In scientific publications, the term "electoral system" is used, as a rule, in a wide and narrow sense. In the first case, this term reflects the structure of social relations that relate to the formation of public authorities. This sphere of relations is quite large. It includes issues of forming a circle of candidates and voters, elective infrastructure, as well as the interaction as a whole, which takes place at each stage of the process. 
Regulation Features
An appropriate system of norms acts as the legal basis for the electoral structure. It is often called a subbranch of state (constitutional) law. However, it should be noted that this regulatory system does not regulate the entire electoral structure. The scope of relations includes some relationships that are managed through corporate acts. These are, in particular, the charters of parties and other political communities. In addition, the regulation of the electoral system is carried out with the help of the electoral traditions and customs of a particular society.
Russian trends
In the Russian Federation at the federal level it is applied proportional majority system election. On January 10, 2003, the Federal Law was adopted. In accordance with it, the president of the country is elected by the majority system (by absolute majority). Until 2005, the formation of the State Duma was carried out in a mixed way.
Innovations
After the adoption of the Federal Law governing the representation of deputies, a proportional election system is used in the formation of the lower house. According to the Law, lists that are able to overcome the seven percent barrier are allowed to the process of distribution of mandates. In this case, certain conditions must be met. In particular, there should be at least 2 lists, and in the aggregate they should collect at least 60% of the vote. The election system in the subjects has its own characteristics. In particular, this concerns the representation of the heads of regions. Previously, they were elected by the majority system by secret ballot on the basis of direct and equal law. Citizens of Russia who live in the territory of the subject could participate in the process. 
Proportional election system
This is one of the forms used in education. representative bodies authorities. The proportional election system is characterized by a special distribution of mandates. In particular, it is carried out in accordance with the number of votes cast for candidate lists. Moreover, they must overcome a certain percentage barrier. The proportional system was used in the formation of the State Duma from 2007 to 2011.
History reference
The proportional system began to take shape in the 19th century with the advent of the party structure. Presumably, she received her first justification in the work of Victor Consideran, published in 1892. The author was a follower of the utopian socialist Fourier. The practical implementation of this electoral system was justified by various mathematicians. In this regard, its variants bear different names. The first country to use the proportional political system was Belgium. This happened in 1899. 
Closed lists for multi-member constituencies
The proportional system can be used in many ways. However, as practice shows, thanks to it, the voting results become more clear.Candidates are placed on the party list in order of preference. They themselves can be open or closed. In the latter case, votes are cast for the entire list, and not for individual candidates. Proportional to them will be allocated and space.
Representatives occupy them in the order in which they are listed. These are the most obvious signs of a proportional electoral system. This formation of lists and the method of voting is used in the formation of the European Parliament in all EU countries. Such a system is used in Israel. Here, the whole country acts as one district, in which there is only one closed list. Since 2007, this method has also been used in Russia. Thus, the State Duma is formed. The election of deputies is carried out in the federal district in proportion to the number of votes cast for the lists. At the same time, the district is the entire Russian Federation.
Open Lists
If such a system is used, then votes are cast depending on the method used. So, either one candidate or two is indicated, or the order of their preference in the list is determined. Such a system is used in the Republic of the Congo, Brazil, the Netherlands and Finland. 
Additional single-member districts
This system is considered "hybrid." It has certain advantages for states with a large population, because it allows you to maintain a balance between national or local interests. There are signs of a proportional electoral system in combination with the structure of single-mandate constituencies. This form of voting is also used in states with a heterogeneous population living in various economic, social, cultural and geographical conditions. In particular, it is used in Great Britain and New Zealand, Mexico and Lesotho, Germany and Bolivia, as well as in Scotland during the formation of the Parliament and the creation of the Legislative Assembly of Wales. Until 2007, it was also used in Russia.
Transmitted Voice
Signs of a proportional system in this case are expressed in the use of the "preference" method. Representatives of the electorate cast their vote for 2 or more candidates. As a result, the selected number is more than the number of places. To win in this case, the candidate needs to collect a minimum quota. It is determined by dividing the total number of votes by the number of available seats +1. For example, if there are 9 vacant places, then the division is carried out by this number plus one, that is, ten. Those candidates who gain the number of votes equal to this result will occupy them. In practice, it is rather rare to distribute all the places according to the results of the first count. At the second stage, the votes that are cast for candidates in excess of the established minimum quota automatically pass to others.
The latter, therefore, get the required amount and also take up space. When using another option for counting votes from candidates who scored the least, they are transferred to the first in the list who have not scored a quota. Thus, he gets the opportunity to take a free place. This whole process lasts until all vacancies are filled. It should be said that, despite the complexity of the calculations, as a result, voters in most cases find their candidate on the list of candidates. Such a system is used in Australia in the formation of the Senate and the House of Representatives of the Capital District of the country and Tasmania, as well as the legislative councils of the states of Victoria, Western and South Australia, South Wales (New). It is also used in states such as Malta, Ireland, and Scotland in the formation of local authorities, as well as in a number of New Zealand counties. 
What are the advantages of this form of representation?
Experts attribute the advantages of the system to the fact that each party receives the number of seats in proportion to the votes cast for it. That is why it is considered the most fair. If the quota is low, then small fractions will also have the opportunity to take up empty seats. An advantage of the system is the fact that different groups of voters can provide vacancies to their representatives. In this regard, the voting result is recognized by the population as fair.
This system allows you to choose candidates whose position is close to their own, and not those who have more chances. When using the open list, representatives of the electorate can cast their ballots for both the candidate and the party. As a result, the influence of factions on the personal composition of their candidates in parliament is reduced. The establishment of a low quota allows a more adequate reflection in the representative body of all the political forces of the country in accordance with their actual impact on the population. Among other things, the percentage of penetration into the state apparatus of representatives of the shadow business or criminal structures that are capable of not entirely legal methods to ensure victory in the regions is quite low. 
Disadvantages of the proportional system
In the case of voting on closed lists, the use of the “steam locomotive principle” is likely. It is, for example, that popular candidates are put at the top of the list. Subsequently, they renounce their mandates, in connection with which unknown people from the end of the list (“wagons”) appear in parliament. In states where form of government favors a constitutional monarchy or parliamentary republic, the formation of the government is carried out by the party that has an advantage in parliament.
In a proportional system, more than in a majority, there is a possibility that not a single fraction will gain an absolute majority. In this regard, there will be a need for the formation of a coalition government. If it consists of ideological enemies, then, presumably, it will become unstable and will not be able to carry out any reforms. In regions where a large number of heterogeneous groups of voters are present, the appearance of numerous small fractions is likely. As a result, the formation of a workable coalition will be difficult. Quoting can reduce this problem.
When using closed lists, there is a weakening of the relationship between the electorate and elected representatives. When using an open voting system, this problem is not. Closed lists give great power to party leaders as they distribute candidates to them. This, in turn, can lead to intra-party dictatorship, trade in places. However, in associations these issues are regulated by special methods. For many voters, the distribution of votes remains unclear. This adversely affects the popularity of the entire system. 
Another area of application
The principle of proportionality is used not only in the electoral system. In general, it is characteristic of many areas of human life. In particular, the system of proportional liability is used in insurance. It relates to compensation payments. The proportional reimbursement system provides for deductions in a predetermined share. Insurance compensation is determined in accordance with the amount of damage. Simply put, not the entire amount is returned, but only the amount of interest by which property was insured.
For example, if the amount is equal to 80% of the assessment of the object, then the same percentage of damage will be paid. The remaining share (20% in this case) will remain at the risk of the insured. The liability limit is limited to the insured amount. The use of this method is supposed to contribute to increasing interest in increasing the insurance amount and premium.As in the case of application in the electoral system, in insurance the principle of proportionality is considered the most fair, and therefore quickly became popular.