Winnebago County Walker Recall: A Probability Analysis of Optical Scan and Touch Screen Vote Counts
Richard Charnin
Aug. 14, 2012
Updated: Oct.27, 2013
Three independent models analyzed the Walker Recall election in Winnebago County. This post focuses on a probability analysis of DRE vs. Optical scanners. Summaries and links to the Cumulative County Vote Share graphical analysis and the County/Muni True Vote Model are also included. The three models confirm the very high probability of fraud.
Assume that the votes cast on Optical scanners and Touch screens are given for a location (ward, precinct). All things being equal, the vote shares should be nearly identical. But if they are not equal, is the difference significant? And if the difference is significant, what is the probability that it would be due to chance?
Note that this is not an exit poll analysis. The probabilities are based on actual recorded votes.
The probability of the discrepancy is a function of the following:
1) number of optical scanners and touch screens
2) vote share percentages on each
If the optical scan ballots are hand-counted, we can calculate the number of touch screen votes and vote shares by subtraction. We can then determine if the difference in vote shares between the touch screens and optical scanner is significant.
This spreadsheet is a probability calculator for the discrepancy between optiscan and touchscreen vote shares in a given ward/precinct.
The Z-score is based on the bell-curve (normal distribution). Z determines the probability of the difference between the touch screen and optical scan vote shares. If
Z = 1.65, the probability is 95.2% that the difference between touch screen and optical scan vote shares was not due to chance. Election Fraud is likely.
Z = 1.96, the probability is 97.5%
Z = 2.33, the probability is 99.0%
Assume that in a given location, we have:
nv = total number of votes
ns = number of optical scan ballots
wv = Walkers total vote
ps = Walker’s vote share on optical scanners
Then we can easily determine
nt = number of TSX (touch screen) votes = nv – ns
pt = Walker’s TSX share
We can then calculate the probability of the difference in vote shares between the optical scanners and touchscreens:
1) Difference in vote shares: Diff = pt-ps
2) Standard error: Std = sqrt [ps*(1-ps)/ns + pt*(1-pt)/nt]
3) Z-score = ABS(Diff) / Std
4) Probability (Diff) = 2-2*NORMSDIST(Z)
The following table is based on the Winnebago County spreadsheet in the 2012 Wisconsin Recall True Vote Model. It shows that the large discrepancies between Opscan and TSX shares in the following locations could not have all been due to chance.
Model 1. Winnebago Muni DRE/Opscan Differential Vote Share Probability (Walker 2-party%)
Location.....Opscan...TSX.....Diff..ZS..Prob
Menasha(3,5,6).65.64% 60.23% -5.41% 1.89 5.82%
Neenah.........63.14% 73.21% 10.08% 1.67 9.45%
Poygan.........62.81% 72.66% 9.85% 2.68 0.74%
Rushford.......58.48% 65.92% 7.44% 2.10 3.59%
Utica..........66.67% 75.17% 8.51% 2.08 3.78%
Neenah(13-16)..60.32% 53.68% -6.63% 1.74 8.20%
Neenah(17-20)..51.31% 64.10% 12.79% 2.77 0.57%
Oshkosh(5).....42.73% 32.98% -9.75% 1.85 6.46%
Oshkosh(15)....50.76% 40.00% -10.76% 2.89 0.38%
Oshkosh(17)....40.48% 47.66% 7.18% 1.91 5.66%
Oshkosh(28A)...44.96% 52.58% 7.61% 1.88 5.98%
Oshkosh(29A)...60.63% 73.68% 13.06% 2.24 2.48%
Poygan Village Votes Pct
2-Party Total
Vote Count.... 662 100%
Optiscan...... 406 61.33%
TSX DRE....... 256 38.67%
Walker
Total Votes... 441 66.62%
Optiscan...... 255 62.81%
DRE TSX....... 186 72.66%
Z-Score....... 2.68
Probability... 0.74% (of 9.85% vote share discrepancy between Optiscan and DRE)
Model 2: Winnebago County Cumulative VoteShares
Note the statistically improbable increase in Walker’s share. https://richardcharnin.wordpress.com/2012/12/09/walker-recall-county-cumulative-vote-trend-by-ward-group/
Model 3: Winnebago True Vote (2-party)
Barrett won the True Vote with 53.5%, a 5000 vote margin.
Walker won the recorded vote with 56.4%, a 9000 vote margin.
Walker needed an implausible 29% of returning Obama 2008 voters to match his recorded vote. https://richardcharnin.wordpress.com/2012/07/24/the-walker-recall-municipal-database-a-true-vote-model/
2008... Share. Votes. Alive Turnout.Votes..... Mix. Barrett Walker Barrett Walker Margin
Obama...55.90% 48,137 45,971 80.00% 36,777.... 51.97% 89.93% 10.07% 33,075 3,702 29,372
McCain..44.10% 37,976 36,267 80.00% 29,014.... 41.00% 06.96% 93.04% 2,020 26,993 -24,973
New..................................4,976..... 7.03% 55.90% 44.10% 2,781 2,194 587
Total......... 86,113 82,238 80.00% 70,766
True Vote........................................... 53.52% 46.48% 37,876 32,890 4,986
Recorded Vote....................................... 43.60% 56.40% 30,885 39,881 -8,996
2012 votes / living 2008 voters:86.05%
2012 voters % of 2008: 82.18%
Est. votes flipped:6,991 18.46%
Sensitivity Analysis
Barrett won all 18 plausible voter turnout and vote share scenarios
2008 Voter turnout in 2012:77.00% 80.00% 83.00%
Required Walker % of Obama:30.08% 29.16% 28.31%
Voter Turnout.......................... Barrett share of
Obama McCain........................... Obama McCain
80% 80%................................. 90% 7%
......Barrett Share of Obama.................. Obama Turnout
Barrett 87.0% 90.0% 93.0%.......McCain...77.0% 80.0% 83.0%
%McCain....Barrett Share........Turnout......Barrett Share
9.96% 53.19% 54.75% 56.31%......... 77% 53.61% 54.28% 54.94%
6.96% 51.96% 53.52% 55.08%......... 80% 52.86% 53.52% 54.19%
3.96% 50.73% 52.29% 53.85%......... 83% 52.11% 52.77% 53.43%
...........Barrett Margin.....................Barrett Margin
9.96% 4,520 6,727 8,934............. 77% 5,112 6,051 6,990
6.96% 2,780 4,986 7,193............. 80% 4,047 4,986 5,925
3.96% 1,039 3,245 5,452............. 83% 2,983 3,921 4,860
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