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Sample of Election Records
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Winning margin, as % of all ballots1.25%2.50%5%10%20%40%
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Error rate to detect0.63%1.25%2.50%5%10%20%
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You can word that as 1 error in this many records1 in 1601 in 801 in 401 in 201 in 101 in 5
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This random sample of ballots gives 63.2% chance of detecting the error (sample = 2 divided by the winning margin)160804020105
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A bigger random sample of ballots gives 90% chance of detecting the error (sample â‰ˆ 4.5 divided by the winning margin)36818491452211
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4.604.604.554.504.404.40
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Winning margin, as % of all ballots1.25%2.50%5%10%20%40%
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Error rate to detect0.63%1.25%2.50%5%10%20%
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Size of random sample
Probability that sample size at left will detect the error rate above
11
10.62%1.25%2.5%5.0%10.0%20.0%
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21.25%2.5%4.9%9.8%19.0%36.0%
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116.7%12.9%24.3%43.1%68.6%91.4%
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2212.9%24.2%42.7%67.6%90.2%99.3%
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4524.6%43.2%68.0%90.1%99.1%100.0%
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9143.5%68.2%90.0%99.1%100.0%100.0%
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18468.5%90.1%99.1%100.0%100.0%100.0%
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36890.0%99.0%100.0%100.0%100.0%100.0%
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50095.6%99.8%100.0%100.0%100.0%100.0%
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1,00099.8%100.0%100.0%100.0%100.0%100.0%
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Winning margin, as % of all ballots1.25%2.50%5%10%20%40%
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Erroneous ballots0.63%1.25%2.50%5%10%20%
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If worst batches are 100% wrong, this fraction of batches are erroneous0.63%1.25%2.50%5%10%20%
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If worst batches are 50% wrong, this fraction of batches are erroneous1.25%2.50%5%10%20%40%
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If worst batches are 25% wrong, this fraction of batches are erroneous2.50%5%10%20%40%80%
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If worst batches are 100% wrong, this random sample of batches gives 90% chance of detecting error36818491452211
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If worst batches are 50% wrong, this random sample of batches gives 90% chance of detecting error184914522115
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If worst batches are 25% wrong, this random sample of batches gives 90% chance of detecting error9145221152
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Sample of batches
Erroneous batches as % of all batches
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1%5%10%20%
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Number of batches in sample
Chance sample will miss all the erroneous batches
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199.00%95.00%90.00%80.00%
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298.01%90.25%81.00%64.00%
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496.06%81.45%65.61%40.96%
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1090.44%59.87%34.87%10.74%
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2081.79%35.85%12.16%1.15%
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4066.90%12.85%1.48%0.01%
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factor
Average number of ballots switched, in batches with switches
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30%25%20%5%
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winning margin as %
Number of batches needed in sample depends on how many ballots switched
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3%2218143
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1%68564510
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0.60%114957618
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54
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error level detectible, at 10% risk, with sample of 20.6820.51%17.09%13.68%3.42%
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error level detectible, at 10% risk, with sample of 140.154.55%3.79%3.03%0.76%
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error level detectible, at 10% risk, with sample of 180.123.60%3.00%2.40%0.60%
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error level detectible, at 10% risk, with sample of 450.051.50%1.25%1.00%0.25%
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ballots switched, in batches with switches25%
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number of batches100.00500.001,000.003,000.00
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1% sample1.005.0010.0030.00
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ballots switched overall
Odds of missing errors
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0.5%98.0%90.4%81.7%54.5%
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1.0%96.0%81.5%66.5%29.4%
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2.0%92.0%65.9%43.4%8.2%
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4.0%84.0%41.8%17.5%0.5%
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8.0%68.0%14.5%2.1%0.0%
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chance of missing errors
error level to give chance of missing as shown at left, assuming up to 25% of batch in error
70
70%7.5%1.7%0.9%0.3%
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67.0%8.3%1.9%1.0%0.3%
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80.0%5.0%1.1%0.6%0.2%
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chance of missing errors
erroneous batches to give chance of missing as shown at left
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70%30.0%6.9%3.5%1.2%
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67.0%33.0%7.7%3.9%1.3%
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80.0%20.0%4.4%2.2%0.7%
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Sample of individual ballots
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Sample size50301503009000Sample size needed for 90% chance of detecting error
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Error levelRisk of missing errors in the image files or CVRs
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5%8%21%0%0%0%100%45
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4%13%29%0%0%0%100%57
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3%22%40%1%0%0%100%76
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2.28%32%50%3%0%0%100%100
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2%36%55%5%0%0%100%114
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1%61%74%22%5%0%100%230
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0.60%74%83%41%16%0%100%383
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Risk of missing the error level shown with sample shownError level
90
11%4.32%7.09%1.46%0.73%0.24%
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10%4.50%7.39%1.52%0.76%0.26%
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good items
errors
cum chance of missing errors
94
Example: total ballots or batches200
95
erroneous ballots or batches10
96
chance of missing error in sample 10.95190100.95
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chance of missing error in sample 20.9497487437189100.9022613065
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chance of missing error in sample 30.9494949495188100.8566925537
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chance of missing error in sample 40.9492385787187100.813205622
100
chance of missing error in sample 50.9489795918186100.7717155393