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Social choice and electoral systems
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Single-winner methodsSingle 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 representationParty-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 systemsBy 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 pathologiesSpoiler 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 Paradoxes of majority rule Tyranny of the majority Discursive dilemma Conflicting majorities paradox
Social and collective choiceImpossibility 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
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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

List of electoral systems used for national elections

Electoral system for national legislatures (lower house or unicameral)
Majoritarian representation (winner-take-all)   Proportional representation  Mixed-member majoritarian representation   Mixed-member proportional representation  Semi-proportional representation (non-mixed)  No election (e.g. Monarchy)

See also

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

References

1. ^ "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. ^ 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. ^ "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. ^ "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)

• Electoral systems
• Electoral systems by outcome type
• Electoral systems by ballot type