A joint Politics and Economics series |
Social choice and electoral systems |
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Mathematicsportal |
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.
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) |
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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 | 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, | Winner-take-all | No | single-winner | candidate | majority | ranked choice (ordinal voting) | 1 (effectively) | — |
Two-round system (TRS) [8] Runoff voting | Non-partisan primary, | 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 remainder Highest averages Binomial 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) | Two-round system + List-PR | 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 | mixed single vote version best-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 |
Electoral system | Subtype / combination | Type of representation | Countries and territories that use it to elect primary (lower) chamber of legislature |
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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 | 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) |
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No election (e.g. Monarchy) |
An election is a formal group decision-making process by which a population chooses an individual or multiple individuals to hold public office.
Proportional representation (PR) refers to any type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions among voters. The essence of such systems is that all votes cast – or almost all votes cast – contribute to the result and are effectively used to help elect someone. Under other election systems, a bare plurality or a scant majority are all that are used to elect candidates. PR systems provide balanced representation to different factions, reflecting how votes are cast.
Party-list proportional representation (list-PR) is a system of proportional representation based on preregistered political parties, with each party being allocated a certain number of seats roughly proportional to their share of the vote.
The two-round system, also called ballotage, top-two runoff, or two-round plurality, is a single winner voting method. It is sometimes called plurality-runoff, although this term can also be used for other, closely-related systems such as instant-runoff voting or the exhaustive ballot. It falls under the class of plurality-based voting rules, together with instant-runoff and first-past-the-post (FPP). In a two-round system, if no candidate receives a majority of the vote in the first round, the two candidates with the most votes in the first round proceed to a second round where all other candidates are excluded. Both rounds are held under choose-one voting, where the voter marks a single favored candidate.
The single transferable vote (STV) or proportional-ranked choice voting (P-RCV), is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternative preferences if their preferred candidate is eliminated or elected with surplus votes, so that their vote is used to elect someone they prefer over others in the running. STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another.
Strategic or tactical voting is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results.
Voting refers to the process of choosing officials or policies by casting a ballot, a document used by people to formally express their preferences. Republics and representative democracies are governments where the population chooses representatives by voting.
In the study of electoral systems, the Droop quota is the minimum number of supporters a party or candidate needs to receive in a district to guarantee they will win at least one seat in a legislature.
In social choice, the negative responsiveness, perversity, or additional support paradox is a pathological behavior of some voting rules, where a candidate loses as a result of having "too much support" from some voters, or wins because they had "too much opposition". In other words, increasing (decreasing) a candidate's ranking or rating causes that candidate to lose (win). Electoral systems that do not exhibit perversity are said to satisfy the positive response or monotonicitycriterion.
The quota or divide-and-rank methods make up a category of apportionment rules, i.e. algorithms for allocating seats in a legislative body among multiple groups. The quota methods begin by calculating an entitlement for each party, by dividing their vote totals by an electoral quota. Then, leftover seats, if any are allocated by rounding up the apportionment for some parties. These rules are typically contrasted with the more popular highest averages methods.
A random ballot or random dictatorship is a randomized electoral system where the election is decided on the basis of a single randomly-selected ballot. A closely-related variant is called random serialdictatorship, which repeats the procedure and draws another ballot if multiple candidates are tied on the first ballot.
An electoraldistrict, sometimes called a constituency, riding, or ward, is a subdivision of a larger state created to provide its population with representation in the larger state's legislature. That body, or the state's constitution or a body established for that purpose, determines each district's boundaries and whether each will be represented by a single member or multiple members. Generally, only voters (constituents) who reside within the district are permitted to vote in an election held there. District representatives may be elected by a first-past-the-post system, a proportional representative system, or another voting method. They may be selected by a direct election under universal suffrage, an indirect election, or another form of suffrage.
In the study of apportionment, the Harequota is the number of voters represented by each legislator under an idealized system of proportional representation, where every legislator represents an equal number of voters and where every vote is used to elect someone. The Hare quota is the total number of votes divided by the number of seats to be filled. The Hare quota was used in the original proposal for a single transferable vote system, and is still occasionally used, although it has since been largely supplanted by the Droop quota.
In electoral systems, a wasted vote is any vote cast that is not "used" to elect a winner, and so is not represented in the outcome. However, the term is vague and ill-defined, having been used to refer to a wide variety of unrelated concepts and metrics. The precise definition of a wasted vote can have a major impact on the conclusions of an analysis. For example, under the narrowest possible definition of a wasted vote, the single transferable vote (STV) can be considered to waste zero votes. However, if the wasted vote definition is expanded even slightly, it is possible for up to 100% of STV votes to be classified as wasted because STV fails the unanimity criterion; that is, it is possible to elect a legislature that every single voter agrees is worse than some alternative.
The single transferable vote (STV) is a proportional representation system that elects multiple winners. It is one of several ways of choosing winners from ballots that rank candidates by preference. Under STV, an elector's vote is initially allocated to their first-ranked candidate. Candidates are elected (winners) if their vote tally reaches quota. After the winners in the first count are determined, if seats are still open, surplus votes — those in excess of an electoral quota— are transferred from winners to the remaining candidates (hopefuls) according to the surplus ballots' next usable back-up preference.
FairVote is a 501(c)(3) organization and lobbying group in the United States. It was founded in 1992 as Citizens for Proportional Representation to support the implementation of proportional representation in American elections. Its focus changed over time to emphasize instant-runoff voting (IRV), a national popular vote, and universal voter registration. It changed its name to the Center for Voting and Democracy in 1993 and to FairVote in 2004.
Semi-proportional representation characterizes multi-winner electoral systems which allow representation of minorities, but are not intended to reflect the strength of the competing political forces in close proportion to the votes they receive. Semi-proportional voting systems are generally used as a compromise between complex and expensive but more-proportional systems and simple winner-take-all systems. Examples of semi-proportional systems include the single non-transferable vote, limited voting, and parallel voting.
An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.
Ranked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked system is one that depends only on which of two candidates is preferred by a voter, and as such does not incorporate any information about intensity of preferences. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them very different properties. In instant-runoff voting (IRV) and the single transferable vote system (STV), lower preferences are used as contingencies and are only applied when all higher-ranked preferences on a ballot have been eliminated or when one of the higher ranked preferences has been elected and surplus votes need to be transferred.
Mixed-member majoritarian representation (MMM) is type of a mixed electoral system combining winner-take-all and proportional methods, where the disproportional results of the winner-take-all part are dominant over the proportional component. Mixed member majoritarian systems are therefore categorized under semi-proportional representation, and are usually contrasted with mixed-member proportional representation (MMP) which aims to provide proportional representation compensation ("top-up") seats.
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