Electoral system

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Method by which voters make a choice between options

Plurality-at-large voting (block voting)

  General ticket (party block voting)

Semi-proportional system

  Limited voting or cumulative voting

  Single non-transferable vote

  Modified Borda count

Proportional system
      Party-list proportional representation

  Single transferable vote

Mixed system
    Mixed-member proportional representation
      Mixed-member majoritarian representation
    Majority bonus/jackpot system
Other

  No election

  Varies by state

  No information

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Electoral systems
Single-winner/majoritarian Plurality First-past-the-post Plurality at-large (plurality block voting) General ticket (party block voting) Multi-round voting Two-round Exhaustive ballot Primary election Nonpartisan unified top-four Majority at-large (two-round block voting) Ranked / preferential systems Instant-runoff (alternative vote) Contingent vote Coombs' method Minimax, Nanson's, ranked pairs, Schulze, Alternative Smith ) Positional voting (Borda count, Nauru/Dowdall method) Bucklin voting Oklahoma primary electoral system Preferential block voting Cardinal / graded systems Score voting Approval voting Combined approval voting Unified primary Usual judgment Satisfaction approval voting Majority judgment STAR voting
Proportional representation Party-list Electoral list open list closed list local lists Apportionment Sainte-Laguë D'Hondt Huntington–Hill Hare Droop Imperiali Hagenbach-Bischoff National remnant Highest averages Largest remainder Proportional forms of ranked voting Single transferable vote Gregory Wright Schulze STV CPO-STV Ranked party list PR Spare vote Proportional forms of cardinal voting Proportional approval voting Sequential proportional approval voting Method of Equal Shares Phragmen's voting rules Biproportional apportionment Fair majority voting Weighted voting Direct representation Interactive representation Liquid democracy
Mixed systems By type of representation Mixed-member majoritarian Mixed-member proportional Non-compensatory mixed systems Parallel voting Majority bonus Compensatory mixed systems Additional member system Mixed single vote (positive vote transfer) Scorporo (negative vote transfer) Mixed ballot transferable vote Alternative Vote Plus Dual-member proportional Rural–urban proportional
Other systems and related theory Semi-proportional representation Single non-transferable vote Limited voting Cumulative voting Binomial voting Other systems Multiple non-transferable vote Double simultaneous vote Proxy voting Delegated voting Indirect STV Liquid democracy Random selection (sortition, random ballot) Supermajority Social choice theory Arrow's theorem Gibbard–Satterthwaite theorem Public choice theory Veto Players List of electoral systems List of electoral systems by country Comparison of electoral systems Effects of electoral systems Political fragmentation Political efficacy Voter turnout
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An electoral system or voting system is a set of rules that determine how elections and

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.

Some electoral systems elect a single winner to a unique position, such as prime minister, president or governor, while others elect multiple winners, such as members of parliament or boards of directors. When electing a

STV or Instant-runoff voting

). Mixed systems and some other electoral systems attempt to combine the benefits of non-proportional and proportional systems.

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. Impossibility proofs such as Arrow's impossibility theorem demonstrate that when voters have three or more alternatives, no preferential voting system can guarantee the race between two candidates remains unaffected when an irrelevant candidate participates or drops out of the election.

Types of electoral systems

Main articles: List of electoral systems and List of electoral systems by country

Plurality systems

Plurality voting is a system in which the candidate(s) with the highest number of votes wins, with no requirement to get a majority of votes. In cases where there is a single position to be filled, it is known as first-past-the-post; this is the second most common electoral system for national legislatures, with 58 countries using it for this purpose,^[1] the vast majority of which are current or former British or American colonies or territories. It is also the second most common system used for presidential elections, being used in 19 countries.^[1]

In cases where there are multiple positions to be filled, most commonly in cases of multi-member constituencies, there are several types of plurality electoral systems. Under

block voting (also known as multiple non-transferable vote or plurality-at-large), voters have as many votes as there are seats and can vote for any candidate, regardless of party, a system used in eight countries.^[1] In limited voting voters are given fewer votes than there are seats to be filled. Gibraltar is the only territory where this system is in use).^[1] Under single non-transferable vote (SNTV) voters can vote for only one candidate, with the candidates receiving the most votes declared the winners; this system is used in Kuwait, the Pitcairn Islands and Vanuatu.^[1] In party block voting, voters can only vote for the list of candidates of a single party, with the party receiving the most votes winning all seats. This is used in five countries as part of mixed systems.^[1]

The

Borda Count is a ranked voting system intended to elect broadly acceptable options or candidates, rather than those preferred by a majority.^[2] Under the Borda Count, lower rakings are given lower weighting. This system is used to elect the ethnic minority representatives seats in the Slovenian parliament.^[3][4] The Dowdall system, a multi-member constituency variation on the Borda count, is used in Nauru for parliamentary elections and sees voters rank the candidates. First preference votes are counted as whole numbers; the second preference votes divided by two, third preferences by three; this continues to the lowest possible ranking.^[5] The totals for each candidate determines the winners.^[6]

Majority systems

First-past-the-post

  Instant-runoff voting

Majority voting is a system in which candidates must receive a majority of votes to be elected, either in a runoff election or final round of voting (although in some cases only a plurality is required in the last round of voting if no candidate can achieve a majority). There are two main forms of majoritarian systems, one conducted in a single round of voting using

ranked voting

and the other using multiple elections, to successively narrow the field of candidates. Both are primarily used for single-member constituencies.

Majoritarian voting can be achieved in a single election using instant-runoff voting (IRV), whereby voters rank candidates in order of preference; this system is used for parliamentary elections in Australia and Papua New Guinea. If no candidate receives a majority of the vote in the first round, the second preferences of the lowest-ranked candidate are then added to the totals. This is repeated until a candidate achieves over 50% of the number of valid votes. If not all voters use all their preference votes, then the count may continue until two candidates remain, at which point the winner is the one with the most votes. A modified form of IRV is the contingent vote where voters do not rank all candidates, but have a limited number of preference votes. If no candidate has a majority in the first round, all candidates are excluded except the top two, with the highest remaining preference votes from the votes for the excluded candidates then added to the totals to determine the winner. This system is used in Sri Lankan presidential elections, with voters allowed to give three preferences.^[7]

The other main form of majoritarian system is the

United States Electoral College

.

An

Swiss Federal Council

. In some formats there may be multiple rounds held without any candidates being eliminated until a candidate achieves a majority.

Proportional systems

Proportional representation is the most widely used electoral system for national legislatures, with the parliaments of over eighty countries elected by various forms of the system.

Party-list proportional representation is the single most common electoral system and is used by 80 countries, and involves voters voting for a list of candidates proposed by a party. In closed list systems voters do not have any influence over the candidates put forward by the party, but in open list systems voters are able to both vote for the party list and influence the order in which candidates will be assigned seats. In some countries, notably Israel and the Netherlands, elections are carried out using 'pure' proportional representation, with the votes tallied on a national level before assigning seats to parties. However, in most cases several multi-member constituencies are used rather than a single nationwide constituency, giving an element of geographical representation; but this can result in the distribution of seats not reflecting the national vote totals. As a result, some countries have leveling seats to award to parties whose seat totals are lower than their proportion of the national vote.

In addition to the

Hagenbach-Bischoff quota

.

rank candidates in a multi-member constituency rather than voting for a party list; it is used in Malta and the Republic of Ireland. To be elected, candidates must pass a quota (the Droop quota being the most common). Candidates that pass the quota are elected. If necessary to fill seats, votes are reallocated from the least successful candidates, as well as surplus votes from successful candidates, until all seats are filled by candidates who have passed the quota or until there are only as many remaining candidates as the number of remaining seats.^[6]

Mixed systems

Additional member system

: list-PR + FPTP

In several countries, mixed systems are used to elect the legislature. These include parallel voting (also known as mixed-member majoritarian) and mixed-member proportional representation.

In non-compensatory, parallel voting systems, which are used in 20 countries,^[1] members of a legislature are elected by two different methods; part of the membership is elected by a plurality or majority vote in single-member constituencies and the other part by proportional representation. The results of the constituency vote have no effect on the outcome of the proportional vote.^[6]

In compensatory mixed-member systems the results of the proportional vote are adjusted to balance the seats won in the constituency vote. The mixed-member proportional systems, in use in eight countries, provide enough compensatory seats to ensure that parties have a number of seats approximately proportional to their vote share.^[1]

Other systems may be insufficiently compensatory, and this may result in

Mixed single vote systems are also compensatory, however they usually use a vote transfer mechanism unlike the seat linkage (top-up) method of MMP and may or may not be able to achieve proportional representation. An unusual form of mixed-member compensatory representation using negative vote transfer, Scorporo, was used in Italy from 1993 until 2006.

Some electoral systems feature a majority bonus system to either ensure one party or coalition gains a majority in the legislature, or to give the party receiving the most votes a clear advantage in terms of the number of seats. San Marino has a modified two-round system, which sees a second round of voting featuring the top two parties or coalitions if there is no majority in the first round. The winner of the second round is guaranteed 35 seats in the 60-seat Grand and General Council.^[9] In Greece the party receiving the most votes was given an additional 50 seats,^[10] a system which was abolished following the 2019 elections.

In Uruguay, the President and members of the General Assembly are elected by on a single ballot, known as the double simultaneous vote. Voters cast a single vote, voting for the presidential, Senatorial and Chamber of Deputies candidates of that party. This system was also previously used in Bolivia and the Dominican Republic.

Primary elections

Indirect elections

Some elections feature an indirect electoral system, whereby there is either no popular vote, or the popular vote is only one stage of the election; in these systems the final vote is usually taken by an

Historically, weighted voting systems were used in some countries. These allocated a greater weight to the votes of some voters than others, either indirectly by allocating more seats to certain groups (such as the Prussian three-class franchise), or by weighting the results of the vote. The latter system was used in colonial Rhodesia for the 1962 and 1965 elections. The elections featured two voter rolls (the 'A' roll being largely European and the 'B' roll largely African); the seats of the House Assembly were divided into 50 constituency seats and 15 district seats. Although all voters could vote for both types of seats, 'A' roll votes were given greater weight for the constituency seats and 'B' roll votes greater weight for the district seats. Weighted systems are still used in corporate elections, with votes weighted to reflect stock ownership.

Rules and regulations

In addition to the specific method of electing candidates, electoral systems are also characterised by their wider rules and regulations, which are usually set out in a country's

Electoral rules place limits on suffrage and candidacy. Most countries's electorates are characterised by universal suffrage, but there are differences on the age at which people are allowed to vote, with the youngest being 16 and the oldest 21. People may be disenfranchised for a range of reasons, such as being a serving prisoner, being declared bankrupt, having committed certain crimes or being a serving member of the armed forces. Similar limits are placed on candidacy (also known as passive suffrage), and in many cases the age limit for candidates is higher than the voting age. A total of 21 countries have compulsory voting, although in some there is an upper age limit on enforcement of the law.^[11] Many countries also have the none of the above option on their ballot papers.

In systems that use constituencies, apportionment or districting defines the area covered by each constituency. Where constituency boundaries are drawn has a strong influence on the likely outcome of elections in the constituency due to the geographic distribution of voters. Political parties may seek to gain an advantage during redistricting by ensuring their voter base has a majority in as many constituencies as possible, a process known as gerrymandering. Historically rotten and pocket boroughs, constituencies with unusually small populations, were used by wealthy families to gain parliamentary representation.

Some countries have minimum turnout requirements for elections to be valid. In Serbia this rule caused multiple re-runs of presidential elections, with the 1997 election re-run once and the 2002 elections re-run three times due insufficient turnout in the

Reserved seats are used in many countries to ensure representation for ethnic minorities, women, young people or the disabled. These seats are separate from general seats, and may be elected separately (such as in Morocco where a separate ballot is used to elect the 60 seats reserved for women and 30 seats reserved for young people in the House of Representatives), or be allocated to parties based on the results of the election; in Jordan the reserved seats for women are given to the female candidates who failed to win constituency seats but with the highest number of votes, whilst in Kenya the Senate seats reserved for women, young people and the disabled are allocated to parties based on how many seats they won in the general vote. Some countries achieve minority representation by other means, including requirements for a certain proportion of candidates to be women, or by exempting minority parties from the electoral threshold, as is done in Poland,^[14] Romania and Serbia.^[15]

History

Pre-democratic

In ancient Greece and Italy, the institution of suffrage already existed in a rudimentary form at the outset of the historical period. In the early monarchies it was customary for the king to invite pronouncements of his people on matters in which it was prudent to secure its assent beforehand. In these assemblies the people recorded their opinion by clamouring (a method which survived in Sparta as late as the 4th century BCE), or by the clashing of spears on shields.^[16]

Early democracy

Voting has been used as a feature of democracy since the 6th century BCE, when democracy was introduced by the

Generally, the taking of votes was effected in the form of a poll. The practice of the Athenians, which is shown by inscriptions to have been widely followed in the other states of Greece, was to hold a show of hands, except on questions affecting the status of individuals: these latter, which included all lawsuits and proposals of ostracism, in which voters chose the citizen they most wanted to exile for ten years, were determined by secret ballot (one of the earliest recorded elections in Athens was a plurality vote that it was undesirable to win, namely an ostracism vote). At Rome the method which prevailed up to the 2nd century BCE was that of division (discessio). But the system became subject to intimidation and corruption. Hence a series of laws enacted between 139 and 107 BCE prescribed the use of the ballot (tabella), a slip of wood coated with wax, for all business done in the assemblies of the people. For the purpose of carrying resolutions a simple majority of votes was deemed sufficient. As a general rule equal value was made to attach to each vote; but in the popular assemblies at Rome a system of voting by groups was in force until the middle of the 3rd century BCE by which the richer classes secured a decisive preponderance.^[16]

Most elections in the early history of democracy were held using plurality voting or some variant, but as an exception, the state of Venice in the 13th century adopted approval voting to elect their Great Council.^[17]

The Venetians' method for electing the Doge was a particularly convoluted process, consisting of five rounds of drawing lots (sortition) and five rounds of approval voting. By drawing lots, a body of 30 electors was chosen, which was further reduced to nine electors by drawing lots again. An electoral college of nine members elected 40 people by approval voting; those 40 were reduced to form a second electoral college of 12 members by drawing lots again. The second electoral college elected 25 people by approval voting, which were reduced to form a third electoral college of nine members by drawing lots. The third electoral college elected 45 people, which were reduced to form a fourth electoral college of 11 by drawing lots. They in turn elected a final electoral body of 41 members, who ultimately elected the Doge. Despite its complexity, the method had certain desirable properties such as being hard to game and ensuring that the winner reflected the opinions of both majority and minority factions.^[18] This process, with slight modifications, was central to the politics of the Republic of Venice throughout its remarkable lifespan of over 500 years, from 1268 to 1797.

Development of new systems

Jean-Charles de Borda proposed the Borda count in 1770 as a method for electing members to the French Academy of Sciences. His method was opposed by the Marquis de Condorcet, who proposed instead the method of pairwise comparison that he had devised. Implementations of this method are known as Condorcet methods. He also wrote about the Condorcet paradox, which he called the intransitivity of majority preferences. However, recent research has shown that the philosopher Ramon Llull devised both the Borda count and a pairwise method that satisfied the Condorcet criterion in the 13th century. The manuscripts in which he described these methods had been lost to history until they were rediscovered in 2001.^[19]

Later in the 18th century,

Perhaps influenced by the rapid development of multiple-winner electoral systems, theorists began to publish new findings about single-winner methods in the late 19th century. This began around 1870, when William Robert Ware proposed applying STV to single-winner elections, yielding instant-runoff voting (IRV).^[22] Soon, mathematicians began to revisit Condorcet's ideas and invent new methods for Condorcet completion; Edward J. Nanson combined the newly described instant runoff voting with the Borda count to yield a new Condorcet method called Nanson's method. Charles Dodgson, better known as Lewis Carroll, proposed the straightforward Condorcet method known as Dodgson's method. He also proposed a proportional representation system based on multi-member districts, quotas as minimum requirements to take seats, and votes transferable by candidates through proxy voting.^[23]

Ranked voting electoral systems eventually gathered enough support to be adopted for use in government elections. In Australia, IRV was first adopted in 1893 and STV in 1896 (Tasmania). IRV continues to be used along with STV today.

In the United States in the early-20th-century

The use of game theory to analyze electoral systems led to discoveries about the effects of certain methods. Earlier developments such as Arrow's impossibility theorem had already shown the issues with ranked voting systems. Research led Steven Brams and Peter Fishburn to formally define and promote the use of approval voting in 1977.^[26] Political scientists of the 20th century published many studies on the effects that the electoral systems have on voters' choices and political parties,^[27][28][29] and on political stability.^[30][31] A few scholars also studied which effects caused a nation to switch to a particular electoral system.^{[32][33][34][35][36]}

The study of electoral systems influenced a new push for electoral reform beginning around the 1990s, when proposals were made to replace plurality voting in governmental elections with other methods. New Zealand adopted mixed-member proportional representation for the 1996 general elections, having been approved in a 1993 referendum.^[37] After plurality voting was a key factor in the contested results of the 2000 presidential elections in the United States, various municipalities in the United States began to adopt instant-runoff voting, although some of them subsequently returned to their prior method. However, attempts at introducing more proportional systems were not always successful; in Canada there were two referendums in British Columbia in 2005 and 2009 on adopting an STV method, both of which failed. In the United Kingdom, a 2011 referendum on adopting IRV saw the proposal rejected.

In other countries there were calls for the restoration of plurality or majoritarian systems or their establishment where they have never been used; a referendum was held in Ecuador in 1994 on the adoption the two round system, but the idea was rejected. In Romania a proposal to switch to a two-round system for parliamentary elections failed only because voter turnout in the referendum was too low. Attempts to reintroduce single-member constituencies in Poland (2015) and two-round system in Bulgaria (2016) via referendums both also failed due to low turnout.

Comparison of electoral systems

Electoral systems can be compared by different means. Attitudes towards systems are highly influenced by the systems' impact on groups that one supports or opposes, which can make the objective comparison of voting systems difficult. There are several ways to address this problem. One approach is to define criteria mathematically, such that any electoral system either passes or fails. This gives perfectly objective results, but their practical relevance is still arguable. Another approach is to define ideal criteria that no electoral system passes perfectly, and then see how often or how close to passing various methods are over a large sample of simulated elections. This gives results which are practically relevant, but the method of generating the sample of simulated elections can still be arguably biased. A final approach is to consider practical criteria, and then assign a neutral body to evaluate each method according to these criteria or evaluate the performance of countries with these electoral systems. The practical criteria include political fragmentation, voter turnout, wasted votes, complexity of vote counting, and barriers to entry for new political movements.^[38] The quality of electoral systems can be measured on outcomes, such as voter turnout,^[39][40] and reduced political apathy. This approach can look at aspects of electoral systems, which the other two approaches miss, but both the definitions of these criteria and the evaluations of the methods are still inevitably subjective.

Arrow's theorem and the Gibbard–Satterthwaite theorem prove that no single-winner system using ranked voting can meet all such criteria simultaneously, while Gibbard's theorem proves the same for all single-winner deterministic voting methods.

According to a 2006 survey of electoral system experts, their preferred electoral systems were in order of preference:^[41]

1. Mixed member proportional
2. Single transferable vote
3. Open list proportional
4. Alternative vote
5. Closed list proportional
6. Single member plurality
7. Runoffs
8. Mixed member majoritarian
9. Single non-transferable vote

Systems by elected body

This section is an excerpt from List of electoral systems by country § Maps.[edit]

Head of state

Lower (or unicameral) house

Upper house

Single-winner system / single-member constituencies (non-proportional)    First past the post /single member plurality (FPTP/SMP)   Two-round system (TRS)   Instant-runoff voting (IRV) Multi-member constituencies, majoritarian (non-proportional)    Block voting (BV) or mixed FPTP and BV   Party block voting (PBV) or mixed FPTP and PBV Multi-member constituencies, semi-proportional   Limited voting (LV) or cumulative voting   Single non-transferable vote (SNTV) or mixed FPTP and SNTV   Modified Borda count Multi-member constituencies, proportional   Party-list proportional representation (list PR)   Single transferable vote (STV)

Mixed non-compensatory (semi-proportional)   Mixed-member majoritarian (MMM): parallel voting (FPTP and list PR)   Mixed-member majoritarian (MMM): parallel voting (TRS and list PR)   Mixed-member majoritarian (MMM): parallel voting (BV/PBV and list PR)   List PR with plurality bonus (MBS)   Parallel voting (SNTV and list PR) Mixed compensatory (proportional or semi-proportional)   Mixed-member majoritarian (MMM) with compensation / scorporo    Additional member system / semi-proportional MMP   Mixed-member proportional representation (MMP)   Majority jackpot (majority of seats reserved for largest party/coalition)

Indirect election   Election by legislature   Election by electoral college or local legislatures   Partly elected by electoral college or local legislatures, partly appointed by head of state Other   No election (e.g. Monarchy)   Appointed by head of state   Varies by federal states or constituencies   No information/Unicameral legislature

See also

Notes

References