Using aggregate measures to identify election night corruption in Japan, Canada, and the United States

Though the Nevada and Texas stories presented above are part of the political lore of the United States, it is noteworthy that there are no examples of similar stories of corrupt campaign officials in Japan facilitating the illegal manufacture or destruction of ballots, sufficient to change an outcome of an election. This lack of such examples in Japan stands out given the notorious corruption of Japanese politics generally. Fortunately, it is possible to go beyond stories and analyze the occurrence of election night corruption by looking for distinctive evidentiary trails such as:

  • 1 a disproportionate number of ultra-close races compared to very close races;
  • 2 one political party winning a disproportionate number of ultra-close races compared to very close races;
  • 3 a correlation between the winners of ultra-close races and their party’s control of the local electoral machinery.

A first and obvious test, then, for election night corruption is to compare the number of ultra-close races (defined as victory margins of less than 0.5 percent) against the number of very close races (victory margins less than 2.5 percent). 1 group races into half-percent categories, creating, for example, 20 categories of victors of those that won by 10 percent or less. These categories can then be compared to see if ultra-close races significantly differ from very close races. Comparing similarly situated races, for example, all races won by 2.5 percent or less, controls for the many factors, legal or illegal, that can affect the closeness of a race generally. Because factors other than election night corruption cannot distinguish between a very close race (victory margin of less than 2.5 percent) and an ultra-close race (victory margin of less than 0.5 percent), the differences that do show up are likely caused, in part, by election night corruption.3

Thus, in jurisdictions in which there is no election night corruption, the distribution of the margins of victory, plotted according to half-percent increments should produce a distribution of only incremental changes between half-percent intervals. These incremental changes would reflect the impact of all of the factors that generally affect the closeness of races. There might be twice as many 1 -percent victories as there are 10-percent victories because races in that jurisdiction are quite competitive. On the other hand, there might be twice as many 10-percent victories as there are 1 -percent victories because one party dominates races in that jurisdiction or because bipartisan gerrymandering has eliminated most of the competitive districts. Under either scenario, however, the changes in half-percent categories moving from 1 percent to 10 percent should be incremental. None of the factors (other than election night corruption) that affect the closeness of races generally are able to distinguish between victories of 0.5 percent and victories of 1 or 2 percent. Thus, if election night corruption is not occurring, the difference between the number of races won by 0.5 percent and races won by 1 percent should be consistent with the trend line of incremental differences between, for example, races with a 1.5-percent and 2-percent margin of victory.

In contrast, if election night corruption is common there will be a sharp break between the number of ultra-close races and the number of very close

Distribution of margins of victory in Japan, Canada, and the United States

Figure 6.1 Distribution of margins of victory in Japan, Canada, and the United States

races, rather than an incremental change between these two categories. Figure 6.1 reports aggregate totals for Japan, Canada, and the United States, scaling the results so that all three countries can be placed in comparable positions on the graph.4 Figure 6.1 also truncates the distribution, showing only the results for the first 20 categories of half-percent increments (all races with a 0-10-percent margin of victory). There is no sharp or disproportionate increase for the ultra-close races (category 1). Japan, in contrast to the United States and Canada, shows a skewing in favor of close races which is explained by the multi-seat electoral system that Japan used until the 1993 elections. However, this trend occurs across all ultra-close and very close races, creating no suggestion that election night corruption occurred. This first cut of the data suggests that election night corruption is not occurring in Japan, the United States, or Canada.

It is possible, however, for significant election night corruption to occur without altering the overall distribution of margins of victory. This can occur if one party disproportionately benefits from election night corruption. For example, election night corruption might be disproportionately used by one party to convert what would have been ultra-close victories for their opponents into ultra-close victories for their candidates. It stands to reason that election night corruption is more likely to be attempted when an opponent’s margin of victory would have been small and easy to reverse. If this scenario is correct, then the total number of ultra-close races would not be disproportionately larger, but the party distribution of ultra-close races would stand out in contrast to the party distribution of very close races. Figures 6.2, 6.3, and 6.4 break down the data for each country reported in Figure 6.1 into partisan groups.

The Japanese data shows a consistent pattern across all percentage groupings of victories. The LDP and affiliated independents maintain a consistent and small advantage over all non-LDP candidates which is consistent with the

Margins of victory in Japan, by political party

Figure 6.2 Margins of victory in Japan, by political party

Margins of victory in Canada, by political party

Figure 6.3 Margins of victory in Canada, by political party

fact that the LDP has won a small majority of the seats over time also. This data shows no evidence of election night corruption.

Similar results are obtained looking at Canadian data, broken down into four party groupings. No strong pattern emerges of one party doing better in ultra-close elections in contrast to very close elections.

The data for the United States, however, is intriguing. There are always more Republican victors than Democratic victors for every category of close races from 0- to 10-percent margins of victory except for the closest category, those candidates who won by less than 0.5 percent of the vote. There, for the only time, do the Democrats win more races than the Republicans. Though it is hard to see in Figure 6.4, there is also a sizeable jump in the number of winners

Margins of victory in the United States, by political party

Figure 6.4 Margins of victory in the United States, by political party

in the ultra-close category for the candidates of other parties, a category that includes all independents and candidates who run on party lines other than the Republican and Democratic parties. Thus, of the three countries, only the United States shows a footprint of possible election night corruption, but are these results just random variation or are they statistically significant? After all, the number of opposition victors in Japan and Conservative Party victors in Canada also drop for the ultra-close category. At what level is it possible to be confident that these patterns aren’t just random noise in the data?

It is possible to use the data to calculate a trend line that will predict the number of ultra-close winners for each party grouping. This predicted number can be compared to the actual number of ultra-close winners, and the difference between these numbers can be assessed to see if the difference is statistically significant, meaning that the results are less likely to be just random noise in the data. Thus, for example, the Democrats in the United States won 365 seats with margins of victory of 2.5 to 3.0 percent. They won 393 seats with margins of 2.0 to 2.5 percent. They also won 383, 385, and 383 seats in the next categories of 1.5-2, 1.0-1.5, and 0.5-1.0 percent. I used a statistical procedure that uses all five observations, weighting later observations more, to predict the number of victors in the 0-0.5-percent margin of victory category. This predicted value was 386.8 victors in the ultra-close category, with a 95-percent confidence interval of the actual number being within the range of 363.5 to 392.1 victors. In reality, the Democrats won 425 seats in this category, suggesting that the number of Democratic victors who won by less than 0.5 percent of the vote is both anomalous and statistically significant. Similar calculations for all nine party groupings are reported in Table 6.1.

The results reported in Table 6.1 seem like stunning evidence of election night corruption occurring only in the United States and being centered in the Democratic Party and in third parties and independents. Indeed, some authors have also speculated that election corruption might be more common in the

Table 6.1 Predicted and actual numbers of ultra-close races, by party in Japan, Canada, and the United States











Democrats US






Republicans US






Other US



+ 16.5



LDP Japan






Other Japan






Liberals Canada













NDP Canada






Other Canada






Democratic Party in the United States (Sabato and Simpson, 1996,299; Fund, 2004, 6-7). Similar drops in the number of Canadian Conservative victors or opposition victors in Japan, in contrast to the US data, are not statistically significant. However, as a robustness check for these results, I calculated every half-percent category of victory between 0 percent and 10 percent victories (a total of 20 categories). For each calculation, 1 used the trend line for the five prior categories. Of a total of 180 calculations (20 calculations for each of 9 party groupings), 64 of these calculations produce statistically significant results. In addition, these results are also affected by the number of categories included in the trend line calculations. 1 used the five previous categories to create trend lines, but slightly different results obtain if only the three previous categories, the ten previous categories, or all previous data are used. These varied results show that the number of victors in a certain margin of victory category are fairly volatile, and calculations of statistical significance should not be the end of the analysis but rather a suggestion of a possible relationship that needs further investigation.

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