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

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

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