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Comparative Election Fraud Detection

∗

Walter R. Mebane, Jr.

†

Kirill Kalinin

‡

August 7, 2009

Abstract

Elections in Russia are widely believed to be fraudulent in various ways, a claim some

support especially by looking at voter turnout, others by looking at vote counts’ digits. We

use polling station level data from the Russian Duma elections of 2003 and 2007 and

presidential elections of 2004 and 2008 to examine how several methods for diagnosing

election fraud complement one another. The methods include estimating the distribution of

turnout, measuring the relationship between turnout and party support and testing for vote

counts’ second digits following the distribution implied by Benford’s Law. Anomalies the

methods detect are worse by the end of the period under study than at the beginning. The digit

test detects anomalies beyond those suggested by a simple idea that turnout in many places

was fraudulently inﬂated.

∗

Prepared for presentation at the Annual Meeting of the American Political Science Association, Toronto, Canada,

Sept 3–6, 2009. A previous version wes presented at the 2009 Annual Meeting of the Midwest Political Science

Association.

†

Professor, Department of Political Science and Department of Statistics, University of Michi-

gan, Haven Hall, Ann Arbor, MI 48109-1045 (E-mail: wmebane@umich.edu).

‡

Ph.D. student, Department of Political Science, University of Michigan (E-mail:

kkalinin@umich.edu).

1

Introduction

The least one can say about national elections in Russia over the most recent election cycles is

that they have become less competitive, with fewer political parties presenting candidates for both

the Duma (federal parliament) and the presidency. The United Russia [UR] party, associated with

Vladimir Putin, has unquestionably become increasingly dominant. But many observers go

further and argue that during the recent period Russian elections have become increasingly unfree

and unfair. Myagkov and Ordeshook (2008) argue that during the past 15 years “falsiﬁcations in

the form of stuffed ballot boxes and artiﬁcially augmented election counts” have become

prevalent throughout the country (see also Myagkov, Ordeshook, and Shaikin 2008, 2009).

Since 2000 there have been increases in institutional barriers that suppress electoral

competition between parties and candidates: tougher registration requirements; the rise of a

parliamentary threshold for parties; cancellation of protest voting; and cancellation of the

minimum electoral threshold. In the electoral campaign there has been excessive positive

informational and ﬁnancial support of candidates favored by the Kremlin along with negative

campaigning against alternative candidates and parties. Administrative changes decreased the

transparency of elections. Electoral commission activities became more closed off from the

public, with independent public observation being canceled and the rights of the legal observers

being frequently violated. The OSCE identiﬁed serious problems in the 2004 election (OSCE

Ofﬁce for Democratic Institutions and Human Rights 2004), and by 2008 problems had become

so severe that international observer groups declined to observe the election (OSCE Ofﬁce for

Democratic Institutions and Human Rights 2008).

Lubarev, Buzin, and Kynev (2007) argue that administrative changes since 2000 increased the

extent to which ofﬁcials from all levels of the government participated in election administration.

Since 2003 both federal and regional administrative resources as well as the mass media have

been deployed in favor of UR, which thereby received substantial informational advantages, and

against its main competitor the KPRF (Communist party) (Buzin and Lubarev 2008). The

Kremlin now controls the appointments of regional executives (each governor can be ﬁred for

1

“loss of trust”), which has made them responsible for delivering “recommended” electoral ﬁgures

to the Kremlin. After gubernatorial elections were canceled in December 2004, by the spring of

2007, 70 of 85 governors had announced they were participating in the party of power (Gel’man

2007). Thus, it appears that the entire regional state apparatus is now at the service of the party of

power, making it one large electoral “political machine.” This operation is characterized by

control over the mass media, administrative pressure on both opposition and voters, and possibly

falsiﬁcations as well. In fact, state ofﬁcials have excessive control over all levels of electoral

commissions, including precincts (UIKs), territorial (TIKs) and regional commissions.

Allegations point to a wide variety of methods used to distort reported votes (Kalinin 2008).

Many of these methods relate to voter turnout and so as markers for fraud may appear ambiguous

to the extent they resemble efforts to boost genuine electoral support. In the 2004 presidential

election, due to the effectiveness of administrative resources and the popularity of Putin, the

outcome of presidential elections was essentially predetermined. As a result, neither of the

opposition parties was promoting its leader as their candidate (Buzin and Lubarev 2008, 26).

Nonetheless a wide variety of methods was used to increase turnout, including forced voting by

absentee certiﬁcates. According to Buzin and Lubarev, in 214 territories the 2004 election was

the ﬁrst election where the turnout rate and the share of votes for the winner simultaneously

exceeded 90 percent (Buzin and Lubarev 2008, 26). This phenomenon occurred frequently in

republics as well as in Rostovskaya, Tumenskaya, Chukotskii and Yamalo-Nenetskii AO.

Voters in Russia do not personally register to vote, but all eligible voters are assigned to

speciﬁc UIKs depending on where they live. There is a permanent gap between the number of

real voters and the “listed voters”—the average number of unaccounted voters in Russia is 2–5

million people—and on election days there are always extensive corrections of the voter lists

(Arbatskaya 2004). The large-scale character of these corrections depends on the speciﬁc ways

the voter lists are formed, methods that differ in different territories. Arbatskaya argues that this

correction of voter lists phenomenon opens the door for administrative tyranny, violating the

democratic rights of citizens Arbatskaya (2004, 224–226).

2

The federal elections of 2007 and 2008 took place under different conditions. The president’s

popularity remained high, and the “party of power” controlled not only the Duma but also many

federal legislatures, encompassing the majority of regional heads, mayors of big cities, and other

representatives of political, administrative and economic elites. Putin had promised not to change

the Constitution to allow himself to stand for reelection, so he was preparing for his successor.

Between 2003 and 2007, the Duma election was changed from a mixed system to a system based

entirely on proportional representation. The UR party list was headed by Putin, and it also

included a majority of the governors. In the absence of any viable political competitors and

Putin’s unique position in UR’s list (he was the only one in its federal list), the 2007 federal

elections were labeled as referendum for the all-national Leader. The lack of competition and the

absence of the “against all” (Protiv vseh) option on the ballot—this protest voting option was

prohibited after the 2004 election—produced a danger of low turnout. According to Buzin and

Lubarev, the main task of federal authorities in 2007 and 2008 was twofold: to provide the victory

of Kremlin candidates, and to provide high turnout (Buzin and Lubarev 2008, 184, 257-258).

Therefore Buzin and Lubarev claim that vote falsiﬁcations were not solely about shifting votes

from one candidate to another, but rather about simultaneously increasing the number of votes

and the number of voters. These goals can be implemented by “stufﬁng” the ballot boxes (vbros)

or “adding ﬁgures to protocols” (pripiska) (Buzin and Lubarev 2008, 184).

Like Myagkov et al. (2009), Lubarev et al. (2007) and Buzin and Lubarev (2008) argue that

direct falsiﬁcations played a much larger role in the federal elections of 2007 and 2008 than they

had in the federal elections and regional elections of the 1990s and early 2000s. Buzin and

Lubarev (2008) present electoral data, observer reports and multiple stories from observers and

ordinary voters that illustrate the growth of crude falsiﬁcations and their widespread character, a

pattern they refer to as “mass administrational electoral technology.” Buzin and Lubarev (2008)

conclude that compared to all other elections, the elections of 2007 and 2008 showed that direct

falsiﬁcations started to affect the results of elections, by affecting the distribution of votes

between the candidates.

3

Myagkov et al. (2009), Lubarev et al. (2007) and Buzin and Lubarev (2008) all emphasize

what they claim is fraudulent voter turnout. Buzin and Lubarev (2008) state that along with

stuffed ballot boxes, the easiest and the most popular technique is to change ﬁgures in UIKs’

protocols by UIKs or even more often by TIKs (territories). Buzin and Lubarev are astonished by

how widespread direct falsiﬁcations are and about the “courage” of falsiﬁcators, who appear

conﬁdent that they are supported by administration and courts (Buzin and Lubarev 2008, 177). As

Buzin and Lubarev point out “the insolence with which the protocols are changed in TIKs,

knowing that the copy is already given out to observers, is explained by their conﬁdence in

impunity, being assured that falsiﬁcators and law machinery, including courts, are acting

together” (Buzin and Lubarev 2008, 177). They argue that the federal elections of 2007 and 2008

showed widespread discrepancies between data derived from UIKs and ofﬁcial data produced by

TIKs and the Gas VIBORI system (the internet-accessible election reporting system).

In this paper we use UIK-level data from the 2003 and 2007 Duma elections and the 2004 and

2008 presidential elections to show that it is useful to augment analysis of Russian elections that

focuses on voter turnout statistics with information about the distribution of the second signiﬁcant

digits in UIK-level vote counts.

Tests of vote counts based on the so-called second-digit Benford’s Law (2BL) distribution

have ﬁgured prominently in work on election forensics (Mebane 2006a,b, 2007b,a, 2008b). The

analysis in Mebane (2007a) ultimately focuses on the conditional means of the second digits in

collections of vote counts, measuring how these means differ from the means expected according

to the 2BL distribution. The conditioning factors in that analysis, which examined data from the

2006 election in Mexico, were the partisan afﬁliations of mayors in Mexican municipalities.

Mebane (2008a) and Kalinin (2008) combined an examination of UIK vote counts second-digit

conditional means with outlier detection methods (Mebane and Sekhon 2004) to try to diagnose

which of several hypothesized methods for fraud may have affected the votes reported for Russian

presidential candidates in 2004 and 2008.

4

Nonparametric Regression 2BL Test

The 2BL test used in this paper involves comparing the arithmetic mean of the vote counts’

second digits to the mean value expected if the digits are 2BL-distributed. This test adapts an idea

used in Grendar, Judge, and Schechter (2007)’s analysis that focuses on the ﬁrst signiﬁcant digit

and is intended to identify what they describe as generalized Benford distributions. Grendar et al.

suggest that data that do not conform to Benford’s law may have ﬁrst digits that match a member

of a speciﬁed class of exponential families. Mebane (2006b) argues that vote counts in general do

not have digits that match Benford’s law at all. In particular, the distribution of the ﬁrst digits of

vote counts is undetermined. Mebane (2006b) demonstrates a pair of naturalistic models that

produce simulated vote counts with second digits but not ﬁrst digits that are distributed roughly as

speciﬁed by Benford’s law. Nonetheless we can use the mean of the second digits to test how

closely the digits match the 2BL distribution. According to Benford’s law, the expected relative

frequency q

j

with which the second signiﬁcant digit is j is (rounded)

(q

0

, . . . , q

9

) = (.120, .114, .109, .104, .100, .097, .093, .090, .088, .085). Given 2BL-distributed

counts, the value expected for the second-digit mean

¯

j is approximately

¯

j

B

=

P

9

j=0

jq

j

= 4.18 7 .

Mebane (2006b) and Mebane (2007a) suggest that vote counts whose second digits follow the

2BL distribution are unproblematic, while departures from the 2BL distribution indicate that some

kind of manipulation has occurred. Whether the manipulation the second-digit test may detect

constitutes any kind of fraud is something that needs to be established by additional evidence.

The test is, ﬁrst, whether

¯

j differs from

¯

j

B

and, second, whether it differs in a way that

depends on observed conditioning factors. The conditioning factor in the current analysis is

reported voter turnout, measured as the proportion of registered voters who voted at each UIK.

1

For vote counts y

i

observed for UIKs indexed by i, we nonparametrically regress the second

digits on the turnout proportion x

i

. To estimate the nonparametric regressions we use the package

sm (Bowman and Azzalini 1997) for the statistical programming environment R (R Development

1

Speciﬁcally the value we use to measure turnout is the sum of the number of ballots given out to voters before

election day, the number given to voters in polling places and the number given to voters outside of polling places

divided by the number of registered voters.

5

Core Team 2005).

Turnout, Votes and Manipulations in Russia 2003–2008

Start by considering some of the facts about the distribution of turnout in recent Russian elections

that support suspicions that the elections were, increasingly, affected by fraud. Figures 1 and 2

display kernel density estimates

2

for UIK-level turnout in the Duma elections of 2003 and 2007

and the presidential elections of 2004 and 2008.

3

Following Myagkov et al. (2009), we consider

separately data from republics and data from other regions (“oblasts”). The ﬁgures mirror results

presented by Buzin and Lubarev (2008, Appendix, Illustration 38), which they attribute to S. A.

Shpilkin.

*** Figures 1 and 2 about here ***

The progression of ﬁgures shows worse distributions in 2007 and 2008 than in the earlier two

years. The distributions are also worse in the presidential election years than in the Duma election

years. The top row of Figure 1 shows the distribution for 2003. For both oblasts and republics

there is a spike of UIKs with turnout at or very near 100 percent. A higher proportion of UIKs in

the republics than in the oblasts have this feature. But in oblasts most of the UIKs have turnout

following a relatively smooth unimodal distribution, and in republics many of the UIKs have

turnout following such a distribution. In 2004 (the second row of 1), the proportion of UIKs with

turnout near 100 percent increases noticeably in oblasts and very substantially in republics. In

oblasts the distribution also exhibits spikes at locations corresponding to the excess of turnout

values at values of 70%, 80% and 90% noticed by Shpilkin and Shulgin (Buzin and Lubarev

2008, 201). The distributions for 2007 (top row of Figure 2) shows spikes of UIKs at or near 100

percent turnout similar to those observed in 2004. In the distribution for oblasts, spikes are

apparent at round number percentages of turnout above 60%. The distributions for 2008 (bottom

row of Figure 2) have proportions of UIKs with turnout at or near 100 percent comparable to

2

These densities are computed using R’s density() function.

3

All vote and turnout data were downloaded from the website of the Central Election Commission of the Russian

Federation, http://www.vybory.izbirkom.ru/region/izbirkom.

6

2004. The distribution for oblasts shows very pronounced spikes at round number percentages of

turnout, and in the distribution for republics a spike is evident near 75% turnout.

Buzin and Lubarev (2008, 201) argue that the only acceptable explanation for the spiked

distributions is a wide-spread adjustment of turnout to speciﬁc “rounded” ﬁgures. Inspecting the

last digits of the original UIK-level turnout counts adds to the impression that many of them are

faked. If the turnout counts reﬂected the natural complex of processes that cause people to vote or

not to vote, we would expect the counts’ last digits to be uniformly distributed (i.e., each digit

zero through nine would occur equally often) (Beber and Scacco 2008). Table 1 shows that the

distribution of the last digits in the actual turnout counts from 2003–2008 is very often far from

uniform. The table shows for each digit the signed square root of the discrepancy between the

observed frequency of the digit and the frequency of 0.1 expected if the distribution is uniform.

4

A value of 2.0 or greater in magnitude represents a signiﬁcant discrepancy. The table shows that

there are always too many zeros, with one exception too few nines, and usually too many ﬁves.

Year 2003 for UIKs in oblasts is the only situation where neither the number of ﬁves nor the

number of nines is signiﬁcantly discrepant from the expected uniform distribution, and that subset

of UIKs is the only one for which the overall Pearson chi-square statistic is not statistically

signiﬁcant at the .05 test level. As measured by the overall chi-squared statistics, the extent of the

discrepancy from the uniform expectation increases monotonically as one moves from 2003 to

2008. Turnout fakery seems to be much worse at the end of the time period than at the beginning.

*** Table 1 about here ***

Myagkov et al. (2009) emphasize the way turnout is associated with votes for the party of

power at the rayon level, and Buzin and Lubarev (2008, 204) discuss similar kinds of relationships

using UIK-level data. Both discussions make the point that where turnout is very high, support

for UR tends also to be very high, and support for other parties—notably the KPRF—tends to be

relatively low. Figures 3–6 illustrate these relationships for these two parties. These ﬁgures show

a solid line representing the nonparametric regression of the vote proportions on the turnout

4

If p

j

is the observed frequency of digit j and N is the number of UIKs, then the signed square root statistic is

sign(p

j

− 0.1)N[(p

j

− 0.1)

2

/0.1]

1/2

.

7

proportions bounded by dashed lines indicating 95% conﬁdence bounds. A dotted line shows the

unconditional mean vote proportion. Figure 3 shows the results for UR in republics, with one plot

for the UIKs in each year. Clearly mean support for UR is much greater in UIKs where turnout is

very high. The increase in mean UR vote share from its approximate ﬂoor (for turnout roughly 50

percent) to its peak at turnout equalling 100 percent is greater in 2003 than in 2007 but also

greater in 2008 than in 2004.

5

Figure 4 shows the results for UR in oblasts. In the Duma election

years, then mean support for UR no longer peaks at turnout equal to 100 percent but instead

reaches a maximum for turnout at around 90 percent. In the presidential election years, mean

support for UR does have a maximum at the highest level of turnout. The gain in mean support

from ﬂoor to maximum is now greater in 2007 than in 2003 and in 2008 than in 2004.

*** Figures 3 and 4 about here ***

Figures 5 and 6, which show the same kinds of scatterplots and nonparametric regression

lines, in contrast show mean support for the KPRF decreasing once turnout increases beyond a

certain level. The relationships for UIKs in republics, in Figure 5, show mean KPRF support

declining throughout the distribution of turnout in 2003, but 2004, 2007 and 2008 a decline in

mean support sets in only for turnout greater than about 60 percent. The decline from ceiling to

minimum is greater in 2003 than in 2007 but greater in 2008 than in 2004. The relationships for

UIKs in oblasts, in Figure 6, show mean KPRF support declining only turnout greater than a

certain level in all four years. In 2003 and 2004 the decline begins once turnout reaches about 80

percent, but in 2007 and 2008 the decline starts when turnout reaches about 50 percent. The

ceiling to minimum declines in mean KPRF support are also larger in 2007 than in 2003 and in

2008 than in 2004.

*** Figures 5 and 6 about here ***

Reported turnout certainly looks suspicious when its distribution and the distribution of

turnout counts’ last digits are viewed on their own, and turnout is clearly related to the mean

support for UR and the KPRF. Plots computed for other parties resemble the ones shown here for

5

For 2003 we use the proportional represntation votes, to match the electoral system in place in 2007.

8

the KPRF. Such a pattern of UR tending to gain support in places where the KPRF and other

parties are tending to lose support strongly suggests that vote switching is possibly occurring.

The 2BL test may provide further evidence on this point. Simulations reported in Mebane

(2006b) and Mebane (2008a) suggest that variations from the 2BL distribution can occur both

when vote counts are artiﬁcially increased and when they are artiﬁcially reduced. As Mebane

(2008a) observes, it is unclear whether an artiﬁcial increase in vote counts will mean that the

mean second digit,

¯

j, also increases, or whether an artiﬁcial decrease implies that

¯

j decreases. But

we might expect that if substantial vote switching is occurring, we should see signiﬁcant

departures from the 2BL expected mean ,

¯

j

B

, for both the receiver party and the donor party in

places where the vote switching is happening. In the current case, we might expect nonparametric

regression lines to show that the expected second digit differs from the 2Bl expected value for

both UR and the KPRF for the same values of turnout, if vote switching is taking place.

Figure 7 shows the ﬁrst of a series of graphs intended to allow such parallel assessments. Each

plot in the ﬁgure shows a solid line representing the nonparametric regression of the second digits

on the turnout proportions, with a pair of dashed lines indicating the boundaries of a 95%

conﬁdence interval. A horizontal dotted line locates

¯

j

B

= 4.187. A rug plot along the bottom of

each plot locates the observed values of turnout. The ﬁrst question is whether there is any range

of turnout values for which the nonparametric regression curve’s conﬁdence interval does not

contain

¯

j

B

. If so, we will then ask whether the same region of discrepancy is found for both UR

and KPRF.

*** Figure 7 about here ***

In all four years in republics, shown in Figure 7, the nonparametric regression curves for the

UR vote counts’ second digits have roughly the same shape, but across the years the regions

where

¯

j signiﬁcantly differs from

¯

j

B

varies somewhat. In 2003,

¯

j differs signiﬁcantly from

¯

j

B

only for turnout in the interval roughly (0.45–0.6).

6

In this region,

¯

j >

¯

j

B

. In 2007,

¯

j differs from

¯

j

B

for roughly the same values of turnout in the same way, but

¯

j also is signiﬁcantly less than

¯

j

B

6

Magniﬁcation is probably needed to see the differences discussed in this section.

9

for turnout in the interval roughly (0.7–0.9). In 2004,

¯

j differs from

¯

j

B

for turnout in the interval

roughly (0.6–0.8), and in that interval

¯

j <

¯

j

B

. For 2008,

¯

j <

¯

j

B

signiﬁcantly for turnout in

roughly (0.65–0.9), and

¯

j >

¯

j

B

signiﬁcantly for turnout greater than roughly 0.975. The graphs

for UIKs in oblasts, shown in Figure 8, show roughly the same pattern as in the republics for 2003

and 2007. For 2004, the oblasts graph shows

¯

j >

¯

j

B

signiﬁcantly for turnout in the interval

roughly (0.3–0.5) and

¯

j <

¯

j

B

signiﬁcantly for turnout in roughly (0.55–0.8). The graph for 2008

is similar. None of the graphs for oblasts shows a signiﬁcant discrepancy between

¯

j and

¯

j

B

at the

very highest levels of turnout.

*** Figure 8 about here ***

Comparing these ﬁgures to those for the second digits of the KPRF vote counts, we see in the

plot for republics (Figure 9) very different patterns. In 2003,

¯

j <

¯

j

B

signiﬁcantly for turnout in

two intervals, roughly (0.3–0.55) and greater than 0.75. The results for 2004 are approximately

similar. In 2007 the lower interval shrinks to roughly (0.55–0.6) and the upper interval is also

slightly smaller (greater than about 0.85). In 2008,

¯

j >

¯

j

B

signiﬁcantly for turnout in roughly

(0.6–0.7), while

¯

j <

¯

j

B

signiﬁcantly for turnout greater than about 0.9.

*** Figure 9 about here ***

The intervals of turnout for which

¯

j 6=

¯

j

B

signiﬁcantly for UR overlap with the intervals for

which

¯

j 6=

¯

j

B

signiﬁcantly for the KPRF in all four years. For 2003, 2004 and 2007, the overlaps

occur for turnout values in the vicinity of 0.5, and

¯

j >

¯

j

B

for UR but

¯

j <

¯

j

B

for the KPRF. For

2008 overlaps occur for most of the turnout values greater than about 0.65, and once again

¯

j −

¯

j

B

has opposite signs for UR and for the KPRF. Such patterns strongly suggest vote switching.

Notably, in every year except 2008, the pattern that suggests vote switching occurs for moderate

levels of turnout and not at the highest levels. The pattern of

¯

j for the KPRF in republics in the

earlier years clearly suggest something irregular was happening in the highest turnout UIKs.

Perhaps, as in some of the simulations reported by Mebane (2006b) and Mebane (2008a), vote

switching was also occurring in those years but it did not rise to levels sufﬁcient to trigger a 2BL

signal in the receiver party’s vote counts.

10

The results for

¯

j for the KPRF for UIKs in oblasts, shown in Figure 10, are similar to those for

republics. With minor differences the comparison between those conditional means and the

conditional means for UR suggest the same kind of conclusion.

*** Figure 10 about here ***

Conclusion

Anomalies the methods detect are worse by the end of the period under study than at the

beginning. The second-digit test detects anomalies beyond those suggested by a simple idea that

turnout in many places was fraudulently inﬂated.

11

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14

Table 1: Distribution of last Digits for UIK Vote Totals in Russian Elections 2003–2008

Year

2003 2004 2007 2008

Digit Repub. Oblast Repub. Oblast Repub. Oblast Repub. Oblast

0 6.2 3.0 9.9 4.7 10.5 7.7 15.4 10.5

1 −2.0 0.1 −1.8 1.3 −0.8 0.1 −1.4 −0.7

2 −0.6 −0.4 1.1 0.5 −1.3 1.7 −2.1 −0.2

3 −1.2 −1.0 −1.8 −0.7 −0.6 −1.4 −1.9 −2.1

4 0.7 −0.3 −3.3 −0.8 −3.4 −1.0 −3.7 −1.3

5 3.1 0.9 2.1 3.3 2.1 −0.2 2.7 0.8

6 −1.8 −0.9 −0.1 0.0 −2.8 −1.8 −1.3 −1.1

7 −0.2 0.9 −2.0 −2.2 −1.1 −0.9 −3.1 0.0

8 −0.7 −1.5 −0.7 −2.1 −0.3 −0.8 −1.4 −1.0

9 −3.5 −0.8 −3.4 −4.0 −2.3 −3.5 −3.2 −4.9

χ

2

L

69.9 15.4 137.2 60.9 144.2 82.0 292.2 143.0

n 17, 008 77, 305 17, 600 77, 824 17, 875 77, 92 8 17, 865 78, 383

Notes: Entries for each digit show signed square roots of chi-squared statistics implied by the null

hypothesis that the total number of votes cast at each UIK (polling station) have uniformly

distributed last digits. The χ

2

L

statistics show the overall Pearson chi-squared statistic (9 degrees

of freedom). n shows the number of UIKs.

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Distribution of Turnout across UIKs, 2003 Oblasts

N = 77757 Bandwidth = 0.0146

Density

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Distribution of Turnout across UIKs, 2003 Republics

N = 17347 Bandwidth = 0.02346

Density

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Distribution of Turnout across UIKs, 2004 Oblasts

N = 77826 Bandwidth = 0.01452

Density

0.2 0.4 0.6 0.8 1.0

0 1 2 3 4 5 6

Distribution of Turnout across UIKs, 2004 Republics

N = 17600 Bandwidth = 0.01942

Density

Figure 1: UIK turnout, 2003 and 2004

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.5 1.0 1.5 2.0 2.5

Distribution of Turnout across UIKs, 2007 Oblasts

N = 77930 Bandwidth = 0.01422

Density

0.0 0.2 0.4 0.6 0.8 1.0

0 1 2 3 4 5 6

Distribution of Turnout across UIKs, 2007 Republics

N = 17875 Bandwidth = 0.02052

Density

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.5 1.0 1.5 2.0

Distribution of Turnout across UIKs, 2008 Oblasts

N = 78384 Bandwidth = 0.01447

Density

0.2 0.4 0.6 0.8 1.0

0 1 2 3 4 5 6

Distribution of Turnout across UIKs, 2008 Republics

N = 17865 Bandwidth = 0.01786

Density

Figure 2: UIK turnout, 2007 and 2008

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8

turnout proportion

Edinaya Rossiya vote proportion

0.2 0.4 0.6 0.8 1.0

0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

turnout proportion

Putin vote proportion

0.0 0.2 0.4 0.6 0.8 1.0

0.65 0.70 0.75 0.80 0.85 0.90 0.95

turnout proportion

EDINAYA ROSSIYA vote proportion

0.2 0.4 0.6 0.8 1.0

0.6 0.7 0.8 0.9

turnout proportion

Medvedev vote proportion

Figure 3: UIK United Russia vote proportion by turnout, 2003, 2004, 2007 and 2008, republics

0.0 0.2 0.4 0.6 0.8 1.0

0.30 0.35 0.40

turnout proportion

Edinaya Rossiya vote proportion

0.0 0.2 0.4 0.6 0.8 1.0

0.60 0.65 0.70 0.75

turnout proportion

Putin vote proportion

0.0 0.2 0.4 0.6 0.8 1.0

0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75

turnout proportion

EDINAYA ROSSIYA vote proportion

0.0 0.2 0.4 0.6 0.8 1.0

0.55 0.60 0.65 0.70 0.75

turnout proportion

Medvedev vote proportion

Figure 4: UIK United Russia vote proportion by turnout, 2003, 2004, 2007 and 2008, oblasts

0.0 0.2 0.4 0.6 0.8 1.0

0.10 0.15 0.20 0.25 0.30 0.35 0.40

turnout proportion

KPRF vote proportion

0.2 0.4 0.6 0.8 1.0

0.00 0.05 0.10 0.15

turnout proportion

Haritonov vote proportion

0.0 0.2 0.4 0.6 0.8 1.0

0.00 0.02 0.04 0.06 0.08 0.10 0.12

turnout proportion

Kommunisticheskaya vote proportion

0.2 0.4 0.6 0.8 1.0

0.05 0.10 0.15 0.20 0.25 0.30

turnout proportion

Zyuganov vote proportion

Figure 5: UIK Communist vote proportion by turnout, 2003, 2004, 2007 and 2008, republics

0.0 0.2 0.4 0.6 0.8 1.0

0.02 0.04 0.06 0.08 0.10 0.12 0.14

turnout proportion

KPRF vote proportion

0.0 0.2 0.4 0.6 0.8 1.0

0.10 0.15 0.20 0.25

turnout proportion

Haritonov vote proportion

0.0 0.2 0.4 0.6 0.8 1.0

0.02 0.04 0.06 0.08 0.10 0.12 0.14

turnout proportion

Kommunisticheskaya vote proportion

0.0 0.2 0.4 0.6 0.8 1.0

0.15 0.20 0.25

turnout proportion

Zyuganov vote proportion

Figure 6: UIK Communist vote proportion by turnout, 2003, 2004, 2007 and 2008, oblasts

0.2 0.4 0.6 0.8 1.0

3.5 4.0 4.5 5.0 5.5 6.0

turnout proportion

2003 Edinaya Rossiya 2d digit

0.2 0.4 0.6 0.8 1.0

3 4 5 6 7 8 9

turnout proportion

2004 Putin 2d digit

0.2 0.4 0.6 0.8 1.0

3 4 5 6 7 8 9

turnout proportion

2007 EDINAYA ROSSIYA 2d digit

0.2 0.4 0.6 0.8 1.0

0 2 4 6 8

turnout proportion

2008 Medvedev 2d digit

Figure 7: UIK United Russia second-digit by turnout, 2003, 2004, 2007 and 2008, republics

0.2 0.4 0.6 0.8 1.0

1 2 3 4 5

turnout proportion

2003 Edinaya Rossiya 2d digit

0.2 0.4 0.6 0.8 1.0

1 2 3 4 5 6

turnout proportion

2004 Putin 2d digit

0.2 0.4 0.6 0.8 1.0

0 2 4 6 8

turnout proportion

2007 EDINAYA ROSSIYA 2d digit

0.2 0.4 0.6 0.8 1.0

1 2 3 4 5 6 7

turnout proportion

2008 Medvedev 2d digit

Figure 8: UIK United Russia second-digit by turnout, 2003, 2004, 2007 and 2008, oblasts

0.2 0.4 0.6 0.8 1.0

0 1 2 3 4

turnout proportion

2003 KPRF 2d digit

0.4 0.6 0.8 1.0

3 4 5 6 7

turnout proportion

2004 Haritonov 2d digit

0.2 0.4 0.6 0.8 1.0

0 2 4 6 8

turnout proportion

2007 Kommunisticheskaya 2d digit

0.2 0.4 0.6 0.8 1.0

0 1 2 3 4 5

turnout proportion

2008 Zyuganov 2d digit

Figure 9: UIK Communist second-digit by turnout, 2003, 2004, 2007 and 2008, republics

0.2 0.4 0.6 0.8 1.0

2 3 4 5 6

turnout proportion

2003 KPRF 2d digit

0.2 0.4 0.6 0.8 1.0

2 3 4 5 6 7

turnout proportion

2004 Haritonov 2d digit

0.2 0.4 0.6 0.8 1.0

0 1 2 3 4 5 6

turnout proportion

2007 Kommunisticheskaya 2d digit

0.2 0.4 0.6 0.8 1.0

0 1 2 3 4 5 6

turnout proportion

2008 Zyuganov 2d digit

Figure 10: UIK Communist second-digit by turnout, 2003, 2004, 2007 and 2008, oblasts