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Electoral Fraud in Russia: Vote Counts Analysis using
Second-digit Mean Tests∗
Walter R. Mebane, Jr.†Kirill Kalinin‡
April 20, 2010
Abstract
Growing authoritarian tendencies in Russian politics pose the problem of
widespread electoral fraud designed to boost electoral support for Kremlin
presidential candidates and parties, and to suppress political competitors. We use
tests based on the second-digits of polling station level data from the Russian Duma
elections of 2007 and presidential election of 2008 to examine the methods used to
distort vote counts and examine whether votes reported at different times during the
day are differently distorted. We find evidence of substantial changes in at least the
location of fraud in Russian elections. In 2008, fraud moved into cities in ways it had
not been present in 2007. We also find signs of “normal politics” at work, meaning
that besides extensive evidence of widespread fraud there is also evidence of people
having switched their votes in order to avoid wasting them on hopeless candidates.
∗Prepared for presentation at the Annual Meeting of the Midwest Political Science Association, Chicago,
IL, April 22–25, 2010.
†Professor, Department of Political Science and Department of Statistics, University of
Michigan, Haven Hall, Ann Arbor, MI 48109-1045 (Phone: 734-763-2220; Fax: 734-764-3522;
E-mail: wmebane@umich.edu).
‡Ph.D. student, Department of Political Science, University of Michigan (E-mail:
kkalinin@umich.edu).
1
Introduction
Growing authoritarian tendencies in Russian politics pose the problem of widespread
electoral fraud designed to boost electoral support for Kremlin presidential candidates and
parties, and to suppress political competitors. Our previous research (Mebane and Kalinin
2009a,b) and work by others (Myagkov and Ordeshook 2008; Myagkov, Ordeshook, and
Shaikin 2008, 2009) focuses on fraudulently inflated turnout. Our current research, again
using polling station level data from the Russian Duma elections of 2007 and presidential
election of 2008, examines the methods used to distort vote counts and examine whether
votes reported at different times during the day are differently distorted. To accomplish
our research objective we apply methods studied in Mebane (2010) that examine the
pattern of digits in vote counts.
Mebane (2010) uses a Monte Carlo simulation study to show that tests based on the
second significant digits of precinct-level vote counts can distinguish votes that were cast
normally from votes that were subject to coercion. Votes being normal refers to both votes
that directly reflect preferences and votes that are changed by voters voting strategically
according to “wasted vote logic”: voters vote not for their most preferred choice but
instead for a lower ranked alternative in order to try to defeat an even lower ranked
alternative that they believe is attracting more votes than their first choice is attracting
(Cox 1994). Votes being coerced means votes are cast regardless of preferences. Mebane’s
simulation study applies to a simple plurality election. In Mebane (2010) the simulation
results are supported by data from several American elections, elections in Mexico and an
election in Iran.
The presidential election in Russia in 2008 is an example of a simple plurality election,
so the results claimed in Mebane (2010) should apply directly. The 2007 Duma election is
different, however, using a proportional representation (PR) election system instead of a
plurality rule. Here we assume Mebane’s simulation results are relevant to PR election
systems, pending a direct demonstration. For both kinds of Russian elections we also
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extend the concept of coercion to include ballot box stuffing: adding entirely phony votes
to a candidate’s total. The rationale for this is that each such vote is not motivated
independently by a set of preferences, only by the preferences of the malefactor; so it seems
reasonable to say they are cast regardless of preferences, in the same sense as the coerced
votes in Mebane (2010).
Exploring Turnout by Time
Previously we studied the relationship between electoral frauds and turnout figures, using
precinct-level data (Mebane and Kalinin 2009a,b). We have undertaken a complex
methodological approach to diagnostics of electoral falsifications in the federal elections of
2003-2004, 2007-2008 in Russia. The methods of diagnostics of electoral falsifications
involved in our research have revealed abnormal zones of the Russian elections with
reference to turnout and, partly, voting. Kernel density plots of turnout have shown excess
occurrence of 100% turnout for republics and the abnormal localized irregularity testifying
that turnout indicators have been provided by Kremlin to regional authorities (Mebane
and Kalinin 2009a,b, Figures 1 and 2). The analysis of last significant figures in numbers of
the voted voters has revealed presence of a considerable quantity of zeros and fives and lack
of nines (Mebane and Kalinin 2009a,b, Table 1). This tendency worsens across elections
from 2003 to 2008. Construction of nonparametric regression of turnout shares and a share
of obtained votes has revealed strong relationships between turnout and the level of
support for each party, which is positive for United Russia and negative for the Communist
Party of the Russian Federation and all other parties (Mebane and Kalinin 2009a,b,
Figures 3–6). These relationships cause suspicions about falsifications in turnout and
voting. Last, as a result of the analysis of nonparametric regression of the second
significant digit and turnout share, the intervals of turnout were constructed which suggest
that “vote switching” most likely took place (Mebane and Kalinin 2009a,b, Figures 7–10).
It has been revealed that similar “vote switching” was carried out not for high levels of
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turnout, but at average levels of turnout.
The general conclusion of the research is that a combination of various methods of
electoral diagnostics is the important way of revealing falsifications of turnout and voting
anomalies. In this paper we further develop our argument by exploring the patterns of
turnout distribution across time for the federal elections of 2007 and 2008. Unlike the
previous paper, which focuses on the diagnostics of electoral frauds related to turnout, in
this paper we emphasize the mechanism by which the anomalies in turnout have been
produced. In other words, we will be addressing the question whether there are any
observed irregularities in turnout which will help us to explain “how” the observed levels of
fraudulent turnout have been reached throughout the day in around 95,000 precincts across
the country during 2007 and 2008 elections.
Unfortunately, there is a lack of relevant literature discussing the distribution of
by-hour turnout during the Russian elections. In her work Arbatskaya, by analyzing
Russian elections 1996–2000 argues that the models of electoral activity of the regional
electorate, on the one hand, are determined by political and administrative factors, such as
the type of elections (regional or federal) and administrative interferences in the electoral
process, on the other hand, by the type of the regions—urban/rural, type of industrial
structure, seasonal effects—contributing to the changes in turnout rates during the day
(Arbatskaya 2004). She makes a strong assumption that the course of voting—i.e. turnout
by time—should follow particular distributions. As a result of her analysis, Arbatskaya
groups regions into two broad categories of turnout activity: passive, predominantly,
Russian regions and rural territories; and active regions, Republics and rural territories.
In this paper we suggest that the observed anomalies in the distribution of turnout
throughout the day in the federal elections of 2007 and 2008 can be attributed to the active
interference of administrative elites with the electoral process.
Let’s first consider specifics of federal elections of 2007 and 2008.
Both elections were vital for the future of the authoritarian regime established under
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Vladimir Putin’s presidency. The 2007 parliamentary elections, labeled as a referendum for
the all-national Leader, were aimed to provide sustainability of the regime by
relegitimating Vladimir Putin, i.e. providing him the level of electoral support comparable
with 2004 elections (2004, 71.31%, and 2007, 64.30%) and thus securing his position for at
least another 4 years. The 2008 presidential elections had to insure the consistency of the
established regime, serving as another referendum, this time through support for Putin’s
crony, today’s Russia’s president Dmitry Medvedev. Most experts agree that Medvedev’s
support in 2008 had to be almost similar to Putin’s, but a bit less—70.28% was his result.
Similarly, turnout levels for Putin in 2007 had to be relatively similar to turnout level for
Putin in 2004, respectively 63.66% and 64.3% (compared to 55.75% in 2003), and for
Medvedev in 2008, 69.7%.
The significance of these both elections for the present Russian political regime made
both the level of turnout and level of electoral support important indicators of the regime’s
sustainability and consistency. In reality, given the fact that the Parliament was always
considered as weak and ineffective by the average Russian voter (as Boris Gryzlov, a leader
of UR memorably said: “Parliament isn’t a place for political discussions”) and presidential
elections were characterized by low competition and the lack of any intrigue—both
elections could have provided low turnout and hence an inferior political outcome to
Kremlin (Buzin and Lubarev 2008, 83–84).
Therefore the wide range of methods to boost turnout figures were introduced, which
included various propaganda methods, increased levels of “controlled” voting (outdoor
voting, voting at home, rising number of absentee certificates), wide scale organization of
precincts at the railway stations/hospitals etc., as well as, open falsifications designed not
solely to shift votes from one candidate to another, but rather to simultaneously increase
the number of votes and the number of voters, implemented by “stuffing” the ballot boxes
(vbros) or “adding figures to protocols” (pripiska ) (Buzin and Lubarev 2008, 184). Buzin
and Lubarev (2008) present electoral data, observer reports and multiple stories from
4
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.”
The administrative implementation of the Kremlin’s strategy of winning/frauding votes
was assigned to the governors. With the abolition of regional elections the governors lost
their independent political base: the political survival of the governor was put entirely
under the Center’s judgment, which has led to local “political machines”, which were quite
independent during Yeltsin’s rule, being co-opted into a nation-wide political “convoy”
(Gel’man 2009). As a result, electoral frauds started to serve as a basic “signaling”
mechanism through which favorable electoral outcomes were aimed to display regional
elites’ loyalty to the Center.
Regional clientelistic networks can serve as vehicles to win national elections both under
decentralized competitive political regime—when patron-clientelistic networks work
autonomously—and under centralized authoritarian political regime—when
patron-clientelistic networks are built into the vertical power structure. Since there was no
perfect coordination in the economy, enterprises took on roles of providers of many social
services. The first secretaries of the regional organizations of the Communist Party of the
Soviet Union tended to play a central role in insuring the regional economy. They
organized informal, off-plan exchanges among enterprises within their regions, and the
regional party bosses had considerable formal and informal control over the personnel in
regional enterprises (Hale 2003). Interestingly, to meet the figures in the plan and not to be
punished the regional bosses also often applied “false accounting” (pripiski), affecting the
measures of the level of regional output (Harrison 2009). No wonder that after the collapse
of the Soviet Union and installation of the market, many such clientelistic ties between the
regional governments and enterprises persisted, though it became harder for regional bosses
to manipulate the enterprises.
By definition, turnout is a ratio between the number of participated voters and the
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number of registered voters in the denominator. Clearly, the increase in turnout rate leads
to the increase in numerator or decrease in denominator. Given this information, we also
need to consider the way strategies of the elites towards the increase of turnout occur in
different types of elections, i.e. parliamentary elections with PR electoral formula and
presidential elections with built in majoritarian formula. Here we argue that despite the
fact that in both elections the goals of increased turnout by the regional elites were similar,
electoral systems will differently affect the strategies of the regional governors. The
majoritarian electoral system which is based on a “winner take all” principle is in contrast
to PR, designed to split ballots proportionately between the parties.
If we consider 2007 parliamentary elections, not only the threat of sanctioning of the
governors, but also the distribution of mandates (seats) between regional groups tied the
level of turnout to the number of mandates, and subsequently motivated the regional
governors to fight for the increase in the level of turnout as far as the number of voters is
concerned in order to provide themselves with the greater number of mandates. Given the
fact that according to PR electoral formula, the regional governors are interested in
increasing the number of voters during the day of elections by using the range of methods
to boost the number of participated voters. Moreover, with the cancellation of the
threshold of turnout for elections to be successful (20%) the governors lost their incentives
to decrease the number of registered voters. These incentives might have eclipsed the
electoral goal of 2007 to provide Putin with equivalent “percentages.”
If we consider presidential elections and its “winner take all setting,” what matters
most is the level of turnout (understood as the percentage), which means that elites will
consider manipulation with a ratio between the number of participated voters and the
number of registered voters. For instance, to meet specific “turnout” percentage the fraud
is more likely to take place before the elections (reduce the lists of participants to secure
higher level of turnout before the election day) or by the end of the day to adjust both
components in such a way as to provide a required percentage of voters. For instance, the
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tremendous decrease in the number of registered voters in 2008 compared to 2007 discussed
by many experts was most likely caused by above-mentioned political reasoning, i.e. the
incentives of the governors to provide the higher level of turnout at the presidential
elections by reducing the denominator (i.e. the number of registered voters), compared to
Duma elections, where the governors were more eager to increase the numerator due to the
fact that it’s linked to the number of mandates distributed (Kornya 2008).
As a result, we expect to see that turnout was manipulated in parliamentary elections
by increasing the number of voters during the day of elections, while for the presidential
election of 2008 the turnout figures were adjusted closer to the end of the day.
Second-digit Benford’s Law (2BL) Testing
In general the digits in vote counts do not follow Benford’s Law, but several examinations
have found Benford’s Law often approximately describes vote counts’ second digits (e.g.
Mebane 2006, 2010). Under Benford’s Law, the relative frequency of each second
significant digit j= 0,1,2,...,9 in a set of numbers is given by
rj=P9
k=1 log10(1 + (10k+j)−1). If vote counts’ second-digits follow Benford’s Law, then
the value expected for the second-digit mean is ¯
j=P9
j=0 jrj= 4.187. We use ˆ
jto denote
the estimated second-digit mean.
The simulation and data in Mebane (2010) suggest that ˆ
jcan support the following
interpretations of what happened in a plurality election that produces a collection of vote
counts. ˆ
j≈¯
joccurs when there is neither strategic voting nor fraud and no other
candidates similar to the candidate are on the ballot. ˆ
j > ¯
j, significantly, suggests that the
candidate gained votes that were switched to the candidate by voters who abandoned their
favorite candidate in order to avoid wasting their votes. In particular, in this case, the
simulation suggests we should see a value ˆ
j= 4.35. A candidate who lost votes through
such strategic vote switching is expected to have a relatively small vote count and ˆ
jmuch
smaller than ¯
j. These patterns count as normal politics. In the case of coercion, the
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candidate who receives the coerced votes should have relatively high vote counts and ˆ
j
much less than ¯
j.
Because these interpretations turn largely on how ˆ
jstands relative to ¯
j, we focus on
differences ˆ
j−¯
j. When ˆ
j−¯
j≈0 or ˆ
j−¯
j≈0.163, we diagnose normal politics. When
ˆ
j−¯
jis significantly less than zero for candidates who receive relatively many votes, then
we diagnose fraud by coercion, by which we mean to cover the possibility of ballot-box
stuffing. When ˆ
j−¯
jis significantly less than zero for candidates who receive relatively few
votes, then we diagnose strategic vote switching if there is another candidate for whom
ˆ
j−¯
j≈0.163. In this case the suggestion is that votes were switched from the candidates
with ˆ
j−¯
j < 0 to the candidate with ˆ
j−¯
j > 0.
A complication in these interpretations is that the simulation of Mebane (2010) is based
on a plurality election, while the Duma election is based on PR. We find a conceptual basis
for the simulation result to be relevant in the Duma threshold of 5 percent for a party to
gain seats in the legislature. We suppose that voters who fear the party they most support
will finish below the threshold will strategically switch their votes to another party that
they expect will finish above the threshold. A constraint on this rule, of course, following
the wasted vote logic, is that no voter votes for the candidate he ranks last in his
preferences. Any voter who does that is coerced.
Data from 2007 and 2008
We use data from polling stations (UIKs)1from the Russian Duma elections of 2007 and
the presidential election of 2008. Data were downloaded from the website of the Central
Election Commission of the Russian Federation, http://www.vybory.izbirkom.ru/.
Table 1 shows the national total votes for each party in our data. Edinaya Rossiya or
United Russia (UR) apparently did very well in both elections, gaining 64.9% of the vote in
2007 and 71.2% in 2008. The Kommunisticheskaya partiya Rossijskoj Federacii or
1UIK, also described by us as a precinct, is uchastkovaya izbiratelnaya komissiya.
8
Communist party (KPRF) came in a distant second, with 11.7% and 18.0% of the votes
respectively in the two elections, and the third-place finisher in both elections was
Liberal’no-demokraticheskaya partiya Rossii (LDPR) with 8.2% and 9.5%, respectively. In
2007 a fourth party alliance, Spravedlivaya Rossiya: Rodina/Pensionery/Zhizn’ (Just
Russia) did only slightly worse than LDPR, gaining 7.8% of the votes nationally. Other
parties did much worse, none others exceeding the 5 percent threshold in 2007.
*** Table 1 about here ***
Even so, LDPR and Just Russia just barely cleared the threshold, so to see signs that
some voters had strategically abandoned them to vote for another party would not be a
great surprise. Given the substantive politics of Russia at the time, we might expect UR to
be the beneficiary of these vote switches.
We separate precincts in republics from precincts in oblasts, and within each class we
separate precincts into three categories: cities; towns; and rural.2Cities are the most urban
areas, such as Moscow and St. Petersburg, while towns are smaller, somewhat urban
locations.
We also separate precincts based on information about the level of turnout reported at
four time points during election day. For 2007 and 2008, turnout percentages are reported
at http://www.vybory.izbirkom.ru/ for each precinct at 10, 14, 17 and 19 hours.3The
polls open at 10 and close at 19 hours. Because we consider that the level of turnout in
2004 (64.3%) was a goal for the regime in 2007 and 2008, we separate those precincts that
had turnout greater than or equal to 65% from precincts that did not. Our suspicion,
naturally, is that the higher turnout values are fraudulent. Precincts that exceeded 65%
turnout in each time period are considered separately. We also highlight precincts where
turnout was reported as 100% or greater at 10 hours.
2The basis for the classification is the name of the territory commission for the precinct. Cities match the
regular expression /Gorod |g\.|,/, towns match / gorod/ and rural territories match neither pattern. An
example of a territory commission that we classified as a city is Ulan-Ud‘e, ZHeleznodorozhnaya in Respublika
Buryatiya. An example of a territory commission that we classified as a town is Majkopskaya gorodskaya in
Respublika Adygeya.
3Times are on a 24-hour clock.
9
We estimate ˆ
jin each category and use the standard error of the mean to help assess
whether ˆ
jdiffers significantly from ¯
j. We use z= (ˆ
j−¯
j)/ˆσˆ
jto measure the difference,
where ˆσˆ
jdenotes the standard error of the mean. We consider that a value of zgreater
than 2.0 in absolute magnitude represents a significant difference. We report results for a
category only if it contains more than 10 precincts.
Table 2 reports results for precincts in republics in 2007. There are separate results for
cities, towns and rural areas, and within each class results reported separately for precincts
that hit the 65% turnout level at different times. The values Nshow the number of
precincts that have a vote count greater than 9 for the respective party (so there is a
second digit to analyze). The four columns for times 10h, 14h, 17h and 19h are not
cumulative, so a precinct that exceeded 65% turnout at 10h is not included in the columns
for subsequent times. The next to last column shows precincts that had turnout less than
65% at the end of the day. The last column shows precincts that had turnout at least 100%
when the polls opened at 10h; any such precinct results are also included in the column for
precincts with turnout greater than or equal to 65% at 10h. In addition to N, two kinds of
statistics are reported for each category of precincts, namely ˆ
j−¯
jand z.
*** Table 2 about here ***
There is evidence of strategic voting according to the modified kind of wasted vote logic
in relation to the threshold of 5 percent required to gain seats in the Duma. Often zis
significantly negative for both Just Russia and LDPR, while zis often significantly positive
or not significantly different from zero for UR. ˆ
j−¯
jis not all that different from 0.163 for
precincts that had turnout less than 65% at 19h. This pattern also holds in Table 3, below,
for oblasts. The interpretation is that in 2007 many voters strategically abandoned Just
Russia or LDPR in order to vote for UR.
There is also some evidence of coercion. Cities with turnout greater than 65% at 19h
and towns with such turnout at 17h have zsignificantly negative for UR. Also negative, but
not significant, are the zvalues for towns at 19h and rural places at 17h and 19h. Evidently
10
in these places there was substantial ballot box stuffing near then end of election day.
Except in rural areas in the middle of the day, the zstatistics are not significant for
KPRF, which suggests that in cities and towns in republics in 2007 that party for the most
part neither gained nor lost votes through strategic switching nor was subject to votes
being added through coercion. In rural areas the story is a bit different. Perhaps the
significant zvalues for precincts that reached 65% turnout during the day indicates places
where votes were stolen from KPRF.
Table 3 shows similar patterns for precincts in oblasts in 2007. The pattern of strategic
vote switching away from Just Russia and LDPR and to UR is apparent, as are the signs of
coercion in favor of UR late in the day, especially in cities and towns. A difference from
republics is that KPRF seems to have benefitted from strategically switched votes in cities
where turnout was less than 65%, but they seem to have lost votes to UR in towns and
maybe rural areas.
For oblasts there are enough precincts with at least 100% turnout at 10h to compute z,
and the pattern that appears in those precincts is clearly one of coercion in favor of UR. z
is significantly negative for UR in towns and rural areas and negative in cities.
*** Table 3 about here ***
Table 4 shows results for UR and KPRF in 2008 in republics. In cities the pattern
differs substantially from 2007. Now there is strong evidence of coercion in precincts where
turnout was less than 65% (z=−5.0). Coercion in favor of UR is also apparent in the z
statistics for cities in precincts with turnout of at least 65% at 17h and 19h. In towns and
rural areas there is a hint of strategic voting in favor of UR in places than had turnout less
than 65%, but coercion is evident in towns that had high turnout during the day. The
value of ˆ
j−¯
jfor KPRF in towns with turnout less than 65% is considerably higher than
that seen in the simulation of Mebane (2010) or in any other data and hence must be
deemed suspicious.
*** Table 4 about here ***
11
Table 5 shows similar patterns for 2008 for precincts in oblasts. There is clear evidence
of extensive coercion for UR in cities and towns. Now KPRF seems to have benefitted from
strategically switched votes in both cities and towns, although ˆ
j−¯
jin cities with less than
65% turnout and in towns with at least 65% turnout at 19h is slightly too high to match
the simulation of Mebane (2010). In rural areas there is some evidence of coercion in favor
of UR during the middle of the day. Precincts with at least 100% turnout now do not
consistently show signs of coercion having affected the vote counts.
*** Table 5 about here ***
Conclusion
Overall the 2BL tests indicate substantial changes in at least the location of fraud in
Russian elections. In 2008, fraud moved into cities in ways it had not been present in 2007.
This finding expands our previous findings (Mebane and Kalinin 2009a,b) that distortions
in turnout were more apparent in 2008 and in 2007, and also reinforces our claim that in
2008 fraudulent manipulation was not confined to areas with excessively high turnout.
But we also find signs of “normal politics” at work, meaning that besides the extensive
evidence of widespread fraud there is also evidence of people having switched their votes in
order to avoid wasting them on hopeless candidates. The pattern in rural areas could be
due to patron-client relationships (Hale 2003, 245). Whether all the candidates in the
election were credible in other senses is a topic beyond our scope here (Gel’man 2006).
There is evidence of more “normal politics” in 2007 than in 2008, although again our
conclusions about this depend on our having applied plurality system simulation results to
a PR system.
Notwithstanding the different context, we see the analysis here as further reinforcing
the finding by Mebane (2010) that “given an appropriate covariate, tests based on vote
counts’ digits can do a lot to give strong suggestions about what happened” in an election.
Here the conditioning on type of place and turnout level at different times of day supplies
12
the covariate.
13
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15
Table 1: Russia, national vote totals by party, 2007 and 2008
Year Party Total Percentage
2007 Edinaya Rossiya (UR) 44,460,295 64.9
Spravedlivaya Rossiya: Rodina/Pensionery/Zhizn’ (Just Russia) 5,372,269 7.8
Patrioty Rossii 613,324 .9
Soyuz Pravyh Sil 663,689 1.0
Grazhdanskaya Sila 730,783 1.1
Agrarnaya partiya Rossii 1,598,092 2.3
Rossijskaya obedinennaya demokraticheskaya partiya Yabloko 1,100,456 1.6
Partiya social’noj spravedlivosti 153,563 2.2
Kommunisticheskaya partiya Rossijskoj Federacii (KPRF) 8,026,122 11.7
Liberal’no-demokraticheskaya partiya Rossii (LDPR) 5,646,622 8.2
Demokraticheskaya partiya Rossii 89,402 1.3
2008 Medvedev (UR) 52,238,287 71.2
Zyuganov (KPRF) 13,217,489 18.0
Bogdanov (DPR) 964,489 1.3
ZHirinovskij (LDPR) 6,972,745 9.5
Note: vote counts based on UIK-level data downloaded from
http://www.vybory.izbirkom.ru/.
Table 2: Russia, republics: 2BL mean deviations for UIK vote counts, 2007
cities t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 2,034 52 161 403 448 933 —
KPRF 1,890 35 99 348 442 928 —
Just Russia 1,744 11 61 320 437 912 —
LDPR 1,725 — 52 325 432 909 —
ˆ
j−¯
jUR −.069 .293 .098 −.046 −.598 .106 —
KPRF −.111 −.159 .338 −.164 −.267 −.070 —
Just Russia −.078 −.551 −.056 .091 −.446 .052 —
LDPR −.392 — −1.053 −.563 −.692 −.141 —
(ˆ
j−¯
j)/ˆσˆ
jUR −1.1.8.5−.3−5.0 1.1 —
KPRF −1.7−.4 1.2−1.1−1.9−.8 —
Just Russia −1.1−.7−.2.5−3.4.5 —
LDPR −5.8 — −2.9−3.5−5.1−1.5 —
towns t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 2,394 — 248 749 406 992 —
KPRF 2,235 — 198 681 387 976 —
Just Russia 1,995 — 164 518 352 968 —
LDPR 1,942 — 135 489 347 979 —
ˆ
j−¯
jUR −.147 — −.296 −.545 −.202 .223 —
KPRF −.089 — −.001 .033 −.131 −.167 —
Just Russia −.211 — −.236 −.172 −.324 −.192 —
LDPR −.391 — −.595 −.361 −.228 −.448 —
(ˆ
j−¯
j)/ˆσˆ
jUR −2.5 — −1.7−5.6−1.4 2.4 —
KPRF −1.5 — .0.3−.9−1.8 —
Just Russia −3.3 — −1.0−1.3−2.1−2.1 —
LDPR −6.2 — −2.7−2.8−1.5−5.0 —
rural t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 13,357 85 5,141 4,232 1,667 2,244 —
KPRF 7,592 12 1,615 2,748 1,276 1,948 —
Just Russia 5,151 12 852 1,689 865 1,741 —
LDPR 4,552 — 619 1,424 830 1,680 —
ˆ
j−¯
jUR −.020 .048 −.016 −.055 −.115 .110 —
KPRF −.190 −.854 −.424 −.223 −.051 −.042 —
Just Russia −.214 −.187 −.504 −.203 −.301 −.042 —
LDPR −.257 — −.672 −.234 −.022 −.242 —
(ˆ
j−¯
j)/ˆσˆ
jUR −.8.2−.4−1.2−1.6 1.8 —
KPRF −5.8−1.2−5.9−4.1−.6−.6 —
Just Russia −5.4−.2−5.2−3.0−3.1−.6 —
LDPR −6.0 — −6.0−3.1−.2−3.5 —
Note: N, number of UIKs with count >9; ˆ
j, mean second digit; ¯
j, mean expected under
2BL; ˆσˆ
j, standard error of ˆ
j;t, turnout percentage; —, fewer than 10 UIKs.
Table 3: Russia, oblasts: 2BL mean deviations for UIK vote counts, 2007
cities t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 18,116 252 590 688 1,110 15,472 172
KPRF 17,731 77 456 658 1,096 15,449 33
Just Russia 17,563 64 396 633 1,070 15,408 29
LDPR 17,683 91 450 639 1,080 15,429 50
ˆ
j−¯
jUR .122 −.255 .111 −.362 −.482 .196 −.304
KPRF .072 .033 −.203 −.116 −.129 .104 .176
Just Russia −.472 −.437 −.117 −.221 −.256 −.506 −.532
LDPR −.416 −.385 .126 −.103 −.011 −.473 −.327
(ˆ
j−¯
j)/ˆσˆ
jUR 5.6−1.4 1.0−3.3−5.5 8.4−1.4
KPRF 3.4.1−1.5−1.0−1.5 4.6.3
Just Russia −22.2−1.2−.8−1.9−3.0−22.4−1.0
LDPR −19.6−1.3.9−.9−.1−20.8−.8
towns t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 9,197 166 309 780 854 7,092 120
KPRF 8,855 36 225 743 831 7,025 11
Just Russia 8,689 29 179 685 817 6,982 —
LDPR 8,881 42 225 743 837 7,038 24
ˆ
j−¯
jUR −.006 −.483 −.074 −.332 −.306 .080 −.554
KPRF −.121 .313 −.121 −.342 −.101 −.102 .540
Just Russia −.333 −.980 −.210 .026 −.216 −.382 —
LDPR −.276 −.449 .021 −.232 −.012 −.320 −.604
(ˆ
j−¯
j)/ˆσˆ
jUR −.2−2.1−.4−3.3−3.1 2.3−2.1
KPRF −4.0.7−.6−3.3−1.0−3.0.6
Just Russia −10.9−2.1−1.0.2−2.2−11.3 —
LDPR −9.1−1.1.1−2.2−.1−9.4−1.1
rural t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 50,156 438 7,035 11,881 7,804 22,957 260
KPRF 41,394 84 3,938 9,218 6,717 21,399 29
Just Russia 35,018 43 2,258 6,889 5,599 20,221 14
LDPR 40,095 119 3,606 8,718 6,463 21,171 56
ˆ
j−¯
jUR .047 −.276 −.051 −.038 .020 .136 −.395
KPRF −.143 −.664 −.323 −.117 −.098 −.134 −1.153
Just Russia −.232 −.676 −.717 −.300 −.165 −.168 −.902
LDPR −.156 −.154 −.296 −.125 −.122 −.155 −.348
(ˆ
j−¯
j)/ˆσˆ
jUR 3.7−2.0−1.5−1.5.6 7.2−2.3
KPRF −10.2−2.2−7.2−3.9−2.8−6.9−2.5
Just Russia −15.2−1.5−12.3−8.8−4.5−8.3−1.1
LDPR −10.9−.6−6.3−4.1−3.4−7.8−.9
Note: N, number of UIKs with count >9; ˆ
j, mean second digit; ¯
j, mean expected under
2BL; ˆσˆ
j, standard error of ˆ
j;t, turnout percentage; —, fewer than 10 UIKs.
Table 4: Russia, republics: 2BL mean deviations for UIK vote counts, 2008
cities t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 1,396 12 100 342 336 608 —
KPRF 1,359 — 84 331 333 608 —
ˆ
j−¯
jUR −.707 −.937 .333 −.760 −1.181 −.589 —
KPRF .128 — .027 .106 .236 .110 —
(ˆ
j−¯
j)/ˆσˆ
jUR −9.6−1.1 1.2−5.5−8.5−5.0 —
KPRF 1.6 — .1.6 1.5.9 —
towns t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 1,693 — 130 743 254 557 —
KPRF 1,656 — 118 729 250 555 —
ˆ
j−¯
jUR −.137 — −.464 −.276 −.164 .182 —
KPRF .121 — −.018 −.056 .301 .321 —
(ˆ
j−¯
j)/ˆσˆ
jUR −2.0 — −2.0−2.7−.9 1.5 —
KPRF 1.7 — −.1−.5 1.6 2.7 —
rural t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 10,089 102 3,222 3,727 1,431 1,538 —
KPRF 7,446 34 1,551 3,106 1,257 1,476 —
ˆ
j−¯
jUR .013 −.246 .083 −.053 .004 .051 —
KPRF −.113 −.834 −.294 −.053 −.119 −.019 —
(ˆ
j−¯
j)/ˆσˆ
jUR .5−.9 1.6−1.1.1.7 —
KPRF −3.4−1.7−4.1−1.0−1.5−.3 —
Note: N, number of UIKs with count >9; ˆ
j, mean second digit; ¯
j, mean expected under
2BL; ˆσˆ
j, standard error of ˆ
j;t, turnout percentage; —, fewer than 10 UIKs.
Table 5: Russia, oblasts: 2BL mean deviations for UIK vote counts, 2008
cities t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 17,291 314 740 1,820 2,324 12,056 234
KPRF 16,939 88 667 1,810 2,319 12,051 34
ˆ
j−¯
jUR −.229 −.156 −.131 −.421 −.665 −.123 −.243
KPRF .198 .347 −.025 .022 .179 .241 .254
(ˆ
j−¯
j)/ˆσˆ
jUR −10.4−.9−1.3−6.7−12.0−4.5−1.3
KPRF 9.0 1.2−.2.3 3.0 9.3.6
towns t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 8,526 53 535 1,245 1,150 5,548 13
KPRF 8,420 38 465 1,230 1,145 5,537 —
ˆ
j−¯
jUR −.186 .341 −.279 −.348 −.579 −.065 2.043
KPRF .137 .128 .067 −.064 .301 .154 —
(ˆ
j−¯
j)/ˆσˆ
jUR −5.8.8−2.2−4.3−6.8−1.6 4.4
KPRF 4.4.3.5−.8 3.5 4.0 —
rural t≥65% t < 65% t≥100%
all 10h 14h 17h 19h 19h 10h
NUR 49,028 481 11,235 14,883 7,664 14,776 296
KPRF 45,524 126 9,304 14,086 7,429 14,589 51
ˆ
j−¯
jUR −.019 .016 −.049 −.050 −.016 .032 .029
KPRF −.009 −.489 −.049 −.006 −.029 .029 −1.089
(ˆ
j−¯
j)/ˆσˆ
jUR −1.4.1−1.8−2.1−.5 1.3.2
KPRF −.7−1.9−1.6−.2−.9 1.2−2.9
Note: N, number of UIKs with count >9; ˆ
j, mean second digit; ¯
j, mean expected under
2BL; ˆσˆ
j, standard error of ˆ
j;t, turnout percentage; —, fewer than 10 UIKs.