicating via cellular telephony (C). Differences on volume of data transmitted and received are accompanied by differences in number of packets of data and causes of termination of sessions. In fact, group A has transmissions with the same number of packets being received and sent (symmetric transmission) with call terminated by totalizing servers. Group B has few packets sent but many received (asymmetrical transmission) and calls terminated by machines. For detailed information on network platforms, protocols used and more see Malpica, Velasco and Martin 1 ().

The voting centers, at the same time, were equally classified as High Traffic centers (A), Low Traffic and Cellular ones, (B) and (C) respectively, according to whether voting machines in a center fell into the three groups mentioned above. In the case of existing mixed wire and cellular transmissions in a center, the classification was made according to the highest number of machines of a particular type A, B or C, in general the number of mixed centers in each category A and B is less than 10% of the total.

There were no voting centers with mixed High (A) and Low (B) Traffic machines. In general, voting centers could have from 1 to 18 machines grouped in electoral tables, which could in turn accommodate from 1 to 3 voting machines. The typical voting center housed 4 machines. In the Venezuelan electoral system, voting centers are arranged into parishes, the latter into municipalities and several municipalities make a state. Venezuela is divided into 24 states.

The rest of this manuscript is organized as follows. We first explore the characteristics of the three groups A, B and C of voting machines comparing the volume of data in bytes transmitted from and toward the totalizing CNE servers relative to the number of votes cast in each machine as reported by CNE. Indeed, the classification on the basis of empirical observation of differences in the pattern of graphs is justified. The results from these exploratory analyses are presented in Section 2.1. We then investigate whether voting centers classified as A, B or C exhibit different distributions of the following variables:

  • The percentage of abstentions per machine nationwide.

  • The percentage of NO votes per machine nationwide.

  • The percentage of NO votes per voting center, compared to what was observed during the presidential elections of 1998 and 2000.

All of these results are presented in Section 2.2. Finally, some brief conclusions are offered in Section 3.



Table 1:
High Traffic—wire Low Traffic—wire Cellular (C) Total
(A) (B)
Voting centers 1,876 1,573 972 4,421
Number of voting
 machines in centers 8,185\tabnoterefa 7,383\tabnoterefa 3,124\tabnoterefb 18,692\tabnoterefc
Number of machines
 in each class 7,535 6,702 4,455 18,692\tabnoterefc
Numbers of votes 3,695,415 3,300,896 1,357,733 8,354,044\tabnoterefd
 and % of total (43.44%) (38.80%) (15.96%)

[*]aIncludes voting machines with cellular transmission. \tabnotetext[**]bIncludes voting machines with High Traffic transmission (0.5%). \tabnotetext[†]cRepresents 98.05% of automated 2004 PRR. \tabnotetext[††]dRepresents 98.20% of automated 2004 PRR.

Figure 1: Graphs of amount of bytes in data emitted and received by each machine versus number of total votes per machine for the group of High Traffic transmission. In the Outgoing data graph representing a sample of 6,579 machines, it is possible to differentiate two subgroups of machines related to two clusters: one superior cloud (G2 with 2,166 machines) and another inferior cloud (G1 with 4,413 machines).

2 Results

The electronic voting machines transmitted via wire, mobile and satellite telephony. The machines transmitting via wire telephony fall into two groups, High Traffic (A) and Low Traffic (B), according to whether the amount of data received plus the amount of data sent is in the range of 23,000 to 63,000 bytes for the High Traffic class and from 1,500 to 7,500 bytes in the Low Traffic class. When the electoral variables by region are studied, it will be corroborated that the classification of High and Low Traffic is bound to the telephone area codes. We find whole municipalities in regional states whose voting machines fall in one or another category. The group of machines that transmitted via cellular is not much different to the wire High Traffic group as far as the pattern of Bytes vs. Votes is concerned and the volume of bytes transmitted but, technologically, they are not comparable to the wire telephony. That is the reason why it is included in this study as a separate group. In the present analysis machines that have communicated via satellite are not mentioned for lack of data.

The classification of High, Low Traffic and Cellular for voting centers corresponds to those centers where most of their machines classified in some of the mentioned classes. It is possible to find around 8% to 9% of machines that communicated via cellular in some of the High and Low Traffic centers; this could be justified by transmissions failures of wire telephony or for a way to speed up the process of data transmission when few wire lines were available. There are no centers where machines transmitted in both High Traffic and Low Traffic groups. The inclusion of cellular transmissions with High or Low Traffic wire transmissions responds to the fact that analyzed electoral variables do not vary significantly among machines in the same center.

Thus, 4,421 voting centers are grouped in 1,876 High Traffic centers housing 8,185 voting machines including cellular machines, 1,573 Low Traffic centers with 7,383 machines including cellular transmissions and 972 Cellular centers having 3,124 machines with the exception of 17 machines that fall into the category of High Traffic wire telephony. The total number of voting machines in this study is 18,692, corresponding to 98.05% of the 19,064 voting machines officially used in the 2004 PRR and for which registries are known through electronic tally reports. Table 1 shows the number of machines and centers with transmission via wire and cellular telephony according to the volume of traffic, and, also, the number of entered effective votes in each category from a universe of 8,505,867 automated votes in the 2004 PRR according to electronic tally reports.

2.1 Incoming and Outgoing Data versus Votes between Electronic Voting Machines and CNE Totalizing Servers

For each group of machines, technological and electoral variables are represented in an plane. The number of total votes by machine reported by official reports is in the -axis and the amount of bytes in the data that left and came into the machines during the transmission is in the -axis. The points on the plane represent individual machines that reported a determined number of total votes, and the data in bytes they emitted to transmit the voting results to CNE totalizing servers (Outgoing data), as well as the data received by the machine from CNE totalizing servers during the established sessions of communication (Incoming data). (See Figures 13.)

Figure 2: Graphs of amount of bytes in data emitted and received by each machine versus number of total votes by machine in 2004 PRR for the group of machines with Low Traffic transmission.
Figure 3: Graphs of amount of bytes in data emitted and received by each machine versus number of total votes by machine in 2004 PRR for the cellular transmission group of machines.

A strong correlation between bytes in the incoming data being transmitted and the amount of votes per machine is observed in High Traffic and Cellular groups of machines (groups A and C). But the behavior of the Low Traffic group of machines (group B) is totally different. A linear relation between number of votes and bytes in the transmitted data may be observed only by a small number of machines framed by a high dispersion of points.

Outgoing data transmissions, on the other hand, show clusters of points with small correlation to the number of votes in groups A and C, but no correlation exists for the horizontal plot on the Low Traffic group.

2.1.1 A—High Traffic transmissions

Within the High Traffic group, it is possible to observe two clearly differentiated clusters in the Outgoing data graph, one that we will call the G1 subgroup and the other the G2 subgroup. These subgroups correspond to points falling into the various parallel straight lines that gather in the Incoming data graph. Subgroup G1 in the Outgoing graph is related to the lower straight lines in the Incoming graph.

The perception of a greater dispersion of points shown in the Outgoing data graph compared to the one in the Incoming data graph is due to different scales involved in the volume of data sizes in both graphs. Dispersion in graphs as well as various straight parallel lines in the Incoming data graph may be related to retransmission of packets of data lost during transmission. One should expect that the higher the number of packets of data to be transmitted the higher would be the possibility of losing some of them during transmission, so they are retransmitted and the number of bytes required for sending the same information should increase. Since the number of bytes in packets would differ, retransmission could produce a random dispersion pattern. Also, some dispersion could be pointing to a mismatch between the number of votes reported by the electronic machines and the actual number of votes transmitted by machines to totalizing servers. This inference relies on the presumption that any difference on data transmission bytes among machines could only be related to the amount of votes being reported since the rest of the information sent from machines had a fixed amount of bytes assigned in the memory by the software according to electoral norms. Parallel lines in graphs may also be produced when more packets of data are transmitted intentionally.

Figure 4: Graphs of amount of bytes in data emitted and received by each machine versus number of total votes per machine for a High Traffic machines sample extracted from the lowest straight line shown in Figure 1. The straight lines show lines of regression with a slope of 47.11 bytes by vote for Incoming data with a 0.2% error and 1.28 bytes by vote for Outgoing data with 6.0% error in the same machines.

In order to determine a typical value of the relations between incoming and outgoing bytes in High Traffic machines with the reported votes by machine, a sample of machines that fall on the lowest straight line with the largest number of points of the Incoming data graph of Figure 1 was taken randomly. In the Outgoing data graph, these machines are in subgroup G1. Then, regressions for Incoming data bytes with respect to votes by machine as well as Outgoing data bytes against votes by machine of the same selected machines were calculated. The graphs for the selected sample regressions are in Figure 4. The linear regressions show a relation between bytes and votes given by the following equations:

Incoming data bytes
Outgoing data bytes

Segregating the High Traffic machines into the above mentioned subgroups, corresponding to the superior cluster (G2) and the inferior cluster (G1) in the Outgoing data graph, it is possible to corroborate that the average of received data bytes by machines in the inferior cloud (G1) is around 27,000 bytes and the one on the superior cloud is of 37,000 bytes, whereas the average in the emitted data is around 6,200 bytes in the first case and of 6,700 bytes in the second one. It is found that these two dissimilar behaviors are simultaneously occurring in machines of the same electoral table in the same voting center for a high number of voting centers. Of the 1,876 High Traffic centers studied, 1,051 centers (56%) correspond to the category of mixed tables, 663 centers (35%) with all machines in the inferior cloud and 162 (9%) in the superior one. It is necessary to notice that the majority of these machines only connected once with the totalizing servers from which it is deduced that the connections were unique and successful.

Proportions for centers with mixed subgroups, inferior and superior subgroup machines respectively, may be considered as originating from a random sample of the universe of High Traffic centers if the probability of occurrence of a machine with traffic in the superior subgroup is 0.33 and for the inferior one is of 0.67 which are the ratios shown by the subgroups to the universe of 6,579 machines (2,166 in superior cloud and 4,413 in the inferior one).

It follows that machines located in the same electoral table using presumably the same source code, the same telephone area codes, sometimes the same telephone line and local networks with the same technology, similar electoral populations and with similar physical conditions behaved in such a different manner in both the reception and emission of data, even though the relations of bytes to vote remained more or less the same. The distributions of votes by machine in both groups differ in average in 10 votes per machine, being greater in the superior subgroup. Nevertheless, there are no statistical differences in the average of percentage of YES and NO votes reported by automated reports.

Figure 5: Graphs of amount of bytes in data emitted and received by each machine versus number of total votes per machine for 14 voting machines transmitting via cellular telephony in the Colegio Internacional de Caracas located in Baruta municipality. The straight lines show lines of regression with a slope of 53.25 bytes by vote for Incoming data with a 0.9% error and 1.28 bytes by vote for Outgoing data with 30% error in the same machines.

It is difficult to technologically explain a behavior so systematically different in the emitted and received data in High Traffic voting machines located in the same electoral table of the same polling center.

2.1.2 B—Low Traffic transmissions

In the Low Traffic group in wire telephony there is no relation between the volume of Outgoing data and the number of votes computed in each machine, suggesting the information transmitted was homogeneous for the machines of this sector. Practically no dispersion is shown in comparison with the behavior in the High Traffic group. This behavior corresponds more to the expected one when only the information on vote totals is transmitted and there are no packets retransmitted.

On the other hand, the Incoming data of voting machines show a regular pattern that depends on the number of votes in the machines only in a small sector. 27.5% of the machines are in the vertical segments of the graph related somehow to number of votes. But the rest of the machines in the horizontal cluster do not show any relation between Incoming data bytes to transmitted votes. This graph also shows a great deal of dispersion. In general, machines in the same electoral table could be located in any one of the two mentioned sectors.

The pattern of Incoming data versus votes in the Low Traffic machines does not seem to respond to the model of individual vote transmission, as it is the case for the High Traffic group. Nevertheless, those machines whose Incoming data bytes are correlated with votes do so in a nonhomogeneous way, the proportional relations between bytes and votes go from 41 to 46 bytes per vote; these proportions are comparable in magnitude to those observed in the High Traffic group but only among machines that differ approximately in 30 votes.

Once again, it can not be technologically explained that machines in the same electoral table have behaviors so differentiated in bytes transmissions; some of them are in the vertical segments of the graph and other ones are in the cluster base.

2.1.3 C—Cellular transmissions

In the Cellular transmissions machines (group C), there is a strong correlation between votes and Incoming data bytes transmitted, much in the fashion of the High Traffic group. The same may be said of the Outgoing data bytes against number of votes in each machine. To illustrate behavior in this group (Figure 5), a particular voting center where transmissions from machines were all through cellular telephony is chosen. This voting center was located in a municipality where the majority of centers fell into the group of Low Traffic transmissions.

The regressions are as follows:

Incoming data bytes
Outgoing data bytes

It is observed that the slopes of straight lines correspond to 53 bytes per vote for the Incoming data versus votes relations and of 1.28 bytes per vote in the slope for Outgoing data versus votes with errors indicating the degree of dispersion. The pattern shown indicates transmission of individual votes as in the case of the High Traffic group. Differences in the volume of data transmission compared to the High Traffic wire telephony are due to differences in transmission technology with data bytes measurements made at different levels.

2.1.4 General results in transmissions

The preceding discussions suggest that either the programming of electronic voting machines for data transmission or the programming in the CNE totalizing servers to handle data transmissions to machines behaved in different ways for two sets of groups of machines, groups A and C compared to group B. Although the transmissions through cellular telephony would not be comparable with that of wire telephony because of differences in technology, the remarkable differences in the volume of data and patterns of transmission between the groups of High and Low Traffic machines in wire telephony cannot be satisfactorily explained under the electoral rules.

Electoral rules required that each machine should do the counting of recorded votes and then its results be transmitted to the totalizing servers. That is, tallies and not individual votes should be transmitted. Transmission of tallies required a fixed amount of bytes per machine, the same is true for the authorizing, acknowledgement answers and transmission certificates sent from totalizing servers to machines; in these cases horizontal straight lines should be expected in Incoming and Outgoing data graphs against votes per machine, with perhaps some variability in the number of bytes mainly for Outgoing data.

Therefore, the dependence of the amount of data bytes on the number of votes is inexplicable under the premise of vote totals transmissions, which was supposed to be the electoral normative. In fact, graphs show clearly a pattern for transmission of individual votes in both directions to and from totalizing servers for the High Traffic and Cellular groups. Also, if the programming software in the machines was the same for all machines, one does not understand either the differences in the types of linear relations with the number of votes reported in every voting machine, or the volumes of data reported in logs since the transmitted information must have equivalent sizes in all wire telephony cases.

Figure 6: Data transmission in municipalities and states. The map shows Venezuela divided by municipalities with some States marked. Full light gray color municipalities include High Traffic wire and Cellular transmissions. Striped gray color regions refer to municipalities containing some parishes with Low Traffic transmissions. The dark gray color municipalities are regions with a majority of Low Traffic transmissions mixed with small percentages of Cellular ones.

On the other hand, a systematic behavior in the transmissions going from machines to servers and also from servers to machines might suggest a programmed intentionality.

Other findings are also consistent with the suggestion of intentional tampering with the vote counting and transmission process. The irregular distribution of groups of machines, mainly in wire telephony, in different parishes and municipalities with no overlapping, cannot be explained reasonably by random technological causes. If the difference in volumes of traffic in wire telephony is due to a technological variable, then it would be difficult to understand why the Aragua state in its totality behaves technologically different to nearby states like Carabobo and Miranda that share the same telephone network. The same occurs between contiguous parishes in the same municipality in Carabobo, Miranda, Merida and Trujillo. A map with occurrences of A, B and C machine groups by municipalities is shown in Figure 6 (Data transmission in municipalities and states).

2.2 Empirical Distributions of Electoral Variables Across the Three Groups of Voting Machines and Centers

In what follows differences and similarities between distributions of several variables for the three groups of voting machines and centers are studied statistically. The reason to carry out this additional analysis is to shed light on the incidence of the differentiation in the voting machines transmissions on electoral results or vice versa.

A priori we could infer that groups A, B and C of the machines would show differences in electoral variables like abstention and vote results because the number of urban voters is higher in group B than in other groups, as we could gather from the geographical distribution of groups of machines. In fact, we should find that the three groups are not random samples of an electoral universe. But then if there was intentional tampering with the votes, the grouping of the machines and centers must be somehow associated with electoral results since there seem to be no technological factors that can explain the groups. On the other hand, if there was an innocent reason for loading two different software packages in either machines or servers, the electoral authorities should have mentioned this fact prior to the election. Suspicions arise mainly because voting machines were connected to totalizing servers at CNE headquarters, before tallies were printed by machines locally. Even more, previously planned audits were not fully carried out and ballot boxes with paper tickets produced by the machines were not allowed to be opened.

In this light, a question of interest is the following: is the linear dependence of Outgoing and Incoming data bytes on votes related to virtual votes and tampering of electoral results? If that was the case for groups A and C, what happened to group B where the linear dependence shows only for 27.5% of the machines?

If vote results were tampered with, it seems logical to think that the made-up voting patterns were not made up during the electoral event but, rather, were determined in advance of the election. If so, an approach to generate plausible distributions of NO and YES votes across the various voting centers would be to mimic what was observed during the 1998 and 2000 presidential elections. Thus, we explore the similarities and the differences between the electoral results reported for the 2004 PRR and those that were obtained during the presidential elections of 1998 and 2000. Clearly, we cannot expect to arrive at any conclusive results, but these comparisons may help explain how, if at all, electoral results were altered in 2004.

Figure 7: Comparison of distributions of NO_Percentage per machine across High, Low Traffic and Cellular groups through box plots. The short horizontal straight lines indicate the position of the means of distributions and standard deviations, the long horizontal straight lines indicate the position of the percentiles (10%, 25%, median, 75% and 90%) of the distribution, and the boxes width shows the relative size of the samples in High, Low Traffic of wire and Cellular telephony. On the right-hand side Q–Q plots are shown for the three empirical distributions showing variances (slopes) for each distribution.

2.2.1 Percentage of NO votes per machine at the national level

The comparisons of percentiles, means and medians for the empirical distributions along with the Van der Waerden test for means are performed. Also, when two distributions show close enough means or medians an analysis of variance is included with its -test to look at the source of differences.

From previous graphs and numerical tables it is deduced that the empirical distributions for NO% per machine in groups A and C are equivalent as much in the functional form as in their main quantiles, see Figure 7. An analysis of variance test comparing means shows there is not statistical difference between groups A and C with (). Their respective means are and .

The B (Low Traffic) distribution has a Mean and Median significantly different from those of groups A and C; these differences go up to around 10 points (20%). These results together with the irregular distributions of types of machines in municipalities and parishes aim at considering that High and Low Traffic groups of machines cannot be considered representative samples of the electoral universe as expected. But the Cellular group not expected to produce electoral results similar to either High or Low traffic groups because of its geographical distribution is not statistically different to the High Traffic group, coinciding with the fact that both share the same pattern of transmission.

The classification of these groups by volume of data transmissions where the High Traffic and Cellular groups share a pattern quite different to the Low Traffic one looks like having influence into the percentage of NO votes per machine.

2.2.2 A comparison to presidential elections of1998 and 2000 by voting centers classified ingroups A, B and C

The next percentage of abstention and empirical distributions for percentage result in various elections for Chavez 1998, Chavez 2000 and NO 2004 PRR per voting center are statistically analyzed. Here we aim to consider the historical electoral evolution of the centers; we want to know how different were those centers in the past compared to the 2004 event, as well as how different were their vote results among groups of centers.

In order to be able to compare the 1998 and 2000 elections with the 2004 PRR event, the percentage of Chavez votes in 1998, 2000 and those of NO in the 2004 PRR are calculated for each voting center and for the same centers. This procedure is needed since the structure of electoral tables was different for those elections. Also, there was a drastic increase of 32.6% in the number of voters between the 2000 and the 2004 electoral events.

Voting centers are classified as the High Traffic group (A) representing 42% of the universe considered in this study, the Low Traffic group (B) with 36% and the Cellular group (C) with 22%. Each group contains 44%, 39% and 17% of A, B and C types of machines respectively. Electoral data are taken from the official results published by the CNE.

In Table 1 the relations between groups of voting centers are detailed.

Comparisons of means and standard deviations of percentage of abstention in each voting center for the 1998, 2000 and 2004 electoral events and their differences between successive events for groups A, B and C are shown in Figure 8.

The number of voting centers analyzed in this section is of 4074: 1759 of them correspond to centers that in 2004 were classified in the High Traffic group, 1492 in the Low Traffic group and 823 in the Cellular one.

Figure 8: Means and differences of % abstention for High, Low Traffic and Cellular groups of voting centers in 1998, 2000 and 2004 electoral events.

In Figure 8 the most striking finding is that differences in percentage of abstention by voting center between the 2000 and 2004 electoral events across groups A, B and C are statistically the same with , when the same measurements between 1998 and 2000 are different for different groups. In 1998 High and Low Traffic groups showed means of abstention per center slightly different being lower in the latter group. As pointed out before, in this group the number of urban voters is higher; traditionally in Venezuela voters in cities tend to participate more in elections than rural ones. Group C behaved quite different compared to the others more in line with a rural behavior. By 2000, the B group showed a small difference with the other two groups; abstention increased more in this group than in the others presumably because there were less Chavez supporters in it, added to the fact that the 2000 event was a presidential re-election after a change of Constitution and just one year and a half of Chavez being elected with high popularity. But what is unexpected is that the difference with the other groups was maintained in 2004 for a Presidential Recall Referendum summoned by voters concentrating in greater numbers precisely in group B. It was expected that abstention would be lower than ingroups A and C, even lower than the one experienced in 1998.

Tables 27 for means, standard deviations and differences in % of abstention across groups of voting centers are shown below.

Comparisons of percentages of Chavez votes distributions in 1998, 2000 and the 2004 NO votes for the High Traffic and Low Traffic groups are shown in Figures 9 and 10 as to visualize similarities in all quantiles between the 2004 PRR and the 2000 presidential election. Tables with means, standard deviations and quantiles for all groups in the three electoral events are also included below.

Level Number Mean Std dev 25%—Q Median 75%—Q
 Traffic—wire 8,205 62.0384 14.6481 53.0 63.51 72.47
 Traffic—wire 7,431 51.8259 19.2504 40.23 54.65 66.59
C—Cellular 3,150 62.3028 15.9224 52.45 63.94 74.54
Table 2: Means, standard deviations and quantiles for percentage of NO votes per machine
Level Number Mean Std dev
A—HighTraffic—1998 1,759 35.69 6.23
B—LowTraffic—1998 1,492 35.05 7.83
C—CellTraffic—1998 1,823 38.32 8.99
A—HighTraffic—2000 1,759 42.43 6.70
B—LowTraffic—2000 1,492 43.94 8.25
C—CellTraffic—2000 1,823 42.99 8.63
A—HighTraffic—2004 1,759 28.35 5.45
B—LowTraffic—2004 1,492 29.71 6.34
C—CellTraffic—2004 1,823 28.41 6.16
Table 3: Means, standard deviations of % abstention per voting center for groups A, B and C

From Figures 9 and 10, it can be perceived that these groups show different empirical distributions in their parameters for the three considered elections. The distributions of votes percentages in High Traffic centers are similar for the 2000 and 2004 electoral events but different from the one in 1998. The analysis of variance shows that the means of High Traffic group distributions for the 2000 and the 2004 electoral events are not statistically different with when percentages of Chavez votes are taken with respect to total votes, that is, null votes are included. When only valid votes are considered, means differ but quantiles above median are almost the same for 2000 and 2004 elections as shown in Figure 9.

Figure 9: Chavez% votes with respect to valid votes only for 2004 High Traffic centers (A) in 1998, 2000 and NO% PRR.
Level Number Mean Std dev
A—HighTraffic 1,759 14.09 5.44
B—LowTraffic 1,492 14.23 6.19
C—CellTraffic 1,823 14.58 7.12
Table 4: Means, standard deviations for differences in % abstention per center between 2000 and 2004 events
Level Number Mean Std dev 25%—Q Median 75%—Q
1998 1,759 58.36 9.90 51.92 58.4 65.27
2000 1,759 64.11 13.1 55.76 64.83 73.13
NO—2004 1,759 62.25 14.25 53.15 63.95 72.41
Table 5: Means, standard deviations and quantiles for High Traffic centers
Level Number Mean Std dev 25%—Q Median 75%—Q
1998 1492 51.62 13.84 43.65 53.94 62.10
2000 1492 54.55 18.53 43.34 57.78 68.71
NO—2004 1492 51.81 19.11 40.61 54.42 66.29
Table 6: Means, standard deviations and quantiles for Low Traffic centers
Level Number Mean Std dev 25%—Q Median 75%—Q
1998 823 51.46 11.80 43.36 51.00 60.19
2000 827 60.39 13.38 52.20 60.62 69.80
NO—2004 827 61.80 15.39 52.57 63.33 73.69
Table 7: Means, standard deviations and quantiles for Cellular centers

There are differences in means in centers classified in the Low Traffic group for the 2000–2004 years. But, comparing quantiles, we could appreciate a nearly constant shift along the entire distribution, a fact that seems surprising. It is found that 2004 NO% PRR in the Low Traffic centers have a mean statistically comparable to the mean in the 1998 election with .

Also, it is interesting to observe that the Cellular group and the Low Traffic group show similar statistical behavior in 1998 but in 2000 and 2004 are quite different. The Cellular group resembles more the High Traffic group in 2004.

It is worth noticing that the 1998, 2000 and 2004 elections should be different from a statistical point of view, since in the first one every voter had to choose from 5 or more options, the second one from a maximum of 4 options and in the Recall Referendum choice was only among 2 options in the automated centers. The differences in the number of options would have to affect the range of votes percentages obtained, thus, the smaller the number of options is the greater the range of votes percentages would be. Although this is observed for the ranges of percentages obtained in the 4074 centers in the 1998, 2000 and 2004 elections (76.42 points), (86.73 points) and (91.08), respectively, when the mentioned centers are classified into the A, B and C groups, group B shows a contraction in the range if the 2000 and the 2004 electoral events are compared. Also, if the standard deviations for each group are historically compared, an increase is observed from 1998 to the 2004 event, nevertheless, the increase from the 2000 to the 2004 PRR is significantly smaller in group B.

Figure 10: Chavez% votes for 2004 Low Traffic centers (B) in 1998, 2000 and NO% PRR.
High Traffic centers DF 1758 Low Traffic centers DF 1491 Cellular centers DF 832
\ccline2-3,4-5,6-7 Distributions ChiSq ChiSq ChiSq
%NO 2004—%Chav 2000
 valid votes 1748.64
%NO 2004—%Chav 2000
 total votes 1587.79
%NO 2004—%Chav 1998
 valid votes 4552.21
%NO 2004—%Chav 1998
 total votes 5413.84
%NO 2000—%Chav 1998
 valid votes 3235.13
%NO 2000—%Chav 1998
 total votes 3810.55
Table 8:

2.2.3 Chi test of comparison of empirical distributions of Chavez’ votes percentages for 1998, 2000 elections and 2004 PRR

As it becomes clear in examining the graphs above, there are similarities between the 2004 PRR and the 2000 elections for automated voting centers in all groups. So, it proceeds to apply statistical tests for comparison of the entire distributions. In this case, the Chi test is used to examine the degree of dependence of data between the 2004 NO% empirical distribution and the 2000 Chavez% distribution. By comparison and reasons of completeness, the Chavez% vote in the 1998 elections for the same voting centers are included as well. Results are shown in Table 8.

Comparisons are made between the empirical percentage distributions in the case when only total valid votes are considered and also, when null votes are included. It occurs for the 1998 and 2000 elections, the 2004 PRR did not have the null option.

It is remarkable that although there was 1 year and 7 months of difference between the 1998 and 2000 electoral events, Chi test of comparison between the corresponding empirical distributions show that they were completely independent events. Nevertheless, the %NO in 2004 PRR cannot be considered totally independent of the %Chavez votes in the 2000 elections for the High Traffic group (), although the first one was an election of two options and the second one had four options. There exist differences in the Low Traffic group when percentages are computed using valid votes only, but when null votes are included similarities () resemble those of the High Traffic and Cellular groups ().

Something to notice is that the population of voters increased significantly, 32.6%, for the 2004 electoral event, but those new voters do not have to behave from the electoral point of view in the same manner as the population of the 2000 election. There are more similarities between the NO% 2004 PRR High Traffic and Cellular groups with the %Chavez 2000 distributions than with the NO% 2004 PRR Low Traffic one. This is unexpected when considering that most of the new voters are in the former groups. Is this indicating a virtual copying of 2000 results in the 2004 PRR event or is just a mere coincidence?

3 Conclusions

The programming of electronic voting machines for data transmission or the programming in the CNE totalizing servers to handle data transmissions appears to have been different in two groups of machines. This difference allowed a classification of machines into High Traffic and Cellular machines with one particular pattern of transmissions, and Low Traffic machines with quite a different pattern. Differences in the patterns of transmission across groups cannot be satisfactorily explained under the electoral rules and technological platforms used. In fact, they point to two different programs being used either in the voting machines, totalizing servers or both. The presence of a linear dependence of transmitted data bytes on votes in both directions in communications between servers and machines suggests that individual votes were interchanged in one group of machines. Nonrandomness in the geographic distribution of groups A, B and C of machines may be showing intentionality in the differentiation, separating municipalities that showed higher concentrations of President Chavez supporters in the 2000 election from the rest. Voting machines in these districts were administered differently than machines in the rest of electoral districts.

We argue that the percentage of NO votes per machine, as well as the percentage of abstentions, exhibit a similar distribution across voting machines in the High Traffic (A) and Cellular (C) groups; the distribution of both variables is rather different, however, when we consider machines in the Low Traffic (B) group. The differences in mean percentage of NO votes and in the percentage of abstentions in machines of group B compared to machines of groups A and C are statistically significant.

The differences in abstention percentages at the center level across the A, B and C groups for the 1998, 2000 and 2004 electoral events support the hypothesis of a nonrandom grouping of centers. When combined with the fact that voting centers of types A and B tended to be located in different nonoverlapping parishes within the same municipalities, this may be taken as an indication that tampering in selected voting centers and selected voting machines may have taken place.

If indeed tampering occurred, an interesting question is whether the 2000 election results may have been approximately reproduced in 2004 to produce a plausible distribution of NO and YES votes in various centers. When we compare the distributions of each type of vote across the elections of 1998, 2000 and 2004 we find that the hypothesis of a linear dependence between results observed in 2000 and those reported for 2004 cannot be rejected. We observe a constant shift of the relative differences of abstentions in centers classified as A, B or C between 2000 and 2004, an unexpected finding.

While we believe that we have put forth persuasive arguments to question the integrity of the voting process during the 2004 PRR, our analyses and conclusions are limited by the fact that voting machines were not calibrated prior to the election. Thus, even though we cannot think of a plausible reason for the differences that were observed in transmission volumes, it is possible that factors totally unrelated to the electoral process may have had an effect on transmission volumes. For the monitoring and auditing system of electronic voting machines to be fully defensible, it would be necessary to calibrate the machines ahead of the event, perhaps by transmitting a test file of known size from randomly chosen machines to randomly chosen servers repeatedly so that the number of bytes used in the transmission can be compared to the file size.

Deciding whether tampering occurred given the evidence is akin to deciding between two competing hypothesis: tampering occurred or tampering did not occur. This decision problem can be formulated as a posterior odds problem, where we weigh the probability of tampering given the evidence against the probability of no tampering given the same evidence. The latter can be thought of the probability of a coincidental outcome that occurs for reasons which have nothing to do with tampering. To compute a posterior odds ratio, we need to be able to evaluate the probability of observing the electoral results (and the rest of the evidence) we observed under the two hypothesis of tampering and no tampering. With the information available to us, we can think of quantifying the conditional probability of the evidence given tampering. But in order to also quantify the probability of observing what we observed if no tampering had occurred, we need information that is not available and that can be obtained through a careful calibration of the voting machines.

Finally, it is worth mentioning that after the 2006 elections that took place in Venezuela, the governing party greatly limited the type and amount of information that would be made available about transmissions between voting machines and the CNE servers. For example, information that was available for earlier elections including log headers for outgoing and incoming data bytes were missing from the transmission logs shared with the public. Further, it is no longer possible to determine the geographic location of each voting machine. Thus, the analyses that we were able to carry out using the 2004 election data cannot be carried out for the 2006 election.


I would like to thank the previous study of telecommunications and electronic voting technology used during the 2004 PRR made by Ing. Horacio Velasco and his team. Also, special thanks to Professor Freddy Malpica who coordinated the investigation group, rendering great insight into solutions of the puzzle presented. Last, I am grateful to Professor Lelys Bravo who gave important recommendations as to the presentation of statistical data and its analysis in the present article. Further thanks go to Professor Hugo Montesinos for long clarifying discussions about the most adequate statistical analysis for the present study.


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