Modification Proposals for a Mixed Compensatory Electoral System: A Model Study

Lyubarev A.E.

Abstract

The article presents an analytical view of strengths and shortcomings of a split-voting mixed compensatory electoral system and proposes several modification proposals. Using the 2018 Smolensk Oblast Duma election as a model, the author analyzes seat allocation in the proposed scenarios. The criteria used in evaluating the results include the views of fairness, ensuring political and territorial representation as well as party, candidate and voter incentives. The author concludes that the model proposing three-seat constituencies and single non-transferable vote in plural voting is the most viable. This model allows parties other than the leading three to secure seats in such a way that all of the parties admitted to seat allocation can directly put at least half of their candidates into the elective body.

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It is generally agreed that an ideal electoral system does not exist. However, researchers keep looking for systems that would qualify as effective for certain political, social and geographical settings.

Many authors consider a mixed compensatory system to be one of the more compelling and promising types of electoral systems that exist today [23; 24; 34; 6: 209–210; 19: 213–243; 26; 14]. This type failed to gain wider currency, however, and different countries use significantly different models of mixed compensatory systems at that. We believe the model that has been in use in the Bundestag election since 1953 (often referred to as the German system or split-voting mixed compensatory system) to be the most viable [36; 18; 19: 213–223; 25; 31]. The same but slightly changed model is used in Landtag elections by the majority of Germany's federated states as well as in parliamentary elections in New Zealand, Scotland, Wales and Greater London Council [7; 10: 72; 17: 27–36; 18: 111–113; 19: 223–225].

At the same time, this system has certain shortcomings that we will address below. In this context, we have earlier proposed some modifications to this system [19: 588–591]. The purpose of this paper is to present a model example that shows how certain modifications may take effect.

Split-voting mixed compensatory electoral system

The electoral system we refer to as "German" essentially gives a voter two voting ballots: the first is used to vote for a party list, while the second is used to vote for a candidate in a single-member constituency. At the same time, the total number of seats gained by the party is determined by the party list vote. The order of priority in seat allocation on the other hand depends on the candidate vote in constituencies. The candidates that win in their constituencies (that is, by beating other candidates) are the first to receive seats (the so-called "direct" seats). It is only after that that party list candidates receive their seats (the so-called "party" seats).

Let us use the 2009 election to the Landtag of Hesse to show what the system looks like in action. The number of seats in the Landtag stands at 110, with 55 elected in single-member constituencies. The election of 2009 resulted in 46 seats going to the Christian Democratic Union (CDU), and 9 seats going to the Social Democratic Party (SPD). In the federated state constituency, the CDU gained 37.2% of the total number of valid ballots, while the SPD received 23.7%. The Free Democratic Party (FDP), The Greens and The Left received 16.2%, 13.7% and 5.4% respectively, while 3.8% of the vote went to the parties that failed to get over the 5% threshold. According to both the currently applied Sainte-Laguë method and the previously applied Hare quota, the 110 seats should have been allocated in proportion to the votes for the five major parties the following way: 42 to the CDU, 27 to the SPD, 19 to the FDP, 16 to The Greens and 6 to The Left. However, the CDU won 46 of the direct seats, so it was unable to gain any less seats. Therefore, the party gained these 46 seats (42 + 4 excess seats). However, four additional ("equalizing") seats were allocated in order to preserve the proportion: two to the SPD and one to the FDP and The Greens each. In other words, the SPD gained 29 seats, the FDP gained 20 The Greens gained 17 and The Left gained 6.

As the result, 118 members ended up in the Landtag instead of 110. At the same time, the CDU gained 45 direct seats, but none of its party list candidates gained any. The SPD gained 9 direct seats while the remaining 20 went to party list candidates. As for the three other parties, only party list candidates gained seats.

While discussing the ways of adapting the German system to Russian context, we pointed out that the number of deputies in Russia is fixed everywhere, which is why there should not be any excess or equalizing seats. Applying the model we developed within the framework of our Electoral Code of the Russian Federation project (ECRF) [9: 54–57, 170, 370–372] to the Hesse election would yield a slightly different result. The 46 seats would be excluded from the allocation process, and the remaining 64 would be reallocated. Such a set of circumstances would give 26 seats to the SPD, 17 to the FDP, 15 to The Greens and 6 to The Left. The SPD would still gain 9 seats for direct candidates and 17 seats for party list candidates.

As can be seen in Table 1, the proportional nature of representation deviates in favor of the CDU, although only ever so slightly. We may regard this case as the leading party gaining excess seats on account of multiple victories in single-member constituencies.

On top of that, let us demonstrate how our model would have worked in the 2016 legislative (Duma) election (assuming vote returns would have remained the same). The results are displayed in Table 2 in comparison with the actual seat allocation based on the mixed non-compensatory (parallel) system that is currently in use in Russia. Given that in constituencies an independent candidate and two candidates from parties that failed to get over the 5% threshold gained one seat each [15: 1054, 1120], 447 seats would have been subject to proportional allocation.

Based on proportion, United Russia would have gained 279 seats, CPRF – 69, LDPR – 67, A Just Russia – 32. That said, party list candidates from all four parties would have gained seats. However, for United Russia, it would have been a smaller number while for the other three parties it would have been bigger.

Since a sizeable percentage of votes went to parties that failed to get over the 5% threshold, all four parties would have gained a share of seats larger than that of votes, while the "bonus" would have been allocated evenly. As the result of actual seat allocation under a parallel system, however, United Russia gained a share of seats far greater than its share of votes while the other three parties gained a much lesser share.

Modification proposals for a split-vote mixed compensatory electoral system

This system faces some criticisms, the bulk of which points out that it may provide room for electoral manipulations in a country with a developing party system. These electoral manipulations are sure to distort the will of the people and undermine the weak party system. Lesotho in particular is often used as an example, where the two leading parties only nominated lists while their satellite parties nominated candidates in constituencies. There is another possible (especially so in Russian context) type of manipulation where candidates from the leading parties run as independents. In such a case, a party essentially gains extra seats, since its "cloaked" candidates are not taken into account [8; 6: 210].

We believe this specific model has one more defect. This defect takes root in a drawback that pertains to the plurality voting system in general, where the only possible winner is a candidate who has strong support in a given territory. Once more, let us look at elections in Germany as an example. Some researchers believe that in Germany, the results of a candidate are largely determined by the party's reputation, and that personality has little influence [12; 25].

The above data from the 2009 elections to the Landtag of Hesse shows that only two parties gained direct seats. Bundestag elections demonstrate a similar situation. For example, since 1961, the FDP only once (in 1990) won in a single-member constituency, and only in one constituency at that. The Green won in one single-member constituency between 2002 and 2017. The Left have been ever so mildly successful in single-member constituencies as well. In the plurality part, only two parties essentially race against one another: the CDU and the SPD.

This effectively means that the main idea behind the German system (where the deputy cabinet staffing depends on whomever constituencies vote for) only works in regards to the two major parties of Germany. In Russia, the same system would work in regards to two (or quite often even one) parties as well. On the other hand, the leading party may be faced with a situation where all the seats go to candidates in constituencies and no one on the list gets a seat (as was the case in Hesse in 2009).

What is more, such a situation may lead to widespread tactical (also referred to as strategic) voting [29; 33]. For example, many of the FDP's voters in single-member constituencies do not vote for the FDP, but for a party that the FDP is planning to enter into an alliance with instead. The voters of The Greens act in a similar fashion [1; 11; 19: 478–483; 21]. Smart Voting strategy, which has been gaining traction in Russia recently, is effectively a variation of tactical voting [2; 3].

This fact prompts a need to adjust the given model, namely its plurality part. In the meantime, it is important to consider the following points.

In a mixed non-compensatory (parallel) electoral system, the majority part has independent value. Election results in this part have a direct influence on the party setup of the elected organ. In a mixed compensatory electoral system, plurality part plays a different role. It should not have any influence on the party setup of the elected parliament (which should be determined entirely by the vote for parties). In this case, the point of the plurality part is to give the majority of seats to voter-supported candidates.

That is exactly why the plurality principle of "winner takes all" should be abandoned, as it is rendered meaningless under the given circumstances. There are two direction such an adjustment could take [19: 588–591].

The first direction. Changing the rules of gaining direct seats in constituencies. General approach: the winners are not the only ones allowed to gain seats, the so-called "best loser rules" rule [13]. We would like to put forward three different options.

Option A. Allocating the seat to the candidate depending on his/her individual result instead of his/her position in the constituency. Another possible provision – depending on the absolute number of votes he/she received. In this case, however, the advantage goes to candidates in larger constituencies (which is especially significant in the Russian Duma election, where it is nearly impossible to achieve constituency equality by the number of voters) or in high-turnout constituencies. It is better to allocate the seat depending on the share of votes from the number of participating voters or from the number of valid ballots. For example, seats could be allocated to all candidates with over 20% of votes.

Option B. Each party admitted to seat allocation is allocated half the seats (or, in case the party gains an odd number of seats, about a half) depending on constituency results. All party candidates will be then queued in descending order, and seats will go to the candidates in the top half.

Option C (combined). If the number of winners from the party amounts to half the seats due to the party or more, seats should be given to these candidates alone (as in the initial proposal, which we shall refer to as "Option 0"). However, if the number of winners is less than a half, the extra direct seats should be allocated to candidates from this party so that the total number of direct seats amounts to half the number due to the party. In case the latter number is an odd one, then it should be a half rounded upwards (as in Option B).

The second direction. Replacing single-member constituency with multiple-member (we believe three-seat constituencies would fit best), where a voter only has one vote (the so-called single non-transferable vote). This will prevent manipulations that seek to gain extra seats: the party that is supported by less than a half of the voters in the constituency will be unable to get all of the three seats (getting two will be problematic as well), regardless of whether its candidates will run as representatives of the party or otherwise.

At the same time, replacing single-member constituencies with multiple-member constituencies with single non-transferable vote should promote allocating direct seats to mid-level parties as well, not just the leading parties. This system allows for a set of circumstances where a constituency is represented by deputies from three different parties.

Both directions blend together fairly well. In other words, it is possible to use three-seat constituencies and at the same time allocate direct seats based on Option A, B or C.

Elections used for the model study

For the model study, we chose the 2018 Smolensk Oblast Duma election. There are several reasons why this particular election fits our purposes.

The number of seats was relatively large, but not that large, standing at 48. At the same time, as is the case in Russia, the election was held under a mixed non-compensatory (parallel) system: 24 seats were allocated depending on the vote returns for party lists in a unified constituency; 24 seats were allocated in single-member constituencies. It should be noted that 24 is evenly divided by 3, which means that for the purposes of our model study, we can replace 24 single-seat constituencies with 8 three-seat constituencies.

Five party lists participated in unified constituency election. All of them got over the 5% threshold and gained seats. At the same time, candidates from the very same five parties ran in single-member constituencies, and no one else did. Most constituencies (19) had candidates from all five parties. CPRF and LDPR had their candidates in all 24 constituencies, United Russia and A Just Russia had their candidates in 23 constituencies, and Russian Party of Pensioners for Social Justice (RPPSJ) had its candidates in 21 constituencies.

A unified constituency produced the following results: 36.3% for United Russia, 22.9% for CPRF, 19.8% for LDPR, 9.3% for RPPSJ, 7.8% for A Just Russia (the percentages were counted based on the number of participating voters). Seat allocation was as follows: 9 to United Russia, 6 to CPRF, 5 to LDPR, 2 to RPPSJ, 2 to A Just Russia. It should be noted that the Tyumen method was used to allocate seats, but the result would still have been the same if the Hare quota was used.

United Russia candidates won in 17 constituencies, while CPRF and LDPR won in 6 and 1 respectively. As a result, United Russia gained 26 seats, CPRF gained 12, LDPR gained 6 while RPPSJ and A Just Russia gained 2 seats each [37; 16: 493, 520].

In order to test the three-seat constituency model, we merged bordering single-seat constituencies into threesomes while taking other geographical features into account. We eventually ended up with 8 three-seat constituencies and gave them the following code names:

· Smolensk-1 – constituencies no. 1, 2 and 3;

· Smolensk-2 – constituencies no. 4, 5 and 6;

· Smolensk-3 – constituencies no. 7, 8 and 9;

· South – constituencies no. 11, 13 and 14;

· Center – constituencies no. 17, 18 and 19;

· East – constituencies no. 21, 22 and 23;

· North – constituencies no. 10, 16 and 20;

· South-East – constituencies no. 12, 15 and 24.

We construct our model on the assumption that vote returns would have been the same if other variations of the mixed system had been used. Naturally, we are fully aware that electoral behavior of parties, candidates and voters would likely have different depending on the variation of the electoral system. However, we consider our hypotheses as initial approximation aimed at demonstrating the most obvious effects of different models.

Single-member constituency models

First, let us see how the seats would have been allocated in the Smolensk Oblast Duma election under the mixed compensatory system set out in the Electoral Code of the Russian Federation project where the seats are allocated using the Hare quota (we shall refer to it as zero option). The results are displayed in Table 3.

As the table suggests, a mixed compensatory system allows for seat allocation where the share of seats for parties is close to the share of votes they received. Under a parallel system, the party that dominates single-member constituencies achieves a disproportionately large representation while outsider parties achieve a disproportionately low representation.

As for seat allocation between candidates, United Russia would have gained only one seat while the rest of the seats would have gone to candidates who had won in constituencies. CPRF would have seen the seats allocate fairly evenly between direct and party list candidates. Only one LDPR candidate would have gained a direct seat while the rest of the seats would have gone to party list candidates. As for RPPSJ and A Just Russia, only party list candidates would have gained seats.

Now let us estimate how the seats would have been allocated had Alternatives A, B and C been applied.

Option A. Direct seats only go to those candidates, who received more than 20% of valid votes.

United Russia has 22 candidates like that, meaning all but one. However, since the number of seats set for this party amounts to 18, one more requirement will have to be introduced. The most logical move in this case would be to give the seats to 18 candidates with highest results (in shares of votes). As the result, out of the 23 candidates running in constituencies, the ones from constituencies no. 6, 7, 8, 19, 21 do not get direct seats. At the same time, it is revealed that candidates in constituencies no. 7 and 21 who were ahead in their constituencies with 30.5% and 30.4% respectively are outrun by candidates in constituencies no. 2, 3 and 5 who lost in their constituencies, but gained 31.0%, 32.6 and 36.0% respectively. Naturally, the rules may be adjusted to give seats to all leading candidates while the percentages are allocated to losing candidates. Nevertheless, we shall stick to the option we singled out earlier.

CPRF has 18 such candidates. In this case, we have to choose only 11 as well. Using the method described above, we elect candidates in constituencies no. 2, 3, 5, 6, 8, 10, 12, 17, 21, 22 and 23. All six winners get on the list.

LDPR has 4 such candidates: a winner (in constituency no. 19) and candidates in constituencies no. 14, 21 and 24.

None of the RPPSJ candidates passed the 20% mark. A Just Russia has three such candidates: in constituencies no. 4, 7 and 19.

Direct seats should therefore go to 36 candidates: two candidates per constituency in one-half of the constituencies and one candidate per constituency in the other half.

Party list seats go to 12 candidates, namely six LDPR candidates, all five of RPPSJ candidates and one A Just Russia candidate.

Option B. Direct seats should be allocated to a half (in case of an odd number, a half rounded upwards) of the candidates derived from the overall number of seats due to the party; the chosen candidates should be those with the best results (measured in vote percentage of the number of valid ballots).

It is then necessary to select nine candidates from United Russia, namely from constituencies no. 10, 11, 12, 14, 15, 16, 18, 20, 24. Six candidates should be selected from CPRF (from constituencies no. 2, 3, 5, 6, 8, 23 – all who won in constituencies). Five candidates should be selected from LDPR (from constituencies no. 2, 14, 19, 21, 24). Three candidates should be selected from RPPSJ (from constituencies no. 8, 22, 23). Eventually, two candidates should be selected from A Just Russia (from constituencies no. 4, 19).

This option results in 25 candidates getting direct seats. At the same time, although five constituencies (no. 1, 7, 9, 13, 17) do not gain any seats, six constituencies (no. 2, 8, 14, 19, 23, 24) gain two seats each.

Option C. Direct seats are allocated to all candidates who were leading in their respective constituencies. However, if a party has less than a half of such candidates, additional direct seats should be allocated to its other candidates (like in Option B).

Under these circumstances, 17 winners from United Russia and 6 winners from CPRF get direct seats. As for the winning candidates from LDPR, RPPSJ and A Just Russia, five, three and two respectively get direct seats. We therefore arrive at 33 direct seats. The condition was that all constituencies get seats, but 9 constituencies get two seats.

The results of all four models are summed up in Table 4.

Three-seat constituency models

When building three-seat constituency models we cannot but provide for extra concessions, as any party may nominate one, two or three candidates in a three-seat constituency.

This is why we have to consider options with varying concessions. In the case of Option 0 (where direct seats are allocated to the three candidates with the best results), we will consider three sub-options:

option 0-1: parties nominate one candidate each in every constituency; their results are the sum of votes obtained by candidates from these parties in the corresponding single-seat constituencies during the actual vote;

option 0-2: United Russia nominates three candidates in every constituency but one (two in the East constituency), and their results correspond with those from the actual vote; other parties nominate one candidate each, their results are the sum of votes obtained by candidates from these parties in the corresponding single-seat constituencies during the actual vote;

option 0-3: parties nominate the same number of candidates as in the actual election (CPRF and LDPR nominate three candidates each in all constituencies, United Russia and A Just Russia nominate three each in seven constituencies and two each in one, RPPSJ nominates three candidates per constituency in five and two candidates per constituency in three) with the results corresponding with those from the actual vote.

Overall, it is possible to come up with many more options, but these three carry the point across clearly enough. The modeling results can be found in Table 5.

The table demonstrates that with the exception of United Russia (and CPRF and LDPR in certain constituencies), there is little incentive for parties to nominate three candidates. Since votes casted for them split, the chances of at least one candidate gaining a seat are close to none. There is a reason why Option 0-3 is similar to the actual results in single-seat constituencies: RPPSJ and A Just Russia do not get any seats, LDPR only gets one and CPRF gets six.

However, if all parties except United Russia nominate one candidate each in every constituency, the odds will be flipped in their favor, regardless of the number of candidates nominated by the leading party. As we observe, CPRF gains eight seats in both Options 0-1 and 0-2, while LDPR gains seven in 0-1 and six in 0-2. A Just Russia gains one seat in both options while RPPSJ does so only in Option 0-2.

We will now consider the same sub-options for Option C, which in this case will go as follows: seats are allocated to all candidates placing first, second or third in their constituencies However, if a party has less than a half of such candidates, additional direct seats should be allocated to candidates who received the biggest share of the number of valid ballots. This is done in order to raise the overall number of direct seats gained by the party to the half of the number of seats it gained overall (in case of an odd number, a half rounded upwards).

It should be reminded that United Russia is due 18 seats. In Options C-1 and C-2, United Russia has 8 winners, so in these cases it gains one additional seat. However, it had only 8 candidates in Option C-1, which is why it cannot get any more direct seats. In Option C-3. United Russia has 17 winners, so no additional direct seats are due.

CPRF is due 11 seats. In Options C-1 and C-2, CPRF has 8 seats, and 6 seats in C3, which is why it does not get any additional direct seats.

LDPR is due 10 seats. It has 7 seats in Option C-1, 6 seats in Option C-2 and only one seat in Option C-3. Therefore, LDPR should be given four more direct seats in Option C-3.

RPPSJ and A Just Russia should be given additional direct seats in all three cases: three (RPPSJ in C-1 and C-3), two (RPPSJ in C-2, A Just Russia in C-3) or one (A Just Russia in C-1 and C-2).

Direct seat allocation results can be found in Table 6. There is a total of 28 direct seats in Options C-1 and C-2 and a total of 33 in Option C-3.

Discussion

Electoral system models may be assessed from different perspectives, such as views of fairness, ensuring representation and political party, candidate and voter incentives. We shall assess the models we have described in this paper from these very perspectives.

The fairness of a system is typically associated with whether high electoral support for a party is reflected in its representation in the parliament [14]. From this perspective, a mixed compensatory system is not much different from a proportional system and has clear advantages over a parallel system, where the plurality part is the source of many significant distortions. This can be observed in Tables 2 and 3 among other things. The phenomenon of a "fabricated majority" (which is when a party that does not have the support of the majority gets more than a half of seats) may be considered one of the more revealing manifestations of unfairness [28; 5; 20].

The idea of fairness is more difficult to apply to seat allocation among candidates. It is quite widely accepted that candidates who take leading positions in their constituencies should get seats (this thesis in particular was used to criticize a draft bill on elections to the State Duma proposed by V.I. Vasilyev and A.E. Postnikov in 1994 [35: 40–41; 27: 106]). This is why Options A and B that presume that a candidate may not get a seat are likely to be seen as unfair.

Another factor at play in terms of fairness is the lost votes, as in votes casted for unelected candidates in constituencies [14]. We can easily calculate this factor. For example, in the case of single-seat constituencies in Option 0, elected candidates gained a total of 44.0% of the overall number of valid votes, meaning 56.0% of votes were lost. Then, the share of lost votes is as follows:

· Option A – 33.4%;

· Option B – 60.5%;

· Option C – 49.5%.

For three-seat constituencies:

· Option 0-1 – 16.4%;

· Option 0-2 – 36.3%;

· Option 0-3 – 55.2%;

· Option C-1 – 11.4%;

· Option C-2 – 30.9%;

· Option C-3 – 48.0%.

We can therefore see that in a three-seat constituency, vote loss is much smaller than in a single-seat constituency if all parties nominate one candidate each. Even if the leading party is the only one to nominate three candidates, vote loss is still smaller in a three-seat constituency than that in a single-seat constituency.

As for the issue of representation, we believe it should be viewed from two perspectives: political and territorial [22]. Then again, from the point of view of political representation, it is essential that the share of votes gained by the party be aligned with the share of seats it gained. This is aspect acts as an argument in favor of the German mixed compensatory system as well. In this aspect, the variations of said system do not differ much from one another.

Territorial representation under a mixed system is ensured by electing candidates in single-seat constituencies. In Russia, dividing the party list into territorial groups may be yet another way of ensuring territorial representation [19: 316–330]. However, this aspect is not addressed in this paper.

Of far greater interest is the possibility of combining political and territorial representation, and not mechanically at that. From this perspective, it is important that the deputy cabinet of each party have territorial representatives on the one hand, and members of different parties become territorial representatives on the other [22]. This essentially single task may be solved by either Options B and C or by replacing single-seat constituencies with three-seat constituencies, although Table 6 shows that a combination of the two approaches works best.

Discussion of party incentives should begin with one of the most critical issues. As we have noted previously, a mixed compensatory system may prompt parties to "hide" their candidates by allowing them to run as a member of a satellite party (that is not set out to pass the threshold) or as an independent candidate. If such a candidate wins in a constituency, he or she is not considered when counting the number of seats gained by a party list and is effectively added to this number.

Here we have to point out that such a move may prove disadvantageous for the party as much as advantageous. There exists something called "contamination" effect, which means that a party's candidate in a constituency raises the result of the party's list in the same territory [13; 4: 225–226]. For this reason, refusing to nominate candidates in constituencies lowers the overall result of the party, including the number of seats it receives. Moreover, it is unlikely that candidates elected outside the party brand will observe party rules much. Nevertheless, we may assume that a party will deem that the advantages of such a move outweigh its disadvantages.

German legislation on Bundestag elections contains a regulation aimed at preventing such manipulations. When allocating seats between party lists, supporting votes for certain types of candidates are not taken into account. These types include voter-nominated candidates, candidates nominated by a party that did not nominate a list in the given federated state and candidates nominated by a party that was not admitted to seat allocation [18: 169; 19: 217; 30: 299]. However, this regulation can only be met in split-ticket voting used in Germany. Russia uses separate ballots for voting in a unified constituency and a single-seat constituency, which makes it impossible to find votes casted for a certain candidate in party ballots. Moreover, this regulation has yet to be applied in Germany itself, so it is unclear what surprises it might have in store. Our Electoral Code of the Russian Federation project proposes a mixed compensatory system that is free of this regulation [19: 230].

We believe that replacing single-seat constituencies with three-seat constituencies (with one vote per voter) substantially reduces the incentive for parties to "hide" their candidates and even more so reduces the negative consequences of said "hiding". This very fact can be observed in our model study.

The leading party has a support level of 37.8%. It gets 18 seats out of 48 (37.5%, see Table 3) under a mixed compensatory system. Even if its direct candidates win in 17 constituencies, it still gains only 18 seats. However, if the very same candidates win as independents, the situation will certainly change. In this case, only 31 seats will have to be allocated among party lists, and the leading party will get 12 seats (assuming that its support level remains unchanged, although it is supposed to drop due to the lack of the "contamination" effect). Still, combined with the 17 seats, there will be a total of 29 "hidden" candidates. The leading party will thus obtain a "fabricated majority".

However, given that the proper tactics are applied by other parties in three-seat constituencies, the "hidden" candidates from the leading party will get only 8 seats. The leading party itself will gain 15 seats in the process of allocating 40 seats. We thus have a total of 23 seats (which is an overestimation that does not take the losses prompted by the absence of candidates in constituencies into account) and no "fabricated majority".

An entirely separate question is as follows: how many candidates does a party nominate? Under a parallel system with single-seat constituencies, stronger parties seek to nominate candidates in all constituencies as each win adds an extra seat. For weaker parties that cannot count on winning in a single-seat constituency, the "contamination" effect turns out to be the only incentive. At the same time, weaker parties often do not have many strong candidates in their ranks, which is why they do not always nominate candidates in every constituency, or at least in the majority.

A mixed compensatory system with single-seat constituencies reduces rather than increases the incentive to nominate candidates in constituencies, as a party does not gain any seats even if its candidate wins. That said, the contamination effect is virtually the only incentive left. The leading party is the only one with any hope of gaining extra seats.

On the other hand, it may be important for a party to incentivize its active core through electoral participation and potential victories. Although there has been little research into it, this factor remains a significant one. Under any variation of a mixed system, a candidate can run in the election either as part of a party list or in a constituency, i.e. directly. Russian and German electoral law permits party-list and direct nomination of a candidate at the same time. Ukraine, on the other hand, banned simultaneous nomination in 1998 [32; 19: 418–420]. A candidate's chances of being elected as part of a party list depend on his or her position on said list above all else. The position is determined by the party's body of power (the situation is a bit more nuanced if the list is open or split into territorial groups). In a constituency, a candidate's success is largely dependent on the candidate themselves.

Party bureaucrats set their sights on having the majority of their candidates elected through a party list, as this makes it easier to manage the deputy cabinet. However, if the party is to develop, it is preferable that it has charismatic candidates who could be successful in their own right. Nevertheless, balance seems most preferable; that is, the balance between promoting charismatic party activists and considering party interests that involve having parliament-suited candidates elected.

From this point of view, applying Option A in a mixed system with single-seat constituencies mostly incentivizes mid-level party candidates: they get the chance to become deputies by simply overcoming a certain threshold (20% in our case) instead of attaining leading positions (which is impossible for them most of the time). As for candidates from weaker parties, most of the time it is quite difficult for them to achieve anything even remotely close to a result like this. That said, none of the RPPSJ candidates got more than 20% in our example.

Options B and C allow candidates from all parties to gain seats depending on their individual results in constituencies. However, in Option B, some winning candidates from stronger parties are stripped from their potential seats. While this option seems most convenient for party bureaucrats, it reduces the incentives for mid-level candidates from these parties. We believe Option C to be the most effective since it incentivizes candidates from all parties while still allowing parties to put the necessary candidates into the elective body through party lists.

Replacing single-seat constituencies with three-seat constituencies with single non-transferable vote significantly increases the chances of mid-level party candidates to get direct seats even in Option 0 (electing three candidates with most votes to represent the constituency). At the same time, mid-level and weaker parties do not have to nominate many candidates: nominating one candidate per three-seat constituency is enough and perfectly reasonable. Stronger parties in such a case may nominate two or even three candidates who will have to compete against one another as well. Whether or not such competition is fitting has to be decided by the party on a case-by-case basis.

When used in isolation, the single non-transferable vote model has a clear disadvantage. Parties have to predict the election results in each constituency with quite a high level of accuracy in order to understand how many candidates to nominate. Nominating too many would mean splitting the votes between them and eventually losing. Nominating too few would mean getting less seats than the party could have [6: 197; 33]. However, using this model as part of a mixed compensatory system takes the edge off this disadvantage significantly since the overall number of seats gained by the party is not determined by the number of seats it gains in constituencies.

It is likely that even the strongest of parties will nominate one candidate per constituency under a mixed compensatory system with three-seat constituencies. On the one hand, it will ensure both the party presence on the constituency ballot and the contamination effect. On the other hand, it will decrease (albeit slightly, most probably) the number of candidates elected from this party in constituencies thus increasing the number of candidates elected through the party list. Our example indicates that in Options 0-1 and C-1, United Russia has an 8:10 ratio of direct and indirect (party-list) seats, while in the case of single-seat constituencies (Options 0 and C) the ratio would have been 17:1.

Option C for three-seat constituencies prompts the candidates to compete for votes even more than Option 0, as candidates receive an opportunity to get a direct seat even without getting into the top 3.

Speaking of voter incentives, we believe that the most essential thing in this case is to reduce the levels of tactical voting. This, in its turn, is most closely related to vote losses described earlier. As was evidenced before, three-seat constituencies significantly reduce vote loss, which means tactical voting incentives are reduced as well. Option C may be used as an additional factor of vote loss reduction.

Considering the issues we have discussed in the paper, we believe that a mixed compensatory electoral system with three-seat constituencies may be considered as the most effective. If said system is used, direct seats go to: 1) candidates placing first, second and third in a constituency; 2) additional direct seats go to candidates from parties admitted to seat allocation based on vote returns for party lists that received less than a half of direct seats (as specified in clause 1) if they (candidates) gained the largest share of votes from valid ballots – this is done so that a party's overall number of direct seats amounts to a half of the overall number of seats it received.

In this case, we cannot but mention that it is impossible to make all constituencies three-seat in a legislative (State Duma) election. Certain constituencies are bound to remain single-seat, as the rule says that any small federative subject in Russia has to be represented as a separate constituency. Quite a few constituencies will remain two-seat for the very same reasons. Nevertheless, a common direction has been established, and three-seat constituencies should replace as many other constituencies as possible. There are no such obstacles in a regional election (except that it is possible that the number of direct seats in a regional parliament is not be divisible by three – but the number can be easily changed), which is why the proposed approach may be fully realized in this case.

That said, Russia is not the only country where the approach is applicable. We believe that the above-mentioned modification proposals for a mixed compensatory system can be used in other countries as well, regardless of whether a variation of a mixed system has already been introduced or the possibility of doing so is being discussed.

Received 17.02.2021, revision received 12.03.2021.

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