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Identifying Electoral Fraud: A Novel Test and New Data From Nigeria
Unformatted Document Text:  type of fraud, which could potentially be traced to named individuals, but are not surprised to find that other mechanisms of fraud could play an important role in areas for which we cannot reject the null of a “clean” election. Figure 9 suggests a similar narrative with respect to differences between urban and rural areas: A number of questionable ward sheets come from Jos-North, a densely populated urban local government area. More generally, we find dubious digit sequences not only in rural, but also in many urban areas, and a logit regression of our indicator of potential manipulation on an indicator for urban areas, coded on the basis of a 2003 map of Plateau state (Satod Cartographic Consultants, 2003), even yields a positive, although statistically insignificant, coefficient. This stands in contrast to the observations of election monitors in 2003, who generally concluded that electoral fraud affected rural areas most severely. Most observers noted that flagrant violations of rules at the polling stations were much more likely to occur in rural as opposed to urban areas, because international election observers were far more prevalent in cities (Kew, 1999). But this suggests that in rural areas, manipulation of return sheets was likely to be unnecessary in areas where fraud occurred. In larger urban areas (like the city of Jos), on the other hand, manipulation of election results was more likely to occur behind closed doors, at ward-level collation centers. Arguably, different types of fraud can serve as substitutes for one another: In urban areas, digit manipulation was more likely to occur on ward sheets than in rural areas, where such fraud was unnecessary. Finally, we assess the extent to which digit pairs exhibit repetition or adjacency across wards. Figures 11 and 12 use data for Nigeria, but are equivalent in design to figure 3. Surprisingly, we find no solid evidence of return sheets with too few digit repetitions, nor do we detect an overabundance of adjacent digits. (Recall that we can expect a small number of wards to exceed the confidence bound purely by chance.) We do, however, find that in a large number of wards, digit pairs do not often enough bridge a distance of more than one. When we look at several columns for each ward return sheet (PDP votes, number of registered voters, and total vote count), we can identify 17 wards in which pairs of non-neighboring digits occur suspiciously infrequently. How can we interpret the fact that pairs of adjacent numerals are sufficiently rare, digit repetition is as common as it should be, and yet we find a good number of return sheets on which pairs of non-adjacent numerals are lacking? We argue that this is, to some ex- tent, a reflection of the statistical power associated with each measure. Even for relatively small wards, the expected number of pairs of non-adjacent digits is fairly large, at least in comparison to the expected number of pairs of repeated or adjacent digits, and so the 95% confidence bound is relatively unforgiving. Small wards need to lack digit repetition or ex- hibit adjacency to a very substantial degree in order for us to be confident enough to reject the null hypothesis of a fair election, while a less extreme insufficiency of non-neighboring digits could push the ward beyond the 95% confidence bound. 5 Conclusion This paper derived and applied a method to detect manipulation of electoral return sheets. We showed that we can expect the last digits of electoral results to occur with equal frequency 20

Authors: Beber, Bernd. and Scacco, Alexandra.
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type of fraud, which could potentially be traced to named individuals, but are not surprised
to find that other mechanisms of fraud could play an important role in areas for which we
cannot reject the null of a “clean” election.
Figure 9 suggests a similar narrative with respect to differences between urban and rural
areas: A number of questionable ward sheets come from Jos-North, a densely populated
urban local government area. More generally, we find dubious digit sequences not only in
rural, but also in many urban areas, and a logit regression of our indicator of potential
manipulation on an indicator for urban areas, coded on the basis of a 2003 map of Plateau
state (Satod Cartographic Consultants, 2003), even yields a positive, although statistically
insignificant, coefficient. This stands in contrast to the observations of election monitors in
2003, who generally concluded that electoral fraud affected rural areas most severely. Most
observers noted that flagrant violations of rules at the polling stations were much more likely
to occur in rural as opposed to urban areas, because international election observers were
far more prevalent in cities (Kew, 1999). But this suggests that in rural areas, manipulation
of return sheets was likely to be unnecessary in areas where fraud occurred. In larger urban
areas (like the city of Jos), on the other hand, manipulation of election results was more
likely to occur behind closed doors, at ward-level collation centers. Arguably, different types
of fraud can serve as substitutes for one another: In urban areas, digit manipulation was
more likely to occur on ward sheets than in rural areas, where such fraud was unnecessary.
Finally, we assess the extent to which digit pairs exhibit repetition or adjacency across
wards. Figures 11 and 12 use data for Nigeria, but are equivalent in design to figure 3.
Surprisingly, we find no solid evidence of return sheets with too few digit repetitions, nor do
we detect an overabundance of adjacent digits. (Recall that we can expect a small number of
wards to exceed the confidence bound purely by chance.) We do, however, find that in a large
number of wards, digit pairs do not often enough bridge a distance of more than one. When
we look at several columns for each ward return sheet (PDP votes, number of registered
voters, and total vote count), we can identify 17 wards in which pairs of non-neighboring
digits occur suspiciously infrequently.
How can we interpret the fact that pairs of adjacent numerals are sufficiently rare, digit
repetition is as common as it should be, and yet we find a good number of return sheets
on which pairs of non-adjacent numerals are lacking? We argue that this is, to some ex-
tent, a reflection of the statistical power associated with each measure. Even for relatively
small wards, the expected number of pairs of non-adjacent digits is fairly large, at least in
comparison to the expected number of pairs of repeated or adjacent digits, and so the 95%
confidence bound is relatively unforgiving. Small wards need to lack digit repetition or ex-
hibit adjacency to a very substantial degree in order for us to be confident enough to reject
the null hypothesis of a fair election, while a less extreme insufficiency of non-neighboring
digits could push the ward beyond the 95% confidence bound.
5
Conclusion
This paper derived and applied a method to detect manipulation of electoral return sheets.
We showed that we can expect the last digits of electoral results to occur with equal frequency
20


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