Overview of the Election Forensics Toolkit
Test using 2024 Election Data from Georgia
Test using 2024 Election Data from Michigan
Test using 2024 Election Data from South Carolina
Overview of the Election Forensics Toolkit
An Election Forensics Toolkit and Guide can be found at https://www.iie.org/publications/dfg-um-publication/. It lists the Principal Investigators as Allen Hicken and Walter Mebane from the University of Michigan. It contains links to a Guide and Working Paper and begins with the following paragraph:
There is an acute need for methods of detecting and investigating fraud in elections, because the consequences of electoral fraud are grave for democratic stability and quality. When the electoral process is compromised by fraud, intimidation, or even violence, elections can become corrosive and destabilizing-sapping support for democratic institutions; inflaming suspicion; and stimulating demand for extra-constitutional means of pursuing political agendas, including violence. Accurate information about irregularities can help separate false accusations from evidence of electoral malfeasance. Accurate information about the scope of irregularities can also provide a better gauge of election quality. Finally, accurate information about the geographic location of malfeasance-the locations where irregularities occurred and how they cluster-can allow election monitors and pro-democracy organizations to focus attention and resources more efficiently and to substantiate their assessments of electoral quality.
The Guide contains the following table of Distribution and Digit Tests on page 9:
Table 1: Distribution and Digit Tests
Value Expected in the
Absence of Fraud or
Test Name Definition Strategic Behavior
------------------ ------ ---------------------------------------------- ------------------
second-digit 2BL to be compared to the mean value Benford's Law 4.187
mean specifies
last-digit mean LastC to be compared to the mean value implied by 4.5
uniformly distributed last digits
count
last-digit 0/5 C05s to be compared to the mean value implied by 0.2
indicator mean uniformly distributed last digits
percentage
last-digit 0/5 P05s to be compared to the mean value implied by 0.2
indicator mean uniformly distributed percentages
skewness Skew the extent to which a variable departs from a 0
normal distribution by being asymmetric
kurtosis Kurt the extent to which a variable departs from a 3
normal distribution by being spread out too
much or not enough
Unimodality test DipT tests whether the distribution of a variable > 0.05
p-value departs from unimodality
There appears to be an online version of the toolkit at this link which mentions Hicken and Mebane and versions of code that mention Mebane at this link and this link. This latter link refers to a "web application sponsored by the USAID and developed by Walter Mebane and Kirill Kalinin" and the code there was used for the following test on precinct data from the 2024 U.S. general election that took place on November 5, 2024.
Test using 2024 Election Data from Georgia (20 counties with the highest populations)
Precinct data was obtained for the 20 most populous Georgia counties (according to this link) from Election Night Reporting data. It was downloaded on December 4, 2024 at 8:17 AM PST via the Media Export link at the bottom of this page of Official Results. That data was then transformed into the proper format for the Election Toolkit via the following R code:
library(tidyverse)
dd <- read_csv("precinct/ga/ga_2024_GE241204_local_precinct.csv")
names(dd) <- c("county","precinct","candidate","votes","voteType","party","office")
ee <- dd[!(dd$precinct %in% c("ALL")),]
ee$party <- toupper(ee$party)
ee <- ee[ee$party %in% c("DEM","REP"),]
ee$district <- ""
ff <- data.frame(ee$county,ee$precinct,ee$office,ee$district,ee$party,ee$candidate,ee$votes)
names(ff) <- c("county","precinct","office","district","party","candidate","votes")
write_csv(ff,"precinct/ga/20241206__ga__GE24__precinct.csv")
ff <- ff[ff$office == "President of the US",]
write_csv(ff,"precinct/ga/20241206__ga__GE24pres__precinct.csv")
ff <- ff[,c(1,2,3,5,7)]
ff <- ff %>% spread(party,votes)
ff$TOTAL <- ff$DEM + ff$REP
write_csv(ff,"precinct/ga/20241204__ga__GE24wide__precinct.csv")
The resulting file was then processed using code from this link. That code is not available as a package and was simply sourced via the following code:
library(tidyverse)
library(boot)
library(hwriter)
library(knitr)
library(kableExtra)
library(xtable)
library(moments)
library(diptest)
source("R/BasicElectionForensics.R")
source("R/BuildMap.R")
source("R/ClusterAnalysis.R")
source("R/ColorSignificance.R")
source("R/ComputeFiniteMixtureModel.R")
source("R/ComputeKlimekModel.R")
source("R/ComputeShpilkinMethod.R")
dat<-read_csv("precinct/ga/20241204__ga__GE24wide__precinct.csv")
dat <- dat[dat$TOTAL >= 10,]
tt <- table(dat$county)
tt <- tt[tt >= 20]
dat <- dat[dat$county %in% names(tt),]
#NB! R=100 to speed up computations for this example.
eldata<-BasicElectionForensics(dat,
Candidates=c("DEM", "REP"),
TotalReg ="TOTAL",
TotalVotes="TOTAL",
Level="county",
Methods=c("_2BL", "LastC", "C05s", "P05s",
"Skew", "Kurt"))
eldata_out <- eldata$html
eldata_out <- gsub("<","<",eldata_out)
eldata_out <- gsub(">",">",eldata_out)
write(eldata_out,file="precinct/ga/eftoolkit_ga10p20_24.htm")
Following is the output of the resultant file (located online at this link):
| Level | Candidate's Name | _2BL | LastC | P05s | C05s | Skew | Kurt | Obs |
| Bibb | DEM | 3.387 | 5.548 | 0.29 | 0.161 | -0.116 | 1.451 | 31 |
| (2.387, 4.355) | (4.645, 6.484) | (0.129, 0.451) | (0.032, 0.29) | (-0.708, 0.522) | (0.732, 1.636) | |||
| Carroll | DEM | 4.536 | 4.786 | 0.107 | 0.179 | 0.583 | 2.544 | 28 |
| (3.394, 5.643) | (3.714, 6) | (-0.036, 0.214) | (0.036, 0.321) | (-0.035, 1.23) | (0.962, 3.465) | |||
| Chatham | DEM | 4.126 | 4.345 | 0.195 | 0.23 | -0.012 | 1.783 | 87 |
| (3.598, 4.666) | (3.759, 4.885) | (0.115, 0.276) | (0.138, 0.31) | (-0.293, 0.306) | (1.448, 1.991) | |||
| Cherokee | DEM | 3.452 | 4 | 0.214 | 0.238 | -0.433 | 2.752 | 42 |
| (2.619, 4.285) | (3.19, 4.81) | (0.095, 0.333) | (0.095, 0.357) | (-1.031, 0.014) | (1.726, 3.51) | |||
| Clarke | DEM | 3.917 | 4.458 | 0.167 | 0.25 | 0.77 | 3.328 | 24 |
| (2.917, 4.833) | (3.583, 5.332) | (0, 0.292) | (0.083, 0.417) | (0.252, 1.77) | (1.437, 4.779) | |||
| Clayton | DEM | 4.1 | 4.329 | 0.271 | 0.186 | -1.459 | 4.993 | 70 |
| (3.457, 4.743) | (3.615, 5) | (0.157, 0.371) | (0.1, 0.271) | (-1.99, -0.977) | (2.332, 6.717) | |||
| Cobb | DEM | 4.007 | 4.892 | 0.216 | 0.155 | 0.333 | 2.271 | 148 |
| (3.527, 4.479) | (4.426, 5.392) | (0.149, 0.284) | (0.095, 0.209) | (0.064, 0.589) | (1.848, 2.6) | |||
| Columbia | DEM | 3.978 | 4.87 | 0.174 | 0.152 | 0.479 | 3.761 | 46 |
| (3.087, 4.847) | (4.043, 5.717) | (0.065, 0.283) | (0.043, 0.239) | (-0.214, 1.279) | (2.056, 4.908) | |||
| Coweta | DEM | 4.625 | 4.208 | 0.042 | 0.125 | 1.089 | 3.192 | 24 |
| (3.333, 5.792) | (2.958, 5.416) | (-0.042, 0.083) | (-0.041, 0.25) | (0.31, 1.781) | (-0.369, 4.674) | |||
| DeKalb | DEM | 3.817 | 4.974 | 0.147 | 0.136 | -0.922 | 2.723 | 191 |
| (3.398, 4.204) | (4.581, 5.382) | (0.094, 0.199) | (0.084, 0.183) | (-1.191, -0.649) | (1.986, 3.267) | |||
| Dougherty | DEM | 3.96 | 4.44 | 0.16 | 0.16 | -0.344 | 1.597 | 25 |
| (2.88, 5) | (3.24, 5.599) | (0, 0.28) | (0, 0.28) | (-0.963, 0.421) | (0.485, 1.915) | |||
| Douglas | DEM | 3.72 | 5.6 | 0.16 | 0.08 | -0.465 | 2.547 | 25 |
| (2.72, 4.68) | (4.56, 6.72) | (0, 0.28) | (-0.04, 0.16) | (-1.192, 0.1) | (1.46, 3.489) | |||
| Effingham | DEM | 4.25 | 4.7 | 0.15 | 0.2 | 0.205 | 2.147 | 20 |
| (3.2, 5.35) | (3.451, 5.95) | (0, 0.3) | (0, 0.35) | (-0.44, 0.933) | (1.09, 2.738) | |||
| Fayette | DEM | 3.111 | 4.222 | 0.222 | 0.194 | 0.328 | 2.348 | 36 |
| (2.278, 3.889) | (3.333, 5.167) | (0.083, 0.333) | (0.028, 0.306) | (-0.274, 0.915) | (1.364, 3.099) | |||
| Forsyth | DEM | 3.966 | 4.103 | 0.276 | 0.138 | 0.018 | 2.101 | 29 |
| (3.103, 4.862) | (3.207, 4.897) | (0.103, 0.414) | (0, 0.241) | (-0.561, 0.647) | (1.249, 2.654) | |||
| Fulton | DEM | 3.952 | 4.694 | 0.218 | 0.214 | -0.696 | 2.059 | 444 |
| (3.704, 4.221) | (4.432, 4.953) | (0.18, 0.259) | (0.173, 0.25) | (-0.881, -0.499) | (1.712, 2.326) | |||
| Gwinnett | DEM | 3.615 | 4.468 | 0.167 | 0.205 | 0.06 | 2.362 | 156 |
| (3.173, 4.045) | (3.994, 4.942) | (0.109, 0.218) | (0.135, 0.269) | (-0.185, 0.279) | (2.007, 2.613) | |||
| Hall | DEM | 3.742 | 4.742 | 0.194 | 0.194 | 1.464 | 6.466 | 31 |
| (2.677, 4.871) | (3.969, 5.548) | (0.065, 0.323) | (0.065, 0.323) | (0.741, 3.032) | (3.011, 11.037) | |||
| Henry | DEM | 4.946 | 4.676 | 0.297 | 0.135 | -0.607 | 2.808 | 37 |
| (4.081, 5.865) | (3.676, 5.649) | (0.136, 0.459) | (0.027, 0.243) | (-1.222, -0.077) | (1.393, 3.743) | |||
| Muscogee | DEM | 3.72 | 4.12 | 0.2 | 0.16 | 0.205 | 1.523 | 25 |
| (2.48, 4.759) | (3, 5.2) | (0.04, 0.36) | (0.04, 0.28) | (-0.538, 0.853) | (0.386, 1.771) | |||
| Paulding | DEM | 3.905 | 4.381 | 0.095 | 0.048 | 0.565 | 3.197 | 21 |
| (2.952, 4.857) | (3, 5.619) | (-0.048, 0.19) | (-0.048, 0.095) | (-0.086, 1.636) | (1.538, 4.784) | |||
| Richmond | DEM | 4.118 | 4.368 | 0.162 | 0.25 | -0.4 | 2.105 | 68 |
| (3.5, 4.721) | (3.662, 5.074) | (0.074, 0.25) | (0.147, 0.353) | (-0.791, -0.028) | (1.368, 2.573) | |||
| Thomas | DEM | 4.1 | 4.85 | 0.3 | 0.25 | 1.41 | 3.833 | 20 |
| (2.65, 5.3) | (3.351, 6.25) | (0.1, 0.5) | (0.05, 0.4) | (0.358, 2.414) | (-1.66, 6.131) | |||
| Whitfield | DEM | 5.391 | 4.043 | 0.13 | 0.261 | 0.977 | 3.184 | 23 |
| (4.13, 6.739) | (2.87, 5.304) | (0, 0.261) | (0.087, 0.435) | (0.35, 1.821) | (0.549, 4.602) | |||
| Bibb | REP | 4.097 | 3.806 | 0.29 | 0.129 | 0.116 | 1.451 | 31 |
| (3.258, 4.871) | (3, 4.645) | (0.129, 0.419) | (0, 0.226) | (-0.524, 0.73) | (0.77, 1.635) | |||
| Carroll | REP | 4.357 | 5.571 | 0.107 | 0.214 | -0.583 | 2.544 | 28 |
| (3.321, 5.393) | (4.537, 6.5) | (0, 0.214) | (0.071, 0.357) | (-1.225, 0.039) | (1.111, 3.462) | |||
| Chatham | REP | 3.701 | 4.667 | 0.195 | 0.149 | 0.012 | 1.783 | 87 |
| (3.115, 4.241) | (4.092, 5.264) | (0.115, 0.276) | (0.069, 0.218) | (-0.278, 0.297) | (1.444, 1.99) | |||
| Cherokee | REP | 5.095 | 4.571 | 0.214 | 0.262 | 0.433 | 2.752 | 42 |
| (4.238, 6) | (3.81, 5.381) | (0.095, 0.333) | (0.119, 0.381) | (-0.014, 1.019) | (1.703, 3.464) | |||
| Clarke | REP | 3.542 | 5.375 | 0.167 | 0.167 | -0.77 | 3.328 | 24 |
| (2.251, 4.667) | (4.333, 6.375) | (0, 0.292) | (0, 0.292) | (-1.782, -0.183) | (1.139, 4.777) | |||
| Clayton | REP | 4.471 | 4.1 | 0.271 | 0.214 | 1.459 | 4.993 | 70 |
| (3.786, 5.143) | (3.4, 4.7) | (0.157, 0.371) | (0.114, 0.314) | (0.999, 1.946) | (2.492, 6.767) | |||
| Cobb | REP | 3.48 | 4.182 | 0.216 | 0.203 | -0.333 | 2.271 | 148 |
| (3.061, 3.851) | (3.676, 4.655) | (0.142, 0.277) | (0.135, 0.264) | (-0.594, -0.039) | (1.792, 2.586) | |||
| Columbia | REP | 4.435 | 4.065 | 0.174 | 0.217 | -0.479 | 3.761 | 46 |
| (3.565, 5.217) | (3.174, 4.913) | (0.065, 0.283) | (0.109, 0.326) | (-1.145, 0.186) | (2.257, 4.901) | |||
| Coweta | REP | 3.875 | 4.333 | 0.042 | 0.25 | -1.089 | 3.192 | 24 |
| (2.667, 5.124) | (3.042, 5.625) | (-0.042, 0.083) | (0.083, 0.417) | (-1.794, -0.365) | (0.092, 4.691) | |||
| DeKalb | REP | 4.403 | 4.618 | 0.147 | 0.173 | 0.922 | 2.723 | 191 |
| (3.953, 4.864) | (4.225, 5) | (0.094, 0.194) | (0.12, 0.225) | (0.649, 1.192) | (1.919, 3.269) | |||
| Dougherty | REP | 4 | 4.16 | 0.16 | 0.16 | 0.344 | 1.597 | 25 |
| (2.92, 4.92) | (3, 5.16) | (0, 0.28) | (0, 0.28) | (-0.391, 1.037) | (0.546, 1.921) | |||
| Douglas | REP | 4.04 | 4.64 | 0.16 | 0.04 | 0.465 | 2.547 | 25 |
| (2.88, 5.16) | (3.68, 5.6) | (0, 0.28) | (-0.04, 0.08) | (-0.063, 1.232) | (1.467, 3.511) | |||
| Effingham | REP | 3.65 | 5.65 | 0.15 | 0.15 | -0.205 | 2.147 | 20 |
| (2.55, 4.7) | (4.55, 6.85) | (0, 0.3) | (0, 0.3) | (-0.889, 0.419) | (0.964, 2.77) | |||
| Fayette | REP | 3.722 | 4.361 | 0.222 | 0.222 | -0.328 | 2.348 | 36 |
| (2.667, 4.639) | (3.389, 5.333) | (0.083, 0.361) | (0.083, 0.36) | (-0.968, 0.266) | (1.325, 3.091) | |||
| Forsyth | REP | 4.414 | 4.172 | 0.276 | 0.207 | -0.018 | 2.101 | 29 |
| (3.414, 5.483) | (3.345, 5.034) | (0.103, 0.448) | (0.069, 0.345) | (-0.619, 0.525) | (1.247, 2.633) | |||
| Fulton | REP | 4.022 | 4.448 | 0.218 | 0.191 | 0.696 | 2.059 | 444 |
| (3.762, 4.303) | (4.183, 4.703) | (0.18, 0.257) | (0.153, 0.225) | (0.523, 0.88) | (1.749, 2.332) | |||
| Gwinnett | REP | 4.032 | 4.109 | 0.167 | 0.218 | -0.06 | 2.362 | 156 |
| (3.603, 4.512) | (3.667, 4.564) | (0.103, 0.224) | (0.147, 0.282) | (-0.297, 0.182) | (2.005, 2.659) | |||
| Hall | REP | 4.613 | 4.871 | 0.194 | 0.194 | -1.464 | 6.466 | 31 |
| (3.614, 5.548) | (3.873, 5.87) | (0.065, 0.323) | (0.065, 0.323) | (-3.055, -0.78) | (3.387, 10.992) | |||
| Henry | REP | 3.757 | 4.108 | 0.297 | 0.189 | 0.607 | 2.808 | 37 |
| (2.919, 4.595) | (3.162, 5.027) | (0.135, 0.432) | (0.054, 0.297) | (0.091, 1.195) | (1.517, 3.804) | |||
| Muscogee | REP | 4.52 | 5.04 | 0.2 | 0.28 | -0.205 | 1.523 | 25 |
| (3.201, 5.76) | (4.04, 6.079) | (0.04, 0.359) | (0.08, 0.44) | (-0.868, 0.506) | (0.492, 1.776) | |||
| Paulding | REP | 3.762 | 4.238 | 0.095 | 0.048 | -0.565 | 3.197 | 21 |
| (2.81, 4.808) | (3.239, 5.381) | (-0.048, 0.19) | (-0.048, 0.095) | (-1.629, 0.198) | (1.109, 4.797) | |||
| Richmond | REP | 3.897 | 4.294 | 0.162 | 0.235 | 0.4 | 2.105 | 68 |
| (3.177, 4.529) | (3.515, 5.059) | (0.059, 0.25) | (0.132, 0.338) | (-0.024, 0.817) | (1.323, 2.602) | |||
| Thomas | REP | 4.45 | 5.5 | 0.3 | 0.15 | -1.41 | 3.833 | 20 |
| (3.151, 5.7) | (4.251, 6.8) | (0.1, 0.5) | (-0.05, 0.3) | (-2.324, -0.346) | (-1.961, 5.995) | |||
| Whitfield | REP | 3.783 | 4.565 | 0.13 | 0.304 | -0.977 | 3.184 | 23 |
| (2.61, 4.999) |
The output appears to consist of pairs of rows with the first pair containing the specified value and the seoond line containing the 95 percent confidence limits). The specified values appear to be red if the 95 percent confidence limits do not include the expected value. For example, the LastC value of 5.548 for DEM for Bibb County is colored red because its 95% confidence limits of 4.645 and 6.484 do not include the expected value of 4.5. LastC is the last digit of the value being measured (in this case, Democrat vote count) and, if it were to contain random digits between 0 and 9, the average would be expected to be 4.5. The histogram below shows the actual distribution of the digits:
As can be seen, there are noticably more occurrances of the digits 8 and 9 than any of the other digits. Also, except for the digit 7, the counts of the digits generally increase from left to right. It should be noted that these counts exclude any precincts with fewer that 10 votes, chiefly to avoid precincts with no votes increasing the count of digit 0.
However, this raises the question of what are the best next steps to take to determine if a red flag is actually a problem. By pure chance, one would expect about 1 out of every 20 values to be outside of the 95% confidence limits. One step might be to look at the actual distribution of the digits as was done here. It would appear that this red flag is based strictly on the average of the digits. However, it's unclear how one could best judge if the distribution of the digits adds or subtracts from the likelihood that this represents a real problem. It might also be possible to make a judgement based on the number of tests that fall outside the 95% confidence limits for a county. For example, the DEM vote count for DeKalb County falls outside the limits in 4 tests (LastC, P05s, C05s, and Skew). In addition, it might make sense to look at the test with smaller confidence limits though it is not clear how to do this in the current code. Of course, the final solution for anomalies in elections is to audit or recount the balance. Still, it would be preferable to do as much other analysis as possible before this. Also, it's not clear whether or not every or most precincts in the flagged county would need to be audited or recounted. These numerical tests would seem very useful in flagging potential problems but it would also seem useful to understand how best to follow up on those counties and values that are flagged.
Regarding the LastC test, following are two other vote counts that had red flags:
Note that, like Bibb County, the counts of the digits generally increase from left to right. Even more interesting distributions can be seen in those vote counts that had red flags for the C05s test:
As can be seen, the distribution counta for the Democrat and Republican votes in both Douglas and Paulding counties is zero for either the 0 or the 5 digit. For the other digit, the distribution count is one except for the Democrat votes in Douglas County for which it is 2. Also interesting is that the expected value of 0.2 falls far outside the confidence limits for all 4 tests. Those 4 tests had upper confidence limits of 0.16, 0.095, 0.08, and 0.095, far less than the expected value of 0.2. Finally, the two counties border each other, just northwest of Fulton County. There are of course differing reasons, some likely bnign, why this may have occurred. But, if there was any human manipulation involved, it could be that the "round digits" of 0 and 5 were unintentially avoided.
The other vote count that failed the C05s test was the Democrat vote count in DeKalb County. As seem in its distribution shown earlier, the counts for the 0 and 5 digits were lower in DeKalb County, same as the prior 4 tests.
Test using 2024 Election Data from Michigan
| Level | Candidate's Name | _2BL | LastC | P05s | C05s | Skew | Kurt | Obs |
| MIEaton | Turnout | 4.455 | 4.295 | 0.295 | 0.25 | -0.535 | 3.064 | 44 |
| (3.682, 5.34) | (3.432, 5.114) | (0.159, 0.432) | (0.114, 0.364) | (-1.209, -0.093) | (1.913, 3.962) | |||
| MIGrand_Traverse | Turnout | 3.949 | 4.128 | 0.128 | 0.205 | -0.613 | 2.923 | 39 |
| (3.206, 4.744) | (3.256, 5.026) | (0.026, 0.205) | (0.077, 0.333) | (-1.205, -0.128) | (1.636, 3.899) | |||
| MIMacomb | Turnout | 4.097 | 4.578 | 0.172 | 0.188 | -0.758 | 3.755 | 308 |
| (3.792, 4.399) | (4.244, 4.909) | (0.13, 0.214) | (0.146, 0.231) | (-1.113, -0.464) | (2.991, 4.649) | |||
| MIOakland | Turnout | 3.988 | 4.558 | 0.187 | 0.191 | -1.599 | 6.38 | 498 |
| (3.743, 4.227) | (4.305, 4.817) | (0.149, 0.219) | (0.157, 0.225) | (-1.894, -1.335) | (5.054, 7.698) | |||
| MIEaton | DEM | 3.932 | 4.909 | 0.227 | 0.091 | 0.229 | 2.172 | 44 |
| (3.114, 4.75) | (4.068, 5.727) | (0.091, 0.341) | (0, 0.159) | (-0.238, 0.832) | (1.364, 2.811) | |||
| MIGrand_Traverse | DEM | 2.846 | 4.846 | 0.154 | 0.128 | 0.147 | 2.503 | 39 |
| (1.924, 3.744) | (3.872, 5.769) | (0.026, 0.256) | (0, 0.231) | (-0.292, 0.654) | (1.588, 3.089) | |||
| MIMacomb | DEM | 4.023 | 4.601 | 0.214 | 0.205 | 0.993 | 4.089 | 308 |
| (3.679, 4.357) | (4.282, 4.916) | (0.169, 0.256) | (0.156, 0.25) | (0.757, 1.252) | (3.264, 4.874) | |||
| MIOakland | DEM | 3.662 | 4.275 | 0.195 | 0.217 | 0.749 | 2.831 | 498 |
| (3.38, 3.912) | (4.014, 4.512) | (0.159, 0.229) | (0.183, 0.251) | (0.625, 0.889) | (2.468, 3.179) | |||
| MIEaton | REP | 4.045 | 4.136 | 0.159 | 0.227 | -0.192 | 2.128 | 44 |
| (3.136, 4.931) | (3.318, 4.977) | (0.045, 0.25) | (0.091, 0.341) | (-0.775, 0.289) | (1.448, 2.712) | |||
| MIGrand_Traverse | REP | 3.821 | 4.436 | 0.179 | 0.103 | -0.08 | 2.468 | 39 |
| (2.949, 4.692) | (3.564, 5.308) | (0.051, 0.282) | (0, 0.179) | (-0.542, 0.385) | (1.573, 3.062) | |||
| MIMacomb | REP | 4.062 | 4.513 | 0.208 | 0.221 | -0.875 | 3.762 | 308 |
| (3.74, 4.396) | (4.182, 4.831) | (0.159, 0.25) | (0.179, 0.266) | (-1.108, -0.651) | (3.042, 4.41) | |||
| MIOakland | REP | 3.716 | 4.42 | 0.211 | 0.215 | -0.664 | 2.727 | 498 |
| (3.473, 3.979) | (4.177, 4.665) | (0.177, 0.245) | (0.177, 0.249) | (-0.79, -0.537) | (2 |
Test using 2024 Election Data from South Carolina
Precinct data was obtained for 6 South Carolina counties from Election Night Reporting data from the following 6 URLs:
These files were downloaded on November 28, 2024 at 1:23 AM PST via the Detail XLS links on the above pages and the election data extracted. That data was then transformed into the proper format for the Election Toolkit via the following R code:
library(tidyverse)
counties <- c("SCAiken","CSChesterfield","SCDarlington",
"SCLee","SCMarlboro","SCSumter")
dd <- read_csv("SClastfocus/20241127__sc__last_focus__precinct.csv")
dd$candidate[dd$office == "Registered Voters"] <- "R_V"
dd$candidate[dd$office == "Ballots Cast"] <- "B_C"
dd$office[dd$office == "Registered Voters"] <- "President and Vice President (Vote For 1)"
dd$office[dd$office == "Ballots Cast"] <- "President and Vice President (Vote For 1)"
ee <- dd[dd$office == "President and Vice President (Vote For 1)",]
ee <- ee[!(ee$precinct %in% c("Failsafe","Failsafe Provisional","Provisional","Total:")),]
ee$party <- substring(ee$candidate,1,3)
ee <- ee[ee$party %in% c("DEM","REP","R_V","B_C"),]
ff <- data.frame(ee$county,ee$precinct,ee$office,ee$party,ee$votes)
names(ff) <- c("county","precinct","office","party","votes")
ff <- ff %>% spread(party,votes)
ff$TOTAL <- ff$DEM + ff$REP
write_csv(ff,"SClastfocus/20241127__sc__last_focus__wide2.csv")
The resulting file was then processed using code from this link. That code is not available as a package and was simply sourced via the following code:
library(tidyverse)
library(boot)
library(hwriter)
library(knitr)
library(kableExtra)
library(xtable)
library(moments)
library(diptest)
source("R/BasicElectionForensics.R")
source("R/BuildMap.R")
source("R/ClusterAnalysis.R")
source("R/ColorSignificance.R")
source("R/ComputeFiniteMixtureModel.R")
source("R/ComputeKlimekModel.R")
source("R/ComputeShpilkinMethod.R")
dat<-read_csv("SClastfocus/20241127__sc__last_focus__wide2.csv")
#NB! R=100 to speed up computations for this example.
eldata<-BasicElectionForensics(dat,
Candidates=c("DEM", "REP"),
TotalReg="R_V",
TotalVotes="B_C",
Level="county",
Methods=c("_2BL", "LastC", "C05s", "P05s",
"Skew", "Kurt"))
eldata_out <- eldata$html
eldata_out <- gsub("<","<",eldata_out)
eldata_out <- gsub(">",">",eldata_out)
write(eldata_out,file="eftoolkit_sc6_24.htm")
Following is the output of the resultant file (located online at this link):
| Level | Candidate's Name | _2BL | LastC | P05s | C05s | Skew | Kurt | Obs |
| SCAiken | Turnout | 3.865 | 5.18 | 0.18 | 0.213 | -0.824 | 4.122 | 89 |
| (3.315, 4.427) | (4.573, 5.787) | (0.101, 0.258) | (0.124, 0.303) | (-1.529, -0.396) | (2.619, 5.948) | |||
| SCChesterfield | Turnout | 3.64 | 4.16 | 0.28 | 0.28 | -0.447 | 2.768 | 25 |
| (2.56, 4.8) | (3, 5.32) | (0.12, 0.44) | (0.08, 0.44) | (-1.223, 0.139) | (1.463, 3.72) | |||
| SCDarlington | Turnout | 4.125 | 5.219 | 0.188 | 0.219 | -0.995 | 3.3 | 32 |
| (3.031, 5.188) | (4.312, 6.188) | (0.032, 0.312) | (0.062, 0.344) | (-1.644, -0.304) | (0.521, 4.67) | |||
| SCLee | Turnout | 4.273 | 3.409 | 0.182 | 0.273 | -0.205 | 2.145 | 22 |
| (3.227, 5.182) | (2.364, 4.409) | (0, 0.318) | (0.091, 0.455) | (-0.822, 0.404) | (0.967, 2.7) | |||
| SCMarlboro | Turnout | 2.933 | 3.733 | 0.2 | 0.2 | -0.355 | 2.589 | 15 |
| (1.467, 4.133) | (2.267, 5.133) | (0, 0.4) | (0, 0.4) | (-1.179, 0.851) | (0.014, 3.732) | |||
| SCSumter | Turnout | 3.776 | 4.397 | 0.172 | 0.241 | -1.215 | 4.365 | 58 |
| (3.052, 4.552) | (3.586, 5.207) | (0.069, 0.276) | (0.121, 0.345) | (-1.891, -0.666) | (2.038, 6.149) | |||
| SCAiken | DEM | 4.618 | 3.764 | 0.191 | 0.202 | 1.555 | 5.913 | 89 |
| (4.034, 5.202) | (3.135, 4.326) | (0.101, 0.27) | (0.124, 0.281) | (1.131, 2.225) | (3.262, 8.025) | |||
| SCChesterfield | DEM | 3.92 | 5.2 | 0.28 | 0.12 | 0.314 | 2.498 | 25 |
| (2.88, 4.92) | (4.2, 6.2) | (0.081, 0.44) | (-0.04, 0.24) | (-0.348, 0.977) | (0.912, 3.32) | |||
| SCDarlington | DEM | 4.344 | 4.219 | 0.156 | 0.281 | 0.653 | 3.07 | 32 |
| (3.344, 5.375) | (3.219, 5.281) | (0.031, 0.281) | (0.125, 0.437) | (0.06, 1.398) | (1.338, 4.334) | |||
| SCLee | DEM | 3.364 | 5.091 | 0.182 | 0.091 | -0.214 | 1.593 | 22 |
| (2.409, 4.273) | (4.092, 6.091) | (0, 0.318) | (-0.045, 0.182) | (-0.911, 0.539) | (0.541, 1.877) | |||
| SCMarlboro | DEM | 3.867 | 4.4 | 0.2 | 0.2 | 0.607 | 3.182 | 15 |
| (2.333, 5.333) | (2.867, 5.932) | (0, 0.333) | (0, 0.4) | (-0.279, 1.733) | (0.894, 4.653) | |||
| SCSumter | DEM | 5.017 | 4.345 | 0.259 | 0.207 | 0.337 | 1.979 | 58 |
| (4.328, 5.707) | (3.517, 5.155) | (0.138, 0.362) | (0.086, 0.293) | (-0.097, 0.737) | (1.219, 2.329) | |||
| SCAiken | REP | 4.36 | 4.551 | 0.157 | 0.213 | -1.53 | 5.793 | 89 |
| (3.753, 5.011) | (3.888, 5.179) | (0.079, 0.225) | (0.124, 0.292) | (-2.12, -1.089) | (3.288, 7.899) | |||
| SCChesterfield | REP | 4.28 | 4.32 | 0.2 | 0.32 | -0.394 | 2.658 | 25 |
| (3.241, 5.36) | (3.121, 5.48) | (0.04, 0.359) | (0.12, 0.48) | (-1.175, 0.21) | (1.289, 3.624) | |||
| SCDarlington | REP | 3.625 | 4.594 | 0.094 | 0.188 | -0.656 | 3.064 | 32 |
| (2.563, 4.594) | (3.562, 5.593) | (0, 0.188) | (0.062, 0.312) | (-1.38, -0.054) | (1.437, 4.31) | |||
| SCLee | REP | 4.682 | 4.409 | 0.227 | 0.227 | 0.362 | 1.829 | 22 |
| (3.318, 6.045) | (3.045, 5.727) | (0.045, 0.409) | (0.045, 0.364) | (-0.317, 1.038) | (0.663, 2.29) | |||
| SCMarlboro | REP | 4.333 | 3.467 | 0.067 | 0.267 | -0.574 | 3.07 | 15 |
| (2.933, 5.733) | (1.802, 4.867) | (-0.067, 0.133) | (0, 0.467) | (-1.67, 0.316) | (1.295, 4.538) | |||
| SCSumter | REP | 4.25 | 4.586 | 0.276 | 0.259 | -0.331 | 1.997 | 58 |
| (3.5, 4.974) | (3.845, 5.345) | (0.138, 0.397) | (0.138, 0.362) | (-0.725, 0.1 |
The output appears to consist of pairs of rows with the first pair containing the specified value and the seoond line containing the 95 percent confidence limits). The specified values appear to be red if the 95 percent confidence limits do not include the expected value. For example, the LastC value of 3.764 for DEM for SCAiken (Aiken County, South Carolina) is colored red because its 95% confidence limits of 3.135 and 4.326 do not include the expected value of 4.5. LastC is the last digit of the value being measured (in this case, Democrat vote count) and, if it were to contain random digits between 0 and 9, the average would be expected to be 4.5. The histogram below shows the actual distribution of the digits:
As can be seen, there are noticably more occurrances of the digits 1 and 2 than any of the other digits. Also, there are almost double the occurances of the first three digits (0, 1, and 2) as the last three digits (7, 8, and 9).
However, this raises the question of what are the best next steps to take to determine if a red flag is actually a problem. By pure chance, one would expect about 1 out of every 20 values to be outside of the 95% confidence limits. One step might be to look at the actual distribution of the digits as was done here. It would appear that this red flag is based strictly on the average of the digits. However, it's unclear how one could best judge if the distribution of the digits adds or subtracts from the likelihood that this represents a real problem. It might also be possible to make a judgement based on the number of tests that fall outside the 95% confidence limits for a county. For example, the DEM vote count for Aiken County falls outside the limits in 3 tests (LastC, Skew, and Kurtosis). In addition, it might make sense to look at the test with smaller confidence limits though it is not clear how to do this in the current code. Of course, the final solution for anomalies in elections is to audit or recount the balance. Still, it would be preferable to do as much other analysis as possible before this. Also, it's not clear whether or not every or most precincts in the flagged county would need to be audited or recounted. These numerical tests would seem very useful in flagging potential problems but it would also seem useful to understand how best to follow up on those counties and values that are flagged.