# Comparative Analysis of Precinct Commission Protocols in the Case of Simultaneous Voting With Different Ballot Types

#### Abstract

Joint elections or elections that require use of multiple ballot types provide an opportunity for research, where one compares protocols for different ballot types within the same precinct election commission (PEC). All this data is related in a certain way: a voter who votes at a given polling station and has a place of residence at another polling station has the right to receive ballots only from the constituency in which their place of residence belongs. Thus, with strict observance of the law, the number of ballots issued in a constituency should not exceed the number of ballots issued in an electoral district covering it geographically. The difference in these numbers shows the migration taking place on election day. If the rules for issuing ballots are violated, then the mentioned ratio is also violated. A comparative analysis of protocols of PECs allows us to draw a conclusion about the quality of compliance with the specified requirement of the law.

## On the correlation between protocols for different ballot types

A comparative analysis of protocols from the same precinct election commission (PEC) for different ballot types always yields interesting results. The point is that if an election is held using two or more types of ballots, there is some correlation between vote returns from different types of ballots. For example, the number of voters who received ballots in a single-seat constituency cannot be greater than the number of voters who received ballots in a single constituency, which territorially includes that single-seat constituency. We assume that cases when a voter refuses to take one of the ballots are extremely rare; this assumption is based on the author's experience working in election commissions. Note that this assumption does not hold for remote voting.

Other examples easily manifest when federal elections are combined with regional or local ones: in the latter two, constituencies are smaller than in the former.

Russian election commissions are well aware that the lines of the same protocol are linked by the so-called "control ratios". The commissions check these control ratios in accordance with the law and methodological materials. PEC supervisors from local administrations do not like it when the "balancing" lines of the protocol, which reflect whether the "main" control ratio is fulfilled, do not contain zeros. Because of this, at the last Duma elections only 2 584 ballots were "lost" in the entire country, and "uncounted" ballots amounted to only 950 out of a total of 198 856 418 (and only those who have no idea of what a Russian election is can believe that).

However, our election commissions know little about the correlation between protocols for different ballot types. Some time ago, the PEC Workbooks issued by the Central Election Commission of Russia (CEC) hinted that it was necessary to check the "inter-protocol" control ratios, but this year there was no mention of it yet again. As a result, electoral commissions did not pay attention to the inconsistencies encountered.

The remarkable facts that emerge from a comparative analysis of protocols for different ballot types allow researchers to evaluate the quality of the work of election commissions and their understanding of the meaning of protocol lines on vote returns. The author of this article brought these facts to the attention of Moscow Election Commission and the CEC several times (see, for example, [2; 3]). In some cases, a comparative analysis of protocols shows clear signs of fabricated vote returns [1].

At a State Duma election, the electoral roll books may include voters who have active suffrage in a federal constituency, but who do not have it in a single-seat constituency. Moreover, sometimes electoral rolls for different elections are combined when elections are joint. When voting is done using several types of ballots, election commissions are faced with the question: What numbers should be put in the first lines of vote return protocols? As experience shows [3], there is no uniform approach to this issue. However, since the first line of the protocol is not used to check the balance of the ballots, senior commissions do not pay attention to it.

The number in the first line of the single-seat constituency protocol must not exceed the number in the first line of the single constituency protocol. That is what happened in all PECs at the 2021 State Duma elections (the only exception was commission No. 433 in Tver Oblast). However, a comparison of the first lines of protocols for different ballot types does not allow us to assess the their accuracy for a simple reason: there is no uniformity and sufficient accuracy in how these lines are filled, so comparison-based conclusions are difficult to make.

In the first part of this paper we will compare PEC protocols in the federal and single-seat constituencies in the 2021 State Duma election. The analysis was conducted using the protocols from 96 325 PECs published in the open-access part of SAS "Vybory".

In the second part, the comparison will be joined by Krasnoyarsk Krai PEC protocols from the 2021 legislative assembly election in krai and single-seat constituencies. We used data from the protocols of 2 161 PECs in Krasnoyarsk Krai for four types of ballots.

The author expresses his deep gratitude to Sergei Shpilkin, who greatly facilitated the collection of this data against the efforts of the CEC to restrict access.

## Remote voting

Let us start with the groundbreaking remote voting. As is known, it was somewhat different for Moscow residents and those in the other 6 regions where it was used. Remote voting protocols for each of the 15 constituencies of Moscow were put together by a special "remote voting precinct election commission" formally located in the Arbat District of Moscow. Protocols for each of the 18 electoral constituencies in the remaining regions were formed in a special "remote e-voting territorial election commission" set up under the CEC. These protocols were called "protocols of e-voting election commissions." In Moscow, these commissions had numbers from 5001 to 5015 and were assigned to specific territorial commissions. In the regions, they had no numbers (for the convenience of our calculations, we put them under number 10000 and assigned to a separate virtual territorial commission). Remote voting precinct commission protocols were included in the summary table of the corresponding constituency.

Table 1 shows the data on all 33 virtual remote voting precinct commissions. The procedure for counting of remote voting data was more or less established by the CEC Resolution No. 26/225-8 of 20 July 2021 [4].

###### Table 1. Comparison of data from PEC remote voting protocols in the federal and single-seat constituencies
 Region Precinct No. TEC (Territorial Election Commission) PEC No. Total number of voters in federal district The total number of voters in single-seat constituency Difference Number of ballots issued in federal district Number of ballots issued in single-seat constituency Difference Number of voters who voted in federal district Number of voters who voted in single-seat constituency Difference Share of difference relative to federal voters Moscow 196 Yaroslavsky District 5001 130978 130978 0 126287 126287 0 122962 119679 3283 2.7% Moscow 197 Mozhaysky District 5002 122408 122408 0 117905 117905 0 114754 111825 2929 2.6% Moscow 198 Sokol District 5003 137036 137036 0 131930 131930 0 128664 120207 8457 6.6% Moscow 199 Maryino District 5004 148444 148444 0 143416 143416 0 139702 135494 4208 3.0% Moscow 200 Altufyevsky District 5005 134841 134841 0 130275 130275 0 127493 119355 8138 6.4% Moscow 201 Danilovsky District 5006 126390 126390 0 121824 121824 0 118728 114287 4441 3.7% Moscow 202 Novo-Peredelkino District 5007 171979 171979 0 166170 166170 0 161641 157016 4625 2.9% Moscow 203 Orekhovo-Borisovo Severnoye District 5008 139704 139704 0 134929 134929 0 131425 126700 4725 3.6% Moscow 204 Perovo District 5009 147637 147637 0 142277 142217 60 138117 134282 3835 2.8% Moscow 205 Ivanovskoye District 5010 123687 123687 0 119526 119526 0 116716 109282 7434 6.4% Moscow 206 Khoroshyovo-Mnyovniki District 5011 128184 128184 0 123592 123592 0 120242 116286 3956 3.3% Moscow 207 Voykovsky District 5012 138144 138144 0 133362 133362 0 130014 126352 3662 2.8% Moscow 208 Arbat District 5013 104716 104716 0 100594 100594 0 97998 92194 5804 5.9% Moscow 209 Tyoply Stan District 5014 126280 126280 0 121658 121658 0 118240 114890 3350 2.8% Moscow 210 Yuzhnoye Butovo District 5015 134337 134337 0 129845 129845 0 126501 122003 4498 3.6% Sevastopol 219 Sevastopol REV219 10000 20772 20772 0 18774 18774 0 18621 18628 -7 0.0% Kursk Oblast 109 Kursk REV109 10000 27571 27571 0 25893 25893 0 25641 25658 -17 -0.1% Kursk Oblast 110 Kursk REV110 10000 23009 23009 0 21607 21607 0 21313 21313 0 0.0% Murmansk Oblast 128 Murmansk REV128 10000 49193 49193 0 46395 46395 0 45995 45984 11 0.0%

The table is not fully displayed Show table

In each of the 15 Moscow constituencies, the number of voters who voted remotely in the federal constituency was a few percent higher than that of voters in the single-seat constituency. That is, 2 to 6 percent of Internet voters voted for a party but refused to vote in a single-seat constituency. Why? And why this phenomenon did not occur in Kursk and Nizhny Novgorod Oblasts, but did in Yaroslavl Oblast?

Another mystery is that Perovsky constituency "issued" 60 ballots fewer for single-seat constituencies than federal ones.

There is a stunning case of Rostov Oblast, where the difference between the number of remotely issued "party" ballots and singe-seat ballots amounted to 152 609. This is explained by the fact that voters in Rostov Oblast (this goes for remote voting as well) included residents of Donetsk and Luhansk Oblasts, who received Russian citizenship under the simplified procedure. It seems that most of these voters were included in the electoral roll of a single constituency, but not of the single-seat constituencies formed in Rostov Oblast.

It is quite easy to imagine that a "savvy" remote voter would refuse to vote on one of the ballots. It is much more difficult to imagine that a voter on the voting premises would refuse a the federal district ballot he or she is entitled to. Therefore, it is natural that the number of "federal" ballots issued should exceed the number of "single-seat" ballots.

Single-seat ballots may not be issued to "mobile" voters (who vote in accordance with Clause 16 of Article 17 of the Federal Law "On Basic Guarantees of Electoral Rights and the Right to Participate in Referendums of Citizens of Russian Federation"), as well as to voters who are temporary residents (who vote in accordance with Clause 17 of Article 17 of the Federal Law). However, some of these voters (we will refer to both categories as "mobile" for short) must receive both ballots if they vote within the constituency that includes their place of residence. Therefore, if single-seat ballots were issued in compliance with the law, the difference between the number of "federal" and "single-seat" ballots issued would be equal to the number of "mobile" voters who voted outside their place of residence.

The difference amounted to 1.3 million people nationwide. Unfortunately, contrary to the law, the CEC's website still does not have complete data on the number of "mobile" voters on display; as of mid-October 2021, the data is lacking for 2663 PECs. According to available data, the total number of voters on electoral rolls at the place of residence is about 2.7 million. This number does not include voters who voted at the place of temporary residence. Given that some of the "mobile voters" did not vote, this means that more than half of those voters received both the federal and single-seat ballots. Therefore, the validity of the issuing procedure for single-seat ballots is called into question.

However, a more convincing fact of the violation of the ballot issuing procedure is that in a large number of PECs, the number of issued "single-seat" ballots exceeds the number of issued "federal" ballots.

If we consider the data on voting outside the voting premises, we find 538 such commissions. Then again, a closer examination reveals that in most such cases, the PEC either made a calculation mistake, or simply put the data in the wrong protocol. But this also means that all the senior commissions did not notice such mistakes. This is especially interesting given the fact that territorial commissions are desperately fighting to have zeros in the balancing lines of the protocol (lines 11 and 12).

Considering this circumstance, it makes sense to compare the total number of ballots issued (for the election in question, it is the sum of lines 3, 4 and 5 of the vote returns protocol) instead of separately comparing the numbers of ballots issued early, outside and within the voting premises.

1551 PECs (1.6% of the total number) issued more "single-seat" ballots than "federal" ones.

At the same time, 963 commissions indicated a difference of 1-3 ballots. It should be noted that such a small difference can only be evidence of a PEC's "sloppiness": it can occur, for example, when a voter forgot to sign for a ballot in a single constituency.

In 316 commissions, the difference amounted to 4-10 ballots, in 219 commissions—to 11-50 ballots, and in 53 commissions the difference exceeded 50 ballots. PEC No. 2418 in Chelyabinsk Oblast indicated a record number of 457 more ballots issued in the single-seat constituency than in the federal one (remember: this is the official data that election managers in Russia might describe as "technical errors").

All this absurd and fraud-indicating data passed through the territorial commissions, then regional commissions, and then through the CEC.

The aforementioned difference was negative in 45 territorial commissions. It should also be noted that in one of the electoral constituencies (Republic of Dagestan—North, No. 10) the difference between the number of "federal" and "single-seat" ballots issued within the voting premises was negative. And all this went under the radars of both regional commissions and the CEC.

It is also interesting to compare the number of voters on the electoral roll who applied to vote at their place of residence ("mobiles") with the difference between the "federal" and "single-seat" ballots issued. If all the other voters of a given PEC were residents of a given polling station (i.e. would have residence registration at that polling station), then the difference between the first and the second number would show the number of nonvoting "mobiles" (minus those "mobiles" who voted outside their polling station, but in their single-seat constituency) and would be non-negative. However, as we pointed out before, full data on the number of "mobiles" is not publicly available. Moreover, some commissions (in places of temporary residence or where non-resident voters vote) fail to meet the presumption that all voters, except for "mobile" voters, are entitled to receive both a "federal" and a "single-seat" ballot. This is why this comparison raises more questions than it answers.

## Comparison of four Krasnoyarsk Krai protocols

To expand our study, we chose protocols from the 2161 PECs in Krasnoyarsk Krai. We compared four protocols:

A: protocol on vote returns in the election to the State Duma in a single (federal) constituency (SFC);

B: protocol on vote returns in the election to the State Duma in the single-seat constituency (SSFC);

C: protocol on vote returns in the election to the Legislative Assembly of Krasnoyarsk Krai in the single (regional) constituency (SRC);

D: protocol on vote returns in the election to the Legislative Assembly of Krasnoyarsk Krai in the single-seat constituency (SSRC);

As is well-known, there are six variants of pairwise comparisons for the four elements. However, there are only three independent differences among these six. Indeed: of the differences

$$\Delta_1 = A - B$$, $$\Delta_2 = C - D$$, $$\Delta_3 = A - C$$, $$\Delta_4 = А - D$$, $$\Delta_5 = B - C$$, $$\Delta_6 = B - D$$

one can select any three, and the other three will be expressed through the selected ones. For example, let us select differences $$\Delta_1$$, $$\Delta_2$$ and $$\Delta_3$$ as independent, then the other differences are expressed through them as

$$\Delta_4 = \Delta_2 + \Delta_3$$, $$\Delta_5 = \Delta_3 - \Delta_1$$, $$\Delta_6 = \Delta_2 + \Delta_3 – \Delta_1$$.

For the reasons outlined in the first sections of this article, we will consider only one indicator — the total number of issued ballots. This number is obtained by adding the numbers in line 3 of the protocol (the number of ballots issued during early voting), line 4 (the number of ballots issued on voting days in the voting room) and line 5 (the number of ballots issued on voting days outside the voting premises). As we proceed, we shall use the following labels: $$\Delta_1$$ for the numerical value of the difference of protocols A and B according to this indicator for a specific PEC; $$\Delta_2$$ for the numerical value of the difference of protocols C and D; $$\Delta_3$$ for the difference of protocols A and C. We should keep in mind that the numbers $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ are assigned to each PEC, which means we have three sets, each with 2161 numbers.

Values $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ have a physical meaning: they are determined as the difference in the number of ballots of different types issued to voters at a given polling station. This difference occurs because some voters are not eligible to receive a certain type of ballot. An incomplete set of ballots is issued to a voter who does not have a place of residence at a given polling station and who is put in the electoral roll under either Clause 16 or Clause 17 of Article 17 of the Federal Law "On Basic Guarantees of Electoral Rights and the Right to Participate in Referendums of Citizens of Russian Federation".

These provisions of the law and the relative location of the electoral districts impose some restrictions on the values of $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$.

Therefore, due to the fact that single-seat constituencies are part of a single constituency, it is obvious that the restrictions must be fulfilled.

(*1) $$\Delta_1 \geqslant 0$$

(*2) $$\Delta_2 \geqslant 0$$ must be met.

Other restrictions are not as obvious and will be covered in the remainder of this section of the article. These restrictions emerge from the requirement that a single regional constituency be part of a single federal constituency, as well as from the mutual arrangement of single-seat federal and single-seat regional constituencies. In the simplest case, single-seat regional constituencies (SSRCs) are included in single-seat federal constituencies (SSFCs), but this is not always the case (for example, in Krasnoyarsk Krai some regional constituencies are spread out over different federal constituencies). Therefore, we will have to consider the general case of the mutual arrangement of SSFCs and SSRCs.

We shall consider the following (which is always abided by in the Russian Federation):

- a single regional constituency (SRC) fully coincides with the territory of the subject of the federation, which is part of the territory of the single federal constituency (SFC);

- one or more single-seat federal constituencies (SSFC), which together cover the entire territory of a subject of the federation;

- single-seat regional constituencies (SSRC) are part of the SRC and collectively cover it in its entirety.

At the same time, a particular SSRC can either be part of one SSFC or overlap with several SSFCs.

In Krasnoyarsk Krai, there are 4 SSFCs and 24 SSRCs. However, 16 SSRC are fully within one of the SSFCs, and these SSRCs include 1240 PECs. 6 SSRCs are divided between two SSFCs and 2 SSRCs are divided between three SSFCs; these 8 SSRCs include the remaining 921 PECs.

Each PEC is assigned to one of the SSFCs and one of the SSRCs (for federal and regional elections, this is a condition that is almost always met; in particular, it was done in Krasnoyarsk Krai for the 2021 election). A voter could receive from one to four ballots — for SFC, SRC, SSFC and SSRC.

We shall assume that voters did not refuse to receive ballots that they could get according to their place of residence (roughly speaking — according to the address in the passport). This assumption is essential to our conclusions. On the other hand, a demonstrative refusal to receive a ballot is extremely rare.

Let us consider an unspecified polling station in Krasnoyarsk Krai. It is assigned to certain SSFC and SSRC. That said, the SSRC may be part of the given SSFC, or it may be assigned to another SSFC. All voters who voted at a given polling station but could not receive a full set of four ballots there are divided into four non-overlapping categories numbering $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$ (see Table 2). Values $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ are generated by the these categories of voters voting, and they are calculated from values $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$.

###### Table 2. Calculation of differences Δ1, Δ2, Δ3 for given polling station
 Voter category No. of voters in this category who voted at given polling station Voting in SFC (protocol A) Voting in SSFC (protocol B) Voting in SRC (protocol C) Voting in SSRC (protocol D) Contribution of one voter to Δ1 Contribution of one voter to Δ2 Contribution of one voter to Δ3 Voter not residing in the krai K0 1 0 0 0 1 0 1 Voter whose place of residence is within the territory of this SSFC, but in another SSRC K1 1 1 1 0 0 1 0 Voter whose place of residence is within the territory of this SSRC, but in another SSFC K2 1 0 1 1 1 0 0 Voter whose place of residence is in Krasnoyarsk Krai, but outside the territories of these SSRCs and SSFCs K3 1 0 1 0 1 1 0 Weighted sum by column K0+K2+ K3 K1+ K3 K0

Abbreviations: SFC – single federal constituency; SRC – single regional constituency; SSFC – single-seat federal constituency; SSRC – single-seat regional constituency.

Values $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$ have a physical meaning: they indicate migration of voters (only those who vote, naturally). $$K_0$$ is the number of voters who did not vote in their federal subject, $$K_1 + K_3$$ is the number of voters who voted in their federal subject, but not in their SSRC, $$K_2 + K_3$$ is the number of voters who voted in their federal subject, but not in their SSFC.

Assuming that ballots were issued only to eligible voters, using values $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$, we can calculate values $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ as functions $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$. These theoretically calculated dependencies can be used in two ways: on the one hand, to evaluate migration (if we assume that the ballots were issued correctly), and on the other hand, to evaluate the correctness of the ballot issuing procedure.

However, before all else, we need to examine the empirical values $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ while taking into account the restrictions that the resulting theoretical dependencies place on them. We have already mentioned two of these restrictions — (*1) and (*2) — and now we shall obtain three more restrictions, which are derivations of the non-negative values $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$.

Table 2 illustrates obtaining the dependence $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ от $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$. $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ are the result of totalling columns 7-9, multiplied by the values in the second column.

By summing up the contributions of the four categories of voters, we get the following:

(1) $$\Delta_1 = K_0 + K_2 + K_3$$

(2) $$\Delta_2 = K_1 + K_3$$

(3) $$\Delta_3 = K_0$$

System (1)–(3) as a system of four indeterminates $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$ is underdetermined. If we take $$K_2$$ as an unrestricted variable, then the solution of this system regarding $$K_0$$, $$K_1$$ and $$K_3$$ is as follows:

(4) $$K_0= \Delta_3$$

(5) $$K_1= -\Delta_1 + \Delta_2 + \Delta_3 + K_2$$

(6) $$K_3=\Delta_1 - \Delta_3 - K_2$$

Since all $$K_0$$, $$K_1$$, $$K_2$$ and $$K_3$$ values are non-negative, then $$\Delta_1$$, $$\Delta_2$$, $$\Delta_3$$ are restricted as follows:

(7) $$\Delta_3 \geqslant 0$$

(8) $$-\Delta_1 + \Delta_2 + \Delta_3 + K_2 \geqslant 0$$

(9) $$\Delta_1- \Delta_3 - K_2 \geqslant 0$$

at some $$K_2 \geqslant 0$$.

As was noted above, Krasnoyarsk Krai has 16 SSRCs, which are entirely located within a certain SSFC. For all 1240 PECs included in these SSRCs, the value of $$K_2 = 0$$. For these precinct commissions, we shall check ratios (7)–(9) when $$K_2 = 0$$, that is, ratios

(*3) $$\Delta_3 \geqslant 0$$

(*4) $$-\Delta_1 + \Delta_2 + \Delta_3 \geqslant 0$$

(*5) $$\Delta_1 - \Delta_3 \geqslant 0$$,

as well as rations (*1) and (*2).

For the remaining 921 commissions, we shall check ratios (*1) – (*3) and (*5). The need to fulfill ratio (*5) for all commissions follows from ratio (9) and the fact that $$K_2 \geqslant 0$$. It is possible that ratio (*4) for these commissions will not be met.

## Results of the comparative analysis of the four protocols

Value $$\Delta_1$$ was less than zero in 41 PECs (1.9% of all PECs), ranging from -1 to -3 in 34 cases, with the minimum value amounting to -12 in one case (PEC No. 468 at Sovetskiy TEC of the city of Krasnoyarsk).

Value $$\Delta_2$$ was less than zero in 35 PECs (1.6% of all PECs), ranging from -1 to -3 in 30 cases, with the minimum value amounting to -37 in one case (PEC No. 300 at Oktyabrskaya TEC of the city of Krasnoyarsk).

Apparently, many PECs did pay attention to the correlation between the protocols for single and single-seat constituencies. There was no comparison of protocols for different elections at all, so the control ratios (*3) – (*5) were barely fulfilled.

Value $$\Delta_3$$ was less than zero in 201 PECs (9.3% of all PECs), while it amounted to between -1 to -3 in 174 PECs. The minimum of this value (-19) was observed at PEC No. 661 in Norilsk.

Ratio (*4) was violated in 113 PECs (this number amounts to 9.1% of the 1240 PECs in which it should be fulfilled). The minimum of this value (-19) was observed in PEC No. 661 in Norilsk (the same PEC that indicated the minimum $$\Delta_3$$ value).

Ratio (*5) was violated in 756 PECs (this number amounts to 35.0% of the total number of 2161 PECs). The minimum of this value (-178) was observed in PEC No. 134 in the territorial commission of the city of Kansk.

## Conclusion

The study shows that, just as many years ago, some PECs neglect the rules of law, at least when issuing ballots. Such violations may be found when voting is done on more than one ballot. At the same time, the inter-protocol control ratios are not complied with. Election commissions that are senior to PECs usually do not pay attention to non-compliance with inter-protocol ratios.

The results of a comparative study of protocols also suggest that the lines of the "upper" part of the protocol on vote returns are not filled in uniformly by PECs, there are mistakes that go undetected by control ratios established by the law and SAS "Vybory".

Pedantic when it comes to ritualistic procedures and proud of the large amount of routine work they perform, our election commissions do not just fail to ensure that the constitutional purpose of elections is fulfilled—they cannot ensure that vote returns are summed up precisely either.