Proportional representation

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Single-winner methods Single vote - plurality methods First preference plurality (FPP) Two-round (US: Jungle primary) Partisan primary Instant-runoff UK: Alternative vote (AV) US: Ranked-choice (RCV) Condorcet methods Condorcet-IRV Round-robin voting Minimax Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin) Antiplurality (el. Coombs) Cardinal voting Score voting Approval voting Majority judgment STAR voting
Proportional representation Party-list Apportionment Highest averages Largest remainders National remnant Biproportional List type Closed list Open list Panachage List-free PR Localized list Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Approval-based committees Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Fractional social choice Direct representation Interactive representation Liquid democracy Fractional approval voting Maximal lottery Random ballot Semi-proportional representation Cumulative SNTV Limited voting
Mixed systems By results of combination Mixed-member majoritarian Mixed-member proportional By mechanism of combination Non-compensatory Parallel (superposition) Coexistence Conditional Fusion (majority bonus) Compensatory Seat linkage system UK: 'AMS' NZ: 'MMP' Vote linkage system Negative vote transfer Mixed ballot Supermixed systems Dual-member proportional Rural–urban proportional Majority jackpot By ballot type Single vote Double simultaneous vote Dual-vote
Paradoxes and pathologies Spoiler effects Spoiler effect Cloning paradox Frustrated majorities paradox Center squeeze Pathological response Perverse response Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting Exaggeration Truncation Turkey-raising Wasted vote Paradoxes of majority rule Tyranny of the majority Discursive dilemma Conflicting majorities paradox
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Positive results Median voter theorem Condorcet's jury theorem May's theorem Condorcet dominance theorems Harsanyi's utilitarian theorem VCG mechanism Quadratic voting
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Proportional representation (PR) refers to any electoral system under which subgroups of an electorate are reflected proportionately in the elected body.^[1] The concept applies mainly to political divisions (political parties) 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.

Exact proportionality is never achieved under PR systems, except by chance. The use of electoral thresholds that are intended to limit the influence of small, extreme parties will reduce proportionality in list systems, and any insufficiency of leveling seats will further reduce proportionality in mixed-member proportional or additional-member systems. Small districts with few seats in each that allow localised representation reduce proportionality in STV or list PR systems. Other sources of disproportionality are electoral tactics, such as party splitting in some MMP systems. Nonetheless, PR systems approximate proportionality much better than other systems^[2] and are more (or completely) resistant to gerrymandering and other forms of manipulation.

Some PR systems do not necessitate the use of parties; others do. The most widely used families of PR electoral systems are party-list PR, used in 85 countries;^[3] mixed-member PR (MMP), used in 7 countries;^[4] and the single transferable vote (STV), used in Ireland,^[5] Malta, the Australian Senate, and Indian Rajya Sabha.^[6][7] Proportional representation systems are used at all levels of government and are also used for elections to non-governmental bodies, such as corporate boards.