# On Manual Recounting of Ballots from Ballot Paper Processing Systems (KOIB)

#### Abstract

Ballot paper processing systems (KOIB) are widely used during elections in Russia. KOIB is a scanner that reads marked paper ballots and automatically tallies the results. Since the voters express doubts in proper operation of KOIB, the law provides for randomized recounting of optical-scan ballots by hand. The current legislation, however, proved to be ineffective. The article discusses the need for randomized recounting of optical-scan ballots by hand and attempts to determine the most efficient sample size.

## On the Issue of KOIB Credibility

The introduction of KOIB to the Russian elections began a long time ago. References to KOIB use during the 1999 Russian legislative election may be found in the book by Arkady Lyubarev called "Elections in Moscow: A 12-Year Experience. 1989–2000" [3: 272]. Along with the introduction of KOIB arose the sentiment of doubt towards the credibility of such counting system. Such sentiment, however, was mostly a consequence of the general mistrust towards election administrators and not the technology per se. It is clear that if there were a lack of trust towards election administrators, the use of any voting and counting system technology would be considered as automation of election fraud by the sceptic voters.

Nevertheless, the integrity of KOIB operation may be easily checked by electoral observers (who are themselves a consequence of the general mistrust towards election administrators) since KOIB still uses paper ballots. Paper ballots in KOIB may be recounted, the amount of votes may be determined by means of a check-up count and compared to the report on voting results (as well as with the voter roll) compiled by KOIB. The legislation has a provision for such a procedure, although its management strategy is far from perfect and either allows avoiding the re-count altogether or set it up in such a way that the re-count will produce rigged results.

In any case, re-counts happened throughout the long history of using KOIB, proving the credibility of operating KOIB in the majority of cases. Moreover, numerous comparative studies of voting results at various polling stations of the same elections has shown a systematic deviation towards opposition and decreased voter turnout at stations equipped with KOIB compared to those without KOIB [1: 162; 2: 250-253]. The pattern was sometimes upset, however [5: 252]. There may also be a connection to the fact that KOIBs were frequently installed in the areas with a more "opposition" leaning population.

The first en-masse use of KOIB happened in 2003. For the next 15 years, the experts had no reasons to doubt the credibility and integrity of KOIB. Moreover, if KOIBs cover a small part of the constituency (the number of KOIBs in Russia gradually increased from roughly a thousand to five thousand in 2018, which constitutes about 1 to 5% of the total number of polling stations in Russia), committing election fraud using KOIB is inefficient since it requires more effort than other methods.

The credibility of KOIB was rising slowly but steadily. The higher it became, the less cases of manual recounting at polling stations there were. It should be pointed out that the legislation does not establish manual recounting as obligatory. The Federal Law "On Basic Guarantees of Suffrage and the Right to Participate in Referendums of Citizens of Russian Federation" (hereinafter referred to as the "Law") states that the manual recounting of votes may be made obligatory either by a law or a decision of the Central Election Commission of the Russian Federation (CEC), or by a decision of commission which administers the elections (it should be noted that not so long ago this right was reserved to CEC only). Electoral commissions provided several arguments to justify their refusal to carry out the mandatory manual recounting procedure. First, KOIBs were never detected to be used for election fraud and second, the Resolutions of CEC already provide for a mandatory recounting under certain circumstances, for example, in case of power shortage or other KOIB malfunctions (although this requirement was not always followed).

## Current Regulations for Manual Recounting of Votes

The Law provides for possibility for manually recounting votes after KOIB processing. There are two cases in which manual recounting may be required:

- on request of persons present during the voting process in case of KOIB malfunction if the precinct election commission (PEC) reaches such a decision (Item 25 of Article 68 of the Law);

- mandatory manual recounting at polling stations chosen by lot.

The second case is regulated by Item 32 of Article 68 of the Law that establishes certain rules for recounting votes. The first rule is as follows:

"In case the electoral commission is using vote counting technology, the vote count is carried out in accordance with Item 24 of the given article. The law [in this case any law] or the decision of the Central Electoral Commission of the Russian federation or any commission that administers the elections or a referendum may provide for the following: at least 5% of the polling or referendum stations (but at least three polling or referendum stations) that used the said technological means shall be chosen for manual votes recounting by lot; the random choice of the polling station for manual recounting of votes shall be made within the territory with one territorial commission; final manual recounting of votes casted at the election or a referendum shall be carried out exclusively by the members of electoral commission bearing the deciding vote. In doing so, the random draw is casted by the higher electoral commission within thirty minutes after the voting has ended, and the results of the draw are immediately brought to attention of every precinct election commission."

The second rule is as follows:

"Based on the outcome of manual vote recounting, either a new report on voting results is compiled, ..., or an act on the initial data matching the recount data is put together... The chairperson of the precinct commission of the polling of referendum station randomly chosen for manual vote recount by lot shall inform the higher commission of the final result immediately after they are determined.

The higher commission that randomly chose the polling or referendum stations for manual vote recount by lot shall immediately make a corresponding decision, including the decision on carrying out manual vote recount on the remaining polling or referendum stations that are located within the same territory upon receiving the report from the precinct commission chairpersons in case at least one of these reports was filed from a polling or referendum station where the manual vote recount showed data mismatch in lines 10, 11, 12 and in the subsequent lines of the data protocol received upon counting the votes automatically and manually."

The current legislation on manual vote recount leaves much to be desired. First, if the random draw is casted immediately after the voting has ended and before the PEC reports are completed, the falsifiers have a chance to decide whether they should put together an "honest" or falsified protocol in the given PEC. Second, the law does not state whether the PECs that were not selected by the random draw should wait for the PECs that were to finish their manual count. This last circumstance is often interpreted by stating that those commissions that were equipped with KOIB but did not carry out the final manual vote recount must wait for the other PECs to finish their final recounts. This, in its turn, is a counter-argument to the very fact of a random draw.

Certain communist deputies attempted to improve upon the legislation that regulated the mandatory final manual vote recount in 2014. They offered to draw lots to determine precincts that would do the manual vote count not immediately after the voting has ended, but after all of the KOIB-equipped precincts put together reports on the results. For some reason, however, the communist bill failed to mention the fact that the recount is not mandatory and is done only upon the commission's decision. The bill was rejected on the first reading.

The Competence Group to the Chairperson of Russian Central Election Commission also attempted to convince the CEC of Russia to adopt a regulation on mandatory manual vote recount at the beginning of 2018. The main argument of opponents to these changes was the fact that precinct election commissions (PECs) that were not randomly selected for recount would have to wait for those that did. We consider this a rather lame argument since it is not directly provided for by law and the generalized final manual vote recount may be done within three days after the election day.

## The Vladivostok Incident

During the repeat gubernatorial election in Primorsky Krai that took place on December 16, 2018 there happened an incident that sparked a new discussion around the need for manual vote count at KOIB-equipped polling stations. Polling stations in Vladivostok used an overall of 80 KOIB-2010 (a 2010 KOIB model) and 65 KOIB-2017 (a 2017 KOIB model). Some electoral observers working at polling stations equipped with KOIB-2010 detected an unusual format of the reports printed by KOIB, namely an irregular font and other deviations from standard report format [4].

It was later revealed that about 2/3 of PECs that used KOIB-2010 displayed the results that were significantly different from the overall polling station results, KOIB-2017-equipped polling stations included. There were grounds for serious concern about the credibility of KOIB-2010 counting ability, especially since a juicy bit of gossip was revealed: apparently the voting results may have been affected by a memory stick that was supposed to serve as a repository for the report on voting results; the memory stick would then be transported from precinct commission to higher commission (the report was printed out from this memory stick). However, it is impossible to dispute the election results based on this data, since the vote recount done a few months later would hardly seem plausible.

It is obvious that the Vladivostok incident yet again sparked the discussion around the necessity of vote recount at KOIB-equipped polling stations.

## Raising Efficiency Levels of Randomized Manual Vote Recount

It is important to recognize that a reliable method of checking the accuracy of the vote count done by KOIB does not require a manual vote recount at all polling stations. Recounting the votes at selected polling stations is enough if the selection is strictly randomized. Let us define the notion of a "reliable checking method." This notion is connected to the notion of probability, which is hardly insignificant, albeit mostly used intuitively. This article has to rely on intuitive interpretation of probability.

The selective manual vote count is done at the polling stations that are chosen randomly by lot (by method of uniform sampling) out of the total number of KOIB-equipped polling stations. This count will either reveal contradictions between the KOIB report and manual report or not. The notion of "contradiction" should be interpreted as a "serious contradiction," meaning attention should be paid to contradictions amounting to several units and not a single unit. What we shall consider election fraud in our report thus comes down to multiple unit contradictions between actual results and results registered in the reports, like, for example, the contradictions described in Item 32 of Article 68 of the Law.

How many (or how big a portion) of polling stations should we select for manual vote count so that in case no contradictions are detected it would be possible to claim there were no contradictions at all? The answer to this question can only be given in probability terms: "There were no contradictions (KOIBs counted the votes correctly) with an X percent probability" or "We can say the votes were counted correctly with an X percent confidence."

Therefore, the first thing we have to determine is the level of confidence we may assign to the allegedly correct count. Two other parameters that determine the sample size of randomly selected polling stations we are supposed to decide by lot are М, which is the total number of KOIB-equipped stations and р, which is the share of the polling stations where election fraud was detected.

Based on this problem statement we may calculate (see Appendix 1) the lowest number of commissions where manual vote recount should be done to be 50, 70 or 90% sure that the remaining commissions did their counting correctly provided that the "checkout" commissions did not reveal any contradictions. It is clear that this digit depends on the М and р parameters.

The results of calculating various М values are displayed in Tables 1-3. Table cells show the number of PECs where the final manual vote recount was supposed to be done (sample size) while the number in the brackets shows the proportion of this number of the total М value to within 1%.

###### Table 1. The number of PECs that require a final manual vote recount to ensure a 50% chance of no electoral fraud
 р=5% р=10% р=20% р~33% р=50% р=90% М=10 - 5(50%) 3(30%) 2(20%) 1(10%) 1(10%) М=40 12(30%) 7(18%) 4(10%) 2(5%) 1(3%) 1(3%) М=180 14(8%) 7(4%) 4(2%) 2(1%) 1(1%) 1(1%)

###### Table 2. The number of PECs that require a final manual vote recount to ensure a 70% chance of no electoral fraud
 р=5% р=10% р=20% p~33% р=50% р=90% М=10 - 7(70%) 5(50%) 3(30%) 2(20%) 1(10%) М=40 18(45%) 10(25%) 6(15%) 3(8%) 2(5%) 1(3%) М=180 23(13%) 12(7%) 6(3%) 3(2%) 2(1%) 1(1%)

###### Table 3. The number of PECs that require a final manual vote recount to ensure a 90% chance of no electoral fraud
 р=5% р=10% р=20% p~33% р=50% р=90% М=10 - 9(90%) 7(70%) 5(50%) 3(30%) 1(10%) М=40 28(70%) 17(43%) 10(25%) 6(15%) 4(10%) 2(5%) М=180 40(22%) 21(12%) 11(6%) 6(3%) 4(2%) 2(1%)

Since there is nothing to say about the р variable, the table contains digits for several of its values. The election in Vladivostok described earlier displayed a p value of about 60%. It may be assumed that it can vary significantly depending on election fraud techniques. This is why we cannot take put cues from high р values only while calculating the sample size necessary for detecting election fraud. In view of this fact and our calculations, we have to conclude that the 5% share established by the law is not big enough.

However, this share may be decreased significantly if the selection is done on a much wider scope than that of a territory with just one territorial commission. This would increase the total number of KOIB-equipped commissions. The tables display that the share of "checkup commissions" may be less than 5% if M=180.

In other words, the current legislation fails to cope with the task of detecting election fraud properly. For large-scale election, KOIBs should be spread around several territorial commissions and the lot should be drawn within all the KOIB-equipped commissions at once.

The proposal made by the communists, which was described earlier, would make a great asset at perfecting the public monitoring procedure. We believe that PECs must hand over the electoral documents to the higher commission immediately after the votes are tallied and the authorized copies of reports are issued. The PECs that are supposed to do manual vote recount on the day following the election day are assigned through a drawing of lots that should be organized after all the reports from all the KOIB-equipped polling station were forwarded to higher commissions. In case contradictions are detected during manual vote count, all the KOIB-equipped commissions shall do a final manual vote recount within the next two days.

## Appendix 1

Let us assume that the vote count by KOIBs in М PEC under Р commissions was incorrect. What is the z probability that the Q number of PECs chosen by lot where the final manual vote recount was done will reveal at least one PEC where the vote count was incorrect? This standard probability problem has the following solution:

$$z(M,P,Q) = 1 - C^Q_{M-P} / C^Q_M$$ , (1)

where $$C^Q_{M-P}$$ is the number of combinations from М-Р along Q, $$C^Q_M$$ is the number of combinations from М along Q.

It should be noted that the function of $$z(M,P,Q)$$ monotonic along Q, which is why the prescribed ž, М and Р will always assist in solving Q, that would result in $$z(M,P,Q)≥ ž$$. In other words, if the М and Р values are known, formula (1) uses the target level of reliability ž thus allowing to calculate the number (and $$q=Q/M$$ share) of commissions that should be inspected to reach this level of reliability.

At the same time, the share of p commissions displayed in Tables 1-3 where the vote calculations were wrong amounts to $$p = P/M$$.