Proportional representation (PR) refers to any of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions among voters. The aim of such systems is that all votes cast contribute to the result so that each representative in an assembly is mandated by a roughly equal number of voters, and therefore all votes have equal weight. Under other election systems, a bare plurality or a scant majority are all that are used to elect candidates. PR systems provide balanced representation to different factions, usually defined by parties, reflecting how votes were cast. Where only a choice of parties is allowed, the seats are allocated to parties in proportion to the vote tally or vote share each party receives.
Mixed-member proportional representation is a type of representation provided by some mixed electoral systems which combine local winner-take-all elections with a compensatory tier with party lists, in a way that produces proportional representation overall. Like proportional representation, MMP is not a single system, but a principle and goal of several similar systems. Some systems designed to achieve proportionality are still called mixed-member proportional, even if they generally fall short of full proportionality. In this case, they provide semi-proportional representation.
In political science, parallel voting or superposition refers to the use of two or more electoral systems to elect different members of a legislature. More precisely, an electoral system is a superposition if it is a mixture of at least two tiers, which do not interact with each other in any way; one part of a legislature is elected using one method, while another part is elected using a different method, with all voters participating in both. Thus, the final results can be found by calculating the results for each system separately based on the votes alone, then adding them together. A system is called fusion or majority bonus, another independent mixture of two system but without two tiers. Superposition is also not the same as "coexistence", which when different districts in the same election use different systems. Superposition, fusion and coexistence are distinct from dependent mixed electoral systems like compensatory (corrective) and conditional systems.
Direct election is a system of choosing political officeholders in which the voters directly cast ballots for the persons or political party that they wanted to see elected. The method by which the winner or winners of a direct election are chosen depends upon the electoral system used. The most commonly used systems are the plurality system and the two-round system for single-winner elections, such as a presidential election, and proportional representation for the election of a legislature or executive.
A majority bonus system is a mixed-member, partly-proportional electoral system that gives extra seats in a legislature to the party with a plurality or majority of seats. Typically, this is done with the aim of providing government stability, particularly in parliamentary systems.
Parliamentary elections were held in Iceland on 25 April 1987. The Independence Party remained the largest party in the Lower House of the Althing, winning 12 of the 42 seats.
Presidential elections were held in the Gambia on 18 October 2001. The result was a victory for the incumbent Yahya Jammeh, who received just over 50% of the vote.
Regional elections were held in France on 16 March 1986. These were the first regional elections in France. French left-wing parties promised the establishment of regional governments in the 1970s. When the Socialist Party was elected to government in 1981, they implemented territorial reform.
General elections were held in Venezuela on 5 December 1993. The presidential elections were won by former president Rafael Caldera of National Convergence, who received 30% of the vote. Democratic Action remained the largest party in the Chamber of Deputies and Senate, which were elected on separate ballots for the first time. Voter turnout was 60%, the lowest since World War II.
A referendum on the use of nuclear power was held in Austria on 5 November 1978. Voters were asked whether they approved a law allowing the peaceful use of nuclear power, particularly relating to the start-up of the Zwentendorf Nuclear Power Plant. Voters narrowly rejected it, with 50.5% voting against. As a result, although the Power Plant was finished, it never operated and has been repurposed for various projects over the years.
Parliamentary elections were held in Brazil on 15 November 1982. The elections were conducted under the military dictatorship. Massive popular street demonstrations led the military dictatorship to stage the elections.
Scorporo is a partially compensatory, mixed-member majoritarian electoral system, sometimes referred to as a negative vote transfer system (NVT) whereby a portion of members are elected in single-member districts (SMDs) and a portion are elected from a list. It may be fully defined as a parallel voting system which excludes a portion of the SMD winners' votes in electing the proportional tier, to result in a more proportional outcome. The exclusion of a portion of the SMD winners' votes is what makes scorporo fundamentally different from parallel voting and somewhat closer to the additional member system in the UK in theory. However, the design proved particularly susceptible to the decoy list strategy, and as a result by 2001 had devolved into a de facto parallel voting system. The scorporo method is only known to have been used in Italy, but a similar version is in used for the National Assembly of Hungary.
The dual-member mixed proportional (DMP) voting method is a mixed electoral system using a localized list rule to elect two representatives in each district. It is similar to other forms of mixed-member proportional representation, but differs from the better-known additional-member system in that all representatives are elected locally in small districts, rather than requiring separate list seats to be filled in large regional or nationwide districts. In the first step, one seat in each district is awarded to the candidate or party with the most votes, as with first-past-the-post voting rules. In the second step, underrepresented parties are assigned secondary seats in the districts in which they won the most votes, which creates an overall proportional result.
A mixed electoral system is one that uses different electoral systems to elect different seats in a legislature. Most often, this involves a winner-take-all component combined with a proportional component. The results of the combination may be mixed-member proportional (MMP), where the overall results of the elections are proportional, or mixed-member majoritarian, in which case the overall results are semi-proportional, retaining disproportionalities from the majoritarian component. Systems that use multiple types of combinations are sometimes called supermixed.
Rural–urban proportional representation (RUP), also called flexible district PR, is a supermixed electoral system which combines the use of single- and multi-member constituencies in a lower tier and top-up seats in an upper tier to meet the different needs of both rural and urban areas, while protecting the objective of proportionality. The term was coined by Fair Vote Canada, which devised a rural–urban system with the intention of meeting the special challenges of Canada's geography, which includes wide-flung, sparsely populated areas.
A mixed single vote (MSV) is a type of ballot in mixed-member electoral systems, where voters cast a single vote in an election, which used both for electing a local candidate and as a vote for a party affiliated with that candidate according to the rules of the electoral system. Unlike most mixed proportional and mixed majoritarian systems where voters cast two votes, split-ticket voting is not possible under MSV. This significantly reduces the possibility of manipulating compensatory mixed systems, at the price of reducing voter choice. An alternative based on the mixed single vote that still allows for indicating different preferences on different levels is the mixed ballot, which functions as a preferential (mixed) single vote.
Mixed-member majoritarian representation (MMM) is type of a mixed electoral system combining winner-take-all and proportional methods, where the disproportional results of the winner-take-all part are dominant over the proportional component. Mixed member majoritarian systems are therefore categorized under semi-proportional representation, and are usually contrasted with mixed-member proportional representation (MMP) which aims to provide proportional representation compensation ("top-up") seats.
The majorityjackpot system (MJS), also known as a majority-minority apportionment, is a mixed-member majoritarian and conditional voting rule. It produces subproportional representation by fixing the final apportionment for a party or alliance that wins a majority of the vote at some level. It differs from the similar majority bonus system in that the total number of seats is fixed, whereas the majority bonus assigns a fixed number of "bonus" seats to the majority party.
Compensation or correction is an optional mechanism of electoral systems, which corrects the results of one part of the system based on some criterion to achieve a certain result, usually to make it more proportional. There are in general two forms of compensation: vote linkage and seat linkage.
The vote linkage or (multi-tier) vote transfer system is type of compensatory mixed electoral system, where votes may be transferred across multiple tiers of an electoral system, in order to avoid wasted votes - in contrast to the more common seat linkage compensatory system. It often presupposes and is related to the concept of the mixed single vote, which means that the same vote can be used in multiple tiers of an electoral system and that a vote for a local candidate may automatically count as a vote for the candidate's party or the other way around. Voters usually cast their single vote for a local candidate in a single-member district (SMD) and then all the wasted votes from this lower tier are added to distribute seats between upper tier candidates, typically national party lists.
Mathematicsportal 
