The 2004 Election:  Analyses, Summaries, Charts, and Spreadsheets
 APPENDICES: How Kerry Votes Were Switched to Bush Votes  Return to Article

NOTICE: Under construction and editing.
This area contains portions of initial article.
Appendix A is new. Appendix A. Notation Index and Definitions

 Notation Key. 2\2 two precincts at a location with two ballot orders 3\3 two precincts at a location with two ballot orders 4\4 two precincts at a location with two ballot orders 5\5 two precincts at a location with two ballot orders b Badnarik B Bush d Peroutka K Kerry K-b Kerry to Badnarik K-B Kerry to Bush K-B P Kerry to Bush vote-switch probability K-b P Kerry to Badnarik cross-vote probability K-bB Kerry to Badnarik or Bush K-d Kerry to disqualified K-d P Kerry to disqualified probability K-K Kerry to Kerry K-p Kerry to Peroutka p disqualified P Probability P = BO Precinct number equals number of ballot orders P > BO Precinct number greater than the number of ballot orders x\x x precincts at a location with equal ballot orders x\x+ x precincts at a location with more than x ballot orders

One of my first impressions about the election results vocabulary was the variation in definitions, sometimes impeding clear discussion. I present this vocabulary discussion in the interest of avoiding confusion from language, and in recognition of probable and known use of these term with different meanings elsewhere. I hope it also serves as a useful primer for readers new to the topic.

ballot order, the sequence of candidates presented to a voter.  This may be on paper ballots, on a voting device, or on a touch screen.  Ballot orders are rotated in elections so each candidate has the same number of occurrences in the order in each position, to defeat a statistical advantage of being first in an order.

ballot position, the relative placement of a candidate in a ballot order sequence, with top being first position.

butterfly ballot, punch card ballot system with candidates displayed on two opposing pages with punch card rows between the candidate names.  In the Florida 2000 Presidential contest, many voters selected the wrong punch card hole in the center because candidates in the same race appeared (and obviously went unnoticed) on the opposite page. Al Gore was second on the left page and the third punch hole, while Buchanan was first on the right page and the second punch hole. Further information and illustrations at Florida 2000 Presidential Vote.

crawl, with reference to punch card voting ballots, the sequence difference between two or more ballot orders. Crawl 1 ballot orders have a difference of one, i.e. bBKdp and BKdpb. Crawl derives from caterpillar ballot.

caterpillar ballot, Ohio's own calamity named with allusion to Florida's infamous butterfly ballot.

wrong-precinct vote, a vote cast in one precinct for a candidate or option and counted using equipment in a different precinct. A wrong-precinct vote may or may not count as intended, unlike a cross-vote.

cross-vote, a vote cast for one candidate/option and counted as a vote for another.

differential,

disparity,

disqualifed, a ballot position without a candidate in Cuyahoga 2004. This postion was intially assigned to Ralph Nader When Nader was disqualified, Ohio Secretary of State Blackwell litigated to preserve the empty position on the ballot.

nonvoter, a person not allowed to vote or a person who does not vote.

non-vote, the difference between ballots cast and total votes counted in a specific race. Non-vote tallies combine the number of voters ignoring a race along with any equipment failures to fully count the votes cast. Non-vote totals can be a useful indicator of voting irregularities, such as spoiled ballots or punch card cross-voting.

undercount, n. the number or percentage of votes cast but not counted, an insufficient count.

undervote, under-vote, the number of voters not participating in the vote for a race or option on the ballot. In general usage, uncounted voting is synonymous with non-votes, and the difference between ballots with uncounted, cast votes and no vote cast is not distinguished.

vote-switch, a cross-vote between two specific candidates, a cross-vote having a double impact of subtracting from one candidate's tally while adding to the other's tally, especially significant with regard to close contenders. Use herein typically references Kerry to Bush vote-switches.

Under-Votes: ballots that contained no selection for a race, resulting when a voter intentionally omits voting for a candidate.

residual Votes, uncounted ballots, plus unmarked ballots, plus over-voted ballots

spoilage,

precinct,

location,

e-vote,

z-score,

undervoting,

undercounting,

non-vote,

probablity,

Ballot Order\Precinct Combinations

#  Appendix B. Ballot Orders and the Number of
Ballot Orders and Precincts per Location.

The following tables present election results data sorted by ballot orders. Each precinct had a specific ballot order. I subdivided the ballot order subsets according to the number of ballot orders at the location of the precinct.  These major subsets and their corresponding notation are introduced in Table C1. Because different subsets have different probabilities of votes being changed by cross-voting, distinguishing the subsets is necessary. The probabilities of cross-voting are explained in detail below, following introduction of the subsets.

 Table C1.  Ballot Orders -- Major Subsets Key. Below, the precincts are represented three times, as distinguished by the three color-coded row groupings. The first column introduces new notation as defined in the second column. all Every precinct. all x\x All locations with 2 or more ballot orders and an equal number of ballot orders and precincts (x=x). all x\x+ All locations where the number of precincts is greater than the number of ballot orders. 2-5\all All locations with more than one ballot order. Precinct cross-voting can alter votes in this subset. 1\all All locations with only one ballot order. wrong-precinct voting cannot alter votes here.

In this table, the results are first analyzed without sorting by ballot orders. The first four rows below present a summary of the major subsets. Then all the precincts are sorted by the number of ballot orders at the location. Each number-of-ballot-orders subset is then subdivided by the same comparative subsets.

When the number of precincts is greater than the number of ballot orders, the cross-vote probabilities change. For example, 2\3+ precincts have a lower vote-switch yield than 2\2 precincts because cross-voters may have the same ballot order in another precinct. Note that the 2\2 precincts are in higher Kerry support areas, amplifying the vote-switch yield. Note also that the indicators of the cross-vote rate, 3rd party and non-votes, are also higher in the 2\2 subset.

These results presented another mystery. Why isn't the pattern normally-distributed, random? What forces are at work skewing this data? It seemed, the more I looked, the more questions arose.

 Locations % Kerry % Bush % b % d % p count all 65.65 32.05 0.277 1.777 0.235 1427 all x\x 66.19 31.30 0.307 1.941 0.307 793 all x\x+ 61.59 36.51 0.247 1.477 0.139 457 The first row is the summary. Below it are the two subsets of the same data. The same subdivision is provided below for locations with 2, 3, and 4 ballot orders. 1\all 73.40 24.05 0.219 2.169 0.162 177 This small subset of 177 precincts includes locations with 1 ballot order and 1, 2, or 3 precincts. What these precincts have in common is one ballot order--no cross-ballot voting can occur at these locations, and even when wrong-precinct voting occurs, the votes count the same as cast. 2\all 69.27 28.04 0.343 2.000 0.346 502 2\2 70.97 26.03 0.377 2.175 0.446 351 2\3+ 65.36 32.65 0.264 1.600 0.116 151 In locations with 2 ballot orders, the subset with only two precincts at the location (2\2) are allocated where Kerry's vote is 5.6% higher (after cross-voting). 3\all 67.59 32.74 0.262 1.723 0.187 465 3\3 64.62 33.12 0.274 1.762 0.251 314 3\4+ 72.56 31.96 0.242 1.643 0.129 151 In the 3 ballot group, Kerry's vote is 7.9% higher with more precincts than ballot orders. 4\all 55.96 42.36 0.228 1.253 0.184 234 4\4 58.71 39.58 0.206 1.315 0.177 108 4\5+ 53.58 44.77 0.247 1.199 0.191 126 In the 4 ballot group, Kerry's vote is 5.1% lower with more precincts than ballot orders. Because the number of locations with 5 precincts is small, I do not subdivide this group. 5\all 53.17 45.41 0.199 1.145 0.068 49 Locations % Kerry % Bush % b % d % p Count

The Cuyahoga County precincts, sorted by ballot orders, are presented in five sections in Table 14 below. Ballot order should be an independent variable, without relation to voting results. This is the premise behind rotation of ballot orders, to make certain that no candidate is favored by order placement.   This sorting of the election results tests that premise.

As was readily seen, locations and ballot-order combination have a far greater impact on the results than does a particular ballot order. The Kerry vote percentage for "all" precincts varies from 65.25 to 66.13 percent when distinguished only by ballot orders. That range increases greatly, from 59.78 to 77.06, when sorted into location subsets. These statistics indicate a non-random pattern in the voting results in relation to presumably rando, independent variables. One consistent pattern is lower Kerry votes where cross-voting can occur, from 6.27 to 12.34% lower.  Another consistent pattern is the difference between locations with the same number of precincts as ballot orders and those with more precincts than ballot orders. Locations with an equal numbers of ballot orders and precincts are found in areas with more Kerry support, from 3.2 to 6.0% more. Correlations are found when the probabilities of cross-voting are considered.

The precinct totals for major subsets are in the lower 4 rows, below the totals in the "all" row. The x\x row represents all precincts where cross-voting can occur AND where the number of precincts equals the number of ballot orders, the sum of 2\2, 3\3, 4\4, and 5\5. The x\x+ row is all the other precincts where cross-voting can occur AND where there are more precincts than ballot orders. Those precinct counts are consistently lower than the x\x subset. In Cuyahoga County, the "no possible cross-voting" scenario is in the extreme minority, less than 1 in 8. In Table 15, the first three rows with counts are locations with only one ballot order. The 1\all row at the bottom sums the precincts with one ballot order, totaling 177 of the 1427 precincts considered.

Table 15 tallies the number of ballot orders and precincts at the polling locations. The notation in Table 15 expands on the notation introduced in Table 13, with a forward slash separating the number of ballot orders and number of precincts (ballot orders\precincts).  Hence, 2\3 represents locations with two ballot orders and three precincts.

 Table 15.  Cuyahoga County Ballot Orders and Precincts. Ballots and Precincts Ballot Orders Totals bBKdp BKdpb KdpbB dpbBK pbBKd 1\1 22 23 35 31 24 137 1\2 6 8 2 15 7 36 1\3 3 0 0 3 0 6 2\2 68 74 71 66 70 352 2\3 41 26 28 18 18 131 2\4 6 2 0 3 9 20 3\3 57 70 55 64 68 314 3\4 23 19 26 17 23 108 3\5 4 5 6 11 4 30 3\6 1 3 0 0 2 6 3\7 0 2 3 2 0 7 4\4 19 19 22 25 23 108 4\5 19 20 20 18 23 100 4\6 3 4 4 3 3 17 4\9 2 3 3 1 0 9 5\5 4 4 4 4 4 20 5\6 2 2 3 3 2 12 5\7 1 2 2 1 1 7 5\10 2 2 2 2 2 10 all 283 288 286 287 283 1427 x\x 148 167 154 159 165 793 x\x+ 104 90 97 79 87 457 2-5\all 252 257 251 238 252 1250 1\all 31 31 35 49 31 177

The precinct totals for the major subsets are in the lower 4 rows, below the totals in the "all" row. The x\x row represents all precincts where cross-voting can occur AND where the number of precincts equals the number of ballot orders, the sum of 2\2, 3\3, 4\4, and 5\5. The x\x+ row is all the other precincts where cross-voting can occur AND where there are more precincts than ballot orders. Those precinct counts are consistently lower than the x\x subset

Pasteboard
Portion of previous version of this writing. Degree of Metamorphosis in the Vote Count

The previous sections presented the differences in the probabilities of vote-switching for different combinations of ballot orders and precincts, factors influencing the degree of metamorphisis in the voting. The only subset with no possible cross-voting or vote-switching is locations with only one ballot order.  Collocated major party candidates, switched-votes, produce the greatest impact on the vote by both subtracting and adding a vote to the contenders.

Sort by Probability of Votes Being Switched.

The next table separates the 2\2 locations into 2 groups, those where the major candidates are collocated on the ballots (locations with P = 0.5) or not so (P = 0.0). The first column in Table 18 is the probability that a cross-vote at a 2\2 location will switch from Kerry to Bush or vice-versa. Simply put, if you are in a P 0.5 location and you cross precincts and punch a vote for Kerry, your vote is switched to Bush or disqualified (P = 0.5), depending on which of the two precincts you vote in. If you are in a precinct in the P = 0.0 location row, a Kerry vote will be tallied for Badnarik or Peroutka and the probability of your vote switching to Bush is zero. (Note the differences in the Badnarik and Peroutka percentages in the different probability categories within the 2\2 group, evidencing the cross-voting pattern.)

 Table 18.  Locations with 2 Ballot Orders and 2 Precincts. Location P Precincts Votes % Kerry % Bush % b % d % p 0.5 222 735 70.30 27.18 0.212 2.161 0.145 0.0 128 710 71.85 24.16 0.690 2.194 1.104

A surprising and alarming aspect of this breakdown is the non-random distribution of the ballot order combinations.

For some reason, the subset where major candidate votes
can be switched is two-thirds larger, 220 precincts to 130.

Since these are precincts with about 3/4 Kerry support, Kerry's loses to cross-voting are proportionately high. The lose is compounded by the higher proportion of precincts where major candidate vote-switching can occur.  At 2\2 P = 0.5 locations, one precinct has a 1.0 probability of Kerry cross-votes going to Bush, and one has 0.0 probability. Therefore 110 of 352 precincts have a 1.0 probability that major candidate cross votes will switch.

The random probability of 0.250 has been augmented
to P = 0.31250 by the ballot order distribution.

Lesson Four:  Disproportionately greater ballot order combinations that

This disparity makes it more difficult to determine how many votes were switched and reduces the number of indicator cross-votes in proportion to undetected switched votes. At this point in the study, I really wondered if someone was intentionally trying to obfuscate the true amount of vote-switching.

Something is very wrong with this election's design. If the designers

Table 19 presents again the 2\3 locations with Kerry-Bush cross-voting. The most striking statistic in this summary is the disproportionate sizes of the precincts. The ballot order with a 1.0 probability that Kerry cross-votes tally for Bush was assigned to precincts on average with 50% more registered voters. For each P = 1.0 precinct there are 2 P = 0.0 precincts at these locations. Given equal sizes of precincts and turnout, the random probability of a Kerry vote being switched to a Bush vote is 0.333. In this subset, the probability that a random Kerry voter's cross-precinct vote would be switched to Bush (0.25) has increased to 0.4220 due to precinct size differences.

Table 20 presents the 3\4 subset, where the random vote-switch probabilities are lower than for the 3\3 subset because 1/6th of cross-precinct votes will be counted for the same candidate as intended. At the same time, in some precincts, the probability that a Kerry vote can be switched to a Bush vote is doubled. In the 3\4 subset, locations have either 1/3, 1/4, 1/6, or 1/12 probability that a Kerry cross-vote will be switched to a Bush vote.

 Table 20. Locations with 3 Ballot Orders and 4 Precincts P Count Votes % Kerry % Bush % b % d % p 1/12 16 6527 62.43 35.91 0.245 1.272 0.138 1/6 28 11856 66.66 31.12 0.245 1.856 0.127 1/4 32 14625 58.61 39.64 0.198 1.409 0.150 1/3 32 12161 70.89 26.86 0.214 1.784 0.255

Once again, the locations with the highest Kerry support have the ballot order combinations with the highest probability of a Kerry cross-vote switching to a Bush vote. Additionally, far more than the random expected percentage of locations have ballot orders with higher probabilities of Kerry to Bush switches. Table 21 presents a comparison of the random and actual number of precincts sorted by K-B vote-switch probability.  Nearly double the expected number of precincts have the highest probability, 0.333.

 Table 21. Random vs. Actual Location Distributions. K-B P = 1/12 1/6 1/4 1/3 Random 16.7% 33.3% 33.3% 16.7% Actual 14.8% 25.9% 29.6% 29.6%

Further analysis of the correlation of Kerry support with the probability that a Kerry cross-vote switches to a Bush vote (K-B probability) revealed the trends seen in the Table 22 below. Variation in the K-B probability has a higher correlation with the number of votes in the subdivisions than with the actual percentage of Kerry support. The K-B probability correlations to the variables are: % Kerry = 0.494, Votes Cast = 0.800, % Non-Votes = 0.426. Note the percent of non-votes. In the precincts with 90% Kerry support, the non-vote is over 3%, compared to less than 1% in precincts with less than 40% Kerry support.

 Table 22.  3\4 Locations Sorted by Kerry Support. % Kerry Support Votes Cast K-B Probability % Non-Votes 90's 8,575 0.228 3.079 80's 7,687 0.216 1.886 70's 11,476 0.245 1.743 60's 9,913 0.208 1.261 50's 12,419 0.243 1.361 40's 5,938 0.210 1.044 < 40 6,608 0.190 0.969

The precincts with zero probability of a vote being switched to a third party candidate indicate the actual support levels of the third party candidates. Table 23 presents the statistics for 2\2 locations. The sorts illustrates the shift from 0.14% support for Peroutka in precincts with no Peroutka cross-voting up to 1.10% support when cross-voting to Peroutka is possible. Obviously, at 2\2 all locations, of the vote going to Peroutka about 0.34% of the 0.48% is cross-voting. In the 111 of 350 precincts with cross-voting to Peroutka, the rate is about 0.95% of votes (1.10 - 0.15).

 Table 23. 2\2 Statistics Sorted by Precinct and Location Probability (Table reflects Jan. '06 Spreadsheet Updates.) Set: Subset: precincts votes % b % B % K % d % p 2\2 all all 350 145,461 0.38 26.12 70.85 2.17 0.48 K-B P=0 all 239 98,146 0.44 25.64 71.05 2.23 0.64 K-B P=0 L P = 0 128 51,011 0.69 24.16 71.85 2.19 1.10 K-B P=0 L P = 0.50 111 47,135 0.18 27.24 70.17 2.26 0.15 K-B P=1 all 111 47,315 0.25 27.12 70.43 2.06 0.14

Pasteboard

Portion of previous version of this writing.

In this table, the results are first analyzed without sorting by ballot orders. The first four rows below present a summary of the major subsets. Then all the precincts are sorted by the number of ballot orders at the location. Each number-of-ballot-orders subset is then subdivided by the same comparative subsets.

When the number of precincts is greater than the number of ballot orders, the cross-vote probabilities change. For example, 2\3+ precincts have a lower vote-switch yield than 2\2 precincts because cross-voters may have the same ballot order in another precinct. Note that the 2\2 precincts are in higher Kerry support areas, amplifying the vote-switch yield. Note also that the indicators of the cross-vote rate, 3rd party and non-votes, are also higher in the 2\2 subset.

These results presented another mystery. Why isn't the pattern normally-distributed, random? What forces are at work skewing this data? It seemed, the more I looked, the more questions arose.

 Locations % Kerry % Bush % b % d % p count all 65.65 32.05 0.277 1.777 0.235 1427 all x\x 66.19 31.30 0.307 1.941 0.307 793 all x\x+ 61.59 36.51 0.247 1.477 0.139 457 The first row is the summary. Below it are the two subsets of the same data. The same subdivision is provided below for locations with 2, 3, and 4 ballot orders. 1\all 73.40 24.05 0.219 2.169 0.162 177 This small subset of 177 precincts includes locations with 1 ballot order and 1, 2, or 3 precincts. What these precincts have in common is one ballot order--no cross-ballot voting can occur at these locations, and even when cross-precinct voting occurs, the votes count the same as cast. 2\all 69.27 28.04 0.343 2.000 0.346 502 2\2 70.97 26.03 0.377 2.175 0.446 351 2\3+ 65.36 32.65 0.264 1.600 0.116 151 In locations with 2 ballot orders, the subset with only two precincts at the location (2\2) are allocated where Kerry's vote is 5.6% higher (after cross-voting). 3\all 67.59 32.74 0.262 1.723 0.187 465 3\3 64.62 33.12 0.274 1.762 0.251 314 3\4+ 72.56 31.96 0.242 1.643 0.129 151 In the 3 ballot group, Kerry's vote is 7.9% higher with more precincts than ballot orders. 4\all 55.96 42.36 0.228 1.253 0.184 234 4\4 58.71 39.58 0.206 1.315 0.177 108 4\5+ 53.58 44.77 0.247 1.199 0.191 126 In the 4 ballot group, Kerry's vote is 5.1% lower with more precincts than ballot orders. Because the number of locations with 5 precincts is small, I do not subdivide this group. 5\all 53.17 45.41 0.199 1.145 0.068 49 Locations % Kerry % Bush % b % d % p Count