# 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
### 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) | 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) 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 (proportional ranked-choice voting) | | semi-proportional / proportional | No | multi-winner | candidate | quota | ranked choice (ordinal voting) | 1 (effectively) | — |
| Instant-runoff voting (IRV) (Alternative vote - AV) (Ranked-choice voting - RCV) (Single-transferable vote - STV) (Hare's method) | contingent vote, supplementary vote, Coombs' method | Winner-take-all | No | single-winner | candidate | majority | ranked choice (ordinal voting) | 1 (effectively) | — |
| Two-round system (TRS) 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) | 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) (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) (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) (mixed single vote - MSV) (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) | | 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

| 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 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) | no | Semi-proportional | Australia, Papua New Guinea |
| Two-round system (TRS) 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 | |
| Party-list proportional representation (list-PR) | Closed list, locally personalized | Proportional | Germany |
| Party-list proportional representation (list-PR) | Open list for some parties | Proportional | Colombia |
| Party-list proportional representation (list-PR) | 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 |
| Party-list proportional representation (list-PR) | 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, South Korea (de facto), Taiwan, Venezuela, Thailand |
| Superposition - non-compensatory combination of FPTP + List-PR Parallel voting, Supplementary member system | FPTP + List-PR (tied votes) | Semi-proportional | Italy |
| Superposition - non-compensatory combination of FPTP + List-PR Parallel voting, Supplementary member system | FPTP + List-PR (proportional to FPTP) | Winner-take-all / Semi-proportional | Pakistan, Tanzania, Zimbabwe |
| Superposition - non-compensatory combination of FPTP + List-PR Parallel voting, Supplementary member system | TRS + List-PR | Semi-proportional | Egypt, Lithuania, Tajikistan |
| Superposition - non-compensatory combination of FPTP + List-PR Parallel voting, Supplementary member system | BV/PBV + List-PR | Semi-proportional | Andorra, Mauritania, Senegal, Monaco |
| Seat-linkage compensatory combination of FPTP + List-PR Additional member system - AMS Mixed-member proportional representation - MMP | FPTP + List-PR | Semi-proportional / Proportional | Bolivia, Lesotho, New Zealand |
| Seat-linkage compensatory combination of FPTP + List-PR Additional member system - AMS Mixed-member proportional representation - MMP | FPTP + List-PR (hybrid) | Semi-proportional | South Korea (de jure) |
| Seat-linkage compensatory combination of FPTP + List-PR Additional member system - AMS Mixed-member proportional representation - MMP | 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 jackpot system | Majority/minority jackpot | Semi-proportional | Armenia |
| Majority jackpot system | Two-round majority jackpot | Semi-proportional / Proportional | San Marino |
* 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)