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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. Electoral systems are used in politics to elect governments, while non-political elections may take place in business,
non-profit organisations A nonprofit organization (NPO) or non-profit organisation, also known as a non-business entity, not-for-profit organization, or nonprofit institution, is a legal entity organized and operated for a collective, public or social benefit, in co ...
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 A candidate, or nominee, is the prospective recipient of an award or honor, or a person seeking or being considered for some kind of position; for example: * to be elected to an office — in this case a candidate selection procedure occurs. * ...
, 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 commission An election commission is a body charged with overseeing the implementation of electioneering process of any country. The formal names of election commissions vary from jurisdiction to jurisdiction, and may be styled an electoral commission, a c ...
s, 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 laws for a political entity such as a country or city. They are often contrasted with the executive and judicial powers of government. Laws enacted by legislatures are usually known ...
, 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. 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 the ...
, block voting, 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. 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 Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Soci ...
or voting theory, and this study can take place within the field of
political science Political science is the scientific study of politics. It is a social science dealing with systems of governance and power, and the analysis of political activities, political thought, political behavior, and associated constitutions and ...
,
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 anal ...
, or
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, and specifically within the subfields of
game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
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


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 per ...
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 the ...
; 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, 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, where voters are given fewer votes than there are seats to be filled (
Gibraltar ) , anthem = " God Save the King" , song = "Gibraltar Anthem" , image_map = Gibraltar location in Europe.svg , map_alt = Location of Gibraltar in Europe , map_caption = United Kingdom shown in pale green , mapsize = , image_map2 = Gibr ...
is the only territory where this system is in use) and
single non-transferable vote Single non-transferable vote or SNTV is an electoral system used to elect multiple winners. It is a generalization of first-past-the-post, applied to multi-member districts with each voter casting just one vote. Unlike FPTP, which is a single-win ...
(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 Iraq–Ku ...
, 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 ...
. In the other main form of block voting, also known as
party block voting The general ticket, also known as party block voting (PBV) or ticket voting, is a type of block voting in which voters opt for a party, or a team's set list of candidates, and the highest-polling party/team becomes the winner. Unless specifically ...
, 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 The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the ...
, is used in
Nauru Nauru ( or ; na, Naoero), officially the Republic of Nauru ( na, Repubrikin Naoero) and formerly known as Pleasant Island, is an island country and microstate in Oceania, in the Central Pacific. Its nearest neighbour is Banaba Island in ...
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 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 Instant-runoff voting (IRV) is a type of Ranked voting, ranked preferential Electoral system, voting method. It uses a Majority rule, majority voting rule in single-winner elections where there are more than two candidates. It is commonly referr ...
(IRV), whereby voters rank candidates in order of preference; this system is used for parliamentary elections in
Australia Australia, officially the Commonwealth of Australia, is a sovereign country comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands. With an area of , Australia is the largest country by ...
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 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 Lanka Sri Lanka (, ; si, ශ්‍රී ලංකා, Śrī Laṅkā, translit-std=ISO (); ta, இலங்கை, Ilaṅkai, translit-std=ISO ()), formerly known as Ceylon and officially the Democratic Socialist Republic of Sri Lanka, is an ...
n 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. An exhaustive ballot 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. 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 Party-list proportional representation (list-PR) is a subset of proportional representation electoral systems in which multiple candidates are elected (e.g., elections to parliament) through their position on an electoral list. They can also be u ...
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 Closed list describes the variant of party-list systems where voters can effectively only vote for political parties as a whole; thus they have no influence on the party-supplied order in which party candidates are elected. If voters had some in ...
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 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
Netherlands ) , anthem = ( en, "William of Nassau") , image_map = , map_caption = , subdivision_type = Sovereign state , subdivision_name = Kingdom of the Netherlands , established_title = Before independence , established_date = Spanish Netherl ...
, 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 highes ...
(of which there are variants including Hagenbach-Bischoff) and the Webster/Sainte-Laguë method. 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 The Hare quota (also known as the simple quota) is a formula used under some forms of proportional representation. In these voting systems the quota is the number of votes that guarantees a candidate, or a party in some cases, captures a seat. T ...
,
Droop quota The Droop quota is the quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation (list PR ...
, the
Imperiali quota The Imperiali quota is a formula used to calculate the minimum number, or quota, of votes required to capture a seat in some forms of single transferable vote or largest remainder method party-list proportional representation voting systems. ...
and the
Hagenbach-Bischoff quota The Hagenbach-Bischoff quota (also known as the Newland-Britton quota or the exact Droop quota, as opposed to the more common rounded Droop quota) is a formula used in some voting systems based on proportional representation (PR). It is used in ...
.
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 p ...
(STV) is another form of proportional representation; in STV, voters rank 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 the island of Ireland. The capital and largest city is Dublin, on the eastern side of the island. ...
. To be elected, candidates must pass a quota (the
Droop quota The Droop quota is the quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation (list PR ...
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 Parallel voting is a type of mixed electoral system in which representatives are voted into a single chamber using two or more different systems, most often first-past-the-post voting (FPTP) with party-list proportional representation (PR). It i ...
(also known as mixed-member majoritarian) and
mixed-member proportional representation Mixed-member proportional representation (MMP or MMPR) is a mixed electoral system in which votes cast are considered in local elections and also to determine overall party vote tallies, which are used to allocate additional members to produce ...
. 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 seats, 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, 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 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 San Marino (, ), officially the Republic of San Marino ( it, Repubblica di San Marino; ), also known as the Most Serene Republic of San Marino ( it, Serenissima Repubblica di San Marino, links=no), is the fifth-smallest country in the world an ...
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. In
Greece Greece,, or , romanized: ', officially the Hellenic Republic, is a country in Southeast Europe. It is situated on the southern tip of the Balkans, and is located at the crossroads of Europe, Asia, and Africa. Greece shares land borders wi ...
the party receiving the most votes was given an additional 50 seats, a system which was abolished following the 2019 elections. 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 A general assembly or general meeting is a meeting of all the members of an organization or shareholders of a company. Specific examples of general assembly include: Churches * General Assembly (presbyterian church), the highest court of pres ...
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 , image_flag = Bandera de Bolivia (Estado).svg , flag_alt = Horizontal tricolor (red, yellow, and green from top to bottom) with the coat of arms of Bolivia in the center , flag_alt2 = 7 × 7 square p ...
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 election 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 ...
s 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 Vote splitting is an electoral effect in which the distribution of votes among multiple similar candidates reduces the chance of winning for any of the similar candidates, and increases the chance of winning for a dissimilar candidate. Vote spl ...
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 List of South American countries by area, second-largest ...
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.


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 List of countries and dependencies by area, seventh-largest country by area, the List of countries and dependencies by population, second-most populous ...
, 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 Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...
, 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 and 2016.


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, the various Condorcet methods ( Copeland's, Dodgson's, Kemeny-Young,
Maximal lotteries Maximal lotteries refers to a probabilistic voting system first considered by the French mathematician and social scientist Germain KrewerasG. Kreweras. ''Aggregation of preference orderings''. In Mathematics and Social Sciences I: Proceedings of t ...
,
Minimax Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for ''mini''mizing the possible loss for a worst case (''max''imum loss) scenario. When ...
, Nanson's, Ranked pairs,
Schulze Schulze is a German surname, from the medieval office of Schulze, or village official. Notable people with the surname include: * Andrew Schulze (1896–1982), clergyman and civil rights activist * William August Schulze, rocket scientist recru ...
), the
Coombs' method Coombs' method or the Coombs ruleGrofman, Bernard, and Scott L. Feld (2004"If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule,"''Electoral Studies'' 23:641-59. is a ranked voting system whi ...
and positional voting. There are also several variants of single transferable vote, including CPO-STV, Schulze STV and the Wright system.
Dual-member proportional representation Dual-member proportional representation (DMP), also known as dual-member mixed proportional, is an electoral system designed to produce proportional election results across a region by electing two representatives in each of the region’s di ...
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 Biproportional apportionment is a proportional representation method to allocate seats in proportion to two separate characteristics. That is, for two different partitions each part receives the proportional number of seats within the total numb ...
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 Cardinal voting refers to any electoral system which allows the voter to give each candidate an independent evaluation, typically a rating or grade. These are also referred to as "rated" (ratings ballot), "evaluative", "graded", or "absolute" ...
allow voters to evaluate candidates independently. The complexity ranges from
approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...
where voters simply state whether they approve of a candidate or not to
range voting Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added (or averaged), and the candidate with the highest total is elected. It has been described by various ...
, where a candidate is scored from a set range of numbers. Other cardinal systems include proportional approval voting, sequential proportional approval voting, satisfaction approval voting, highest median rules (including the majority judgment), and the D21 – Janeček method where voters can cast positive and negative votes. Historically,
weighted voting Weighted voting can exist in a policy or law making body in which each representative has a variable voting power (weighted vote) as determined by the number principals who have made that person their proxy, or the population or the electorate t ...
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 Rhodesia (, ), officially from 1970 the Republic of Rhodesia, was an unrecognised state in Southern Africa from 1965 to 1979, equivalent in territory to modern Zimbabwe. Rhodesia was the ''de facto'' successor state to the British colony of So ...
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
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 pr ...
or
electoral law Election law is a branch of public law that relates to the democratic processes, election of representatives and office holders, and referendums, through the regulation of the electoral system, voting rights, ballot access, election management b ...
. 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 A polling place is where voters cast their ballots in elections. The phrase polling station is also used in American English and British English, although polling place is the building
and the availability of
online voting Electronic voting (also known as e-voting) is voting that uses electronic means to either aid or take care of casting and counting ballots. Depending on the particular implementation, e-voting may use standalone ''electronic voting machines'' ( ...
, postal voting, and absentee voting. Other regulations include the selection of voting devices such as paper ballots, machine voting or
open ballot system An open ballot system is a voting method in which voters vote openly, in contrast to a secret ballot, where a voter's choices are confidential. The open ballot system was the norm prior to Australia adopting the secret ballot in 1856. It was al ...
s, and consequently the type of
vote counting systems Vote counting is the process of counting votes in an election. It can be done manually or by machines. In the United States, the compilation of election returns and validation of the outcome that forms the basis of the official results is call ...
, 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 sta ...
, 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 Compulsory voting, also called mandatory voting, is the requirement in some countries that eligible citizens register and vote in elections. Penalties might be imposed on those who fail to do so without a valid reason. According to the CIA World F ...
, although in some there is an upper age limit on enforcement of the law. Many countries also have the
none of the above "None of the above" (NOTA), or none for short, also known as "against all" or a "scratch" vote, is a ballot option in some jurisdictions or organizations, designed to allow the voter to indicate disapproval of the candidates in a voting syste ...
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 Redistribution (re-districting in the United States and in the Philippines) is the process by which electoral districts are added, removed, or otherwise changed. Redistribution is a form of boundary delimitation that changes electoral distri ...
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 first,
second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ea ...
and
third Third or 3rd may refer to: Numbers * 3rd, the ordinal form of the cardinal number 3 * , a fraction of one third * 1⁄60 of a ''second'', or 1⁄3600 of a ''minute'' Places * 3rd Street (disambiguation) * Third Avenue (disambiguation) * Hi ...
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 A quorum is the minimum number of members of a deliberative assembly (a body that uses parliamentary procedure, such as a legislature) necessary to conduct the business of that group. According to '' Robert's Rules of Order Newly Revised'', 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 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 Europe, Central, Eastern Europe, Eastern, and Southeast Europe, Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, S ...
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 Hu ...
.


History


Pre-democratic

In
ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cu ...
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 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 Sparta ( Doric Greek: Σπάρτα, ''Spártā''; Attic Greek: Σπάρτη, ''Spártē'') was a prominent city-state in Laconia, in ancient Greece. In antiquity, the city-state was known as Lacedaemon (, ), while the name Sparta referr ...
as late as the 4th century BCE), or by the clashing of
spear A spear is a pole weapon consisting of a shaft, usually of wood, with a pointed head. The head may be simply the sharpened end of the shaft itself, as is the case with fire hardened spears, or it may be made of a more durable material fastene ...
s on
shield A shield is a piece of personal armour held in the hand, which may or may not be strapped to the wrist or forearm. Shields are used to intercept specific attacks, whether from close-ranged weaponry or projectiles such as arrows, by means of ...
s.


Early democracy

Voting has been used as a feature of democracy since the 6th century BCE, when democracy was introduced by the
Athenian democracy Athenian democracy developed around the 6th century BC in the Greek city-state (known as a polis) of Athens, comprising the city of Athens and the surrounding territory of Attica. Although Athens is the most famous ancient Greek democratic ci ...
. 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
lawsuit - A lawsuit is a proceeding by a party or parties against another in the civil court of law. The archaic term "suit in law" is found in only a small number of laws still in effect today. The term "lawsuit" is used in reference to a civil act ...
s 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 , 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 A democracy is a political system, or a system of decision-making within an institution or organization or a country, in which all members have an equal share of power. Modern democracies are characterized by two capabilities that differentiat ...
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 Regions of Italy, region. It is built on a group of 118 small islands that are separated by canals and linked by over 400  ...
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 Jean-Charles, chevalier de Borda (4 May 1733 – 19 February 1799) was a French mathematician, physicist, and Navy officer. Biography Borda was born in the city of Dax to Jean‐Antoine de Borda and Jeanne‐Marie Thérèse de Lacroix. In 1 ...
proposed the
Borda count The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the ...
in 1770 as a method for electing members to the
French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at ...
. His method was opposed by the
Marquis de Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal pu ...
, 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 Ramon Llull (; c. 1232 – c. 1315/16) was a philosopher, theologian, poet, missionary, and Christian apologist from the Kingdom of Majorca. He invented a philosophical system known as the ''Art'', conceived as a type of universal logic to pro ...
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 The Constitution of the United States is the supreme law of the United States of America. It superseded the Articles of Confederation, the nation's first constitution, in 1789. Originally comprising seven articles, it delineates the natio ...
, 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 Fathers of the United States, Founding Father who served as the third president of the United States from 18 ...
, and Daniel Webster. 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 highes ...
, 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 p ...
(STV) method was devised by
Carl Andræ Carl may refer to: * Carl, Georgia, city in USA * Carl, West Virginia, an unincorporated community *Carl (name), includes info about the name, variations of the name, and a list of people with the name * Carl², a TV series * "Carl", an episode of ...
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 continental mainland. It comprises England, Scotland, Wales and ...
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. 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 ...
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 and
French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...
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 proposed applying STV to single-winner elections, yielding
instant-runoff voting Instant-runoff voting (IRV) is a type of Ranked voting, ranked preferential Electoral system, voting method. It uses a Majority rule, majority voting rule in single-winner elections where there are more than two candidates. It is commonly referr ...
(IRV). Soon, mathematicians began to revisit Condorcet's ideas and invent new methods for Condorcet completion;
Edward J. Nanson Edward John Nanson (13 December 1850 – 1 July 1936) was a mathematician known for devising Nanson's method, a Condorcet-compliant variation of the Borda count using successive elimination to find a winner. He was born in England and receive ...
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 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. 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 Australia, officially the Commonwealth of Australia, is a sovereign country comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands. With an area of , Australia is the largest country by ...
, 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, some municipalities began to use Bucklin voting, although this is no longer used in any government elections, and has even been declared unconstitutional in
Minnesota Minnesota () is a state in the upper midwestern region of the United States. It is the 12th largest U.S. state in area and the 22nd most populous, with over 5.75 million residents. Minnesota is home to western prairies, now given over t ...
.


Recent developments

The use of
game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...
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 Steven J. Brams (born November 28, 1940 in Concord, New Hampshire) is an American game theorist and political scientist at the New York University Department of Politics. Brams is best known for using the techniques of game theory, public choi ...
and
Peter Fishburn Peter Clingerman Fishburn (September 2, 1936 – June 10, 2021) was an American mathematician, known as a pioneer in the field of decision theory. In collaboration with Steven Brams, Fishburn published a paper about approval voting in 1978. Biog ...
to formally define and promote the use of
approval voting Approval voting is an electoral system in which voters can select many candidates instead of selecting only one candidate. Description Approval voting ballots show a list of the options of candidates running. Approval voting lets each voter i ...
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 Electoral reform is a change in electoral systems which alters how public desires are expressed in election results. That can include reforms of: * Voting systems, such as proportional representation, a two-round system (runoff voting), instant ...
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 coun ...
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 Instant-runoff voting (IRV) is a type of Ranked voting, ranked preferential Electoral system, voting method. It uses a Majority rule, majority voting rule in single-winner elections where there are more than two candidates. It is commonly referr ...
, 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 File:2005 Events Collage V2.png, From top left, clockwise: Hurricane Katrina in the Gulf of Mexico; the Funeral of Pope John Paul II is held in Vatican City; " Me at the zoo", the first video ever to be uploaded to YouTube; Eris was discover ...
and
2009 File:2009 Events Collage V2.png, From top left, clockwise: The vertical stabilizer of Air France Flight 447 is pulled out from the Atlantic Ocean; Barack Obama becomes the first African American to become President of the United States; Protests ...
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 continental mainland. It comprises England, Scotland, Wales and ...
, 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 political science, voter turnout is the participation rate (often defined as those who cast a ballot) of a given election. This can be the percentage of registered voters, eligible voters, or all voting-age people. According to Stanford Univ ...
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 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 syste ...
and the
Gibbard–Satterthwaite theorem In social choice theory, the Gibbard–Satterthwaite theorem is a result published independently by philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a si ...
prove that no system using ranked voting can meet all such criteria simultaneously, while
Gibbard's theorem In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three propertie ...
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 Electoral systems are the rules for conducting elections, a main component of which is the algorithm for determining the winner (or several winners) from the ballots cast. This article discusses methods and results of comparing different electora ...
*
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 operat ...
* List of electoral systems by country *
Matrix vote The matrix vote is a voting procedure which can be used when one group of people wishes to elect a smaller number of persons, each of whom is to have a different assignment. Examples of its use are #when an association elects its executive committ ...
*
Spoiler effect Vote splitting is an electoral effect in which the distribution of votes among multiple similar candidates reduces the chance of winning for any of the similar candidates, and increases the chance of winning for a dissimilar candidate. Vote spl ...
*
Psephology Psephology (; from Greek el, ψῆφος, psephos, pebble, label=none) or political analysis is a branch of political science, the "quantitative analysis of elections and balloting". As such, psephology attempts to explain elections using the ...


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