List of voting systems

A voting system (or electoral system) is a set of rules that determine how elections and referendums are conducted and how their results are determined.

Some voting systems elect candidate or option a single winner. 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.

## Contents

* 1 List of voting systems by types
* 2 List of electoral systems used for national elections
* 3 See also
* 4 References

## List of voting systems by types

Name of electoral system

other names (other names that may sometimes refer to other systems)

| Variations  | Type of representation  | Mixed?  | Single/multi-winner  | List / candidate-based system

(if multi-winner)

| Type of decision rule  | Type of ballot  | Number of votes / voter  | Number of tiers

(if mixed)

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

Single-member plurality (SMP/SMDP)

| two-round system with lower than 50% requirement in first round  | majoritarian | no  | single-winner  | candidate  | plurality | single choice  | 1  |
General ticket(Plurality) party-block voting (PBV) |  | majoritarian | no  | multi-winner  | list | plurality | single choice  | 1  |
Plurality block voting (BV)

plurality-at-large voting

(multiple non-transferable vote, MTNV)

|  | majoritarian | 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 votesupplementary vote  | majoritarian | no  | single-winner  | candidate  | majority  | ranked choice (ordinal voting)  | 1 (effectively)  |
Two-round system (TRS)[8]

Runoff voting

| non-partisan primarymulti-round voting  | majoritarian | no  | single-winner  | candidate  | majority  | single choice  | 1 (each round)  |
Two-round block voting(majority block voting)(multiple non-transferable vote, MNTV) |  | majoritarian | 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 votingRange voting |  | 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)  |  |
Party-list proportional representation (party-list PR)

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)  |
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  | list or candidate  | plurality | single choice  | 1  | 1

## List of electoral systems used for national elections

## See also

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

## References

1. ↑ "First past the post" (in en). Ministry for Culture and Heritage. 13 January 2016. https://nzhistory.govt.nz/politics/fpp-to-mmp/first-past-the-post.
2. ↑ George Howatt, Democratic Representation under the Hare-Clark System – The Need for Seven-Member Electorates
3. ↑ "How RCV Works". https://www.fairvote.org/how_rcv_works.
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. http://dl.acm.org/citation.cfm?id=2028012.2028015. Retrieved 11 June 2022.
5. ↑ "Alternative Vote" (in en-US). https://www.electoral-reform.org.uk/voting-systems/types-of-voting-system/alternative-vote/.
6. ↑ FairVote.org. "Ranked Choice Voting / Instant Runoff". https://www.fairvote.org/rcv.
7. ↑ Pacuit, Eric (3 August 2011). Voting Methods. https://plato.stanford.edu/archives/fall2019/entries/voting-methods/. Retrieved 11 June 2022.
8. ↑ "Two-Round System". https://www.electoral-reform.org.uk/voting-systems/types-of-voting-system/two-round-system/.
9. ↑ Brams, Steven; Fishburn, Peter (1978). "Approval Voting". American Political Science Review 72 (3): 831–847. doi:10.2307/1955105.
10. ↑ "Parallel —". https://aceproject.org/main/english/es/ese01.htm.
11. ↑ "Additional-member system: Politics". Encyclopædia Britannica. http://www.britannica.com/topic/additional-member-system. 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.
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. https://era.library.ualberta.ca/items/e3ab993a-d264-4d30-b819-290ab5fd6b62. Retrieved June 11, 2022.

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