An electoral system (or voting system) is a set of rules that determine how elections and referendums are conducted and how their results are determined.
Some electoral systems elect a single winner (single candidate or option), while others elect multiple winners, such as members of parliament or boards of directors.
The study of formally defined electoral methods is called social choice theory or voting theory, and this study can take place within the field of political science, economics, or mathematics, and specifically within the subfields of game theory and mechanism design.
List of electoral systems by types
Key
Name (abbr.) and other names of the system (other names that may sometimes refer to other systems) Type of representation: the most common division of electoral systems Winner-take-all system (also called majoritarian representation): includes all single-winner systems; no guaranteed minority representation Proportional representation Semi-proportional representation Other: sortition, etc. Mixed system (yes/no): A systems composed of multiple other electoral systems, usually containing at least one proportional and one winner-take all system. Superposition/parallel voting Coexistence Fusion Correction Conditional Supermixed Single-winner/multiple winner system List / candidate (personal election, also called nominal election) based system Type of ballot single choice (voter can cast only one vote, whether for a candidate or for a party) multiple choice (voter can cast multiple votes) cumulative(voter can cast more than one vote for a candidate) ranked (preferential voting; ordinal voting) (allows vote transfers) score (cardinal voting) Decision rule No quotas Plurality (candidate or candidates with most votes wins, even if not majority of votes) Quota (candidates must at least reach the quota to be certain of election) Notable quotas Absolute majority (candidates must receive support at least half of voters Hare quota Droop quota Largest remainder method (supplemental method to using quotas) Multi-round voting (common supplemental method to using absolute majority Pairwise comparisons Simple majority rule Other Randomization Number of votes/voter Number of tiers: number of levels e.g. local, regional, state, national
Systems +Name(s)VariationsType of representationMixed?Number of WinnersList-based OR candidate-based systemDecision RuleType of ballotNumber of votes / voterFirst-past-the-post (FPTP/FPP) Single-member plurality (SMP/SMDP)two-round system with lower than 50% requirement in first round1General ticket Party-block voting (PBV)1Plurality block voting (BV) plurality-at-large voting
(multiple non-transferable vote, MTNV)limited party block votingmultiple choicevaries (equal to number of winners)Limited voting (LV) limited block voting
partial block voting
(multiple non-transferable vote, MNTV)limited party block votingmultiple choicevaries (less than number of winners)Single non-transferable vote (SNTV)1Single transferable vote (STV) Hare–Clark electoral systemGeorge Howatt, Democratic Representation under the Hare-Clark System – The Need for Seven-Member Electorates
(proportional ranked-choice voting)ranked choice (ordinal voting)1 (effectively)Instant-runoff voting (IRV) (Alternative vote - AV)
(Ranked-choice voting - RCV)
(Hare's method)contingent vote, supplementary vote, Coombs' methodmajorityranked choice (ordinal voting)1 (effectively)Two-round system (TRS) Runoff votingNon-partisan primary, multi-round votingmajority majoritarian1 (each round)Two-round block voting (majority block voting)(multiple non-transferable vote, MNTV)majoritymultiple choicevaries (equal to number of winners)(each round)Multiple transferable vote (MTV) (Preferential block voting)majorityranked choice (ordinal voting)=number of winners, effectivelyExhaustive ballotmajority1Cumulative votingpanachage (certain types)cumulative ballot>1Approval voting (AV)block approval votingmultiple choiceany number (max. one for one candidate)Score voting Range votingApproval voting (score voting 0–1)score ballot(cardinal voting)Borda countranked choice (ordinal voting)Condorcet methodCopeland's method, Dodgson's method, Kemeny–Young method, Minimax, Nanson's method, ranked pairs, Schulze method, Tideman's alternative methodsmajority against every candidateranked choice (ordinal voting)Party-list proportional representation list-PRLargest remainderHighest averagesBinomial voting Closed List Open List1 (effectively)Superposition - non-compensatory combination of FPTP + List-PR(Supplementary member system)
(Parallel voting)
(Mixed-member majoritarian representation - MMM) |Two-round system + List-PR mixed single vote version
|(+ single-winner in districts) | + list |mixed non-compensatory | |2 (each tier) |- |Seat-linkage compensatory combination of FPTP + List-PR(Additional member system - AMS)
(Mixed-member proportional representation - MMP) |mixed single vote versionbest-loser mixed-member proportional
|(+ single-winner in districts) | + list |mixed compensatory | |2 (each tier) |- |Vote-linkage compensatory combination of FPTP + List-PRPositive vote transfer system (PVT)
(mixed single vote - MSV)
(Additional member system - AMS)negative vote transfer(+ single-winner in districts) + listmixed compensatory1Dual member proportional (DMP)1
List of electoral systems used for national elections
Electoral systemSubtype / combinationType of representationCountries and territories that use it to elect primary (lower) chamber of legislatureFirst-past-the-post (FPTP/FPP)Single-member plurality (SMP/SMDP)noWinner-take-all (single-winner)Antigua and Barbuda, Azerbaijan, Bahamas, Bangladesh, Barbados, Belarus, Belize, Bhutan, Botswana, Canada, Côte d'Ivoire, Dominica, Gambia, Ghana, Grenada, Jamaica, India, Kenya, Liberia, Madagascar, Malawi, Malaysia, Maldives, Micronesia, Myanmar, Nigeria, St. Kitts and Nevis, St. Lucia, Palau, Samoa, Solomon Islands, Trinidad and Tobago, Turkmenistan, Uganda, United Kingdom, St. Vincent and the Grenadines, ZambiaGeneral ticketParty-list plurality block voting (PBV)noWinner-take-allSingaporePlurality block voting (BV)plurality-at-large votingnoWinner-take-allLaos, Lebanon, Mauritius, Oman, Syria, Tonga, Tuvalu, VietnamLimited voting (LV)limited block votingnoSemi-proportionalSingle non-transferable vote (SNTV)noSemi-proportionalSingle transferable vote (STV)noSemi-proportional / ProportionalIreland, MaltaInstant-runoff voting (IRV)noSemi-proportionalAustralia, Papua New GuineaTwo-round system (TRS)Runoff votingnoWinner-take-all (single-winner)FranceTwo-round block voting majority block votingnoWinner-take-allBorda countnoSemi-proportionalNauruModified cumulative votingnoSemi-proportionalNorfolk IslandParty-list proportional representation (list-PR)Closed listProportionalClosed list, locally personalizedProportionalGermanyOpen list for some partiesProportionalColombiaOpen listProportionalAlbania, Algeria, Austria, Belgium, Brazil, Bulgaria, Chile, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Fiji, Finland, Iceland, Indonesia, Jordan, Kosovo, Latvia, Netherlands, Norway, Peru, Poland, Sierra Leone, Slovakia, Slovenia, Sri Lanka, Suriname, SwedenPanachageProportionalEcuador, El Salvador, Honduras, Liechtenstein, Luxembourg, SwitzerlandSuperposition - non-compensatory combination of FPTP + List-PR Parallel voting, Supplementary member systemFPTP + List-PR (two votes)Semi-proportionalCameroon, D.R.Congo, Japan, Kazakhstan, Kyrgyzstan, Nepal, Philippines, Russia, South Korea (de facto), Taiwan, Venezuela, ThailandFPTP + List-PR (tied votes)Semi-proportionalItalyFPTP + List-PR (proportional to FPTP)Winner-take-all / Semi-proportionalPakistan, Tanzania, ZimbabweTRS + List-PRSemi-proportionalEgypt, Lithuania, TajikistanBV/PBV + List-PRSemi-proportionalAndorra, Mauritania, Senegal, Monaco''Seat-linkage compensatory combination of FPTP + List-PRAdditional member system - AMS
Mixed-member proportional representation - MMP |FPTP + List-PR |Semi-proportional / Proportional |Bolivia, Lesotho, New Zealand |- |FPTP + List-PR (hybrid) |Semi-proportional |South Korea (de jure) |- |FPTP + List-PR (limited disproportionality) |Semi-proportional |Mexico |- |Vote-linkage'' (compensatory) combination of FPTP + List-PRFPTP + List-PRSemi-proportionalHungaryMajority bonus systemList-PR with plurality bonusSemi-proportionalGreeceMajority jackpot systemMajority jackpotWinner-take-all / Semi-proportionalDjiboutiMajority/minority jackpotSemi-proportionalArmeniaTwo-round majority jackpotSemi-proportional / ProportionalSan Marino
See also Comparison of electoral systems Sortition Indirect voting Liquid democracy
Notes
References