The paper
David Cottrell, Michael C. Herron, and Sean J. Westwood (2018). An exploration of Donald Trump's allegations of massive voter fraud in the 2016 General Election. Electoral Studies 51, 123–142.
doi:10.1016/j.electstud.2017.09.002 (opens in a new tab) · No public replication archive
Main text
p. 126, Section 3.1
Published
We drop counties not present in the Associated Press election returns database, meaning, the state of Alaska and Kalawao County, Hawaii.
Correction
We drop counties not present in the Associated Press election returns database, meaning, the state of Alaska and Kalawao County, Hawaii. Our 2016 county returns are the counts in this database at each county's last report; the latest reports, from counties in California, Michigan and Wisconsin, arrived about 19.4 days after polls closed, around November 28, 2016 (Section 3.4). These are unofficial counts. In California they precede certification: counties there were still counting ballots after that date, and the state certified its results on December 16, 2016.
Basis Section 3.4 places the last AP county reports about 28,000 minutes after polls closed, and the list of data sources gives no snapshot date. These counts enter every county regression (Tables 1–3 and 7–11) and Figs. 1–2. The AP counts used in the article are not public, so the number of votes missing from them, and whether the shortfall varies with a county's non-citizen share, cannot be measured.
p. 129, Section 3.2
Published
Contrary to Trump's claims, we find that, in California, New Hampshire, and Virginia counties with disproportionately many non-citizens, Clinton actually attracted fewer voters and lost vote share relative to Obama (coefficients for relevant interaction terms are negative and statistically significant at conventional confidence levels).
Correction
Contrary to Trump's claims, we find that, in California, New Hampshire, and Virginia counties with disproportionately many non-citizens, Clinton actually attracted fewer voters relative to Obama, and her vote-share gain over Obama rose less with the non-citizen share than it did in other states (coefficients for relevant interaction terms are negative and statistically significant at conventional confidence levels). Within these three states, the implied vote-share slope on the non-citizen share is −1.885, and Table 7 does not show that it differs from zero.
Basis A negative interaction shows only that the slope in California, New Hampshire and Virginia is lower than the slope in other states. In Table 7, column 2, the within-state vote-share slope is 3.720 + (−5.605) = −1.885. The article does not print the covariance of the two estimates, and the printed standard errors allow any p-value for this slope from .006 to .70. The turnout half of the sentence stands: in Table 8, column 2, the within-state slope is 11.781 + (−26.634) = −14.853, and even the largest standard error the printed ones allow (5.496) gives p = .007. The conclusion that these three states show no evidence of non-citizen voter fraud is unaffected.
p. 129, Section 3.2
Published
These interactions are both statistically significant and negative in our turnout model and in our vote-share model, implying that Clinton received fewer votes and less vote share in these locations.
Correction
These interactions are both negative and statistically significant in our vote-share model (Table 7), implying that Clinton's vote-share gain over Obama rose less with the non-citizen share in these locations than elsewhere. In our turnout model (Table 8), neither interaction is statistically significant: −0.725 (5.465) for counties that border Mexico and −0.613 (1.914) for battleground states.
Basis Table 8 prints both turnout interactions without stars; they are 0.13 and 0.32 times their standard errors (p = .89 and .75). The vote-share interactions in Table 7 (−14.995* and −4.170*) are significant as printed. The reading of a negative interaction follows the correction to the preceding paragraph.
p. 135, Section 3.3.2, Fig. 5b
Published
In the context of the busing theory, though, we would have expected the opposite relationship in Fig. 5b compared to what is pictured there. Our plots above shed light on the busing hypotheses (they are not consistent with it) [...]
Correction
In the context of the busing theory, though, a negative relationship in Fig. 5b is what we would have expected: Election Day voters bused in for Hassan would raise regular voting relative to absentee voting and lower Ayotte's gain over 2010. Taken at face value, the pattern pictured there points in the direction the busing theory predicts. Our plots above shed light on the busing hypotheses (Figs. 4 and 5a are not consistent with it, and Fig. 5b leans weakly toward it) [...]
Basis The horizontal axis of Fig. 5b is a town's change in regular ballots minus its change in absentee ballots, and the vertical axis is the change in Ayotte's share from 2010 to 2016. Busing would place towns at high values of the first and low values of the second, which is a negative relationship.
p. 136, Table 4
Published
Fraction regular ballots 2016 0.106 (0.041)
Correction
Fraction regular ballots 2016 0.106** (0.041)
Basis The estimate is 2.59 times its standard error (p = .0104), which meets the table's threshold for ** (p < 0.05). The rounding of the printed numbers also allows p just below .01, so ** is the level they guarantee. The text on this page reads the coefficient as a finding: towns with more election day voters were disproportionately pro-Ayotte.
p. 137, Section 3.4
Published
In other cases, a county reported initial results based on a small set of precincts, later updated results (often many times) based on more precincts, and finally produced a full set of results based on all precincts in the county. [...] Other counties took a few hours before their results were finalized.
Correction
In other cases, a county reported initial results based on a small set of precincts, later updated results (often many times) based on more precincts, and finally reported results from all precincts in the county; these last reports precede certification and do not include ballots counted afterward. [...] Other counties took a few hours to reach their last report.
Basis See the correction to p. 126.
p. 137, Section 3.4
Published
Wisconsin was extremely close and ended up completing a recount, which added 162 votes to Trump.
Correction
Wisconsin was extremely close and ended up completing a recount, which added 131 votes to Trump's margin.
Basis In the recount the Wisconsin Elections Commission certified on December 12, 2016, Trump gained 844 votes and Clinton 713, which raised Trump's margin from 22,617 to 22,748, the final margin the article gives on p. 138 (FOX6 News Milwaukee, “Counting complete: President-elect Donald Trump declared the winner after recount in Wisconsin,” December 12, 2016; Wisconsin Public Radio, “Wisconsin completes presidential recount,” December 12, 2016).
p. 137, Section 3.4
Published
In battleground states, 12 flips were from Clinton to Trump. This is the opposite of what we would expect if the election were rigged against Trump. [...] In two states—Florida and Pennsylvania—flips actually increased Trump's lead.
Correction
In battleground states, 14 of these 24 flips were from Clinton to Trump and 10 from Trump to Clinton. This is the opposite of what we would expect if the election were rigged against Trump. [...] In three states—Florida, Iowa, and Pennsylvania—flips actually increased Trump's lead.
Basis From Table 6. A flip from Clinton to Trump raises Trump's margin and a flip from Trump to Clinton lowers it, so the 11 counties with one flip and a positive net Trump gain (Florida 1, Iowa 7, Pennsylvania 3) flipped from Clinton to Trump, and the 7 with a negative gain flipped from Trump to Clinton. Consecutive flips alternate in direction, so each of the 3 counties with two flips (Hillsborough, Staunton, and Sauk) had one flip each way. Iowa's seven flips raised Trump's lead by 12,911 votes in total.
pp. 137–138, Section 3.4
Published
Looking at just the last two reports from each county (in counties with more than two reports), there were flips in just three counties—Hillsborough County in New Hampshire, Dubuque County in Iowa, and Sauk County in Wisconsin—with these flips decreasing Donald Trump's margin by 856 votes. This number of votes is insufficient to have swayed the election in New Hampshire, Iowa, or Wisconsin (where the final margins were 2,736 votes, 147,314 votes and 22,748 votes, respectively).
Correction
Looking at just the last two reports from each county (in counties with more than two reports), there were flips in just three counties—Hillsborough County in New Hampshire, Dubuque County in Iowa, and Sauk County in Wisconsin—and each of these flips moved the county's lead from Clinton to Trump, increasing Donald Trump's margin by more than 2,068 votes in total. Flips toward Trump could not have swung New Hampshire, Iowa, or Wisconsin against him (where the final margins were 2,736 votes, 147,314 votes and 22,748 votes, respectively).
Basis Trump carried all three counties in the certified returns (Hillsborough 100,013 to 99,589, Dubuque 23,460 to 22,850, Sauk 14,791 to 14,692; MIT Election Data and Science Lab, county presidential returns 2000–2016), so a flip between a county's last two reports gave Trump the lead and raised his margin. Table 6 lists Dubuque's only flip above 75% of precincts reporting as a Trump gain of 2,068 votes, and the final flips in Hillsborough and Sauk add to that. The AP report-level counts are not public, so the exact total cannot be computed.
p. 139, Table 7
Published
NH-CA-VA −0.042 (0.364) [...] Battleground state −0.223 (0.365) [...] Note: p < 0.1; *p < 0.05; *p < 0.01. Intercepts and state fixed effects not displayed.
Correction
NH-CA-VA (absorbed by the state fixed effects) [...] Battleground state (absorbed by the state fixed effects) [...] Note: p < 0.1; *p < 0.05; *p < 0.01. Intercepts and state fixed effects not displayed. NH-CA-VA and Battleground state do not vary within states, so the state fixed effects absorb them and they have no estimable coefficient; their interactions with % Non-Citizen are estimated.
Basis Section 3.2 defines both indicators at the state level, and every model in Tables 7–9 includes state fixed effects. A coefficient printed for either main effect can only be an arbitrary contrast between states.
p. 140, Table 8
Published
NH-CA-VA −0.958** (0.425) [...] Battleground state −4.608* (0.444)
Correction
NH-CA-VA (absorbed by the state fixed effects) [...] Battleground state (absorbed by the state fixed effects)
Basis See the correction to Table 7 (p. 139); the same note applies.
p. 140, Table 8, significance stars
Published
Table 8, estimates printed without stars: “% No college degree” 21.292 (11.518) in column 3; “% Black, no college degree” −21.920 (11.939) in column 1; “% Mormon” 6.040 (1.718) and 6.499 (1.753) in columns 2 and 3; “% Evangelical Christian” 3.539 (0.608), 3.632 (0.595) and 3.569 (0.607) in columns 1–3.
Correction
“% No college degree” 21.292* (11.518) in column 3; “% Black, no college degree” −21.920* (11.939) in column 1; “% Mormon” 6.040* (1.718) and 6.499* (1.753) in columns 2 and 3; “% Evangelical Christian” 3.539* (0.608), 3.632* (0.595) and 3.569* (0.607) in columns 1–3.
Basis Stars follow the table's note (p < 0.1; *p < 0.05; *p < 0.01), with p-values from the ratio of each printed estimate to its standard error, as in the correction to Table 10 (p. 141). The first two estimates have p = .065 and .066; the % Mormon and % Evangelical Christian estimates are at least 3.5 times their standard errors, and Tables 7 and 9 print * on every estimate in these two rows. The rounding of the printed numbers allows no other level for these seven estimates, and every star printed in Table 8 agrees with this rule. The text does not discuss these rows of Table 8.
p. 140, Table 9
Published
NH-CA-VA −2.133* (0.386) [...] Battleground state −3.162* (0.394)
Correction
NH-CA-VA (absorbed by the state fixed effects) [...] Battleground state (absorbed by the state fixed effects)
Basis See the correction to Table 7 (p. 139); the same note applies.
p. 141, Table 10
Published
Table 10, printed without stars on most estimates, including “Log median household income” 1.267 (0.349) and “% White” 45.998 (10.511) in column 1 and “% Non-citizen” 19.160 (3.866) in column 2.
Correction
Corrected Table 10. 23 estimates gain the stars their printed values imply, including % Non-citizen in column 2, 19.160* (3.866), the association the text on p. 133 describes as significant.
Corrected Table 10: regression analyses of vote share and turnout differences, 2008 baseline. Estimates and standard errors as printed; stars restored from the printed numbers. Note: p < 0.1; *p < 0.05; *p < 0.01. Intercepts and state fixed effects not displayed. Variable (1) Difference in vote share (2) Difference in turnout % Unemployed −26.245* (4.250) −8.997* (5.384) Log median household income 1.267* (0.349) 5.731* (0.445) % Employed in manufacturing −0.932 (1.144) −5.701* (1.595) % Urban 0.025* (0.003) 0.010** (0.004) % Male −14.832* (4.079) 17.885* (5.720) % White 45.998* (10.511) 23.061* (11.982) % Black 23.178** (10.639) 5.631 (12.082) % Hispanic 39.073* (11.326) 41.723* (12.955) % Asian 4.206 (11.086) −7.096 (12.681) % No college degree 33.586* (11.986) 20.990 (13.503) % White, no college degree −70.975* (12.183) −34.505** (13.769) % Black, no college degree −22.783* (12.267) −10.212 (13.784) % Hispanic, no college degree −41.118* (13.086) −43.379* (14.838) % Asian, no college degree 3.824 (13.447) 25.031 (15.301) % Mormon 5.985* (1.881) 12.816* (3.274) % Evangelical Christian 5.432* (0.606) 5.531* (0.879) % Jewish −17.627* (3.611) −13.830* (4.122) % Muslim 17.320* (5.009) 19.560* (6.144) % Foreign born citizen 1.907 (3.268) −1.733 (3.775) % Non-citizen 4.941 (3.300) 19.160* (3.866) Observations 3111 3111 R2 0.897 0.742 Adjusted R2 0.894 0.736 Basis Stars follow the table's note (p < 0.1; *p < 0.05; *p < 0.01), with p-values from the ratio of each printed estimate to its standard error. Where the rounding of the printed numbers allows more than one level, the table shows the lowest: % Urban in column 2 ( or *). Every star printed in the published table agrees with this rule.
p. 142, Data sources
Published
The Associated Press, election services. Data: 2016 election returns by county. [...]
Correction
The Associated Press, election services. Data: 2016 election returns by county, as recorded in the AP database at each county's last report. The latest reports arrived around November 28, 2016, before certification in some states. [...]
Basis See the correction to p. 126.