A referendum to recall President Hugo Chávez was held in Venezuela in August of 2004. In the referendum, voters were to vote YES if they wished to recall the President and NO if they wanted him to continue in office. The official results were 59% NO and 41% YES. Even though the election was monitored by various international groups including the Organization of American States and the Carter Center (both of which declared that the referendum had been conducted in a free and transparent manner), the outcome of the election was questioned by other groups both inside and outside of Venezuela. The collection of manuscripts that comprise this issue of Statistical Science discusses the general topic of election forensics but also focuses on different statistical approaches to explore, post-election, whether irregularities in the voting, vote transmission or vote counting processes could be detected in the 2004 presidential recall referendum. In this introduction to the Venezuela issue, we discuss the more recent literature on post-election auditing, describe the institutional context for the 2004 Venezuelan referendum, and briefly introduce each of the five contributions.

On August 15th, 2004, Venezuelans had the opportunity to vote in a Presidential Recall Referendum to decide whether or not President Hugo Chávez should be removed from office. The process was largely computerized using a touch-screen system. In general the ballots were not manually counted. The significance of the high linear correlation (0.99) between the number of requesting signatures for the recall petition and the number of opposition votes in computerized centers is analyzed. The same-day audit was found to be not only ineffective but a source of suspicion. Official results were compared with the 1998 presidential election and other electoral events and distortions were found.

A simple and quick general test to screen for numerical anomalies is presented. It can be applied, for example, to electoral processes, both electronic and manual. It uses vote counts in officially published voting units, which are typically widely available and institutionally backed. The test examines the frequencies of digits on voting counts and rests on the First (NBL1) and Second Digit Newcomb–Benford Law (NBL2), and in a novel generalization of the law under restrictions of the maximum number of voters per unit (RNBL2). We apply the test to the 2004 USA presidential elections, the Puerto Rico (1996, 2000 and 2004) governor elections, the 2004 Venezuelan presidential recall referendum (RRP) and the previous 2000 Venezuelan Presidential election. The NBL2 is compellingly rejected only in the Venezuelan referendum and only for electronic voting units. Our original suggestion on the RRP (Pericchi and Torres, 2004) was criticized by The Carter Center report (2005). Acknowledging this, Mebane (2006) and The Economist (US) (2007) presented voting models and case studies in favor of NBL2. Further evidence is presented here. Moreover, under the RNBL2, Mebane’s voting models are valid under wider conditions. The adequacy of the law is assessed through Bayes Factors (and corrections of p-values) instead of significance testing, since for large sample sizes and fixed α levels the null hypothesis is over rejected. Our tests are extremely simple and can become a standard screening that a fair electoral process should pass.

We present a simulation-based study in which the results of two major exit polls conducted during the recall referendum that took place in Venezuela on August 15, 2004, are compared to the official results of the Venezuelan National Electoral Council “Consejo Nacional Electoral” (CNE). The two exit polls considered here were conducted independently by Súmate, a nongovernmental organization, and Primero Justicia, a political party. We find significant discrepancies between the exit poll data and the official CNE results in about 60% of the voting centers that were sampled in these polls. We show that discrepancies between exit polls and official results are not due to a biased selection of the voting centers or to problems related to the size of the samples taken at each center. We found discrepancies in all the states where the polls were conducted. We do not have enough information on the exit poll data to determine whether the observed discrepancies are the consequence of systematic biases in the selection of the people interviewed by the pollsters around the country. Neither do we have information to study the possibility of a high number of false or nonrespondents. We have limited data suggesting that the discrepancies are not due to a drastic change in the voting patterns that occurred after the exit polls were conducted. We notice that the two exit polls were done independently and had few centers in common, yet their overall results were very similar.

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.

This study analyzes diverse hypotheses of electronic fraud in the Recall Referendum celebrated in Venezuela on August 15, 2004. We define fraud as the difference between the elector’s intent, and the official vote tally. Our null hypothesis is that there was no fraud, and we attempt to search for evidence that will allow us to reject this hypothesis. We find no evidence that fraud was committed by applying numerical maximums to machines in some precincts. Equally, we discard any hypothesis that implies altering some machines and not others, at each electoral precinct, because the variation patterns between machines at each precinct are normal. However, the statistical evidence is compatible with the occurrence of fraud that has affected every machine in a single precinct, but differentially more in some precincts than others. We find that the deviation pattern between precincts, based on the relationship between the signatures collected to request the referendum in November 2003 (the so-called, Reafirmazo), and the YES votes on August 15, is positive and significantly correlated with the deviation pattern in the relationship between exit polls and votes in those same precincts. In other words, those precincts in which, according to the number of signatures, there are an unusually low number of YES votes (i.e., votes to impeach the president), is also where, according to the exit polls, the same thing occurs. Using statistical techniques, we discard the fact that this is due to spurious errors in the data or to random coefficients in such relationships. We interpret that it is because both the signatures and the exit polls are imperfect measurements of the elector’s intent but not of the possible fraud, and therefore what causes its correlation is precisely the presence of fraud. Moreover, we find that the sample used in the audit conducted on August 18 was neither random nor representative of the entire universe of precincts. In this sample, the Reafirmazo signatures are associated with 10 percent more votes than in the non-audited precincts. We built 1,000 random samples in non-audited precincts and found that this result occurs with a frequency lower than 1 percent. This result is compatible with the hypothesis that the sample for the audit was chosen only among those precincts whose results had not been altered.

The best way to reconcile political actors in a controversial electoral process is a full audit. When this is not possible, statistical tools may be useful for measuring the likelihood of the results. The Venezuelan recall referendum (2004) provides a suitable dataset for thinking about this important problem. The cost of errors in examining an allegation of electoral fraud can be enormous. They can range from legitimizing an unfair election to supporting an unfounded accusation, with serious political implications. For this reason, we must be very selective about data, hypotheses and test statistics that will be used. This article offers a critical review of recent statistical literature on the Venezuelan referendum. In addition, we propose a testing methodology, based exclusively on vote counting, that is potentially useful in election forensics. The referendum is reexamined, offering new and intriguing aspects to previous analyses. The main conclusion is that there were a significant number of irregularities in the vote counting that introduced a bias in favor of the winning option. A plausible scenario in which the irregularities could overturn the results is also discussed.

Motivated by the practice of exploratory research, we formulate an approach to multiple testing that reverses the conventional roles of the user and the multiple testing procedure. Traditionally, the user chooses the error criterion, and the procedure the resulting rejected set. Instead, we propose to let the user choose the rejected set freely, and to let the multiple testing procedure return a confidence statement on the number of false rejections incurred. In our approach, such confidence statements are simultaneous for all choices of the rejected set, so that post hoc selection of the rejected set does not compromise their validity. The proposed reversal of roles requires nothing more than a review of the familiar closed testing procedure, but with a focus on the non-consonant rejections that this procedure makes. We suggest several shortcuts to avoid the computational problems associated with closed testing.

Goeman and Solari [Statist. Sci. 26 (2011) 584–597] have addressed the interesting topic of multiple testing for exploratory research, and provided us with nice suggestions for exploratory analysis. They defined properties that an inferential procedure should have for exploratory analysis: the procedure should be mild, flexible and post hoc. Their inferential procedure gives a lower bound on the number of false hypotheses among the selected hypotheses, and moreover whenever possible identifies elementary hypotheses that are false. The need to estimate a lower bound on the number of false hypotheses arises in various applications, and the partial conjunction approach was developed for this purpose in Biometrics 64 (2008) 1215–1222 (see also Philos. Trans. R. Soc. Lond. Ser. A 367 (2009) 4255–4271 for more details). For example, in a combined analysis of several studies that examine the same problem, it is of interest to give a lower bound on the number of studies in which the finding was reproduced. I will first address the relation between the method of Goeman and Solari and the partial conjunction approach. Then I will discuss possible extensions and address the issue of exploration in more general settings, where the local test may not be defined in advance or where the candidate hypotheses may not be known to begin with.

We develop new tools for formal inference and informal model validation in the analysis of spatial point pattern data. The score test is generalized to a “pseudo-score” test derived from Besag’s pseudo-likelihood, and to a class of diagnostics based on point process residuals. The results lend theoretical support to the established practice of using functional summary statistics, such as Ripley’s K-function, when testing for complete spatial randomness; and they provide new tools such as the compensator of the K-function for testing other fitted models. The results also support localization methods such as the scan statistic and smoothed residual plots. Software for computing the diagnostics is provided.

Eugenio Regazzini was born on August 12, 1946 in Cremona (Italy), and took his degree in 1969 at the University “L. Bocconi” of Milano. He has held positions at the universities of Torino, Bologna and Milano, and at the University “L. Bocconi” as assistant professor and lecturer from 1974 to 1980, and then professor since 1980. He is currently professor in probability and mathematical statistics at the University of Pavia. In the periods 1989–2001 and 2006–2009 he was head of the Institute for Applications of Mathematics and Computer Science of the Italian National Research Council (C.N.R.) in Milano and head of the Department of Mathematics at the University of Pavia, respectively. For twelve years between 1989 and 2006, he served as a member of the Scientific Board of the Italian Mathematical Union (U.M.I.). In 2007, he was elected Fellow of the IMS and, in 2001, Fellow of the “Istituto Lombardo—Accademia di Scienze e Lettere.” His research activity in probability and statistics has covered a wide spectrum of topics, including finitely additive probabilities, foundations of the Bayesian paradigm, exchangeability and partial exchangeability, distribution of functionals of random probability measures, stochastic integration, history of probability and statistics. Overall, he has been one of the most authoritative developers of de Finetti’s legacy. In the last five years, he has extended his scientific interests to probabilistic methods in mathematical physics; in particular, he has studied the asymptotic behavior of the solutions of equations, which are of interest for the kinetic theory of gases. The present interview was taken in occasion of his 65th birthday.