Mathematics of electoral systems

On the eve of the elections to the State Duma on December 4, 2011, we publish an article about which electoral system seems to be the most optimal experts for Russia. This analysis is a logical continuation of the article by Sergey Spilkin about the “election mathematics” (TRV-hunger, No. 21, October 27, 2009) and was prepared specifically for the TRV-hobby doct. polit. Sciences, professor of comparative political science of the European University in St. Petersburg, director of the Gelix Center Grigory Grigory.

One of the elementary truths of institutional analysis states that in conditions of authoritarianism, institutions do not matter. Indeed, the rules of the game are meaningless if the game is not according to the rules. It is not surprising that in recent years, mathematical modeling has been used in the study of Russian policy almost exclusively for the diagnosis of falsifications. It is clear, however, that in world research practice this direction is secondary. One of the main directions is associated with a quantitative analysis of the effects of electoral systems. And since democratization in Russia, in my opinion, is inevitable, one should not forget about this topic. Sooner or later, we will have to choose an electoral system that would work, and not only created the appearance of democracy, and worked in an optimal way.

In this note, I want to contribute to the solution of this problem by modeling possible results of Russian elections when using different electoral systems. At the same time, I use the data of the latest relatively free all -Russian elections, which was in December 2003. The significance of these elections is that it was after them that the political monopoly of “United Russia” arose in the Duma, which paved the way to the authoritarian transformation of the political system.

The mechanism of this process will be obvious from the lower. But, since my goal is not so much in a retrospective analysis as in the search for the optimal design of the electoral system, I also offer several hypothetical distributions of places when using various methods, and I also evaluate these distributions using a standard disproportionality index (inconsistencies between voters' preferences and the final distributions of places) proposed by Michael Gallaher. It is determined by the formula

Where V is a percentage of votes, and s. - The percentage share of places in a separate batch.

The 2003 elections were held both according to party lists and in the districts. Therefore, I inform the index values ​​in different versions - list (LSQ 1 ), district (LSQ 2 ), and also give the average from these values ​​(LSQ3). The results are presented in the table. In all models, including a proportional component, the method of simple quota and the highest residues, which is used today in the federal elections, is accepted as the method of distribution of mandates. The size of the barrier barrier is 5 %. I note that if in 2003 the current barrier was used 7 %, then the results would not have changed.

In the first two columns of the table, the results of the 2003 elections are given in percentage shares of votes filed for party lists and in 225 single -member districts, as well as shares of votes “against all” and invalid ballots. It is worth paying attention to the fact that such voting methods were especially popular in the districts. As can be seen from the data, the real level of popularity of “United Russia” among voters clearly did not allow her to get a “constitutional majority”. And if this still happened, then due to the effects of the electoral system.

Model 1 is a real distribution of seats after the 2003 elections. They were carried out according to a mixed unrelated electoral system, in which the results are summed up separately on lists and districts and do not affect each other in any way. At the same time, the list elections are held in the national district, covering the entire territory of the country. On the meaning of this detail, I will dwell below. Now it is enough to state that the electoral system allowed United Russia to get a little less than half of the places.

Where did the "constitutional majority" come from? The fact is that the vast majority of deputies elected in single -mandate districts after the election entered the United Russia faction. The results of this are presented in the model 2, where the Party of Power already has 62.4 % of the seats, and the level of imbalance is enormous. The “United Russia” did not have enough places that were not enough to two -thirds due to the entry into its fraction of deputies elected from small parties - such as the People’s Party of the Russian Federation (NPRF) and the ATP.

With a purely proportional system in the national district, as model 3 shows, United Russia would have to be content with a simple majority - however, quite sufficient to control the legislative agenda of the day. If the elections were carried out only in single -mandate districts (model 4), then in the Duma it would be slightly less than 50 % of the “united Russia” and more than 30 % of “independent”. But after their attachment to the United Russia fraction (model 5), its advantage would become colossal, and the average level of imbalance would exceed 33 %.

The representativeness of such a Duma could only be discussed with a fair amount of irony.

The ability of the majority system to give extremely imbalances has been known for a long time. It is all the more strange that votes are still heard with the requirements to abandon the proportional system in favor of majority. The fact is that if a proportional system is used in conditions of authoritarianism, then the disadvantages arise from the conditions, and not from this system itself. If in modern Russia the elections were held according to majority rules, then United Russia would simply win everything without exception.

Models 7 and 8 give a hypothetical distribution of places when using a mixed related electoral system. This system, which has long been used to this day in Germany (it is also called the “mixed member-proportional”), does not differ from the mixed unrelated in Russia in Russia that voters vote separately for party lists and for candidates in the districts. The difference is that the election results are summarized according to proportional rules, however, the places are filled out not in the order of priority of candidates on the list, but primarily departed to party candidates who won the districts. If the party has the right to a larger number of places (and this, as a rule, is exactly so), then the remainder is filled out of the list. If the party wins more places in the districts than it should be based on the results of proportional elections, and especially if independent candidates win the districts, then the size of the parliament simply increases to the missing number of places. In Germany, however, this is extremely rare. In essence, a mixed connected system is proportional. Often it is defined as a "personalized proportional system."

As can be seen from the table, a mixed connected system really gives highly proportional results. Moreover, it allows the voter to vote both for the party and for individual candidates, thus expanding the possibilities of choosing. It is not surprising that she has many supporters, including in Russia. In particular, it is precisely such a system that is laid down in the draft of the electoral code prepared by A.E. Lyubarev under the auspices of the Voice association.

However, this system has a drawback, which, in my opinion, completely eliminates its use in Russia. The fact is that in conditions of an immature party system, it opens up too wide the scope for manipulations. Simply put, if in 2003 such rules were in force in Russia, then all candidates in the districts would go as independent, and after the elections they joined the party factions. Due to this, the faction (as well as the total number of deputies) would double. This does not happen in Germany, because the party belonging of candidates serves as the main guideline for voters, and they would not forgive the parties of such manipulations. In Russia, there are no obstacles to this. It is clear that the representativeness of the Duma would be undermined. It is also clear that the result would be a complete chaos in the party system.

As an alternative, one can consider a purely proportional system used not in the national district, but in the districts of small and medium sizes. I must say that it is such a proportional system that exists in the vast majority of countries. Models 8 and 9 present possible results (before and after the transition of independent ones) if the elections were carried out according to the proportional system in 83 districts formed on the basis of the current constituent entities of the Federation. At the same time, the value of the districts would vary from 1 (in 12 small regions where, thus, a majority system - mainly republics and autonomous districts) to 29 (Moscow), the average value - 5.4. The results were modeled by aggregation by regions of all votes filed for party lists and candidates.

Resume

As follows from the presented data, in terms of the level of imbalance of the tangible difference between a mixed system and a proportional system in small districts. But at the same time, the latter excludes manipulative party strategies and, unlike a mixed related system, creates incentives for the organizational development of parties. I think that this option should have stopped when choosing an optimal electoral system.

The proportional system in small districts allows you to balance the basic principles of representation: party-ideological and territorial. If the voter votes for a party list, then this list is small. You need minimal efforts to find out the biographical details of all candidates, evaluate their political positions and decide whether they deserve trust. In addition, this system allows you to choose a parliament in which the main political forces receive a worthy representation, but the total number of parties is relatively small. This increases the effectiveness of parliamentary work. There are additional advantages.

Firstly, in the small-sized districts there is no need to install a barrier for passing parties to parliament. Small parties, if they do not enjoy strong support in individual districts, are cut off automatically. Secondly, such a system would really participate in the elections not only to party nominees, but also to independent candidates. Contrary to a common misconception, a proportional system does not exclude this. Thirdly, such a system would allow you to completely get rid of one of the shameful phenomena of Russian political life-“steam locomotives”.

The order in which the vacant deputy mandates are filled out at the expense of the waiting list from the party list was borrowed in Germany at one time. It is also used in many other countries. It is quite obvious, however, that in Russia its use led to tremendous abuses. It must be canceled. In a single district, there are no alternative deputies with the size of 450 (or 225) deputies, but in the districts of a small magnitude when the current deputy could simply be held repeated elections. Finally, the radical reduction in the magnitude of the proportional districts would eliminate the excessive impact on the results of the all -Russian elections of those regions where the voter turnout is very high.

In conclusion, I note that a mixed related system still has undoubted advantages, and if it were possible to find a technical way to block the incentives for manipulations built into it, then it could become a quite acceptable option.