Precincts (Secciones) and Polling Stations

The basic unit of Mexico’s electoral geography is the sección electoral (subsequently precinct). Every precinct contains one or more polling stations (henceforth PS), depending on the number of voters registered in the precinct. To provide a sense for the magnitudes: there were 62,692 precincts and 129,238 PSs in the 2012 presidential election. The average precinct covers about 1,200 registered voters. A strictly-enforced maximum of 750 registered voters can be assigned to vote at any given PS. This maximum determines the total number of polling stations needed in an election. Registered citizens are apportioned equally across the PSs in a precinct. For example, in a precinct containing 752 citizens, two PSs will exist, with 376 citizens assigned to each. The first PS in a precinct is known as the básica (basic) PS, the second PS is called contigua 1 (contiguous 1), the third is contigua 2, and so on. Within a given precinct, polling stations are expected to have about the same number of total votes and vote shares across parties because voters are assigned to them in a quasi-random way.

Mexican law requires that votes be tallied by randomly selected citizens who function as polling-station workers (henceforth PW). This is a very challenging logistical feat. Each PS is allocated four acting PWs and three substitute PWs (the number is greater in concurrent elections). To be eligible, a citizen must not work for a political party and must be able to read and write, among other things. The general functions of the PW team for a given PS are to staff the PS during Election Day, to make sure only those eligible to vote at the PS do so, to count the votes by hand after the close of voting, and to fill out the acta that same evening. PWs are trained by INE. The procedure for allocating PWs to PSs is described later in the paper.

Political parties are entitled to send official party representatives to sit at the PSs along with PWs. They can observe the work of the PW, but they have no formal role in the ballot counting or in the filling out of the actas.

Education

Does the quality of vote tallies depend on the education/numeracy of the citizens selected to function as PW? Ex ante, we are agnostic on this point. Lower educational attainment could make it more difficult for poll workers to successfully complete their tallying tasks without mistakes. At the same time, anecdotal evidence has led some INE officials to believe that PWs with lower educational attainment take their vote-tallying tasks more seriously and therefore exert greater effort than their more-educated peers. Simply regressing the extent of inconsistencies on the educational attainment of PWs could potentially be subject to concerns about omitted variable bias. To mitigate this possibility, because the average level of education in the population is likely different across precincts, we focus on variation in educational attainment across PSs within a precinct. In addition, we use an exogenous source of within-precinct variation in the educational attainment of PWs based on the procedure used to allocate PWs across PSs.

The allocation begins with a list of citizens recruited to be PW at a given precinct. These PWs are allocated to the various PSs within their precinct according to a strict rule: The person with the highest educational attainment is named President of the first PS in the precinct (“casilla básica”); the second most-educated person is named President of the second PS (“casilla contigua 1”), and so on. Once all PSs in the precinct have been assigned a President, the next most-highly educated person in the pool is assigned to be Secretary of the first PS; the next one is named Secretary of the second PS, and so forth. The assignment procedure continues until every PS has a full set of PWs (either four or six PWs, plus substitutes, depending on the number of concurrent elections).Footnote ¹⁰

This allocation rule has the consequence that the team of PWs assigned to the first polling station (básica) in a precinct has a higher level of educational attainment—both position by position as well as on average—than the PW team assigned to the second polling station (contigua 1), which in turn has a higher level of education than the team assigned to the third polling station (contigua 2), and so on. Figure A4 in the Appendix shows that, indeed, PSs within a precinct are ranked by education. Part (b) in that figure shows that on average, PWs working at first-ranked (básica) polling stations have approximately 0.6 more years of education than second-ranked (contigua 1) polling stations, 0.9 more than third-ranked polling stations, and 1.0 more than fourth-ranked polling stations. Crucially, this variation is entirely due to the allocation rule, and it is therefore plausibly orthogonal to potentially confounding traits of the polling stations. On this basis, we implement the following instrumental-variables strategy:

(1)$$ AbsNumIn{c}_{pste}^j={X}_{\mathrm{pst}}^{\prime}\alpha +{\beta}^j{S}_{\mathrm{pst}}+{n}_{\mathrm{st}}+{u}_{\mathrm{pst}\mathrm{e}}\kern1.00em $$

and

(2)$$ {\displaystyle \begin{array}{ccc}{S}_{\mathrm{pst}}={X}_{\mathrm{pst}}^{\prime }{\pi}_0+1\left({B}_{\mathrm{pst}}\right){\pi}_1+{n}_{\mathrm{st}}+{e}_{\mathrm{pst}},& & \end{array}} $$

where j indexes the type of inconsistency, $$ {S}_{\mathrm{pst}} $$ is the average years of educational attainment of the PW team at PS $$ p $$ in precinct $$ s $$ in election-year $$ t $$, $$ {X}_{\mathrm{pst}} $$ is a matrix of covariates that includes the average age and the fraction who are female of the PW team for PS $$ p $$ in precinct $$ s $$ in election year $$ t $$ as well as various traits of the recruiter who recruited and trained the PWs in all PSs in precinct $$ s $$,Footnote ¹¹$$ 1\left({B}_{\mathrm{pst}}\right) $$ is an indicator that PS $$ p $$ in precinct $$ s $$ in election year $$ t $$ is the first PS (básica), and $$ {n}_{\mathrm{st}} $$ are precinct–year dummies. The coefficients of interest are the $$ {\beta}^j $$.

The first stage is very strong, as expected, with $$ {\pi}_1=0.743 $$, a t-statistic above 180, and an F-statistic of 5,871 (Table A9). The reason for this strong first stage, even when errors are clustered at the precinct level, is that the number of observations is very large and the allocation rule is followed strictly. Table 1 displays the second-stage estimates. An additional year of average education in a PS reduces the absolute number of inconsistencies of type 1 by 0.60, of type 2 by 0.79, of type 3 by 0.04, and of type 4 by 0.38. These represent 7, 7, 1, and 5% of the corresponding means. These estimates are statistically significant, except in the case of type-3 inconsistencies. These results imply that selecting PWs with greater educational attainment would result in vote tallies with fewer inconsistencies.Footnote ¹²

Difficulty

Insofar as education, numeracy, or training matter for the quality of vote tallying, one would expect that more difficult tallies should on average exhibit more inconsistencies than easier ones. To explore this possibility, we construct a measure of the difficulty of the tallying task. One natural measure of tallying difficulty is the arithmetical difficulty of a sum. The first type of inconsistency requires that PWs perform a sum. The sum generally involves a “large” number (i.e., the number of votes cast in a PS, which is usually in the hundreds) and a “small” one (i.e., the number of party representatives who cast votes in the PS, usually smaller than 10). We classify such a sum as “difficult” if it involves carrying one over and as “easy” if it does not.Footnote ¹³ We construct a dummy variable that takes the value of 1 when the sum that a PW needs to perform is “difficult” and the value of 0 when it is “easy.” Close to 35% of the tallies contain difficult sums.

We believe the difficulty of the sum, thus defined, can be regarded as exogenous with respect to inconsistencies in the tally. For one thing, it depends to a large extent on the last digit of the total number of votes cast in a PS. Crucially, whether turnout is low or high should have no bearing on the last digit of the total number of voters. Still, we check for balance on observables between those tallies where the sum in question is difficult versus those where it is easy. Table 2 presents the results of the balance tests. Each of the first four columns represents the regression of a predetermined covariate on the difficulty dummy. These covariates are a dummy indicating whether the PS is the first one (básica) in the precinct or not, the average years of education of PWs in the PS, the share of male PWs within the team at the PS, and the average age of the PW team at the PS. As before, the estimates are based on variation across PSs within a precinct (i.e., they include precinct fixed effects). As expected, there is no difference in any of the covariates between PSs with a difficult versus an easy sum.

Table 2. Effect of Tallying Difficulty on Tally Quality

Note: Columns 1–4 display balance tests, where a predetermined covariate is regressed on the difficulty dummy: $$ \mathrm{Predetermine}{d}_{\mathrm{pste}}=\alpha +\upgamma \mathrm{DifficultyDumm}{y}_{\mathrm{pste}}+{n}_{\mathrm{st}}+{\epsilon}_{\mathrm{pste}} $$. Such covariates include an indicator for whether the PS is first-ranked (basica), the average education of PWs at the PS, the fraction of male PWs at the PS, and the average age of PWs at the PS. Variables are indexed by PS $$ p $$, precinct $$ s $$, election year $$ t $$, and election-type $$ e $$. The unit of observation is an acta. Columns 5 and 6 show the effect on inconsistencies of type 1; the dependent variable in these two last columns is $$ \mathrm{AbsNumIn}{c}_{\mathrm{pste}}^1 $$, the absolute number of inconsistencies of type 1. Standard errors are clustered at the precinct–year level shown in parentheses below coefficient estimates. *** P < 0.01, ** p < 0.05, * p < 0.10.

Column 5 displays the effect of the difficulty indicator on the extent of inconsistencies of type 1 (the type that involves the aforementioned sum). A difficult sum, in comparison with an easy one, increases the extent of inconsistencies by 1.5—that is, 17% of the average extent of inconsistencies of type 1. To further probe whether our measure of difficulty indeed relates to the kinds of skills that presumably correlate with formal education, we study whether the effect of difficulty on inconsistencies is moderated by the education of the PW. In column 6 we interact the difficulty dummy with the average educational attainment of the PW team in the relevant PS. As before, the main effect of average education is negative. The effect of difficulty, however, is a function of education. Every additional year of educational attainment reduces the effect of difficulty on the extent of inconsistencies by 0.31. The coefficient on the difficulty dummy is 5.3, implying that the effect of difficulty on inconsistencies is completely nullified when the average level of educational attainment among PS workers is about 16 to 17 years.

Workload

The final cause of tally quality that we test is the workload faced by poll workers. The issue of workload figures prominently in current debates in Mexico. On Election Day, a PW spends about 12 hours staffing and managing her assigned precinct and then about three additional hours tallying up the votes and filling out the tally forms (Figure A10). The INE is concerned that excessive workload could lower the quality of the vote tallies.Footnote ¹⁴ They may be justified: a large literature in psychology and neuroscience shows that attention, self-control, and cognitive function in general are subject to fatigue through mechanisms such as glucose depletion.Footnote ¹⁵ In fact, the rule that polling stations should have no more than 750 voters was motivated by the desire to limit workload and reduce PW mistakes, and INE is considering implementing electronic voting to further reduce the burden on PWs.Footnote ¹⁶ Academics and policy makers have similarly used a workload argument to support electronic voting,Footnote ¹⁷ but unfortunately there seems to exist no quantitative evidence for or against the workload conjecture.

The ideal experiment to test the workload hypothesis would allocate more (or fewer) voters randomly to some polling stations and measure how this translates into more or fewer mistakes in the tally for the PS. We approximate the notional experiment through a natural experiment. Specifically, we exploit the previously mentioned fact that precincts are capped at 750 registered voters by law. If the number of registered voters in a precinct exceeds 750, an additional PS is added and the voters are apportioned equally across all the PSs in that precinct. This rule, therefore, generates a discontinuity in the number of registered voters assigned to each PS at precinct sizes that are multiples of 750 where we can apply a regression discontinuity (RD) methodology. For instance, a precinct with 750 registered voters only has one PS, while a precinct with 751 registered voters has two PSs, respectively, with 375 and 376 registered voters each. This legal cap on PS size is followed strictly (Figure A6).

To estimate the causal effect of workload on the extent of inconsistencies, we implement a regression discontinuity analysis. In the online Appendix we present McCrary density tests (Figure A7) and smoothness/balance tests (Figure A8 and Table A10), which lend strong support to the RD identification assumptions. Figure 2 presents the main results graphically, separately for each of the four types of inconsistencies. The horizontal axes describe the number of registered voters in a precinct, while the vertical axes represent the extent (absolute number) of inconsistencies (one inconsistency type is shown in each panel). The vertical lines indicate the number of registered voters at which an additional PS is to be added, inducing the jump in the number of registered voters per PS in the precinct that we use to identify causality. The regression estimates corresponding to the figure are provided in Table A11 in the Appendix.

Note: This figure presents regression discontinuity graphs exploiting the legal rule that no PS can have more than 750 registered voters. The x-axis plots the number of registered voters in a precinct. The vertical red lines indicate the number of registered voters at which another PS is added to the precinct, and the y-axis displays the number of inconsistencies of each type. The dots report bin averages (30-point width size bins). The RD equation consists of a linear model with a 375 bandwidth of each cutoff. The shading represents 95% confidence intervals.

Figure 2. Effect of Workload on Tally Quality (Regression Discontinuity Analysis)

The pattern that emerges from the figure is quite clear: workload—the number of ballots to be tallied— causes inconsistencies. The figure shows, for example, that number of inconsistencies is halved at 751 registered voters and again decreases sharply at 1,501 registered voters. In between the discontinuity points, the slope (inconsistencies per registered voter) is positive and practically linear. This pattern is present for each of the four types of inconsistencies. Respectively, the extent of inconsistencies for types 1, 2, 3, and 4 decreases by 5.5, 7.6, 1.9, and 4.0 at the 751 discontinuity (the mean extent of inconsistencies just below the 751 cutoff is roughly 10, 14, 5, and 7 for each of the types 1–4, respectively). These are substantial decreases, and they are all precisely estimated (with t-statistics above 5).

Generally speaking, one might postulate two simple models of inconsistencies as a function of workload. The first is simply that each vote has some probability of being erroneously tallied, independently of how many votes have been counted before it. This model would imply that the level of mistakes increases proportionally to the workload (i.e., to the number of votes counted). A second model, consistent with fatigue explanations, is that mistakes are a convex (instead of linear) function of total votes. In this case, the likelihood that an additional vote is miscounted would increase with the number of votes counted previously by the PW team on election night. This distinction has important policy implications. In the second model, further reductions in the number of registered voters per PS—a policy measure that INE has considered—would reduce the extent of inconsistencies, but this would not be true in the first model.

Figure 2 suggests that the relationship between workload and inconsistencies is in fact linear, at least within the range of workloads we observe. To investigate this further, we redefine the dependent variable as the ratio of the extent of inconsistencies over the workload (number of votes counted) in a PS. We find (Figure A9) that the slope is practically flat and there is no jump in inconsistencies at the discontinuity points—that is, the rate of inconsistencies per vote counted is approximately constant.Footnote ¹⁸

Tally Quality and Ballot Recounts

Inconsistent vote tallies provide a legal basis for ballot recounts in Mexico and other countries (Table A12). In a sample of 177 countries, 92% have legal provisions that contemplate the possibility of ballot recounts (Figure A12). Mexican electoral law establishes the causes that can give rise to a recount. For purposes of this paper, the law establishes that if there are inconsistencies in a vote tally, an official political party representative can request a recount. The electoral authorities cannot choose to perform a recount based on tally inconsistencies without the explicit request of a political party representative. In practice, more than one-third of PSs with tally inconsistencies do not get recounted.

Recounts are political ammunition often used to question election results. In Mexico politicians frequently cite tally inconsistencies as evidence of fraud and to request recounts. Serra (Reference Serra2014), for example, relates that extensive recounts requested by the runner-up in the 2006 presidential election in Mexico did not change the electoral results, but they were used as the basis for accusing the authorities of having committed election fraud and for mobilizing over one million people to the streets in protest.Footnote ²⁰

To study the relationship between inconsistencies and recounts, we create a dummy variable indicating whether a PS was subject to a recount. The share of PSs subject to a recount ranges in our data between 27% (in the 2009 legislative elections) and 62% (in the 2015 legislative elections). The mean over the five national elections in our data is 48.6%. We estimate the relationship between the presence of inconsistencies and the likelihood of a recount using the following linear probability model:

(3)$$ {\displaystyle \begin{array}{ccc}1{\left( PS\_ Recounted\right)}_{pste}=\alpha +{\beta}^j1\left( AbsNumIn{c}_{pste}^j>0\right)+{n}_{st}+{\epsilon}_{pste,}& & \end{array}} $$

where $$ 1{\left( PS\_ Recounted\right)}_{pste} $$ is a dummy variable indicating that PS $$ p $$ in precinct $$ s $$ in year $$ t $$ and election-type $$ e $$ was recounted and 1($$ AbsNumIn{c}_{pste}^j>0 $$) is a dummy variable indicating that the number of inconsistencies of type $$ j=1,..,4 $$ in absolute value was greater than zero. For this analysis, we use this indicator of the presence of inconsistencies, instead of a measure of their extent, because it is their presence that the law marks as grounds for requesting a recount.Footnote ²¹ The unit of observation is a PS vote tally. We include precinct-year fixed effects ($$ {n}_{\mathrm{st}} $$) to control for location-specific variables like education, socioeconomic status of the neighborhood, and local strength of the political parties.

Table 3 presents the results. Columns 1–4 show that the presence of each of the four types of inconsistency is individually strongly related to the likelihood of recount, with effect sizes ranging between 8.8 and 26.0 percentage points. Column 5 shows that the presence of any inconsistency in the vote tally is associated with a 25 percentage point greater probability of a recount.

Table 3. Recounts vs. Tally Quality (OLS and IV Estimates)

Note: This table shows estimates from Equation 3. The dependent variable in all columns is a dummy indicating whether a PS was subject to a recount. In columns 1–4 the main explanatory variable is an indicator for the respective inconsistency being present $$ 1( AbsNumIn{c}_{pste}^j>\mathrm{0}),j=1,2,3,4 $$). In columns 5–6, the explanatory variable is an indicator for any of the four types of inconsistency being present. Column 6 instruments this dummy with an indicator variable for whether the PS is the first-ranked (basica) within its precinct, while column 5 is plain OLS. We include controls for gender, education, and age of PS workers. All regressions include precinct–year-level fixed effects. Standard errors are clustered at precinct–year level. *** p < 0.01, ** p < 0.05, * p < 0.10.

We emphasize that these estimates are identified based on variation between different PS within one same precinct. In other words, if the vote tally for one PS displays no inconsistencies and the tally for another PS in the same precinct does, the latter is about 25 percentage points more likely to be recounted than the former. In order to give a causal interpretation to the regression estimates, it is sufficient to assume that the various PSs within a precinct would have had the same probability of being recounted if none had displayed inconsistencies. We believe this is a reasonable assumption in light of the fact that PSs in a precinct are generally located in the same physical space (e.g., a school building), and precincts cover a narrow geographical space.

Nevertheless, we additionally implement an instrumental variables strategy. We instrument for inconsistencies with the allocation rule that determines which poll workers are assigned to which PSs within a precinct. Above we showed that a dummy variable indicating whether a PS is the first one in the precinct (básica) predicts inconsistencies.Footnote ²² The exclusion assumption is that, within a precinct, this dummy variable may only cause recounts via its effect on inconsistencies. We find no reason to believe otherwise. Column 6 of Table 3 presents the instrumental variables estimator. The result that inconsistencies cause recounts stands. In fact, the IV point estimate is larger than the comparable one based on the OLS regression (column 5).Footnote ²³ The result is also robust to controlling for other major causes of recounts in the law.Footnote ²⁴ In sum, the analysis furnishes evidence that inconsistencies in the vote tallies are an important cause of recounts.

Inconsistencies and Trust in the Electoral Authority

“Inconsistencies make it easy to sow doubts about elections and difficult to clear such doubts,” writes Schedler (Reference Schedler2009). Once they get into the public eye, inconsistencies in vote tallies can undermine trust in election outcomes and in the electoral system itself—often with the help of political rhetoric. In the Mexican case, the political use of recounts was on display in both the 2006 and the 2012 elections. Serra (Reference Serra2012) concludes that, as a result, “several institutions lost public support, especially the electoral ones.”

Media coverage of inconsistencies typically takes place in the context of partisan calls for recounts and of the recount processes themselves. To establish the fact that recounts are indeed covered by the media, we conducted a keyword search of seven major national Mexican media outlets during the six-month period following the 2018 elections. We found 157 articles mentioning vote recounts, equivalent to 22 news items per outlet in the period covered. We conducted additional searches of local media with similar results (described in the Appendix). While both media coverage and the scholarly literature suggest the possibility that recounts may erode trust in electoral institutions, this is ultimately an empirical question to which we now turn.

Having shown in the previous section that inconsistencies are an important cause of recounts, we now focus on the relationship between recounts and trust in the impartiality of electoral authorities. We measure trust through an original survey of approximately 77,000 Mexican citizens conducted in 2017 in the states of Estado de México, Veracruz, Coahuila, and Nayarit.Footnote ²⁵ Respondents were asked to state the extent to which they agree with the statement that “INE is impartial and does not favor any political party.” Answer options consisted of a five-point scale: strongly agree (= 5), agree (= 4), neither agree nor disagree (= 3), disagree (= 2), and strongly disagree (= 1). Even with these many surveys, the data are too sparse to compute polling-station-level averages. This means that we cannot apply the instrumental variables strategy used in the previous section, which was predicated on comparing across polling stations within a precinct. Instead, the analyses in this section are based on comparisons across precincts.

To probe causality we follow six strategies. First, we use a selection-on-observables approach, controlling for large sets of covariates. We also run specifications with state, district, and municipality fixed effects. Second, we implement a variety of placebo checks on alternative outcome variables that we would not expect to be influenced by recounts. Third, we implement a sensitivity analysis that gauges the plausibility that our findings might be spuriously caused by omitted variable bias. Fourth, we implement an instrumental variables strategy. Fifth, we implement a front-door analysis as suggested by Pearl (Reference Pearl1995). Finally, we exploit heterogeneity in the margin of victory to test for a specific causal mechanism.

We begin by estimating a plain regression of trust in INE’s impartiality, measured in 2017, on the fraction of PSs in a precinct that experienced recounts in 2015, using the following model:

(4)$$ {\displaystyle \begin{array}{ccc} INE\_ Impartia{l}_s=\alpha +\beta FraccRecounte{d}_s+{X}_s^{\prime}\gamma +{\nu}_{s,}& & \end{array}} $$

where $$ INE\_ Impartia{l}_s $$ is the precinct-$$ s $$ average of the trust question, $$ FraccRecounte{d}_s $$ represents the fraction of PSs presenting recounts in precinct $$ s $$, and $$ {X}_s $$ is a matrix of precinct-level controls that vary across specifications.

Results are shown in Table 4. Columns 1–4 (top of the table) include progressively larger sets of control variables: 15 sociodemographic controls, then the whole battery of 27 controls, and then these same 27 with additional geographic fixed effects (see the table notes for the specific regressors used). The first column shows that the greater the fraction of PSs with recounts in a precinct, the lower the perceived impartiality of the INE among those surveyed in that precinct. Comparing a precinct where no PSs display recounts with one where all PSs do, perceptions of INE impartiality are lower in the latter by 0.065, or about 13.5% of a standard deviation of the dependent variable in the regression sample. The result survives the inclusion of additional controls: the coefficient is –0.035 (p < 0.05) in the specification with municipality fixed effects and 27 precinct-level control variables (column 4). In this case, identification is based on comparing precincts within a municipality (there are 212 municipalities in the regression sample). The fact that the estimate is still large and statistically significant after including close to 250 regressors and using only within-municipality variation substantially decreases the likelihood that the estimated association is spurious.Footnote ²⁶ Also, the fact that the dependent variable is measured two years after the explanatory variable argues against the possibility of reverse causality. The result is also robust to repeating the analysis with the individual-level survey data. Column 6 displays the estimates for a regression in which the dependent variable is the individual respondent’s trust in the electoral authorities. Controls include all precinct-level variables (basic controls). In addition, we control for a large set of individual-level covariates including: age, education, gender, having an email account, being a WhatsApp user, having gone to public (vs. private) school, knowing any of the poll workers at one’s polling station, being married (vs. single), satisfaction with democracy, owning a smartphone, having donated money the previous year, having donated blood the previous year, having signed a petition to government in the most recent two years, having paid taxes in the most recent two years, having participated in a neighborhood committee, having participated in a protest, having volunteered for a social cause, having communicated about politics in social media, and having voted in an election in the last six years. The coefficient on the recounts variable is fully robust.

Table 4. Trust in Electoral Authority and Recounts

Note: Part A of this table presents estimates of Equation 4, INE_Impartial_s = α+β Fracc Recounted_s + X’_s γ + v_s, where INE_Impartial_s is the precinct-B average of answers to the trust question in our 2017 survey (except for column 6, where individual-level data are used and errors clustered at the precinct level; see text), FraccRecounted is the fraction of PSs recounted in precinct B in 2015, and -B is a matrix of precinct-level (or higher level) controls. To assess robustness, different columns use different sets of controls and geographic fixed effects. Basic controls: (at precinct level from Census) average years of schooling, % born in another State, number Catholic, number of persons with no health insurance, working population, number of houses/apartments with dirt floor, with electricity, or with low assets; (for registered voters) schooling of PWs at the PS, age of PWs at the PS, % women of PWs at the PS, number of registered voters, (from election results) %PAN, %PRI, %PRD. Full controls = Basic controls + % satisfied with democracy, % with smartphone, % donated money last year, % donated blood last year, % signed petition to government this or last year, % paid taxes this or last year, % participated in neighborhood committee, % participated in a protest, % volunteered for a social cause, % talked about politics in social media, % voted in an election in the last six years. To conduct a “placebo” analysis, Part B changes the dependent variable to the precinct-B average of the extent of agreement with the following statements: (1) INE is impartial and does not favor any party; (2) Voting is a civic duty; (3) I would have preferred not to be asked to be a poll worker; (4) Men are better bosses and leaders than women; (5) We Mexicans should donate our time and fight for transparent elections; (6) I feel taken into account in the political decisions of the country.

As an alternative strategy to explore the possibility of confounding by omitted factors, we implement a series of placebo tests. Prior research shows that political attitudes in different realms tend to correlate across geographically close persons and also within persons. Such correlation could stem from common unobserved factors such as public-mindedness, generalized trust, and/or social capital. Insofar as such deeper factors also drive vote recounts, they would generate a spurious association between recounts and trust in INE, and in the same way one would expect they would also generate spurious correlation between recounts and other attitudes. We repeat the main regression analysis described above using different (placebo) attitudes as dependent variables: voting viewed as a civic duty, willingness to fight for transparent elections, feeling of being taken into account in the political decisions of the country, preferences for being tapped to be a poll worker, and men are better bosses and leaders than women (responses to these items are on the same agree-disagree scale as for the trust-in-INE item). The bottom part of Table 4 presents placebo estimates of Equation 4 using the same controls as column 4 of the top part of the table. It shows that recounts are not associated with any of these alternative attitudes. Instead, recounts only affect trust in INE’s impartiality. This is remarkable in light of the fact that trust in INE is indeed substantially correlated with all the other alternative dependent variables.Footnote ²⁷ Omitted variables could still bias the estimates, but they would have to be of a peculiar kind, inducing correlation with trust in INE but not with any other of the attitudes we tested.

As a further probe of causality, we use tally inconsistencies as an instrument for recounts. Specifically, we measure the share of recounted PSs within a precinct with the fraction of PSs in the precinct that presented inconsistencies. That is, we focus only on the variation in recounts due to inconsistencies. The first stage is powerful, with an F-statistic greater than 900. The IV estimate for attitudes about INE’s impartiality is reported in column 5 in the top part of Table 4.Footnote ²⁸ The estimated effect is somewhat larger than that the OLS equivalent. We view this analysis as an additional piece of evidence consistent with a causal interpretation.

As an alternative approach to exploring whether the estimates are causal, we implement a sensitivity analysis that asks: how strong would omitted confounders have to be to fully account for the estimated association between recounts and trust? Following Oster (Reference Oster2019), we find that omitted confounding would have to be more than 6.1 times more important than the set of basic controls, or 5.2 times more important than the full set of controls, suggesting that omitted variable bias is unlikely to account for the estimated relationship (details are provided in the Appendix).Footnote ²⁹

As a further robustness check, we implement front-door adjustment, as developed by Pearl (Reference Pearl1995), to estimate the causal effect of inconsistencies on trust. A key advantage of front-door adjustment is that it does not rely on the assumption that inconsistencies cause trust only via recounts, which is the exclusion restriction we relied on for the instrumental variables analysis presented in column 5 of Table 4. (See Appendix for further details). The front-door estimate indicates that a precinct where all PSs display some inconsistencies, compared with one where none do, is causally associated with lower trust in the electoral authorities by 3.2%.

As a final robustness test, we explore the implications of a specific mechanism consistent with our causal story: that recounts undermine trust in INE because they are spun and publicized by politicians and political parties for political ends. Specifically, we test the hypothesis that politicians have stronger incentives to use recounts politically in tight races (for example, in order to influence the outcome or appease their political base). This hypothesis implies that recounts should erode trust in INE more in tighter races.Footnote ³⁰ We test this hypothesis and find that recounts indeed matter more for trust in tighter races (Table A13).

In sum, all the estimation methods that we implement obtain similar results under different assumptions, substantially raising our confidence in a causal interpretation for the negative association between recounts and trust in INE. It is still possible, of course, for the observed association to be spurious. However, any argument to that effect would have to point to a confounding mechanism specific to trust in electoral authorities but not to other electoral and political attitudes. It would additionally have to confound tally inaccuracies and trust in INE’s impartiality, it could not rely on omitted variables we actually control for, including the fine-grained geographical fixed effects, and it would have to be many times stronger in its causal effects than all the included covariates together. Finally, whatever the confounding mechanism, it would have to be consistent with the finding that the relationship between recounts and trust is stronger in more-competitive races. We view a causal interpretation (i.e., that recounts erode trust in INE) as the most parsimonious one given the evidence.

We believe that tally inconsistencies could potentially have additional negative effects beyond their effects on trust in electoral institutions, such as increased social polarization and unrest, and a general long-term erosion of democratic values;Footnote ³¹ they could also deny the rightful winner of her place. We leave these issues as open questions for future research.