List of electoral systems explained

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
• 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)
    • Absolute majority (candidates must receive support at least half of voters
  • Other
    • Pairwise comparisons
• 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

!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							1
General ticketParty-block voting (PBV)								1
Plurality block voting (BV)plurality-at-large voting (multiple non-transferable vote, MTNV)	limited party block voting						multiple choice	=number of winners
Limited voting (LV)limited block voting partial block voting (multiple non-transferable vote, MNTV)	limited party block voting						multiple choice
Single non-transferable vote (SNTV)								1
Single transferable vote (STV)Hare–Clark electoral system^[2] (proportional ranked-choice voting)^[3]							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					majority	ranked choice (ordinal voting)	1 (effectively)
Two-round system (TRS)^[8] Runoff voting	Non-partisan primary,multi-round voting					majority majoritarian		1 (each round)
Two-round block voting(majority block voting)(multiple non-transferable vote, MNTV)						majority	multiple choice	=number of winners (each round)
Multiple transferable vote (MTV)(Preferential block voting)						majority	ranked choice (ordinal voting)	=number of winners, effectively
Exhaustive ballot						majority		1
Cumulative voting	panachage (certain types)						cumulative ballot	>1
Approval voting (AV)^[9]	block approval voting						multiple choice	any number(max. one for one candidate)
Score voting Range voting	Approval voting (score voting 0-1)						score ballot(cardinal voting)
Borda count							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					majority against every candidate	ranked choice (ordinal voting)
Party-list proportional representationlist-PR	Largest remainderHighest averagesBinomial voting							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-PRmixed single vote version			(+ single-winner in districts)	+ list	mixed non-compensatory		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			(+ single-winner in districts)	+ list	mixed compensatory		2 (each tier)	2
Vote-linkage compensatory combination of FPTP + List-PRPositive vote transfer system (PVT)^[12] (mixed single vote - MSV^[13]) (Additional member system - AMS)	negative vote transfer			(+ single-winner in districts)	+ list	mixed compensatory		1	2
Dual member proportional (DMP)^[14]								1	1

List of electoral systems used for national elections

See main article: articles and List of electoral systems by country.

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) 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 ticketParty-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)	no	Semi-proportional	Australia, Papua New Guinea
Two-round system (TRS)Runoff voting	no	Winner-take-all (single-winner)	France
Two-round block votingmajority 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-PRParallel 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-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
	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

See also

• Comparison of electoral systems
• Sortition
• Indirect voting
• Liquid democracy

References

1. Web site: 13 January 2016 . First past the post . 25 May 2022 . nzhistory.govt.nz . . en . 24 May 2022 . https://web.archive.org/web/20220524111637/https://nzhistory.govt.nz/politics/fpp-to-mmp/first-past-the-post . live .
2. George Howatt, Democratic Representation under the Hare-Clark System – The Need for Seven-Member Electorates
3. Web site: How RCV Works . FairVote . 2022-06-11 . 2022-05-25 . https://web.archive.org/web/20220525013704/https://www.fairvote.org/how_rcv_works . live .
4. 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 . 11 June 2022 . 3 October 2018 . https://web.archive.org/web/20181003061635/https://dl.acm.org/citation.cfm?id=2028012.2028015 . live .
5. Web site: Alternative Vote . 2019-05-30 . www.electoral-reform.org.uk . en-US . 2019-05-28 . https://web.archive.org/web/20190528095548/http://www.electoral-reform.org.uk/voting-systems/types-of-voting-system/alternative-vote/ . live .
6. Web site: FairVote.org . Ranked Choice Voting / Instant Runoff . 12 April 2021 . FairVote . 7 January 2021 . https://web.archive.org/web/20210107140218/https://www.fairvote.org/rcv . live .
7. Pacuit . Eric . 3 August 2011 . Voting Methods . plato.stanford.edu . 11 June 2022 . 21 November 2021 . https://web.archive.org/web/20211121171052/https://plato.stanford.edu/archives/fall2019/entries/voting-methods/ . live .
8. Web site: Two-Round System . 7 Nov 2019 . Electoral Reform Society . 12 December 2021 . https://web.archive.org/web/20211212121424/https://www.electoral-reform.org.uk/voting-systems/types-of-voting-system/two-round-system/ . live .
9. Brams . Steven . Fishburn . Peter . 1978 . Approval Voting . American Political Science Review . 72 . 3 . 831–847 . 10.2307/1955105 . 1955105. 251092061 .
10. Web site: Parallel — . 2022-04-21 . aceproject.org . 2022-04-27 . https://web.archive.org/web/20220427030522/https://aceproject.org/main/english/es/ese01.htm . live .
11. Encyclopedia: Additional-member system: Politics . . 24 March 2016 . 8 April 2020 . https://web.archive.org/web/20200408184541/http://www.britannica.com/topic/additional-member-system . live .
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 . 10.1080/00344893.2014.902222 . 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 . 10.7939/r3-qppp-b676 . June 11, 2022 . December 4, 2020 . https://web.archive.org/web/20201204001722/https://era.library.ualberta.ca/items/e3ab993a-d264-4d30-b819-290ab5fd6b62 . live .