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Proportional representation (PR) refers to a type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions (political parties) among voters. The essence of such systems is that all votes cast – or almost all votes cast – contribute to the result and are effectively used to help elect someone – not just a bare plurality, or (exclusively) the majority – and that the system produces mixed, balanced representation reflecting how votes are cast.
In the context of voting systems, PR means that each representative in an assembly is elected by a roughly equal number of voters. In the common case of electoral systems that only allow a choice of parties, the seats are allocated in proportion to the vote share each party receives.
The term "Proportional representation" may also be used to mean fair representation by population as applied to states, regions etc. However, representation being proportional in terms of population size are not considered to make an electoral system proportional the way the term is usually used. For example, the US House of Representatives has 435 members, who each represent a roughly equal number of people and each state is allocated a number of members in accordance with its population size, thus producing fair representation by population. But members of the House are elected in first-past-the-post elections: first-past-the-post is not proportional by vote share as it has only one winner. Meanwhile, PR electoral systems are typically proportional to both population (seats per district) and vote share (typically party-wise). The European Parliament gives each member state a number of seats roughly based on its population size (see degressive proportionality) and further, in each member state the election must be held using a PR system (with proportional results based on vote share).
The most widely used families of PR electoral systems are party-list PR, used in 85 countries, mixed-member PR (MMP), used in 7 countries, and the single transferable vote (STV), used in Ireland, Malta and Australian Senate. All PR systems require multi-member voting districts, meaning votes are pooled to elect multiple representatives at once. Pooling may be done in various multi-member districts (in STV and most list PR systems) or in single countrywide – so called at-large – district (in other list-PR systems). A country-wide pooling of votes to elect more than a hundred members is used in Angola, for example. For large districts, party-list PR is more often used. A purely candidate-based PR system, STV, has never been used to elect more than 21 in a single contest to this point in history. Some PR systems use at-large pooling or regional pooling in conjunction with single-member districts (such as the New Zealand MMP and the Scottish additional member system), others use at-large pooling in conjunction with multi-member districts (Denmark). In these cases pooling is used to allocated the so called leveling seats (top-up) to compensate for the disproportional results produced in single-member districts using FPTP (MMP/AMS) or to polish the fairness produced in multi-member districts using list PR (Denmark's MMP). PR systems that achieve the highest levels of proportionality tend to use as general pooling as possible (typically country-wide) or districts with large numbers of seats.
Due to various factors, perfect proportionality is rarely achieved under PR systems. The use of electoral thresholds (in list-PR or MMP), small districts with few seats in each (in STV or list-PR), absence or insufficient number of leveling seats (in list-PR, MMP or AMS) may produce disproportionality. Other sources are electoral tactics that may be used in certain system, such as party splitting in some MMP systems. Nonetheless, PR systems approximate proportionality much better than other systems and are more resistant to gerrymandering and other forms of manipulation.