The 2004 Election: Analyses, Summaries, Charts, and Spreadsheets 
The
2004 Ohio Presidential Election: Cuyahoga County Analysis
In a
subset of 166,953 votes, one of every 34 Ohio voters, the KerryBush margin Preface Simply put, Ohio votes were NOT all counted as cast. Many votes were miscounted, and Kerry votes were counted for Bush. Numerous questions have been raised about the fairness of the 2004 Presidential election in the United States of America (US). In this study I focus on one election issue, punch card crossvoting—how votes cast one way were counted other than as intended, as a vote for a different candidate or option. Punch card voting has been replaced and, with so many election issues, this most egregious of flaws—counting votes wrong—has seemingly been overshadowed by evoting and reform concerns. I also focus on a particular region with onetenth of the Ohio vote, Cuyahoga County, where recount crimes have detracted from miscounting the vote. The 2004 recount issue focused attention away from crossvoting. Crossvotes recount the same and, hence, are an entirely distinct issue. In 2000, the US postelection focus was on Florida, on fairness of punch card voting, on vote count accuracy, and on incomplete counting. In 2004, Ohio's failure to replace punch card voting with improved systems is just one of many issues raised with regard to the Ohio 2004 Presidential election. Other Ohio fairness, fraud, and irregularity issues include politicization of process, voter registration fraud, voter purging and suppression including racial discrimination and unfair voting machine distribution, the exit poll inaccuracy, electronic voting security, paperless evoting, evote flipping, the high percentage of and unequal distribution of undervotes, uncounted provisional ballots, vote count secrecy, recount crimes and irregularities, and official loss of and/or destruction of evidence. This article and the appendices combine, with additional material, earlier versions cited in academic references. In a separate file, I present a 2004 Ohio Presidential Election Results Summary and various Ohio datasets. Seveneights of voters
in heavilyDemocratic Cuyahoga County,
more
than one of every eight
Download vote_switching.ppt featuring
highlights from the study.
The contents links allow readers familiar with some aspects of the issue to focus on specific topics. The subject is complex, and introductory material is conveyed throughout the topics and in the appendices. This topic required defining vocabulary and creating new notations. These are defined throughout the article and discussed in the appendix. Miscounted votes in Ohio came to my attention via press coverage. An incident came to light due to very high returns for thirdparty candidates in several Cuyahoga County precincts:
"How many votes were switched?" should be an easy number to define, I initially surmised. Wrongprecinct voting occurred at a surprisingly high rate. Instead of immediate clear answers, trying to tally the miscounting led down a long path with many more questions, taxed my knowledge of statistics and quantitative methods, necessitated developing new methods, and produced unexpected findings of unfairness in the election process—all providing a political education my political science classes never even considered. The evidence raises suspicions about intentional manipulation of the election process directed at changing the outcome in favor of Bush. I soon wondered, "Were ballots fraudulently switched?" For Ohio punch card voting, accurate tally is dependent on precinct chain of custody, from giving the voter a ballot until central tabulation. Ballots must be cast and counted in their own precinct. Many votes were counted for the wrong candidate or ballot option, and a significant portion of the crossvoting resulted in Kerry votes tallied as Bush votes. The 2004 Presidential election hinged on the Ohio results. According to unadjusted exit polls, Kerry won Ohio. Instead, with a 3.35 percent difference between the tallies, the results gave the victory and the presidency to Bush. With these circumstances, evidence of miscounted voting and KerrytoBush vote switching have particular importance in determining the actual intent of Ohio voters, the reasons for the exit poll discrepancy, and the validity of the 2004 US Presidential election result. Crossvoting also impacted other races. Analysis of past elections and other counties and races may reveal more punch card crossvoting. I present evidence of crossvoting and of how Kerry disproportionately lost votes to crossvoting. I report how ballot order combinations favored Kerry to Bush crossvoting. I present methods developed to determine how many votes were switched, miscounted, or not counted at all. I report the impact of crossvoting and present evidence of the degree of miscounted voting. Finally, statistical tests are applied to the data. Analysis of election results—because every respondent has been polled—is, largely, descriptive statistics, enabling robust statistical analysis without some margin of error problems of sample polling used in inferential statistics. 
The first question I tried to answer was, "How many votes were switched?" Cuyahoga County reported, for the 1432 of 1435 precincts included in this study, 1,003,435 registered voters cast 600,467 votes at precincts, 10.76% of the Ohio vote. Since John Kerry received 65.67 percent of these (394,354 votes), on average Kerry would lose two votes to wrongprecinct voting for every vote Bush loses. This, of course, assumes random distribution of ballot order combinations, crossvoting, and voteswitching in relation to candidate support and other variables. It also assumes ballots were counted in precinct as cast, not switched between precincts later to alter votes. With candidate support varying widely in precincts, where wrongprecinct voting occurs determines the ratio of lost votes and the proportion of voteswitching. The cases following illustrate the variable impact of wrongprecinct voting. Table 6 displays results for the most egregious of obvious crossvoting locations, Benedictine High School. Here major candidates were not collocated. Up to 215 people in precinct 1806 crossvoted for Kerry in precinct 1814, punching the third position using the precinct 1814 voting machines. Those 215 Kerry votes counted for Peroutka (Kp) due to the Kp ballot order collocation. Also, up to 164 Kerry voters from 1814 punched the first position, Kerry in precinct 1806. Those 164 ballots counted as Badnarik votes, the first position in precinct 1814. Meanwhile, Bush lost 10 votes to Peroutka in precinct 1814.
The Benedictine High School tally demonstrates how the number of votes lost to crossvoting is proportional to candidate support. The greater the candidate's support, the greater the negative impact of crossvoting. Kerry lost about 38 times more votes than Bush, 379 votes or 37% of his vote in this location, about 1/1,000th of his votes in the entire county. Kerry votes would increase by up to 60% without this crossvoting. In these precincts Kerry had 96% support, so 24 of 25 random crossvotes would be Kerry voters. Table 7 illustrates two precincts where Bush and Kerry votes can be switched by wrongprecinct voters punching the third position of the ballot order. Kerry voters from precinct 2908 punch the third position (K) on 2909 machines, in their precinct a Bush vote. These Kerry crossvoters cast a voteswitch between the major contenders—the one vote that counts twice.
Table 8 presents the voting results. The precinct 2909 Kerry crossvoters voting in 2908 tallied for disqualified (Kd) in their own precinct. Bush voters from precinct 2908 voting in precinct 2909 voted the second position, Badnarik (b) in their own precinct, while Bush votes from precinct 2909 voteswitch to Kerry in 2908.
Conclusively, thirdparty "cast" votes average less than one vote per precinct. In all those precincts with zero probability of a Kerry crossvote counting for Badnarik, Badnarik garnered a mere 0.20%, compared with 1.02% in precincts with a 1.0 probability of Kerry crossvotes counting for him, a fivefold increase. For Peroutka, the percentage jumps nearly tenfold from 0.168 to 1.604. Figure 1 illustrates the pattern. Now, presumably 14 Bush voters in precinct 2908 crossvoted in precinct 2909, where punching the second candidate counted for Badnarik in their precinct. Bush probably lost 14 votes, 14 of the 15 votes counted for Badnarik.
Badnarik votes increase fivefold and Peroutka votes jump over ninefold. KerryBush switchedvotes are not as readily apparent, obfuscated by higher percent returns, so this example employs hypothetical proportions. Assuming candidate support in the location is 2:1 and that an equal proportion of Kerry voters crossvoted, then 28 precinct 2908 Kerry voters would punch the third position in 2908 and mistakenly voteswitch to Bush. If in precinct 2908, Badnarik gained 14 Bush votes while 28 Kerry votes switched to Bush, the margin between Bush and Kerry changed by 42 votes in Bush's favor, a 17% shift. Comparing Table 8 and Table 9 illustrates how crossvoting hypothetically altered the Kerry's vote by an 11.67% drop, to 65.26% from 73.72%.
Of course, in a hypothetical scenario assuming random crossvoting, voters from 2909 also crossvote. For these voters, the ballot order combination creates different results. In position 3, Bush voters cast votes counted for Kerry while Kerry crossvoters punch disqualified. The number of disqualified votes indicates the maximum number of Kerry crossvoters, up to 24. Assuming all 24 of the precinct 2909 disqualified votes are Kerry crossvoters and, once again, half as many Bush voters also crossvoted, Bush gets back his 12 votes and Kerry nets 12. Accounting for these crossvotes, precinct 2909 voting would have resulted as shown in Table 10.
For the two precincts, Kerry should have garnered 70.03%. Instead he received only 63.72%, a drop of 6.3%. Bush started with 25.7% and ended with 26.0%, or a gain of only 0.315%. The Kerry margin over Bush shrinks by 6.0%. But this scenario began using understated, aftercrossvote results to determine the Bush and Kerry voter proportions! There likely were actually 3 Kerry voters for every Bush voter, so for every 14 Bush crossvoters there should be about 3 times as many Kerry crossvoters. Our first order computation only used twice as many. Recalculating with the 3:1 voter ratio, the Kerry lead increases by 78 votes in the two precincts, a net impact of a 10.87% shift in the margin. The Ohio raw exit polls' disparity with the Kerry vote is 3.35%. By comparison, if a net 1.05% of Ohio Kerry votes switched to Bush, the election outcome was altered. The net impact of crossvoting is significant, especially with switchedvotes. The degree of impact of crossvoting seen in this scenario and the thirdparty crossvoting above certainly brings into question the validity of the election results. The Euclid voting location, in Table 11 below, illustrates twoballotorders without Bush and Kerry collocation. Bush crossvotes count as d or p, Kerry crossvotes count as p or b. In precinct 3943, it appears Kerry lost up to 93 votes to Peroutka. Kerry is collocated with Peroutka, Bush with disqualified. There are no disqualified votes in precinct 3943, so no Bush voters crossvoted. If the ballot order in this case had instead switched Kerry votes to Bush votes, with only one party crossvoting, no direct evidence would exist of crossvoting at the location, excepting statistical evidence of course. In the light of such possible hidden voteswitching, this case is particularly alarming. It illustrates how voteswitching can be completely hidden, unrelated to minor candidate and nonvote results. Was voteswitching intended in this instance? Did someone switching ballots err, thinking this ballotswitch changed Kerry votes to Bush? And undetected at that! This instance forces the question, "How did oneparty crossvoting occur?"
This location also forces the question, "Were up to 93 ballots switched to a different precinct after voting and before counting?" I do not know. Disparity of precinct populations (72 votes to 403) may have driven voters to empty machines in the smaller precinct. But why only Kerry voters? Did poll workers distinguish party affiliations and manipulate wrongprecinct voting? Or, did someone switch the ballots after the voting? If this case is not fraudulent, then Kerry lost up to 93 votes to Peroutka because, suspicious and improbable as it is, only Kerry voters in 3943 crossvoted. A smoking gun like this should cause an election irregularity investigation. Why this did not, and still does not, is a mystery. These examples evidence crossvoting and possible election fraud, and more evidence is interwoven in the following sections. The amount of crossvoting is expected to be random when accidental and unwitting, but if manipulated to alter the outcome, of course the expectation is that it will be nonrandom and biased. Precinct level analysis indicates crossprecinct voting is not randomly distributed, producing one more mystery not easily answered, especially not from data, "Why is crossvoting unevenly distributed?"
Crossvoting changes the results substantially. Crossvoting favors the candidate with the least support. Not every ballot order combination switches major candidate votes. Every switchedvote 'counts' twice! 
Cuyahoga nonvotes included any candidate votes not counted (i.e. hanging chads, other spoilage) and no vote cast for president. In some states, the undervote percentage is well below one percent. Ohio recorded near the highest rate in 2004. Ohio's statewide nonvote rate for evoting was near normal, at 0.76% compared to 1.90% for punch card voters. However, precinct level analysis indicates that many punch card precincts had normal nonvoting percentages. Nonvoting distribution is skewed rather than random and correlates with Kerry support. Figure 3 illustrates the nonvote results for precincts sorted by the level of Kerry support. The nonvote rate is more than three times the normal expectation in precincts with highest Kerry support. Suspiciously, where crossvoting reduces Kerry's vote the most, the nonvote rate is highest. The rate jumps significantly in precincts which reported more than 70% Kerry support.
Figure 4 displays Bush and nonvotes percentages for all Cuyahoga precincts with over 3.6% nonvotes. This sort represents 11.0% of the ballots cast and 27.7% of the nonvotes. Nonvoting is over four times normal in these precincts. Nearly all have over 75% Kerry support, many have over 90% Kerry support. Bush's mean tally in this group is 10.25%.
In Cuyahoga County, Kerry lost a very high, nonrandom proportion of the uncounted votes. This crossvoting/undercounting concentration where it lowers Kerry's tally the most raises suspicion of irregularities and presents yet another mystery, "Why is undervoting concentrated in locations with the highest Kerry support?" It appears Kerry was robbed of votes! 
Multiple ballot order locations constituted 87.6% of the Cuyahoga precincts. Using standard probability (P) notation, the probability that a voter could crossvote, based on actual number of ballots cast, was P = 0.875. Seven of eight ballots were cast at precincts with possible crossvoting, and over 525,000 votes were recorded, 9.2% of Ohio's vote reporting 64.6% Kerry support after the crossvoting. The Cuyahoga County multiple ballot order locations represent 12.75% of Ohio's reported Kerry votes. In summary, seveneights of voters in Cuyahoga County—including more than one of every eight Ohio Kerry voters—could have voted at an adjacent precinct using the wrong ballot order. Of the 525,172 possible crossvoters, 260,988 could voteswitch KerryBush at an adjacent precinct. I wondered, "How many Kerry votes were switched to Bush?" Probability calculations are unabashedly simple. Flip a coin with two sides, the probability that one side will be up is 1/2. For two mutually exclusive events such as heads or tails, P = 0.50. Given five vote options with more precincts than ballot orders at some locations, the probabilities are more complex and yet readily determined. Table 12 presents the random probabilities of major candidate collocation. Of course, at individual locations, the precinct probabilities differ according to which ballot orders are combined with which others. Locations with three precincts and two ballot orders, for example, can have two precincts that switch Kerry votes to Bush votes and only one switching Bush votes to Kerry votes, hence the voteswitching probabilities are KB P = 2/3 or BK P = 1/3. Conversely, where voters can wrongprecinct vote using the same ballot order as their own precinct, the probability that wrongprecinct voters will crossvote is reduced.
When flipping a coin, we are assured that the number of heads and tails are equal. The odds are 50/50, heads or tails, for 100 coin tosses ONLY if both heads and tails are on the coin 100 times! With dice, the odds are one of six, etc. Cuyahoga County election officials decided how many and which candidates were collocated at which locations, who appeared together for each roll of the dice, how many sides the dice had, even which candidate appeared on several sides. A complex pattern of skewed probabilities emerged from analysis of the actual ballot order combinations. Initial analysis revealed that Kerry received 8.9% fewer votes at locations where voters could crossvote. Further inquiries demonstrated that ballotorder combinations, but not ballot orders, had a surprising correlation to the results. When all precincts are sorted by the five ballot orders, the Kerry vote percentage varies normally, from 65.3 to 66.1 percent. That range increases significantly, varying from 60 to 77 percent, when all precincts are sorted instead by ballot order and precinct combinations. The next section addresses this variation in relation to precinct and location crossvote outcome probabilities. Table 13 and Figure 5 illustrate the distribution of crossvoter subsets using percentage of the whole. Almost all voters had nonrandom probabilities of crossvote outcome. The largest subset, 2\2 locations with 27.7% of crossvoters, always has 1.0 probability of location crossvote outcome since only one other candidate can be in the same ballot position. Over 3/4ths of potential crossvoters, 77.6%, voted at locations with only one or two possible crossvote outcomes. Only 1.7% of crossvotes, those at locations with five precincts and five ballot orders, had equal probability (P = 0.25) a crossvote counted for one of four other candidates.

Crossvote outcome varies by precincts rather than locations, therefore I defined crossvote outcome probabilities for each precinct. Analysis with precincts sorted by crossvote probability reveals the impact of crossvoting—both by accounting for how crossvotes tally and by distinguishing voteswitching. I codified wrongprecinct voting using Cuyahoga's majority voter, the Kerry voter. Hence, the shorthand notation Kb, KB, Kd, and Kp represents the four crossvotes, and KK represents wrongprecinct voting or ballot switching with the same ballot order. For example, KB P = 1.0 represents KerryBush voteswitch probability equals 1.0. The datasets use this notation and display analyses of probability sorted subsets. Table 14 presents probabilities of voteswitching at precincts with collocated major candidates. As is readily seen, when the number of ballot orders at the location increases, the voteswitching probability decreases. Random crossvoting has a certain outcome only at locations with two ballot orders. Crossvote outcome can also be certain when nonrandom, if the voter is directed to crossvote or when ballots are precinct switched after votes are cast. At the central tabulation site, these location crossvote limitations do not apply of course, since any two precinct's ballots can be switched. Analysis using location probability subsets identifies location related chain of custody error.
At locations with more precincts than ballot orders, some wrongprecinct votes count as intended. Table 15 presents crossvote probabilities for the ballot order\precinct (BO\P) subsets. The + notation, 2\2+, 3\3+, etc., represents locations with more precincts than ballot orders. The greater the number of precincts, the less likely the wrongprecinct vote counts as intended. Given the subset probabilities in Tables 14 and 15, reconsider the subset population distribution in Table 13. Ballot order subset distribution favors the probability of voteswitching. The two largest groups, the 2/2 and 3/3 locations—over half the population, have P = 1.0 crossvote probability—meaning their KK P = 0.0.
In Cuyahoga County 2004, voters were rolls of the dice, and each vote was an event—one roll of the dice with alarming odds a vote counted opposite the voter's intention. Actual voter numbers in each probability subset, not the precinct averages, define precise overall probabilities and size disparity skews even random crossvote outcome probability. Table 16 presents 2\3 locations sorted by KerryBush voteswitch probability. One striking statistic in this small subset is the disproportionate sizes of the precincts. The ballot order with a 1.0 probability that Kerry crossvotes tally for Bush was assigned to precincts on average with 50% more voters.
If KB P = 1.0
ballot orders are assigned to larger precincts, Table 17 presents countywide crossvote outcome probabilities. The official results indicate 39,388 of 525,172 Kerry wrongprecinct voters would vote as intended, so overall KK P = 0.075. Two specific pairings of crossvotes, Kerry with disqualified and Badnarik with Peroutka, is clearly illustrated by the probabilities. Figure 1 and Table 2 also illustrate probability pairing patterns (further discussed below). In Table 17 the skewed probabilities of the 2\2 subset reflect the overall population size disparities seen in Figure 6 below. The ballot orders were combined such that Kerry and Bush are collocated most often. Significantly more ballot combinations switch Kerry crossvotes to Bush and to disqualified than to the third party candidates. In the largest subset, the 2\2 subset with crossvote outcome P = 1.0, the imbalance is most exaggerated with KB skewed from the random expectation of P = 1/4 to P = 1/3.
Outcome probabilities of wrongprecinct voting favor Kerry to Bush voteswitching.
An important aspect of descriptive statistics is initial examination, assessing basic properties of the data. Finding natural divisions or subsets in a dataset enables comparative analyses. Pairing is an important analytic tool. For example, pairing allows survey of whether wives and husbands agree rather than just whether men and women agree. As seen in the wrongprecinct voting examples (Tables 8 to 11), when Kerry crossvotes switch to Bush for one precinct, an adjacent precinct crossvotes Kerry to disqualified. In like manner, Kerry crossvotes to Badnarik and to Peroutka are paired. These pairings determine crossvote outcome patterns, and examination of the vote results for evidence of the patterns can measure crossvoting and voteswitching. Table 18 presents a comparison between random probability and the actual KB and Kb crossvote probability for the major ballot order and precinct combinations. Note the number of voters in each subset and the relation of the voter numbers to the probabilities, number of voters correlates positively with KB P (0.47) and negatively with Kb P (0.52). The pattern of ballot order combinations favors the KB voteswitch probability. The only subset with a skew slighting voteswitching to Bush is locations with 2 ballot orders and more precincts. Due to crossvote outcome pairing, the Kd and Kp probabilities closely parallel KB and Kb respectively.
Figure 6 presents all precincts with 1.0 crossvote probability sorted by outcome of Kerry crossvotes. The pairing of crossvote outcome probability is apparent by subset sizes. The precinct count and voter population data illustrate the subset deviations from normal distribution. While 123 precincts voteswitch Kerry to Bush, only 76 crossvote Kerry to Badnarik. If the distribution of ballot order combinations were normal, the precinct count and voter numbers subsets would equal near 25% each. Nonrandom distribution of ballot order combinations skews the crossvote outcome probabilities, heavily favoring KB voteswitching. The combinations of ballot orders and precincts favor Kerry to Bush voteswitching. 
Random crossvoting should be just that, random, and an expectation of normal distribution follows. In Cuyahoga County, not only do the combinations of ballot orders and precincts favor Kerry to Bush voteswitching, crossvoting is most evidenced in areas with highest Kerry support. A nonrandom pattern is expected if crossvoting results from manipulations to deprive Kerry of votes. Figure 7 illustrates how precincts with higher voteswitch probability are located in areas of significantly higher Kerry support.
Figure 8 demonstrates how Kerry crossvoting to disqualified is apparently highest in precincts with the highest probability a Kerry crossvoter voted disqualified. Because KerryBush voteswitching is paired with Kd crossvoting at the locations, this crossvoting trend also indicates greater KB voteswitching in areas of highest Kerry support. Nonvotes in Cuyahoga County represents ballots without a vote for President, spoiled ballots, as well as crossvote ballots punched for this unusual, uncounted, nocandidate option. Just as probability sorting evidenced thirdparty crossvoting, a correlation likewise exists for Kd crossvoting probability and nonvote results. For all precincts, Kerry support also correlates (0.42) to the percentage of nonvotes. If about half of nonvoting is Kerry crossvoting, then near one percent of nonvotes were Kerry votes—an alarming amount relative to the number of switched votes needed to reverse the election outcome.
Figure 9 illustrates the relation of ballot order combinations to candidate support. The combinations with the highest probability of voteswitching are located in areas of highest Kerry support. Figure 10 illustrates how the largest populations subsets are the high Kerry support areas with the highest probability of crossvoting. These variables combine to maximize voteswitching in Kerry areas. The factors presented in Tables 5 to 10 must be considered as a whole. Their interrelationships raise strong suspicions of purposeful arrangement of precincts and ballot orders in areas of high Kerry support to facilitate altering the outcome of the election.
On election morning, the dice were loaded and ready. Kerry's losses to random crossvoting were disproportionately high due to higher Kerry support, then compounded by the larger subsets with the highest probabilities concentrated in higher Kerry support areas, then further compounded by a higher proportion of voteswitching precincts. The higher proportion of voteswitching precincts also reduces the proportion of obvious indicator crossvotes to disqualified and the thirdparty candidates, effectively a builtin obfuscation. Roll those dice, and add the possibility of intentional irregularities and ballot switching.
Something is very wrong
with this election's design. If the designers 
To infer the degree of crossvoting and voteswitching, I shifted analysis from descriptive parameters to comparisons of crossvote outcome subsets. Probability sorting provides a refinement for statistical analysis. Crossvote probabilites isolate outcome subsets, providing comparisons to quantify crossvoting. Descriptive analysis revealed the population subsets, how precincts and probability outcomes are paired, and how distinct ballot order combinations present different possible methods for analysis. Precinct pairing at locations facilitates analysis because an expectation of near equal average candidate support exists for geographically adjacent precincts. Probability pairing provides additional useful subsets. Distinct probability sorts of the same population enables further comparisons. Sorting precincts by crossvote outcome produced direct evidence of crossvoting, as depicted again below in Figure 1 illustrating 2\2 precincts sorted by Kerry crossvotes. Sorting by the probability Kerry crossvotes count for Badnarik (Pb P = 1.0) illustrates the fivefold increase in Badnarik votes. Sorting the same precincts by Kp P = 1.0 illustrates 9.5 times more Peroutka votes. Figure 1 clearly infers crossvoting due to Kerry crossvotes. The inferred amount of crossvoting in this comparison is based on an expectation, the vote rate in all the other (P = 0) 2\2 precincts. Vote results significantly depart from expectations in these paired subsets, with under 10% of voters reporting over 38% of Peroutka votes plus over 23% of Badnarik votes. The Kp P = 1.0 subset with 4.9% of possible crossvoters records 34% of the Peroutka votes and the Kb = 1.0 subset with 4.8% of possible crossvoters records 20% of the Badnarik vote.
Descriptive statistics of election results is like a census break down, based on a full tally of a population. Of course, a census does not depend on precinct chain of custody. In a census analogy, a biologist recording parent pairs knows there is an error if there are more fathers than mothers. For election results, the precise 50% ratio of genetic pairings is not expected and precinct combinations are more complex than genetic pairings. Nonetheless, deviation from expected values infers the degree of "error" and statistical methods can quantify crossvoting and voteswitching. Unlike with voteswitching, minor candidate voting is low, therefore one to two percent crossvoting is obvious. Contrastingly, higher levels of major candidate voting can obfuscate significant voteswitching. Variations in candidate support levels influences a complex set of vote result expectations and can further obfuscate irregularities. In Table 19, over onehalf million Cuyahoga County voters, nearly onetenth of the Ohio votes, are sorted by probability of KerryBush voteswitching. The voteswitch probability subsets present a 10% difference in Kerry margin; precincts with some probability of KerryBush voteswitching (KB > 0) have a 10% lower Kerry margin than those with zero possibility. "What portion of this difference is due to voteswitching?" is obviously a necessary analysis. What is the expected difference in the subsets, if any? The margin difference of 27,418 votes is significant, 5.22% of these voters. By comparison, the official Ohio results give Bush a 2.1% victory. (A spreadsheet presents the Table 19 dataset.) The results in Table 19 are unexpected given the data in Figure 7, illustrating precincts with higher KerryBush voteswitch probability correlated to areas of higher Kerry support. Skewed results are expected given the data in Figure 9, illustrating the Kerry support correlation with ballot order combinations. The average number of precincts per location is different for these two subsets, 3.84 for the KB P > 0 subset and 2.94 for KB P = 0. Locations with four and five precincts average lower Kerry support, and their predominant distribution in the KB P > 0 subset skews any expectation of equal results. Understanding the descriptive statistics, especially subsets and their respective variables, is an important first step when considering if subset vote averages are expected to be equal or varied due to variations in neighborhood candidate support. Comparing more delimited subsets can refine expectations that central tendency, dispersion, symmetry, and shape of the data subsets will be equal. While adjacent precincts differ in how ballot chain of custody errors count, their candidate support levels are expected to average near equal. Subsets with paired precincts at each location should average near equal results, and, therefore, provide more conclusive analyses. Different location subsets also present distinct analytic possibilities and problems, and this variation allows addressing diverse questions. The 2\2 population is large and has one possible Kerry crossvote outcome per precinct, providing various definitive comparisons. The 5\5 population is small, a statistical negative, and lacks comparative subsets with identical crossvote probabilities for each precinct. The 4\4 locations provide equal crossvote probabilities, and the precincts provide delimited crossvote probabilities. The 3\3 locations also have several, delimited crossvote probabilities. Locations with three or four ballot orders uniquely allow comparisons of the same data sorted using distinct probability subsets. Locations with more precincts than ballot orders present small, statistically less robust subsets and more complicated determination of expectations. Locations with three precincts and two or three ballot orders reported 166,953 votes representing 1/34th of the Ohio votes (Table 20). At locations with KB P = 0.50 there are two adjacent, paired precincts, at least one with KB P = 0.0. The average Kerry vote is equal for the 2\3 and 3\3 locations when subsets are sorted by Kb crossvote probability. A significant, 6.0% disparity in Kerry margins emerges with the alternate KB probability sort. Bush support increases 3.09% where Kerry crossvotes count for Bush, and Kerry support increases 2.91% with no KerryBush voteswitch probability. (A spreadsheet presents the Table 20 data.) In a subset of 166,953 votes, one of every 34 Ohio voters, the KerryBush margin shifts six percent when the population is sorted by outcomes of wrongprecinct voting. The 4\4 subset consists of 27 identical locations, each with four precincts and four ballot orders. In this subset, the expectation prevails that precinct Kerry results average near the same. One precinct per location cannot voteswitch while three can. Table 21 presents the 4\4 probability matrix with two distinct sorts of the same precincts. Table 22 presents a results comparison for the same probability sorts. The threefourths of precincts where a Kerry crossvote can count for Bush (KB P = 1/3) have a 6.29% lower Kerry margin. The 4\4 locations present about the same 6% Kerry margin disparity seen in the 2\3 and 3\3 subset above. Again, the Kerry and Bush results are near equal as expected when sorted by Kb probability. If crossvoting is random and inadvertent, a statistical expectation prevails, that crossvoting will be approximately equal to probability. Notably in the 3\3 and 4\4 population, thirdparty rates do not increase comparable to the 2\2 subset shown in Figure 1. Instead, the shift is in Kerry and Bush votes. Kerry to third party crossvoting is concentrated at locations where voteswitching is not possible. When the 4\4 population is sorted by Kb probabilities, Kerry voting is equal. Sorting the same population by voteswitching probability distinguishes a 6.3% difference in Kerry margins. This result infers about three percent of Kerry votes were switched to Bush. Random crossvoting can NOT explain the disparities revealed by comparison of distinct crossvote probability subsets. Fraudulent KerryBush voteswitching cannot be ruled out. In a subset of 47,404 votes, the KerryBush
margin
shifts 6.3% Statistics offers inferential methods to test populations against expectations. Unlike in genetic pairing, precisely the same Kerry vote cannot be expected for all precincts. Significance testing determines if variable differences are outside the range of expectation. Population characteristics are parameters and sample characteristics are statistical. Known values of populations, precise descriptive statistics, are often unknown and polling (sampling) is employed to hypothesize population characteristics. With election results, the population parameters are known and the subsets are known samples, providing robust, reliable testing to evidence irregularities. A ttest quantifies difference in a standardized, easytocompare, probability format. A paired ttest of all 1,255 crossvoting precincts indicates an astounding 0.862 probability Peroutka and Badnarik voters are the same population. The actual probability so many voters for different candidates test probable as the same populations is infinitely miniscule. The test results positive with such high probability because the Peroutka and Badnarik vote patterns are largely the same population, Kerry crossvoters. Kerry crossvotes counted as Peroutka and Badnarik votes out weights their actual vote patterns. For every Kb precinct, an adjacent precinct crossvotes Kp, and at locations where one precinct crossvotes, this unusual application of a ttest evidences the other is likely doing so also. Ttests comparing locationpaired precinct data reinforce evidence of a strong correlation between locations and Kerry to thirdparty crossvoting. Ttests applied to Kerry and Bush vote results in Table 20 and Table 22 support the evidence of KerryBush voteswitching. Ttest results and more subset comparisons are highlighted in the spreadsheets.
From the Conyers Report: "...
it is imperative that we examine any and all factors that may have 
Statistical analysis can reveal patterns produced by crossvoting or voteswitching. A potentially useful aspect of the election results for determining numbers of crossvotes, particularly those not evident using results for one race, might be statistical comparison with downticket races using crossvoting probability sorts as defined herein. Precinctlevel pairing of crossvoting in diverse races can be analyzed, especially so where voteswitching produces a down ticket pattern not correlated with party. Also, comparison with 2006 evoting results may reveal patterns of change correlating to punch card crossvoting in previous elections, especially regarding spoilage rates. Given the number of miscounted 2004 votes in Cuyahoga County, results in other Ohio counties and other elections need to be analyzed for irregularities, especially wherever more than one ballot order was employed at a punch card voting location. The same needs to be accomplished for past Ohio elections. The results herein bring into question all past Ohio punch card voting. The methods presented enable a review of past punch card voting for ballotbox stuffing as discussed herein, either casting at or switching ballots to the wrong precinct. This study has not considered the history of decisions that created the Cuyahoga County election. Given the irregularities noted, the decisions in that process, particularly organization of precincts, ballot orders, and locations, and why these factors combined as they did to Bush's advantage, should receive official review in the light of the postelection results evidencing crossvoting. Because the situation resulted in election results different from the votes cast, an official inquiry into all aspects of the process should take place. In particular, the strong correlation between minority populations and both nonvote percentages and crossvoting also requires a civil rights investigation. I did not anticipate the complexities of Cuyahoga County's election organization or the resultant amount of work required to fully and accurately answer the questions first posed. The number of Ohio Kerry votes switched to Bush votes remains to be fully quantified statewide. While a precise answer may not be attainable everywhere, statistical analysis can provide a useful answer. Crossvote outcome probability sorting quantified obvious chain of custody error in the results. The degree of miscounting is far more than I initially thought, more than would be expected under random circumstances, and not random at all. The degree of voteswitching exceeding the election margin in several large subsets is especially alarming. Given the Presidential election hinged on the Ohio result, crossvoting certainly deserves further investigation for all precincts in Ohio. Until all previous punch card elections in Ohio are analyzed, how flawed Ohio elections were remains a mystery. April 28 , 2008. Analyses and research continues. I will continue updating this page. Highlighted cells in the spreadsheets display analyses not yet presented herein. More charts are also found in the spreadsheets and spreadsheets will update also. 
The 2004 Ohio Presidential voting results do not accurately reflect voter intentions. In Cuyahoga County, the election was flawed and the design appears to have been manipulated. At locations with several ballot orders in use, many votes were cast by voters crossing precincts, hence counted other than as intended. At precincts with the highest Kerry support, the percentage of uncounted votes is inexplicably high. The obvious inference—intentional manipulation produced concentrated undercounting, crossvoting, and voteswitching in areas of highest Kerry support—cannot be ignored in the face of the evidence and statistics. The possibility that ballots were switched to different precincts, postvoting to effect voteswitching, must be considered in a complete chain of custody context. Many individual ballots resulted in a voteswitch, a twovote margin difference from the intended result. Switchedvotes cast for Kerry and counted for Bush had twice the impact as their actual occurrence, by each subtracting one from Kerry and adding one to Bush. Bush and Kerry votes also went uncounted as nonvotes or were miscounted as minor candidate votes. A high percentage of all Cuyahoga County votes were cast at locations with multiple ballot orders. The manner in which precincts and ballot orders were combined increased the probability of a Kerry crossvote being recorded as a Bush vote. Quantitative analyses of candidate votes and of nonvote percentages evidence the crossvoting and the patterns of crossvoting and voteswitching. Sorting locations and precincts to their specific crossvoting probability subsets reveals intended voting patterns and the degree of crossvoting. The combinations of ballot orders and precincts at polling locations enables quantitative analysis of crossvoting and voteswitching. The complexity of the election's organization—the great number of combinations of ballot orders and locations—also makes the task of determining the number of crossvotes laborious and complex. While that process is not concluded herein, the procedures so far taken in this study define the process. This process may be more easily applied to other Ohio counties given lesscomplex ballot order combinations. Any official inquiry into the 2004 irregularities needs to be independent of political interests, and monitored by political interests. The fact that the irregularities discussed herein are known and have been reported to multiple jurisdictions and law enforcement entities, and yet no official inquiry into the election has occurred, illustrates the broader failure of the current election process and judicial system to respond to election fraud and irregularities or to hold officials accountable for their actions. Polling places should never have been arranged such as in Ohio, with multiple ballot orders and separate casting and counting devices. Measures are required to prevent the possibility of similar future flawed election designs. To this end, control of elections should be removed from competing political interests and actors to politicallyindependent processes, with at the least, independent and political oversight of elections. Many more conclusions remain to be made as study and analysis continues. The 2004 Ohio election ballots must be preserved to allow further investigations. If this study illustrates anything, hopefully it is the degree to which this problem has not yet been fully considered, and the complete failure of officials to respond. During an era of new voting system technologies and reforms, careful consideration of past errors may prove useful in avoiding their repetition and in preventing future abuses of process and power. The 2004 Ohio Presidential election remains to be fully investigated. The blatant evidence of irregularities and unfairness of organization continues to be ignored by most jurisdictional authorities informed of the evidence. I thank those few authorities pursuing this matter further. 
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