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An electoral system or voting system is a set of rules that determine how elections and
referendums A referendum (plural: referendums or less commonly referenda) is a direct vote by the electorate on a proposal, law, or political issue. This is in contrast to an issue being voted on by a representative. This may result in the adoption of a ...
are conducted and how their results are determined. 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. 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
legislature A legislature is an assembly with the authority to make law Law is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior,Robertson, ''Crimes against humanity'', 90. with its p ...
, areas may be divided into constituencies with one or more representatives. Voters may vote directly for individual candidates or for a list of candidates put forward by a
political party A political party is an organization that coordinates candidates to compete in a particular country's elections. It is common for the members of a party to hold similar ideas about politics, and parties may promote specific ideological or p ...
or
alliance An alliance is a relationship among people, groups, or states that have joined together for mutual benefit or to achieve some common purpose, whether or not explicit agreement has been worked out among them. Members of an alliance are called ...
. There are many variations in electoral systems, with the most common systems being
first-past-the-post voting In a first-past-the-post electoral system (FPTP or FPP), formally called single-member plurality voting (SMP) when used in single-member districts or informally choose-one voting in contrast to ranked voting, or score voting, voters cast thei ...
,
block voting Block voting or bloc voting refers to electoral systems in which multiple candidates are elected at once and a group (voting bloc) of voters can force the system to elect only their preferred candidates. Block voting may be used at large (in a si ...
, the two-round (runoff) system,
proportional representation Proportional representation (PR) refers to a type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to geographical (e.g. states, regions) and political divis ...
and
ranked voting The term ranked voting (also known as preferential voting or ranked choice voting) refers to any voting system in which voters rank their candidates (or options) in a sequence of first or second (or third, etc.) on their respective ballots. Ra ...
. Some electoral systems, such as mixed 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 Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...
, or mathematics, and specifically within the subfields of game theory and
mechanism design Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts a ...
. Impossibility proofs such as
Arrow's impossibility theorem Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral syst ...
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


Plurality systems

Plurality voting Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member pe ...
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 In a first-past-the-post electoral system (FPTP or FPP), formally called single-member plurality voting (SMP) when used in single-member districts or informally choose-one voting in contrast to ranked voting, or score voting, voters cast thei ...
; this is the second most common electoral system for national legislatures, with 58 countries using it for this purpose,Table of Electoral Systems Worldwide
IDEA
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. In cases where there are multiple positions to be filled, most commonly in cases of multi-member constituencies, plurality voting is referred to as
block voting Block voting or bloc voting refers to electoral systems in which multiple candidates are elected at once and a group (voting bloc) of voters can force the system to elect only their preferred candidates. Block voting may be used at large (in a si ...
, multiple non-transferable vote or plurality-at-large. This takes two main forms: in one form voters have as many votes as there are seats and can vote for any candidate, regardless of party – this is used in eight countries. There are variations on this system such as
limited voting Limited voting (also known as partial block voting) is a voting system in which electors have fewer votes than there are positions available. The positions are awarded to the candidates who receive the most votes absolutely. In the special case ...
, where voters are given fewer votes than there are seats to be filled (
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is the only territory where this system is in use) and single non-transferable vote (SNTV), in which voters can vote for only one candidate in a multi-member constituency, with the candidates receiving the most votes declared the winners; this system is used in
Kuwait Kuwait (; ar, الكويت ', or ), officially the State of Kuwait ( ar, دولة الكويت '), is a country in Western Asia. It is situated in the northern edge of Eastern Arabia at the tip of the Persian Gulf, bordering Iraq to the nort ...
, the Pitcairn Islands and
Vanuatu Vanuatu ( or ; ), officially the Republic of Vanuatu (french: link=no, République de Vanuatu; bi, Ripablik blong Vanuatu), is an island country located in the South Pacific Ocean. The archipelago, which is of volcanic origin, is east of no ...
. In the other main form of block voting, also known as party block voting, voters can only vote for the multiple candidates of a single party, with the party receiving the most votes winning all contested positions. This is used in five countries as part of mixed systems. 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 depending on how many seats there are in their constituency. 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. The totals achieved by each candidate determine the winners.Glossary of Terms
IDEA


Majority systems

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 election using
ranked voting The term ranked voting (also known as preferential voting or ranked choice voting) refers to any voting system in which voters rank their candidates (or options) in a sequence of first or second (or third, etc.) on their respective ballots. Ra ...
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 Papua New Guinea (abbreviated PNG; , ; tpi, Papua Niugini; ho, Papua Niu Gini), officially the Independent State of Papua New Guinea ( tpi, Independen Stet bilong Papua Niugini; ho, Independen Stet bilong Papua Niu Gini), is a country i ...
. 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 The contingent vote is an electoral system used to elect a single representative in which a candidate requires a majority of votes to win. It is a variation of instant-runoff voting (IRV). Under the contingent vote, the voter ranks the cand ...
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. The other main form of majoritarian system is the
two-round system The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resu ...
, which is the most common system used for presidential elections around the world, being used in 88 countries. It is also used in 20 countries for electing the legislature. If no candidate achieves a majority of votes in the first round of voting, a second round is held to determine the winner. In most cases the second round is limited to the top two candidates from the first round, although in some elections more than two candidates may choose to contest the second round; in these cases the second round is decided by plurality voting. Some countries use a modified form of the two-round system, such as
Ecuador Ecuador ( ; ; Quechua: ''Ikwayur''; Shuar: ''Ecuador'' or ''Ekuatur''), officially the Republic of Ecuador ( es, República del Ecuador, which literally translates as "Republic of the Equator"; Quechua: ''Ikwadur Ripuwlika''; Shuar: ' ...
where a candidate in the presidential election is declared the winner if they receive 40% of the vote and are 10% ahead of their nearest rival, or Argentina (45% plus 10% ahead), where the system is known as
ballotage The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resul ...
. An
exhaustive ballot The exhaustive ballot is a voting system used to elect a single winner. Under the exhaustive ballot the elector casts a single vote for their chosen candidate. However, if no candidate is supported by an overall majority of votes then the candid ...
is not limited to two rounds, but sees the last-placed candidate eliminated in each round of voting. Due to the potentially large number of rounds, this system is not used in any major popular elections, but is used to elect the Speakers of parliament in several countries and members of the
Swiss Federal Council The Federal Council (german: Bundesrat; french: Conseil fédéral; it, Consiglio federale; rm, Cussegl federal) is the executive body of the federal government of the Swiss Confederation and serves as the collective head of state and governm ...
. In some formats there may be multiple rounds held without any candidates being eliminated until a candidate achieves a majority, a system used in the
United States Electoral College The United States Electoral College is the group of presidential electors required by the Constitution to form every four years for the sole purpose of appointing the president and vice president. Each state and the District of Columbia a ...
.


Proportional systems

Proportional representation Proportional representation (PR) refers to a type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to geographical (e.g. states, regions) and political divis ...
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 Open list describes any variant of party-list proportional representation where voters have at least some influence on the order in which a party's candidates are elected. This is as opposed to closed list, which allows only active members, par ...
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 Israel (; he, יִשְׂרָאֵל, ; ar, إِسْرَائِيل, ), officially the State of Israel ( he, מְדִינַת יִשְׂרָאֵל, label=none, translit=Medīnat Yīsrāʾēl; ), is a country in Western Asia. It is situated ...
and the
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, 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
electoral threshold The electoral threshold, or election threshold, is the minimum share of the primary vote that a candidate or political party requires to achieve before they become entitled to representation or additional seats in a legislature. This limit can ...
(the minimum percentage of the vote that a party must obtain to win seats), there are several different ways to allocate seats in proportional systems. There are two main types of systems: highest average and largest remainder. Highest average systems involve dividing the votes received by each party by a series of divisors, producing figures that determine seat allocation; for example the
D'Hondt method The D'Hondt method, also called the Jefferson method or the greatest divisors method, is a method for allocating seats in parliaments among federal states, or in party-list proportional representation systems. It belongs to the class of highest ...
(of which there are variants including Hagenbach-Bischoff) and the
Webster/Sainte-Laguë method The Webster method, also called the Sainte-Laguë method () or the major fractions method, is a method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system. The metho ...
. Under largest remainder systems, parties' vote shares are divided by the quota (obtained by dividing the total number of votes by the number of seats available). This usually leaves some seats unallocated, which are awarded to parties based on the largest fractions of seats that they have remaining. Examples of largest remainder systems include the Hare quota, Droop quota, the Imperiali quota and the Hagenbach-Bischoff quota.
Single transferable vote Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate ...
(STV) is another form of proportional representation; in STV, voters
rank Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking, such as: Level or position in a hierarchical organization * Academic rank * Diplomatic rank * Hierarchy * ...
candidates in a multi-member constituency rather than voting for a party list; it is used in
Malta Malta ( , , ), officially the Republic of Malta ( mt, Repubblika ta' Malta ), is an island country in the Mediterranean Sea. It consists of an archipelago, between Italy and Libya, and is often considered a part of Southern Europe. It lies ...
and the
Republic of Ireland Ireland ( ga, Éire ), also known as the Republic of Ireland (), is a country in north-western Europe consisting of 26 of the 32 Counties of Ireland, counties of the island of Ireland. The capital and largest city is Dublin, on the eastern ...
. To be elected, candidates must pass a quota (the Droop quota being the most common). Candidates that pass the quota on the first count are elected. Votes are then reallocated from the least successful candidates, as well as surplus votes from successful candidates, until all seats have been filled by candidates who have passed the quota.


Mixed systems

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, there are two methods by which members of a legislature are elected; 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. In compensatory mixed-member representation the results of the proportional vote are adjusted to balance the seats won in the constituency vote. In mixed-member proportional systems, in use in eight countries, there is enough compensation in order to ensure that parties have a number of seats proportional to their vote share. Other systems may be insufficiently compensatory, and this may result in
overhang seat Overhang seats are constituency seats won in an election under the traditional mixed member proportional (MMP) system (as it originated in Germany), when a party's share of the nationwide votes would entitle it to fewer seats than the number of ...
s, where parties win more seats in the constituency system than they would be entitled to based on their vote share. Variations of this include the Additional Member System, and
Alternative Vote Plus The alternative vote plus (AV+), or alternative vote top-up, is a semi-proportional voting system. AV+ was devised by the 1998 Jenkins Commission which first proposed the idea as a system that could be used for elections to the Parliament of ...
, in which voters cast votes for both single-member constituencies and multi-member constituencies; the allocation of seats in the multi-member constituencies is adjusted to achieve an overall seat total proportional to parties' vote share by taking into account the number of seats won by parties in the single-member constituencies.
Mixed single vote The mixed single vote (MSV) or positive vote transfer system (PVT) is a mixed-member electoral system, where voters cast a single vote in an election, which used both for electing a local candidate and as a vote for a party affiliated with that ...
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 ''Scorporo'' (, ) is a partially compensatory, mixed-member majoritarian electoral system, sometimes referred to as a negative vote transfer system (NVT) whereby a portion of members are elected in single-member districts (SMDs) and a portion ...
, was used in Italy from 1993 until 2006. Some electoral systems feature a
majority bonus system The majority bonus system (MBS) is a form of semi-proportional representation used in some European countries. Its feature is a majority bonus which gives extra seats or representation in an elected body to the party or to the joined parties with ...
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 The Grand and General Council ( it, Consiglio Grande e Generale) is the parliament of San Marino. The council has 60 members elected for a five-year term. History From the fifth century San Marino was ruled by an assembly composed by all t ...
. In
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the party receiving the most votes was given an additional 50 seats, a system which was abolished following the
2019 elections The following elections were scheduled to occur in 2019. The International Foundation for Electoral Systems has a calendar of upcoming elections around the world, and the National Democratic Institute also maintains a calendar of elections in coun ...
. In
Uruguay Uruguay (; ), officially the Oriental Republic of Uruguay ( es, República Oriental del Uruguay), is a country in South America. It shares borders with Argentina to its west and southwest and Brazil to its north and northeast; while bordering ...
, 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 The Dominican Republic ( ; es, República Dominicana, ) is a country located on the island of Hispaniola in the Greater Antilles archipelago of the Caribbean region. It occupies the eastern five-eighths of the island, which it shares with ...
.


Primary elections

Primary elections are a feature of some electoral systems, either as a formal part of the electoral system or informally by choice of individual political parties as a method of selecting candidates, as is the case in
Italy Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical ...
. Primary elections limit the risk of vote splitting by ensuring a single party candidate. In
Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the second-largest country in South America after Brazil, th ...
they are a formal part of the electoral system and take place two months before the main elections; any party receiving less than 1.5% of the vote is not permitted to contest the main elections. In the United States, there are both partisan and non-partisan
primary elections Primary elections, or direct primary are a voting process by which voters can indicate their preference for their party's candidate, or a candidate in general, in an upcoming general election, local election, or by-election. Depending on the c ...
.


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 electoral college. In several countries, such as
Mauritius Mauritius ( ; french: Maurice, link=no ; mfe, label= Mauritian Creole, Moris ), officially the Republic of Mauritius, is an island nation in the Indian Ocean about off the southeast coast of the African continent, east of Madagascar. It ...
or
Trinidad and Tobago Trinidad and Tobago (, ), officially the Republic of Trinidad and Tobago, is the southernmost island country in the Caribbean. Consisting of the main islands Trinidad and Tobago, and numerous much smaller islands, it is situated south of ...
, the post of President is elected by the legislature. In others like
India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
, the vote is taken by an electoral college consisting of the national legislature and state legislatures. In the
United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...
, the president is indirectly elected using a two-stage process; a popular vote in each state elects members to the electoral college that in turn elects the President. This can result in a situation where a candidate who receives the most votes nationwide does not win the electoral college vote, as most recently happened in
2000 File:2000 Events Collage.png, From left, clockwise: Protests against Bush v. Gore after the 2000 United States presidential election; Heads of state meet for the Millennium Summit; The International Space Station in its infant form as seen from S ...
and
2016 File:2016 Events Collage.png, From top left, clockwise: Bombed-out buildings in Ankara following the 2016 Turkish coup d'état attempt; the Impeachment of Dilma Rousseff, impeachment trial of Brazilian President Dilma Rousseff; Damaged houses duri ...
.


Systems used outside politics

In addition to the various electoral systems in use in the political sphere, there are numerous others, some of which are proposals and some of which have been adopted for usage in business (such as electing corporate board members) or for organisations but not for public elections. Ranked systems include
Bucklin voting Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking ...
, the various
Condorcet method A Condorcet method (; ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever ...
s (
Copeland's Copeland's is a restaurant chain started by New Orleans native Al Copeland in 1983. It offers New Orleans-style cuisine and a casual sit-down family friendly atmosphere. Significantly expanding in the 1990s, it claimed more than 40 locations in ...
, Dodgson's, Kemeny-Young, Maximal lotteries, Minimax, Nanson's,
Ranked pairs Ranked pairs (sometimes abbreviated "RP") or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. The ranked-pairs procedure can also be used to create ...
, Schulze), the Coombs' method and
positional voting Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair i ...
. There are also several variants of single transferable vote, including
CPO-STV CPO-STV, or the Comparison of Pairs of Outcomes by the Single Transferable Vote, is a ranked voting system designed to achieve proportional representation. It is a more sophisticated variant of the Single Transferable Vote (STV) system, designed ...
,
Schulze STV Schulze STV is a draft single transferable vote (STV) ranked voting system designed to achieve proportional representation.Markus SchulzeFree Riding and Vote Management under Proportional Representation by Single Transferable Vote/ref> It was in ...
and the
Wright system The Wright system is a refinement of rules associated with proportional representation by means of the single transferable vote (PR-STV) electoral system. It was developed and written by Anthony van der Craats, a system analyst and life member of ...
. Dual-member proportional representation is a proposed system with two candidates elected in each constituency, one with the most votes and one to ensure proportionality of the combined results. Biproportional apportionment is a system whereby the total number of votes is used to calculate the number of seats each party is due, followed by a calculation of the constituencies in which the seats should be awarded in order to achieve the total due to them. Cardinal electoral systems allow voters to evaluate candidates independently. The complexity ranges from approval voting where voters simply state whether they approve of a candidate or not to range voting, where a candidate is scored from a set range of numbers. Other cardinal systems include
proportional approval voting Proportional approval voting (PAV) is a proportional electoral system for selecting committees. It is an extension of the D'Hondt method of apportionment that additionally allows for personal votes (voters vote for candidates, not for a part ...
,
sequential proportional approval voting Sequential proportional approval voting (SPAV) or reweighted approval voting (RAV) is an electoral system that extends the concept of approval voting to a multiple winner election. It is a simplified version of proportional approval voting. Pr ...
,
satisfaction approval voting Satisfaction approval voting (SAV) is an electoral system that extends the concept of approval voting to a multiple winner election. It was proposed by Steven Brams and Marc Kilgour in 2010. Paper presented at the Annual National Conference of th ...
, highest median rules (including the
majority judgment Majority judgment (MJ) is a single-winner voting system proposed in 2007 by Michel Balinski and Rida Laraki. It is a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating. Unlike other v ...
), and the
D21 – Janeček method D21 – Janeček method, also known as Democracy 2.1, is an approval voting electoral system for single-winner voting, which giving each voter multiple 'positive' and 'negative' votes. It is similar to cumulative voting and combined approval voting ...
where voters can cast positive and negative votes. 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 The Prussian three-class franchise (German: ''Preußisches Dreiklassenwahlrecht'') was an indirect electoral system used from 1848 until 1918 in the Kingdom of Prussia and for shorter periods in other German states. Voters were grouped by distric ...
), or by weighting the results of the vote. The latter system was used in colonial Rhodesia for the
1962 Events January * January 1 – Western Samoa becomes independent from New Zealand. * January 3 – Pope John XXIII excommunicates Fidel Castro for preaching communism. * January 8 – Harmelen train disaster: 93 die in the wor ...
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
constitution A constitution is the aggregate of fundamental principles or established precedents that constitute the legal basis of a polity, organisation or other type of entity and commonly determine how that entity is to be governed. When these princ ...
or electoral law. Participatory rules determine candidate nomination and
voter registration In electoral systems, voter registration (or enrollment) is the requirement that a person otherwise eligible to vote must register (or enroll) on an electoral roll, which is usually a prerequisite for being entitled or permitted to vote. The r ...
, in addition to the location of polling places and the availability of online voting, postal voting, and
absentee voting An absentee ballot is a vote cast by someone who is unable or unwilling to attend the official polling station to which the voter is normally allocated. Methods include voting at a different location, postal voting, proxy voting and online votin ...
. Other regulations include the selection of voting devices such as paper ballots, machine voting or open ballot systems, and consequently the type of vote counting systems, verification and auditing used. Electoral rules place limits on suffrage and candidacy. Most countries's electorates are characterised by
universal suffrage Universal suffrage (also called universal franchise, general suffrage, and common suffrage of the common man) gives the right to vote to all adult citizens, regardless of wealth, income, gender, social status, race, ethnicity, or political stan ...
, 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. Many countries also have the none of the above option on their ballot papers. In systems that use
constituencies An electoral district, also known as an election district, legislative district, voting district, constituency, riding, ward, division, or (election) precinct is a subdivision of a larger state (a country, administrative region, or other polity ...
, 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 In representative democracies, gerrymandering (, originally ) is the political manipulation of electoral district boundaries with the intent to create undue advantage for a party, group, or socioeconomic class within the constituency. The m ...
. 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 first, second and third attempts to run the election. The turnout requirement was scrapped prior to the fourth vote in 2004. Similar problems in
Belarus Belarus,, , ; alternatively and formerly known as Byelorussia (from Russian ). officially the Republic of Belarus,; rus, Республика Беларусь, Respublika Belarus. is a landlocked country in Eastern Europe. It is bordered by ...
led to the 1995 parliamentary elections going to a fourth round of voting before enough parliamentarians were elected to make a quorum.
Reserved seats Several politico-constitutional arrangements use reserved political positions, especially when endeavoring to ensure the rights of women, minorities or other segments of society, or preserving a political balance of power. These arrangements can ...
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 Jordan ( ar, الأردن; tr. ' ), officially the Hashemite Kingdom of Jordan,; tr. ' is a country in Western Asia. It is situated at the crossroads of Asia, Africa, and Europe, within the Levant region, on the East Bank of the Jordan Rive ...
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 ) , national_anthem = " Ee Mungu Nguvu Yetu"() , image_map = , map_caption = , image_map2 = , capital = Nairobi , coordinates = , largest_city = Nairobi ...
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 Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...
,
Romania Romania ( ; ro, România ) is a country located at the crossroads of Central, Eastern, and Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, Serbia to the southwest, Moldova to the east, and ...
and
Serbia Serbia (, ; Serbian: , , ), officially the Republic of Serbia (Serbian: , , ), is a landlocked country in Southeastern and Central Europe, situated at the crossroads of the Pannonian Basin and the Balkans. It shares land borders with Hungar ...
.


History


Pre-democratic

In
ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean Sea, Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of Classical Antiquity, classical antiquity ( AD 600), th ...
and
Italy Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical ...
, the institution of suffrage already existed in a rudimentary form at the outset of the historical period. In the early
monarchies A monarchy is a form of government in which a person, the monarch, is head of state for life or until abdication. The political legitimacy and authority of the monarch may vary from restricted and largely symbolic (constitutional monarchy), ...
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.


Early democracy

Voting has been used as a feature of democracy since the 6th century BCE, when democracy was introduced by the Athenian democracy. However, in Athenian democracy, voting was seen as the least democratic among methods used for selecting public officials, and was little used, because elections were believed to inherently favor the wealthy and well-known over average citizens. Viewed as more democratic were assemblies open to all citizens, and selection by lot, as well as rotation of office. 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 Ostracism ( el, ὀστρακισμός, ''ostrakismos'') was an Athenian democratic procedure in which any citizen could be expelled from the city-state of Athens for ten years. While some instances clearly expressed popular anger at the ci ...
, 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 Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member per ...
that it was undesirable to win, namely an ostracism vote). At
Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...
the method which prevailed up to the 2nd century BCE was that of division (). 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 (), 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. Most elections in the early history of democracy were held using plurality voting or some variant, but as an exception, the state of
Venice Venice ( ; it, Venezia ; vec, Venesia or ) is a city in northeastern Italy and the capital of the Veneto region. It is built on a group of 118 small islands that are separated by canals and linked by over 400 bridges. The isla ...
in the 13th century adopted approval voting to elect their Great Council.J.J. O'Connor & E. F. Robertso
The history of voting
MacTutor History of Mathematics archive
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.Miranda Mowbray & Dieter Gollmann (2007
Electing the Doge of Venice: Analysis of a 13th Century Protocol
/ref> This process, with slight modifications, was central to the politics of the
Republic of Venice The Republic of Venice ( vec, Repùblega de Venèsia) or Venetian Republic ( vec, Repùblega Vèneta, links=no), traditionally known as La Serenissima ( en, Most Serene Republic of Venice, italics=yes; vec, Serenìsima Repùblega de Venèsia, ...
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 method A Condorcet method (; ) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever ...
s. 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. Later in the 18th century, apportionment methods came to prominence due to the United States Constitution, which mandated that seats in the
United States House of Representatives The United States House of Representatives, often referred to as the House of Representatives, the U.S. House, or simply the House, is the lower chamber of the United States Congress, with the Senate being the upper chamber. Together they ...
had to be allocated among the states proportionally to their population, but did not specify how to do so.Apportionment: Introduction
American Mathematical Society
A variety of methods were proposed by statesmen such as Alexander Hamilton,
Thomas Jefferson Thomas Jefferson (April 13, 1743 – July 4, 1826) was an American statesman, diplomat, lawyer, architect, philosopher, and Founding Father who served as the third president of the United States from 1801 to 1809. He was previously the natio ...
, and
Daniel Webster Daniel Webster (January 18, 1782 – October 24, 1852) was an American lawyer and statesman who represented New Hampshire and Massachusetts in the U.S. Congress and served as the U.S. Secretary of State under Presidents William Henry Harrison ...
. Some of the apportionment methods devised in the United States were in a sense rediscovered in Europe in the 19th century, as seat allocation methods for the newly proposed method of party-list proportional representation. The result is that many apportionment methods have two names; ''Jefferson's method'' is equivalent to the
D'Hondt method The D'Hondt method, also called the Jefferson method or the greatest divisors method, is a method for allocating seats in parliaments among federal states, or in party-list proportional representation systems. It belongs to the class of highest ...
, as is ''Webster's method'' to the Sainte-Laguë method, while ''Hamilton's method'' is identical to the Hare largest remainder method. The
single transferable vote Single transferable vote (STV) is a multi-winner electoral system in which voters cast a single vote in the form of a ranked-choice ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternate ...
(STV) method was devised by Carl Andræ in
Denmark ) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of Denmark , establish ...
in 1855 and in the
United Kingdom The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the European mainland, continental mainland. It comprises England, Scotlan ...
by Thomas Hare in 1857. STV elections were first held in Denmark in 1856, and in
Tasmania ) , nickname = , image_map = Tasmania in Australia.svg , map_caption = Location of Tasmania in AustraliaCoordinates: , subdivision_type = Country , subdi ...
in 1896 after its use was promoted by
Andrew Inglis Clark Andrew Inglis Clark (24 February 1848 – 14 November 1907) was an Australian founding father and co-author of the Australian Constitution; he was also an engineer, barrister, politician, electoral reformer and jurist. He initially qualified as a ...
. Party-list proportional representation began to be used to elect European legislatures in the early 20th century, with
Belgium Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to th ...
the first to implement it for its 1900 general elections. Since then, proportional and semi-proportional methods have come to be used in almost all democratic countries, with most exceptions being former
British British may refer to: Peoples, culture, and language * British people, nationals or natives of the United Kingdom, British Overseas Territories, and Crown Dependencies. ** Britishness, the British identity and common culture * British English, ...
and French colonies.


Single-winner revival

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 William Robert Ware (May 27, 1832 – June 9, 1915), born in Cambridge, Massachusetts into a family of the Unitarian clergy, was an American architect, author, and founder of two important American architectural schools. He received his o ...
proposed applying STV to single-winner elections, yielding instant-runoff voting (IRV). 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 The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method (also called Total Vote Runoff or TVR). Both methods are designed to satisfy the ...
. Charles Dodgson, better known as
Lewis Carroll Charles Lutwidge Dodgson (; 27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet and mathematician. His most notable works are '' Alice's Adventures in Wonderland'' (1865) and its sequ ...
, proposed the straightforward Condorcet method known as
Dodgson's method Dodgson's method is an electoral system proposed by the author, mathematician and logician Charles Dodgson, better known as Lewis Carroll Charles Lutwidge Dodgson (; 27 January 1832 – 14 January 1898), better known by his pen name Lewis ...
. 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. 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 continues to be used along with STV today. In the United States in the early-20th-century
progressive era The Progressive Era (late 1890s – late 1910s) was a period of widespread social activism and political reform across the United States focused on defeating corruption, monopoly, waste and inefficiency. The main themes ended during Am ...
, some municipalities began to use
Bucklin voting Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking ...
, although this is no longer used in any government elections, and has even been declared unconstitutional in Minnesota.


Recent developments

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 Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral syst ...
had already shown the issues with
Ranked voting The term ranked voting (also known as preferential voting or ranked choice voting) refers to any voting system in which voters rank their candidates (or options) in a sequence of first or second (or third, etc.) on their respective ballots. Ra ...
systems. Research led Steven Brams and Peter Fishburn to formally define and promote the use of approval voting in 1977. Political scientists of the 20th century published many studies on the effects that the electoral systems have on voters' choices and political parties, and on political stability. A few scholars also studied which effects caused a nation to switch to a particular electoral system. 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 New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 smaller islands. It is the sixth-largest island count ...
adopted mixed-member proportional representation for the 1993 general elections and STV for some local elections in 2004. 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 The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Europe, off the north-western coast of the European mainland, continental mainland. It comprises England, Scotlan ...
, 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 The two-round system (TRS), also known as runoff voting, second ballot, or ballotage, is a voting method used to elect a single candidate, where voters cast a single vote for their preferred candidate. It generally ensures a majoritarian resu ...
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 create imprecisely defined criteria, and then assign a neutral body to evaluate each method according to these criteria. 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 system using ranked voting can meet all such criteria simultaneously, while Gibbard's theorem proves the same for all deterministic voting methods. Instead of debating the importance of different criteria, another method is to simulate many elections with different electoral systems, and estimate the typical overall happiness of the population with the results, their vulnerability to strategic voting, their likelihood of electing the candidate closest to the average voter, etc. According to a 2006 survey of electoral system experts, their preferred electoral systems were in order of preference: #Mixed member proportional #Single transferable vote #Open list proportional #Alternative vote #Closed list proportional #Single member plurality #Runoffs #Mixed member majoritarian #Single non-transferable vote


Systems by elected body


See also

* Comparison of electoral systems *
Election An election is a formal group decision-making process by which a population chooses an individual or multiple individuals to hold public office. Elections have been the usual mechanism by which modern representative democracy has opera ...
* List of electoral systems by country * Matrix vote * Spoiler effect * Psephology


References


External links


ACE Electoral Knowledge NetworkThe International IDEA Handbook of Electoral System Design
IDEA {{Authority control Comparative politics Voting theory Public choice theory Psephology Social choice theory Elections