-한국 내 보도 의식한 듯 초판보다 강한 어조로 분석
-결론은 "Taken together the eforensics estimates and EFT and spikes tests exhibit anomalies that strongly suggest the Korea 2020 legislative election data were fraudulently manipulated."
[파이낸스투데이=서울] 대한민국의 4.15 총선 부정의혹과 관련하여 논란이 계속되고 있는 가운데 부정선거 탐지 분야 세계적인 권위자로 평가받고 있는 미국 미시건 대학 월터 미베인 교수의 논문 수정본 Anomalies and Frauds in the Korea 2020 Parliamentary이 공개됐다.
월터 미베인(Walter R. Mebane, Jr.)은 Anomalies and Frauds in the Korea 2020 Parliamentary 라는 수정 보고서를 내면서 우리나라의 지난 4.15 총선과 관련된 조작의 의혹을 다시 제기하고 있다. 초판 보다는 다소 강한 표현을 사용한 것으로 평가된다.
이번 보고서는 지난달 28일에 이은 두번째 버젼으로 "Frauds in the Korea 2020 Parliamentary Election" 라는 제목에서 Anomalies and Frauds in the Korea 2020 Parliamentary 라는 제목으로 수정되어 나왔으며, 사기성과 비정상적인 통계수치에 대해 학문적인 입장에서 다루고 있다.
미베인 교수는 보고서에서 2020년 대한민국의 국회의원선거에 비정상과 조작이 있는 것 같다는 결론을 내렸다. 초판에서 선관위의 자료를 그대로 대입하는 과정에서 있었던 약간의 오류를 수정하여 입력해 보니 오히려 부정선거의 의혹이 더욱 강화된 것으로 나타났다. 그러면서 통계는 조작이 있었다는 증거는 아니며, 추가적인 조사를 통해 조작의 증거를 찾아야 한다고 전하고 있다.
8번의 부정선거를 모두 맞힌 현직 미시간 대학교 교수이자 해당 분야 최고의 석학임을 감안할 때, 대한민국의 선거가 사기와 비정상 이라고 밝힌 미베인의 보고서는 중도성향을 갖고 있는 국민들에게는 충격적인 반향을 몰고 올 것으로 보인다.
다음은 보고서 전문이다.
Anomalies and Frauds in the Korea 2020 Parliamentary
The 2020 parliamentary election in Korea is controversial, with fraud allegations. I examine data from the election using eforensics, tests from the Election Forensics Toolkit and the spikes test. This paper improves on a previous version (“Frauds in the Korea 2020 Parliamentary Election,” April 29, 2020) by using updated complete data and by adding Election Forensics Toolkit and spikes test results. The estimates and tests all exhibit anomalies that suggest the election data were fraudulently manipulated.
The statistical model implemented in eforensics1 oﬀers evidence that fraudulent votes occurred in the election that may have changed some election outcomes. The statistical model operationalizes the idea that “frauds” occur when one party gains votes by a combination of manufacturing votes from abstentions and stealing votes from opposing parties. The Bayesian speciﬁcation2 allows posterior means and credible intervals for counts of “fraudulent” votes to be determined both for the entire election and for observed individual aggregation units.
It is important to keep in mind that “frauds” according to the eforensics model may or may not be results of malfeasance and bad actions. How much estimated “frauds” may be produced by normal political activity, and in particular by strategic behavior, is an open question that is the focus of current research. Statistical ﬁndings such as are reported here should be followed up with additional information and further investigation into what happened. The statistical ﬁndings alone cannot stand as deﬁnitive evidence about what happened in an election.
Figure 1 shows the distribution of turnout and vote proportions across aggregation units.3 Each turnout proportion is (Number Valid)/(Number Eligible), and each vote 1https://github.com/UMeforensics/eforensics_public 2Ferrari, McAlister and Mebane (2018) and http://www.umich.edu/~wmebane/efslides.pdf 3Vote and eligible voter count data come from the ﬁle korea election regional 21 eng.sqlite at https://github.com/freedomfighter2022/koreaelection2020, downloaded May 6, 2020 18:48. “The proportion is (Number Voting for Party)/(Number Eligible).4 The data include counts for n = 19131 units. 329 “abroad oﬃce” observations have zero eligible voters but often a small number of votes—the largest number is 23—and are omitted from the plots. One “prevote in” unit with zero voters and zero votes is also omitted. Figure 1(a) uses vote proportions deﬁned based on Democratic Party votes, and Figure 1(b) uses vote proportions deﬁned based on the votes received by the party with the most votes in each constituency. Fraud allegations have focused on the Democratic Party, but a principled way to analyze the single-member district (SMD) election data is to consider that frauds potentially beneﬁted the leading candidate in each constituency. In the ﬁgure diﬀerences
between the two distributions are apparent, but both share a distinctive multimodal pattern. There appear to be clusters of observations that share distinctive levels of turnout and votes, some with low, medium, high and very high turnout. The diagonal edge feature in the plots results from using Number Eligible as the denominator for both proportions: when the party receives nearly all the valid votes, then the observation is near that diagonal.
Figures 2 and 3 show that the diﬀerent clusters in Figure 1 correspond with observations that are administratively distinctive. Figure 2 displays data for Democratic
Party votes, and Figure 3 shows data for constituency leader votes. The four sets of units that have distinctive distributions are district-level, election-day units that are not abroad (Figures 2(a) and 3(a)), voting post, election-day units (Figures 2(b) and 3(b)), abroad
source data (Excel ﬁles) of the 21st general election of Korea was pulled from
https://www.nec.go. kr/portal/bbs/view/B0000338/40935.do?menuNo=200185” (Lee 2020). I determined constituency information using the tables of “Electoral District and Eupmyeon-dong” at http://info.nec.go.kr/ main/showDocument.xhtml?electionId=0020200415&topMenuId=BI&secondMenuId=BIGI05 and the lists of winners at http://info.nec.go.kr/main/showDocument.xhtml?electionId=0020200415&topMenuId= EP&secondMenuId=EPEI01. Google Translate helped me by translating the Korean sources into English in my Chrome browser. 4“Number Valid” is the number voting for any candidate, and “Number Eligible” is sum people in korea election regional 21 eng.sqlite. Candidates are mapped from the candidate table of korea election regional 21 eng.sqlite to parties, which in the party table in korea election regional 21 eng.sqlite are numbered as 3, 5, 7, 9, 11, 532, 616, 695, 1195, 3006, 4133, 10237, 11069, 11955, 13243, 13316, 13318, 13321, 13323, 13676, 17524, 18267, then votes for any of those parties are summed for each aggregation unit observation to produce “Number Valid” for that unit.
Figure 2: Korea 2020 Parliamentary Election Data Plots, Democratic Party
Figure 3: Korea 2020 Parliamentary Election Data Plots, Constituency Leaders
I estimate the eforensics model separately for the two deﬁnitions of leading party votes. Covariates for turnout and vote choice include indicators for pre-vote, voting post, abroad and disabled-ship status and ﬁxed eﬀects for the 253 constituencies included in the data. The two speciﬁcations agree that 506 aggregation units are fraudulent, but 664 additional units are fraudulent in the Democratic party speciﬁcation and 988 additional units are fraudulent in the constituency-leading party speciﬁcation.
As Table 1 shows, key parameter estimates are similar in the models. Parameters for the probabilities of incremental and extreme frauds (π2, π3) are very slightly greater in the constituency leader speciﬁcation, and coeﬃcients for the turnout equation (τ0–τ4) are similar. Coeﬃcients for vote choice (β0–β4) diﬀer, reﬂecting the diﬀerences in vote proportions being modeled. Figure 4 uses plots by subset of Democratic party focused observations to illustrate which observations are fraudulent according to the eforensics model with the Democratic party focused speciﬁcation. Nonfraudulent observations are plotted in blue and fraudulent observations appear in red.
The frequencies of fraudulent and not fraudulent units appear in the note at the bottom of the ﬁgure. Visually and by the numbers, frauds occur most frequently for pre-vote units (43.1% are fraudulent), next most frequently for for district-level, election-day, not abroad unts (3.14% fraudulent) then next most frequently voting post election day units (.925% are fraudulent). None of the abroad units are fraudulent.
Figure 5 uses plots by subset of constituency-leader focused observations to illustrate which observations are fraudulent according to the eforensics model with the constituency-leader focused speciﬁcation. Nonfraudulent observations are plotted in blue and fraudulent observations appear in red. The frequencies of fraudulent and not fraudulent units appear in the note at the bottom of the ﬁgure. Visually and by the numbers, frauds occur most frequently for pre-vote units (22.6% are fraudulent), next most frequently for voting post election day units (2.09% are fraudulent) then next most frequently for district-level, election-day, not abroad unts (.920% fraudulent). None of the abroad units are fraudulent.
I use a counterfactual method to calculate how many votes are fraudulent.5 Table 2 reports the observed counts of eligible voters, valid votes and votes for the (a) Democratic party and (b) constituency-leading party totaled over all units in the analysis, along with fraudulent vote count totals. The total of “manufactured” votes is reported separately from the total number of fraudulent votes: manufactured votes are votes that the model estimates should have been abstentions but instead were observed as votes for the leading party.
Both posterior means and 95% and 99.5% credible intervals are reported. The results show that for the Democratic-Party-focused speciﬁcation over all about 1,382,524 votes are fraudulent, and of the fraudulent votes about 1,030,562 are manufactured (the remaining 351,962 are stolen—counted for the leading party when they should have been counted for a diﬀerent party). Overall, according to the eforensics model, about 9.6% of the votes for Democratic Party candidates are fraudulent. The results show that for the constituency-leading-focused speciﬁcation over all about 1,404,919 votes are fraudulent, and of the fraudulent votes about 1,105,458 are manufactured (the remaining 299,461 are stolen—counted for the leading party when they should have been counted for a diﬀerent party).
Overall, according to the eforensics model, about 8.7% of the votes for constituency-leading candidates are fraudulent.
Fraudulent vote occurrence varies over constituencies. Counts of frauds by aggregation unit appear in a supplemental ﬁle6, but I use the unit-speciﬁc fraudulent vote counts from the constituency-leader focused speciﬁcation to assess whether the number of fraudulent votes is ever large enough apparently to change the winner of a constituency contest.
For 226 constituencies it is not, but for 27 constituencies the number of fraudulent votes is large enough apparently to change the winner of the constituency contest. In 14 instances the apparently fraudulently winning party is the “Democratic Party,” in 11 instances it is 5For a description of the method see “approach two” described at http://www.umich.edu/~wmebane/ efslides.pdf. 6See the original R output ﬁles wrkef2a Korea2020dAC 1d.Rout and wrkef2a Korea2020daAC 1d.Rout in Korea2020ef2.zip for the numbers of fraudulent votes at each aggregation unit.
Note: observed counts and total fraud posterior means and credible intervals based on eforensics model estimates. n = 18801.the “Future Integration Party” and in two instances it is “Independent.”77The particular constituencies that have these conditions can be identiﬁed by matching constituencies sequentially in “list of winners” tables available from http://info.nec.go.kr/main/showDocument. xhtml?electionId=0020200415&topMenuId=EP&secondMenuId=EPEI01 (as of May 9, 2020 17:12 EST). Province constituency-sequence-number (party posterior mean fraudulent): Chung-cheong bukdo 2 (DP 5321.9 fraudulent), Chungcheongnam-do 4 (FIP 3115.4 fraudulent), Chungcheongnam-do 5 (FIP 2574.6 fraudulent), Chungcheongnam-do 6 (FIP 2554.8 fraudulent), Chungcheongnam-do 1 (DP 5381.3 fraudulent), Gyeongsangnam-do 15 (DP 7573.1 fraudulent), Gyeongsangnam-do 5 (FIP 3697.5 fraudulent), Seoul 43 (FIP 6627.6 fraudulent), Seoul 48 (DP 11947.6 fraudulent), Seoul 45 (FIP 6240.1 fraudulent), Seoul 46 (FIP 7214.7 fraudulent), Seoul 4 (FIP 5166.0 fraudulent), Busan 7 (DP 2385.7 fraudulent), Busan 3 (FIP 5138.3 fraudulent), Busan 8 (DP 4055.7 fraudulent), Busan 12 (DP 2854.2 fraudulent), Busan 15 (FIP 6716.0 fraudulent), Daegu Metropolitan City 8 (I 4372.3 fraudulent), Incheon Metropolitan City 3 (I 1176.3 fraudulent), Incheon Metropolitan City 5 (DP 4056.5 fraudulent), Daejeon 7 (DP 4505.1 fraudulent), Daejeon 2 (DP 4458.2 fraudulent), Gyeonggi-do 8 (FIP 6255.3 fraudulent), Gyeonggi-do 9 (DP 8463.6 fraudulent), Gyeonggi-do 27 (DP 4187.1 fraudulent), Gyeonggi-do 49 (DP 4538.8 fraudulent), Gyeonggi-do 44 (DP 9679.8 fraudulent). In the “list of winners” tables, as translated by Google Translate, the constituency winner is
Given two speciﬁcations, which one is better? Probably neither model is correct, strictly speaking, even beyond the generality that no model is ever correct, but some are useful. If frauds only ever beneﬁt the Democratic Party, then those frauds may have induced apparent frauds when we constrain frauds to beneﬁt only constituency-leading candidates, because many of these do not aﬃliate with the Democratic Party. Similarly if only constituency-leading candidates beneﬁt from frauds, then eforensics may be producing misleading results when we constrain frauds to beneﬁt only the Democratic Party.
Or perhaps other candidates—or several in each constituency—beneﬁt from frauds and both speciﬁcations are producing misleading results. Possibly, of course, there are no frauds and something else is going on.
Caveats are many. The most basic caution is to keep in mind that “frauds” according to the eforensics model may or may not be results of malfeasance and bad actions. If some normal political situation makes the apparently fraudulent aggregation units appear fraudulent to the eforensics model and estimation procedure, then the frauds estimates may be signaling that “frauds” occur where in fact something else is happening. In particular there maybe something benign that leads many of the pre-vote units to have a turnout and vote choice distribution that diﬀers so much especially from the distribution for election-day voting post units, the latter comprising the bulk of the data.
Likewise something benign may distinguish the election-day voting post units that the eforensics model identiﬁes as fraudulent. Beyond that general caution, there may something about the particular data used for the analysis that triggers the “fraud” ﬁndings—for instance, the vote totals in the data for constituency-leading candidates do not always match totals reported in “lists of winners.” And there may be something about the model speciﬁcation that should be improved that would produce diﬀerent results.
designated as associated with (“Party Name”) “Democratic Party” (DP), “Future Integration Party” (FIP) or “Independent” (I).
2 Election Forensics Toolkit and Spikes
I use the Election Forensics Toolkit (EFT, a website developed as part of a USAID-funded project) (Hicken and Mebane 2015; Mebane 2015) to look at features of the ward data.
The EFT results add to the impression that the election results are manipulated. Results for ﬁve tests (see Hicken and Mebane 2015 for explanations of the tests)
computed using the entire set of aggregation units all together appear in Table 3. The DipT statistics for Turnout shows there is signiﬁcant multimodality, a result that matches what can be seen visually in Figure 1. The P05s statistic for Turnout is signiﬁcantly below the expected value of .2: this does not match the excessively high value of P05s that occurs in the case of signalling in Russia (Kalinin and Mebane 2011; Kalinin 2017), but it is diﬃcult to think of natural processes that would produce frequencies of percentages that end in 0 or 5 that are too low. The 2BL statistics diﬀer signiﬁcantly from the expected value of 4.187, but the values that occur for the candidates’ votes match what we observe given strategic turnout and voting with multiparty competition (Mebane 2013a), so these
2BL statistics do not support a diagnosis that there are frauds.
Table 3: Distribution and Digit Tests, Korea 2020
Note: statistics and tests based on aggregation unit observations. “2BL,” second-digit mean; “LastC,” last-digit mean; “P05s,” mean of variable indicating whether the last digit of the rounded percentage of votes for the referent party or candidate is zero or ﬁve; “C05s,” mean of variable incicating whether the last digit of the vote count is zero or ﬁve. “Obs,” number of aggregation unit observations. Values in parentheses are 95% nonparametric bootstrap conﬁdence intervals. Point estimates in red diﬀer signiﬁcantly from the values expected if there are no anomalies.
Given the SMD election rules, an approach that potentially produces sharper insights regarding the constituency contests is to compute the EFT statistics separately for each constituency. The counterbalancing concern is statistical power: overall there are n = 18801 aggregation unit observations, but the median size of constituencies is 66 aggregation units with sizes ranging from a minimum of 38 units to a maximum of 183 units. In most cases with such sample sizes bootstrap conﬁdence intervals for the EFT statistics (Hicken and Mebane 2015; Mebane 2015) are too wide to support ﬁnding signiﬁcant diﬀerences from the
values of the statistics that are expected if there are no anomalies. Nonetheless Figure 6 shows that many constituencies have signiﬁcantly anomalous values for the 2BL, LastC and P05s statistics.8 The plots of the 2BL statistic show several values that are either too big or too small to explain as results of electors’ strategic behavior (Mebane 2013a). The LastC statistics, motivated by Beber and Scacco (2012), show many too-large or too-small values.9 The P05s statistics show a few constituencies with excessively high values, in line with the usual understanding of how the percentages are often used to signal, but many more have signiﬁcantly small values. Moreover both Turnout and the votes for the candidates exhibit many signiﬁcantly anomalous P05s statistics. The many signiﬁcant P05s statistics suggest the data are artiﬁcial (cf. Mebane 2013b).
8The C05s statistics, not shown, exhibit similar frequencies of signiﬁcant anomalies. The signiﬁcance test results used to color points in Figure 6 are obtained by checking whether the nonanomalous expected values are contained in 95% conﬁdence intervals obtained using bootstrap methods. The EFT software is not designed to support ﬁnding exact p-values that might be used to implement adjustments for multiple testing. 9A qualiﬁcation to note is that LastC does not exclude aggregation units that have counts less than 100. Beber and Scacco (2012) advocate excluding such counts. In the Democratic-Party-focused data, 1463 units have fewer than 100 votes for the Democratic Party candidate, with a median of one such unit per constituency (max 83). For the constituency-leader-focused data, 603 units have fewer than 100 votes for the constituency leading candidate, with a median of one such unit per constituency (max 22).
Figure 6: Korea 2020 Election Forensics Toolkit by Constituency Plots
Note: statistics and tests based on aggregation unit observations, analyzed by constituency. Constituencies are matched to numbers in the Appendix. “2BL,” second-digit mean; “LastC,” last-digit mean; “P05s,” mean of variable indicating whether the last digit of the rounded percentage of votes for the referent party or candidate is zero or ﬁve. Red points diﬀer signiﬁcantly at level α = .05 from the values expected if there are no anomalies.
The spikes model tests for deviations in the proportions of votes for candidates in a more general way than does the P05s test, relative to a ﬂexible and empirically grounded null distribution (Rozenas 2017). Figure 7 shows graphics that identify the ranges of polling stations the model estimates are fraudulent.
Vertical gray bars in the graph indicate which aggregation units have suspicious votes: the aggregation units with vote proportions for (a) the Democratic Party or (b) the constituency leader that match the highlighted vote shares are suspicious. The results reinforce the ﬁndings for P05s in Table 3 and Figure 6 in that Figure 7 shows an excess of proportions near (a) .05 or (b) .07 and .38. The spike at 1.0 in Figure 7(b) matches the signiﬁcantly high values of P05s in Figure 6(i), for constituency-leading candidates, but the spike at 1.0 in Figure 7(a) is not matched by the P05s ﬁndings for Democratic Party candidates. The spikes test in this case appears to be more sensitive, in that the P05s test is restricted to reporting only a single average value while the spikes test assesses an entire distribution.
Figure 7: Korea 2020 Spikes Tests Plots
Taken together the eforensics estimates and EFT and spikes tests exhibit anomalies that strongly suggest the Korea 2020 legislative election data were fraudulently manipulated.
“Such conclusions are always subject to the caveat that apparent frauds may really be consequences of strategic behavior, but that ambiguity can sometimes be mitigated by exploiting a multiplicity of statistics.... An election fraud will not necessarily trigger all of the statistics and tests, but we think a genuine fraud will in general set oﬀ many of them” (Hicken and Mebane 2015, 39).
Statistical ﬁndings such as are reported here should be followed up with additional information and further investigation into what happened. The statistical ﬁndings alone cannot stand as deﬁnitive evidence about what happened in the election.
List of constituencies:10 1, Busan 1; 2, Busan 10; 3, Busan 11; 4, Busan 12; 5, Busan
13; 6, Busan 14; 7, Busan 15; 8, Busan 16; 9, Busan 17; 10, Busan 18; 11, Busan 2; 12,
Busan 3; 13, Busan 4; 14, Busan 5; 15, Busan 6; 16, Busan 7; 17, Busan 8; 18, Busan 9; 19,
Chung-cheong bukdo 1; 20, Chung-cheong bukdo 2; 21, Chung-cheong bukdo 3; 22,
Chung-cheong bukdo 4; 23, Chung-cheong bukdo 5; 24, Chung-cheong bukdo 6; 25,
Chung-cheong bukdo 7; 26, Chung-cheong bukdo 8; 27, Chungcheongnam-do 1; 28,
Chungcheongnam-do 10; 29, Chungcheongnam-do 11; 30, Chungcheongnam-do 2; 31,
Chungcheongnam-do 3; 32, Chungcheongnam-do 4; 33, Chungcheongnam-do 5; 34,
Chungcheongnam-do 6; 35, Chungcheongnam-do 7; 36, Chungcheongnam-do 8; 37,
Chungcheongnam-do 9; 38, Daegu Metropolitan City 1; 39, Daegu Metropolitan City 10;
40, Daegu Metropolitan City 11; 41, Daegu Metropolitan City 12; 42, Daegu Metropolitan
City 2; 43, Daegu Metropolitan City 3; 44, Daegu Metropolitan City 4; 45, Daegu
Metropolitan City 5; 46, Daegu Metropolitan City 6; 47, Daegu Metropolitan City 7; 48,
Daegu Metropolitan City 8; 49, Daegu Metropolitan City 9; 50, Daejeon 1; 51, Daejeon 2;
52, Daejeon 3; 53, Daejeon 4; 54, Daejeon 5; 55, Daejeon 6; 56, Daejeon 7; 57, Gangwon-do
1; 58, Gangwon-do 2; 59, Gangwon-do 3; 60, Gangwon-do 4; 61, Gangwon-do 5; 62,
Gangwon-do 6; 63, Gangwon-do 7; 64, Gangwon-do 8; 65, Gwangju 1; 66, Gwangju 2; 67,
Gwangju 3; 68, Gwangju 4; 69, Gwangju 5; 70, Gwangju 6; 71, Gwangju 7; 72, Gwangju 8;
73, Gyeonggi-do 1; 74, Gyeonggi-do 10; 75, Gyeonggi-do 11; 76, Gyeonggi-do 12; 77,
Gyeonggi-do 13; 78, Gyeonggi-do 14; 79, Gyeonggi-do 15; 80, Gyeonggi-do 16; 81,
Gyeonggi-do 17; 82, Gyeonggi-do 18; 83, Gyeonggi-do 19; 84, Gyeonggi-do 2; 85,
Gyeonggi-do 20; 86, Gyeonggi-do 21; 87, Gyeonggi-do 22; 88, Gyeonggi-do 23; 89,
Gyeonggi-do 24; 90, Gyeonggi-do 25; 91, Gyeonggi-do 26; 92, Gyeonggi-do 27; 93,
Gyeonggi-do 28; 94, Gyeonggi-do 29; 95, Gyeonggi-do 3; 96, Gyeonggi-do 30; 97,
10Constituencies can be identiﬁed fully by matching constituencies sequentially using “list of winners” tables available from http://info.nec.go.kr/main/showDocument.xhtml?electionId=0020200415& topMenuId=EP&secondMenuId=EPEI01.
Gyeonggi-do 31; 98, Gyeonggi-do 32; 99, Gyeonggi-do 33; 100, Gyeonggi-do 34; 101,
Gyeonggi-do 35; 102, Gyeonggi-do 36; 103, Gyeonggi-do 37; 104, Gyeonggi-do 38; 105,
Gyeonggi-do 39; 106, Gyeonggi-do 4; 107, Gyeonggi-do 40; 108, Gyeonggi-do 41; 109,
Gyeonggi-do 42; 110, Gyeonggi-do 43; 111, Gyeonggi-do 44; 112, Gyeonggi-do 45; 113,
Gyeonggi-do 46; 114, Gyeonggi-do 47; 115, Gyeonggi-do 48; 116, Gyeonggi-do 49; 117,
Gyeonggi-do 5; 118, Gyeonggi-do 50; 119, Gyeonggi-do 51; 120, Gyeonggi-do 52; 121,
Gyeonggi-do 53; 122, Gyeonggi-do 54; 123, Gyeonggi-do 55; 124, Gyeonggi-do 56; 125,
Gyeonggi-do 57; 126, Gyeonggi-do 58; 127, Gyeonggi-do 59; 128, Gyeonggi-do 6; 129,
Gyeonggi-do 7; 130, Gyeonggi-do 8; 131, Gyeonggi-do 9; 132, Gyeongsangbuk-do 1; 133,
Gyeongsangbuk-do 10; 134, Gyeongsangbuk-do 11; 135, Gyeongsangbuk-do 12; 136,
Gyeongsangbuk-do 13; 137, Gyeongsangbuk-do 2; 138, Gyeongsangbuk-do 3; 139,
Gyeongsangbuk-do 4; 140, Gyeongsangbuk-do 5; 141, Gyeongsangbuk-do 6; 142,
Gyeongsangbuk-do 7; 143, Gyeongsangbuk-do 8; 144, Gyeongsangbuk-do 9; 145,
Gyeongsangnam-do 1; 146, Gyeongsangnam-do 10; 147, Gyeongsangnam-do 11; 148,
Gyeongsangnam-do 12; 149, Gyeongsangnam-do 13; 150, Gyeongsangnam-do 14; 151,
Gyeongsangnam-do 15; 152, Gyeongsangnam-do 16; 153, Gyeongsangnam-do 2; 154,
Gyeongsangnam-do 3; 155, Gyeongsangnam-do 4; 156, Gyeongsangnam-do 5; 157,
Gyeongsangnam-do 6; 158, Gyeongsangnam-do 7; 159, Gyeongsangnam-do 8; 160,
Gyeongsangnam-do 9; 161, Incheon Metropolitan City 1; 162, Incheon Metropolitan City
10; 163, Incheon Metropolitan City 11; 164, Incheon Metropolitan City 12; 165, Incheon
Metropolitan City 13; 166, Incheon Metropolitan City 2; 167, Incheon Metropolitan City 3;
168, Incheon Metropolitan City 4; 169, Incheon Metropolitan City 5; 170, Incheon
Metropolitan City 6; 171, Incheon Metropolitan City 7; 172, Incheon Metropolitan City 8;
173, Incheon Metropolitan City 9; 174, Jeju Special Self-Governing Province 1; 175, Jeju
Special Self-Governing Province 2; 176, Jeju Special Self-Governing Province 3; 177,
Jeollabuk do 1; 178, Jeollabuk do 10; 179, Jeollabuk do 2; 180, Jeollabuk do 3; 181,
Jeollabuk do 4; 182, Jeollabuk do 5; 183, Jeollabuk do 6; 184, Jeollabuk do 7; 185,
Jeollabuk do 8; 186, Jeollabuk do 9; 187, Jeollanam-do 1; 188, Jeollanam-do 10; 189,
Jeollanam-do 2; 190, Jeollanam-do 3; 191, Jeollanam-do 4; 192, Jeollanam-do 5; 193,
Jeollanam-do 6; 194, Jeollanam-do 7; 195, Jeollanam-do 8; 196, Jeollanam-do 9; 197,
Sejong Special Self-governing City 1; 198, Sejong Special Self-governing City 2; 199, Seoul
1; 200, Seoul 10; 201, Seoul 11; 202, Seoul 12; 203, Seoul 13; 204, Seoul 14; 205, Seoul 15;
206, Seoul 16; 207, Seoul 17; 208, Seoul 18; 209, Seoul 19; 210, Seoul 2; 211, Seoul 20; 212,
Seoul 21; 213, Seoul 22; 214, Seoul 23; 215, Seoul 24; 216, Seoul 25; 217, Seoul 26; 218,
Seoul 27; 219, Seoul 28; 220, Seoul 29; 221, Seoul 3; 222, Seoul 30; 223, Seoul 31; 224, Seoul
32; 225, Seoul 33; 226, Seoul 34; 227, Seoul 35; 228, Seoul 36; 229, Seoul 37; 230, Seoul 38;
231, Seoul 39; 232, Seoul 4; 233, Seoul 40; 234, Seoul 41; 235, Seoul 42; 236, Seoul 43; 237,
Seoul 44; 238, Seoul 45; 239, Seoul 46; 240, Seoul 47; 241, Seoul 48; 242, Seoul 49; 243,
Seoul 5; 244, Seoul 6; 245, Seoul 7; 246, Seoul 8; 247, Seoul 9; 248, Ulsan Metropolitan City
1; 249, Ulsan Metropolitan City 2; 250, Ulsan Metropolitan City 3; 251, Ulsan
Metropolitan City 4; 252, Ulsan Metropolitan City 5; 253, Ulsan Metropolitan City 6.
Beber, Bernd and Alexandra Scacco. 2012. “What the Numbers Say: A Digit-Based Test for Election Fraud.” Political Analysis 20(2):211–234.
Ferrari, Diogo, Kevin McAlister and Walter R. Mebane, Jr. 2018. “Developments in Positive Empirical Models of Election Frauds: Dimensions and Decisions.”
Presented at the 2018 Summer Meeting of the Political Methodology Society, Provo, UT, July 16–18.
Hicken, Allen and Walter R. Mebane, Jr. 2015. “A Guide to Election Forensics.” Working paper for IIE/USAID subaward #DFG-10-APS-UM, “Development of an ElectionForensics Toolkit: Using Subnational Data to Detect Anomalies.” http://www.umich.edu/~wmebane/USAID15/guide.pdf.
Kalinin, Kirill. 2017. “The Essays on Election Fraud in Authoritarian Regimes: III. Theory of Loyalty: Signaling Games of Election Frauds.” Ph.D. dissertation, University of Michigan.
Kalinin, Kirill and Walter R. Mebane, Jr. 2011. “Understanding Electoral Frauds through Evolution of Russian Federalism: from “Bargaining Loyalty” to “Signaling Loyalty”.”Paper presented at the 2011 Annual Meeting of the Midwest Political Science Association,Chicago, IL, March 31–April 2.
Lee, Paul. 2020. “Personal communication.” Email message of April 29, 2020.
Mebane, Jr., Walter R. 2013a. “Election Forensics: The Meanings of Precinct Vote Counts’Second Digits.” Paper presented at the 2013 Summer Meeting of the Political Methodology Society, University of Virginia, July 18–20, 2013.
Mebane, Jr., Walter R. 2013b. “Using Vote Counts’ Digits to Diagnose Strategies and Frauds:Russia.” Paper prepared for the 2013 Annual Meeting of the American Political ScienceAssociation, Chicago, August 29–September 1.
Mebane, Jr., Walter R. 2015. “Election Forensics Toolkit DRG Center Working Paper.” Working paper for IIE/USAID subaward #DFG-10-APS-UM, “Development of
an Election Forensics Toolkit: Using Subnational Data to Detect Anomalies.” http://www.umich.edu/~wmebane/USAID15/report.pdf.
Rozenas, Arturas. 2017. “Detecting Election Fraud from Irregularities in Vote-Share Distributions.” Political Analysis 25(1):41–56.
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