List of electoral systems

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

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Key

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  • 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
  • Mixed system (yes/no): A systems composed of multiple other electoral systems, usually containing at least one proportional and one winner-take all system.
  • Single-winner/multiple winner system
  • List / candidate (personal election, also called nominal election) based system
  • Decision rule
    • No quota
      • 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)
    • Other
  • 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)
  • Number of votes/voter
  • Number of tiers: number of levels e.g. local, regional, state, national

Systems

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Name(s) Variations Type of representation Mixed? Single/multi-winner List-based OR candidate-based system Type of decision rule Type of ballot Number of votes / voter Number of tiers

(if mixed)

First-past-the-post (FPTP/FPP)[1]

Single-member plurality (SMP/SMDP)

two-round system with lower than 50% requirement in first round Winner-take-all No single-winner candidate plurality single choice 1
General ticket

Party-block voting (PBV)

Winner-take-all No multi-winner (one slate) list plurality single choice 1
Plurality block voting (BV)

plurality-at-large voting

(multiple non-transferable vote, MTNV)

limited party block voting Winner-take-all No multi-winner candidate plurality multiple choice =number of winners
Limited voting (LV)

limited block voting

partial block voting

(multiple non-transferable vote, MNTV)

limited party block voting semi-proportional No multi-winner candidate plurality multiple choice <number of winners
Single non-transferable vote (SNTV) semi-proportional No multi-winner candidate plurality single choice 1
Single transferable vote (STV)

Hare–Clark electoral system[2]

(proportional ranked-choice voting)[3]

semi-proportional / proportional No multi-winner candidate quota ranked choice (ordinal voting) 1 (effectively)
Instant-runoff voting (IRV)[4]

(Alternative vote - AV)[5]

(Ranked-choice voting - RCV)[6]

(Single-transferable vote - STV)

(Hare's method)[7]

contingent vote,

supplementary vote, Coombs' method

Winner-take-all No single-winner candidate majority ranked choice (ordinal voting) 1 (effectively)
Two-round system (TRS)[8]

Runoff voting

Non-partisan primary,

multi-round voting

Winner-take-all No single-winner candidate majority majoritarian single choice 1 (each round)
Two-round block voting

(majority block voting)(multiple non-transferable vote, MNTV)

Winner-take-all No multi-winner candidate majority multiple choice =number of winners (each round)
Multiple transferable vote (MTV)

(Preferential block voting)

majoritarian No multi-winner candidate majority ranked choice (ordinal voting) =number of winners, effectively
Exhaustive ballot majoritarian No single-winner /multi-winner candidate majority single choice 1
Cumulative voting panachage (certain types) majoritarian / semi-proportional No single-winner /multi-winner candidate plurality cumulative ballot >1
Approval voting (AV)[9] block approval voting majoritarian No single-winner /multi-winner candidate plurality multiple choice any number

(max. one for one candidate)

Score voting
Range voting
Approval voting (score voting 0-1) majoritarian / semi-proportional No single-winner /multi-winner candidate plurality score ballot(cardinal voting)
Borda count majoritarian / semi-proportional No single-winner /multi-winner candidate plurality ranked choice (ordinal voting)
Condorcet method Copeland's method,

Dodgson's method, Kemeny–Young method, Minimax, Nanson's method, ranked pairs, Schulze method, Tideman's alternative methods

majoritarian No single-winner candidate majority against every candidate ranked choice (ordinal voting)
Party-list proportional representation

list-PR

Largest remainderHighest averagesBinomial voting semi-proportional / proportional No multi-winner list (+ candidate, if open list) quota or divisor method single choice 1 (effectively)
Superposition - non-compensatory combination of FPTP + List-PR

(Supplementary member system)

(Parallel voting)[10]

(Mixed-member majoritarian representation - MMM)

Two-round system + List-PR

mixed single vote version

semi-proportional Yes multi-winner(+ single-winner in districts) candidate + list mixed non-compensatory single choice 2 (each tier) 2
Seat-linkage compensatory combination of FPTP + List-PR

(Additional member system - AMS)[11]

(Mixed-member proportional representation - MMP)

mixed single vote versionbest-loser mixed-member proportional semi-proportional / proportional Yes multi-winner(+ single-winner in districts) candidate + list mixed compensatory single choice 2 (each tier) 2
Vote-linkage compensatory combination of FPTP + List-PR

Positive vote transfer system (PVT)[12]

(mixed single vote - MSV[13])

(Additional member system - AMS)

negative vote transfer semi-proportional / proportional Yes multi-winner(+ single-winner in districts) candidate + list mixed compensatory single choice 1 2
Dual member proportional (DMP)[14] semi-proportional / proportional Yes multi-winner (one elected by First-past-the-post voting; the other due to party list PR system list or candidate plurality (votes cast outside district have an effect) single choice 1 1

List of electoral systems used for national elections

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Electoral system Subtype / combination Type of representation Countries and territories that use it to elect primary (lower) chamber of legislature
First-past-the-post (FPTP/FPP)[1]
Single-member plurality (SMP/SMDP)
no Winner-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, Zambia
General ticket

Party-list plurality block voting (PBV)

no Winner-take-all Singapore
Plurality block voting (BV)

plurality-at-large voting

no Winner-take-all Laos, Lebanon, Mauritius, Oman, Syria, Tonga, Tuvalu, Vietnam
Limited voting (LV)

limited block voting

no Semi-proportional
Single non-transferable vote (SNTV) no Semi-proportional
Single transferable vote (STV) no Semi-proportional / Proportional Ireland, Malta
Instant-runoff voting (IRV)[4] no Semi-proportional Australia, Papua New Guinea
Two-round system (TRS)[8]

Runoff voting

no Winner-take-all (single-winner) France
Two-round block voting

majority block voting

no Winner-take-all
Borda count no Semi-proportional Nauru
Modified cumulative voting no Semi-proportional Norfolk Island
Party-list proportional representation (list-PR) Closed list Proportional
Closed list, locally personalized Proportional Germany
Open list for some parties Proportional Colombia
Open list Proportional Albania, 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, Sweden
Panachage Proportional Ecuador, El Salvador, Honduras, Liechtenstein, Luxembourg, Switzerland
Superposition - non-compensatory combination of FPTP + List-PR

Parallel voting, Supplementary member system

FPTP + List-PR (two votes) Semi-proportional Cameroon, D.R.Congo, Japan, Kazakhstan, Kyrgyzstan, Nepal, Philippines, Russia, Taiwan, Venezuela, Thailand
FPTP + List-PR (tied votes) Semi-proportional Italy
FPTP + List-PR (proportional to FPTP) Winner-take-all / Semi-proportional Pakistan, Tanzania, Zimbabwe
TRS + List-PR Semi-proportional Egypt, Lithuania, Tajikistan
BV/PBV + List-PR Semi-proportional Andorra, Mauritania, Senegal, Monaco
Seat-linkage compensatory combination of FPTP + List-PR

Additional member system - AMS[11]

Mixed-member proportional representation - MMP

FPTP + List-PR Semi-proportional / Proportional Bolivia, Lesotho, New Zealand
FPTP + List-PR (hybrid) Semi-proportional South Korea
FPTP + List-PR (limited disproportionality) Semi-proportional Mexico
Vote-linkage compensatory combination of FPTP + List-PR FPTP + List-PR Semi-proportional Hungary
Majority bonus system List-PR with plurality bonus Semi-proportional Greece
Majority jackpot system Majority jackpot Winner-take-all / Semi-proportional Djibouti
Majority/minority jackpot Semi-proportional Armenia
Two-round majority jackpot Semi-proportional / Proportional San Marino
Electoral system for national legislatures

(lower house or unicameral)

  Majoritarian representation (winner-take-all)
  No election (e.g. Monarchy)

See also

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References

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  1. ^ a b "First past the post". nzhistory.govt.nz. Ministry for Culture and Heritage. 13 January 2016. Archived from the original on 24 May 2022. Retrieved 25 May 2022.
  2. ^ George Howatt, Democratic Representation under the Hare-Clark System – The Need for Seven-Member Electorates
  3. ^ "How RCV Works". FairVote. Archived from the original on 2022-05-25. Retrieved 2022-06-11.
  4. ^ a b Cary, David (1 January 2011). "Estimating the Margin of Victory for Instant-runoff Voting". Proceedings of the 2011 Conference on Electronic Voting Technology/Workshop on Trustworthy Elections. EVT/WOTE'11: 3. Archived from the original on 3 October 2018. Retrieved 11 June 2022.
  5. ^ "Alternative Vote". www.electoral-reform.org.uk. Archived from the original on 2019-05-28. Retrieved 2019-05-30.
  6. ^ FairVote.org. "Ranked Choice Voting / Instant Runoff". FairVote. Archived from the original on 7 January 2021. Retrieved 12 April 2021.
  7. ^ Pacuit, Eric (3 August 2011). "Voting Methods". Archived from the original on 21 November 2021. Retrieved 11 June 2022 – via plato.stanford.edu. {{cite journal}}: Cite journal requires |journal= (help)
  8. ^ a b "Two-Round System". Electoral Reform Society. Archived from the original on 12 December 2021. Retrieved 7 Nov 2019.
  9. ^ Brams, Steven; Fishburn, Peter (1978). "Approval Voting". American Political Science Review. 72 (3): 831–847. doi:10.2307/1955105. JSTOR 1955105. S2CID 251092061.
  10. ^ "Parallel —". aceproject.org. Archived from the original on 2022-04-27. Retrieved 2022-04-21.
  11. ^ a b "Additional-member system: Politics". Encyclopædia Britannica. Archived from the original on 8 April 2020. Retrieved 24 March 2016.
  12. ^ Bochsler, D (2014). "Which mixed-member proportional electoral formula fits you best? Assessing the proportionality principle of positive vote transfer systems". Representation. 50: 113–127. doi:10.1080/00344893.2014.902222. S2CID 153691414.
  13. ^ Golosov, G. V. (2013). "The Case for Mixed Single Vote Electoral Systems". The Journal of Social, Political, and Economic Studies.
  14. ^ Graham, Sean (April 4, 2016). "Dual-Member Mixed Proportional: A New Electoral System for Canada". doi:10.7939/r3-qppp-b676. Archived from the original on December 4, 2020. Retrieved June 11, 2022. {{cite journal}}: Cite journal requires |journal= (help)