Evidence of Vote Flipping in GOP Primary Elections

all votes should be made public whilst remaining private.
1) the qualified voter should have a unique id.
the vote(s) cast will then be able to become public knowledge visavis publishing on a website.
this will allow the voter to verify their own vote by finding the unique id.

ex: joan smith votes w/ an id of her choosing - this id is known only to joan.
2)her vote is published on a website along w/ all other votes and totals.
3) joan smith verifies that her vote is registered the way she voted.

this would make all vote totals an absolute and not some mystery cloud coughed up by a machine programmed by...

This is what Ron Paul gets for associating with such a lowlife political machine.
If he did not, he might have a shot

Originally posted by ChaoticOrder
reply to post by OccamsRazor04

 

I don't know what this analysis has to do with rural areas and small areas. It seems to me like you are referencing a different analysis, I haven't payed attention to all of them. But this one is simply showing statistical anomalies compared to historical data...

edit on 23-5-2012 by ChaoticOrder because: (no reason given)

Well maybe you should keep up, so you would understand. When the author did a RANDOM sampling the line went flat. This is exactly what you would expect. Here is a quote from the 2012 New Hampshire primary.

As can be seen, by the time you have counted 40% of all the ballots, the line goes flat: you have a reliable predictor of the candidate's final result.

The author then decided, hey, I wont do random sampling, I am going to CHERRY PICK my sample and start with SMALL RURAL areas that are more likely to vote for Paul.

Now let's order the precincts by number of votes cast and let's start counting from the smallest all the way to the largest.

The second he moved away from random sampling his graphs lost all credibility. In fact if the "author" switched and decided to start with larger populated areas we would see a decline of Romney as the Paulites comitted voter fraud.

Originally posted by Grambler
I believe your wrong. If I'm not mistaken, the graphs shown listed the counties by ALPHABETICAL order, not precinct size. Your confusing this study with the one in the previous thread about South Carolina, but clearly that doesn't apply.

You are mistaken, look up at my last post. When he looked at counties in alphabetical order there was a reliable trend. The author then scrapped the RANDOM alphabetical order and started to use county size, starting with the smallest first. He cherry picked the data to get the results he wanted, it's obvious.

There is a zero correlation between the alphabetical order of the precinct and the cumulative result of the candidate.

Now let's order the precincts by number of votes cast and let's start counting from the smallest all the way to the largest.

Translation I need to find a way to manipulate the data to get the result I want. Here's something I just found. I saw Romney was KILLING Paul and Paul comitted voter fraud to attempt to catch up. All you have to do is start with larger counties first, and work your way to the smaller ones. The blatant fraud of Paul is astounding.

Originally posted by Masterjaden
Don't be so quick to listen to OutKast....

He does switch, but the last three graphs are from the same ordering and show that historical analysis shows that it should be flat and the current one is skewed...

Jaden

Author has already shown a willingness to cherry pick data, who is to say he did not do the same here. Author even admits this does not happen everywhere.

The anomaly affects some counties, but others retain the historical complete absence of correlation

Detecting Statistical Data Anomalies in Republican Primary Election 2012 Results (v. 1.0, 06/24/2012)


I. Introduction

This report summarizes methodology for detecting statistical data anomalies in the election results, as well as provides some statistical inferences for specific datasets. These data anomalies can be attributed to election fraud, which is described here from this angle. The analysis is performed on the data sets from the Republican Primary Elections 2012 on the state and/or county level. The report is prepared for a broad audience, and does not require special knowledge base in mathematics.

Soon after the elections, state or county Election Divisions release detailed reports with precinct-by-precinct vote counts (Statements of Vote). For the purposes of this analysis, these reports have to be collected and converted in to tabular format for each precinct as rows with the following columns:

1. Congressional district or county unique name (optional).
2. Precinct unique name (optional).
3. Total number of registered voters in the precinct (optional).
4. Total number of vote tally for each candidate in the precinct (mandatory).
5. Total number of “over votes” and “under votes” in the precinct (optional).

After this data preparation stage, statistical analysis can be done in Microsoft Excel. The methods and data sources will be described later in the report.


II. Hypothesis Description

First, let’s summarize the theory of election fraud and how it impacts the results. Altering election results leaves statistical traces (or anomalies) in the datasets. Regardless whether the fraud is committed electronically or physically, eliminating these anomalies is virtually impossible. There are two types of election fraud:

1. Vote injection
2. Vote flipping

Let’s analyze their statistical impact on the election results data sets:

1. The votes for a particular candidate can be illegally injected in a particular precinct. Most likely, such an injection will not lead the vote tally (the total number of votes that was cast for all candidates) to exceed the total number of registered voters in this precinct. Otherwise, fraud detection would be trivial. However, such an injection causes both the vote tally and the number of votes in favor of this particular candidate to increase at the same time. In other words, statistically speaking, the correlation between these two counts increases. Maintaining such correlation at its original level across all precincts would be virtually impossible, especially considering the fact that such activity is illegal, and thus cannot be managed perfectly.
2. Votes for a particular candidate can be stolen from another candidate in a particular precinct. There are two reasons to perform votes flipping in the precincts with larger vote tally. First, this risky operation will have bigger impact on the final result if conducted in “large” precincts (measured by the vote tally), since more votes can be flipped per precinct, and, therefore, the number of flipped precincts can be reduced, while keeping the target total vote for this candidate fixed. Second, detection in larger precincts is harder. If voters detect fraud in a small precinct, they can easily get together, sign affidavits, and file a lawsuit. For example, if a precincts records only two votes for a candidate, while five friends from this precinct voted together for that candidate, the fraud becomes trivially detectable. By the way, the similar line of arguments is can be used to explain why the primary election results may significantly differ from the results of straw polls, caucuses, and conventions.

Thus, based on the above arguments, election fraud is more likely to occur in precincts with higher “officially” recorded vote tally. This is a hypothesis, which can be tested. I am not aware of other factors that would justify higher vote percentages for a particular candidate in precincts with higher vote tally. This anomaly becomes especially pronounced if it is observed across many states (counties) and favors the same candidate, regardless of its rank in the official vote count. Note that the number of registered voters is not used in this hypothesis. While performing these tests, the researcher must remember about these two statistical rules:

< to be continued>

Detecting Statistical Data Anomalies in Republican Primary Election 2012 Results (v. 1.0, 06/24/2012)

< continued, part 2 >


1. Selection bias. When a hypothesis is tested 100 times with 95% confidence level, then it can be falsely rejected in roughly 5 cases out of 100. Obviously, if it is rejected 60 times out of 100, then most of these rejections are true. This rule is applicable when we need to decide whether to test election fraud hypothesis on the state level once or test it many times for each county.
2. Power of the test. When a hypothesis is tested on a large data sample, the false hypothesis is more likely to be correctly rejected. That’s why testing on the state level is preferable than on the county level. However, if the magnitude of the anomaly (aka fraud) is large, then even relatively smaller sample (like county) will provide strong statistical evidence for its existence. The third method to increase power is to use larger significance criterion (0.05 versus 0.01). But this third method increases the probability of rejecting the true hypothesis, and thus it should be used only as a last resort to improve power of the test, if necessary.


III. Statistical Methods

When the data set is defined and prepared, the following tests should be run either on the state or county level:

1. Confidence interval for the Pearson correlation coefficient between vote tally (the sum of votes for all candidates) and votes cast for each candidate in each precinct.
2. Maximum likelihood estimator for the point estimate of the true number of votes cast for each candidate. This population estimate is inferred from a sample, which is incrementally drawn without replacement from the array of precincts ordered by the vote tally. Another order is possible, but only vote tally order shows the anomaly.
3. One-side hypothesis test (using cumulative distribution function of the Hypergeometric distribution) on the number of votes cast for each candidate. This test performed for each cumulative votes sum in the ordered arrays of precincts. The ordering can be as follows: random, alphabetical by precinct name, or vote tally. Anomaly will be detected in the last ordering only.

Let’s look at the intuition behind each of these methods, which essentially test the same hypothesis about presumptive election fraud that is traceable by the statistical data anomaly:

1. Correlation shows linear relation between two variables. It ranges from -1 to 1. Zero correlation implies non-existence of linear relation, while positive correlation means that a candidate is likely to gets more vote percentage in the precincts with larger vote tally. The “point estimate” of correlation can be computed from a sample (subset of precincts) or entire population (all precincts in a state or a county). Then, a “confidence interval” can be constructed around this point estimate. For example, let the point estimate be 0.3, and let the 99% confidence interval be between 0.2 and 0.4. It means that we statistically confirmed positive correlation. If we apply our hypothesis about election fraud being linked with this correlation, we can statistically confirm this fraud on the state-wide or county level. Alternatively, a two tail hypothesis test can be used, with the “null” hypothesis stating that the correlation is zero. In this case, Student-T distribution has to be used for transformed sample correlation. Let’s summarize the steps to compute the confidence interval for the correlation:
a. Compute arithmetic mean (average) vote tally count across all precincts, and then compute normalized ratios of vote tally counts (for each precinct) divided by this average.
b. Compute ratios for each candidate for each precinct by dividing these individual vote counts by the vote tally count within each precinct.
c. Compute arithmetic mean and standard deviation for all normalized vote tally counts from “a”, and normalize them by subtracting this mean, and then dividing by the standard deviation for each of them.
d. Compute arithmetic mean and standard deviation for all ratios from “b”, and normalize them by subtracting this mean, and then dividing by the standard deviation for each of them.
e. Compute Pearson correlation between the vote tally statistic from “c” and all statistics from “d” for each candidate. This is the “point estimate” correlation.
f. Apply Fisher’s transformation to these point estimate correlations to get approximately standard normal random variable.
g. Construct confidence interval around this standard normal random variable, and then invert that transformation (using hyperbolic tangent function) back into the interval for the correlation.

Excel has the following built-in functions for this analysis: “CORREL”, “NORM.INV”, “TANH”, “AVERAGE”, “STDEV.S”, and “COUNT”. By the way, this correlation is visually apparent from the plot as well.

Detecting Statistical Data Anomalies in Republican Primary Election 2012 Results (v. 1.0, 06/24/2012)

< continued, part 3>


2. Hypergeometric distribution allows making probabilistic statements about random samples’ properties based on the entire population, or inferences about the entire population based on a specific instance of a random sample. For example, suppose that the total vote tally (population) in the state is 100, and candidate A actually got 60 votes. Let’s assume that we have drawn a random sample without replacement from this population, which is somewhat similar to a exist poll (assuming that it is perfectly random and truthful). If our random sample has size 10, then the probability that 6 respondents voted for the candidate A is 0.2643, the probability that at most 6 respondents voted for the candidate A is 0.6258, and the probability that at least 6 respondents voted for the candidate A is 0.6386. Alternatively, one can infer number 60 form the above sample of size 10 with 6 votes for A with the following formula: floor (6 * (100 + 1) / 10). But this is just a point estimate. There are at least two methods to construct the confidence sets (similar to confidence intervals) around point estimates for the hypergeometric distribution: “test-method” and “likelihood-method”. These methods are important for analyzing the exit polls results, but they are not the focus of this report for now. However, even the point estimate of the vote counts for each candidate can show potential fraud-based bias in favor of or against one or several candidates. Specifically, if the precincts are ordered by the vote tally, and the population point estimate of vote counts keeps on increasing for one candidate while decreases or flat for other candidates, then this serves as another indication of the suspicious positive correlation, but viewed from a different angle. The averages can be computed for deviations of these point estimate vote percent results for each precinct (starting from the one with at least one cumulative vote for each candidate) from the “official” results. These are the rough corrections of the official results towards the actual results.
3. Finally, let’s look at the third method to detect the same data anomaly. This time we run a series of one-sided hypothesis tests on the vote percentages for each candidate. If we run these tests on the precincts that are sorted either randomly or alphabetically by country and/or precinct name, then the anomaly is not detected. However, if precincts are sorted by the vote tally, then the anomaly is extremely pronounced in favor of one specific and the same candidate across states and counties. The following list describes steps to reproduce this analysis:
a. After ordering precincts by the vote tally, compute precinct cumulative sums of vote counts and vote percentages for each candidate and for the whole vote tally. You may think of these sums as incremental exit polls results.
b. Run two hypothesis tests for each candidate at each ordered precinct row with the cumulative counts. Use Excel function “HYPGEOM.DIST” to run these tests. The following example illustrates the point. Suppose that the state-wide vote tally is 100, and the candidate Bad “officially” got 40 votes, while the candidate Good “officially” got 30 votes. We do not know how many votes these two candidates actually got. Let’s assume that we added up all “official” votes from 35% percent of precincts with the smallest vote tally. These precincts have only 20 votes cast, and 10 of them were for Mr. Good, while only 5 of them were for Mr. Bad. Evidently, Mr. Bad has to catch up in order to get his 40%, since he has only 25% so far. Meanwhile, we can run a hypothesis test on Mr. Bad: the “null” hypothesis is that he will eventually get at least 40 votes (40%), and an alternative hypothesis is that he will get less than 40% of votes. Since Mr. Bad has a long way to go to catch up, we will reject the “null” hypothesis (say, at 99% confidence level), and we will concluded that Mr. Bad actually got less than 40 votes in total. This is called upper-tail hypothesis test. We can run a lower tail hypothesis test for Mr. Good, who was a victim of vote flipping. In this case, we will reject a “null” hypothesis (say, at 99% confidence level) that Mr. Good’s vote count was less than or equal to 30. Obviously, both tests should and can be applied to both candidates.
c. Finally, we compute the percentage of the “null” hypothesis rejections for both test types for all candidates across all precincts. If we observe that rejection occurred in 97% of precincts for one candidate and in 0.4% of precincts of another one (or the other way around), then we can make statistical inference with respect to these candidates’ election results. The inference can be reinforced by running the test on different states and counties and observing the same anomaly over and over again for the same candidate.

Detecting Statistical Data Anomalies in Republican Primary Election 2012 Results (v. 1.0, 06/24/2012)

< continued, part 4>


IV. Statistical Analysis Results

The previous section describes methods, which were applied to the following data sets:

1. State of Ohio. Official Republican Primary Election Results. March 6, 2012. Precinct count: 9,649. Votes count for all Republican candidates: 1,213,879.
2. State of Oklahoma. Official Republican Primary Election Results. March 6, 2012. Precinct count: 1,961. Votes count for all Republican candidates (including under/over votes): 286,707.

The official election results were the following:

1. Ohio: Newt Gingrich (8.99%); Jon Huntsman (0.33%); Ron Paul (5.75%); Rick Perry (0.38%); Mitt Romney (23.38%), Rick Santorum (22.76%).
2. Oklahoma: Ron Paul (9.63%); Rick Perry (0.45%); Rick Santorum (33.78%); Mitt Romney (28.03%); Michele Bachman (0.33%); Newt Gingrich (27.46%); Jon Huntsman (0.26%); Over Votes (0.02%); Under Votes(0.05%).

The following are the correlations’ 99% confidence intervals and point estimates for pairwise correlations between each precinct relative vote tally and the percentage of each candidate votes in each precinct:

1. Ohio: Newt Gingrich (0.0108; 0.0370; 0.0632); Jon Huntsman (-0.0971; -0.0710; -0.0449); Ron Paul (-0.2289; -0.2039; -0.1786); Rick Perry (-0.1149; -0.0890; -0.0629); Mitt Romney (0.2506; 0.2750; 0.2990), Rick Santorum (0.0089; 0.0351; 0.0612).
2. Oklahoma: Ron Paul (-0.1442; -0.0868; -0.0288); Rick Perry (-0.1502; -0.0928; -0.0349); Rick Santorum (-0.1673; -0.1103; -0.0525); Mitt Romney (0.2768; 0.3296; 0.3805); Michele Bachman (-0.1073; -0.0495, 0.0087); Newt Gingrich (-0.0687; -0.0106; 0.0476); Jon Huntsman (-0.0729; -0.0148; 0.0434); Over Votes (-0.0699; -0.0118; 0.0464); Under Votes (-0.0830; -0.0250; 0.0332).

Let’s assume that the number of actual votes cast for each candidate equals or exceeds the official vote count. The following are the percentages of these “null” hypothesis rejections (across all ordered precincts) with the 95% confidence level for the cumulative results:

1. Ohio: Newt Gingrich (0.00%); Jon Huntsman (3.47%); Ron Paul (0.00%); Rick Perry (0.12%); Mitt Romney (97.23%), Rick Santorum (3.52%).
2. Oklahoma: Ron Paul (0.00%); Rick Perry (0.00%); Rick Santorum (0.05%); Mitt Romney (96.74%); Michele Bachman (0.00%); Newt Gingrich (0.20%); Jon Huntsman (0.05%); Over Votes (2.55%); Under Votes (0.00%).

Let’s assume that the number of actual votes cast for each candidate equals or less than the official vote count. The following are the percentages of these “null” hypothesis rejections (across all ordered precincts) with the 95% confidence level for the cumulative results:

1. Ohio: Newt Gingrich (65.61%); Jon Huntsman (83.74%); Ron Paul (99.24%); Rick Perry (97.94%); Mitt Romney (1.71%), Rick Santorum (84.49%).
2. Oklahoma: Ron Paul (98.06%); Rick Perry (92.81%); Rick Santorum (95.82%); Mitt Romney (1.38%); Michele Bachman (81.29%); Newt Gingrich (70.58%); Jon Huntsman (10.30%); Over Votes (21.42%); Under Votes (48.50%).

The cross-precinct averages for the differences between the point estimate vote percent results for each ordered precinct (with at least one cumulative vote for each candidate) from the “official” results:

1. Ohio: Newt Gingrich (+0.08%); Jon Huntsman (+0.21%); Ron Paul (+2.44%); Rick Perry (+0.30%); Mitt Romney (-3.64%), Rick Santorum (+0.62%).
2. Oklahoma: Ron Paul (+1.19%); Rick Perry (+0.26%); Rick Santorum (+3.03%); Mitt Romney (-5.30%); Michele Bachman (+0.10%); Newt Gingrich (+0.65%); Jon Huntsman (+0.04%); Over Votes (+0.01%); Under Votes (+0.02%).

Detecting Statistical Data Anomalies in Republican Primary Election 2012 Results (v. 1.0, 06/24/2012)

< continued, part 5>

V. Conclusions

Statistical analysis of the Republican Primaries results from 2012 in Ohio and Oklahoma show strong statistical evidence of data anomalies for one candidate in both cases. Moreover, this candidate is the same in both states. If we assume causal relation between statistically significant positive correlation (as defined and explained in section II of this report) and election fraud (vote injection and/or vote flipping), then the latter can be attributed to this candidate’s election results. This would imply that this candidate is very likely to take the second rank in Ohio’s election (as opposed to the first rank), and the third rank in Oklahoma’s election (as opposed to the second one). Presumably, this rank switching was an objective of this fraud. In addition, statistical analysis shows that other candidates were supposed to get more votes than the official count. Both tests were performed on very large samples, which were essentially entire statistical populations represented by the whole state in each case. This fact means high power of the test, as well as lack of selection bias. Moreover, the same pattern was detected in both randomly selected states. Other research reports indicate that this anomaly exists in many more states, and thus additional states must be analyzed to reinforce this statistical evidence of election fraud even more. Individual counties may need to be analyzed as well, in order to pinpoint the ones that contribute to this election fraud on the extreme scale.


VI. Data Sources

1. Ohio Election Results, March 6, 2012: www.sos.state.oh.us...
2. Oklahoma Election Results, March 6, 2012: www.ok.gov...