Condorcet methods
121-401: Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Voting refers to the process of choosing officials or policies by casting
242-512: A ballot , a document used by people to formally express their preferences. Republics and representative democracies are governments where the population chooses representatives by voting. The procedure for identifying the winners based on votes varies depending on both the country and the political office. Political scientists call these procedures electoral systems , while mathematicians and economists call them social choice rules . The study of these rules and what makes them good or bad
363-403: A legislature , areas may be divided into constituencies with one or more representatives or the electorate may elect representatives as a single unit. Voters may vote directly for an individual candidate or for a list of candidates put forward by a political party or alliance . There are many variations in electoral systems. The mathematical and normative study of voting rules falls under
484-400: A majority bonus system to either ensure one party or coalition gains a majority in the legislature, or to give the party receiving the most votes a clear advantage in terms of the number of seats. San Marino has a modified two-round system, which sees a second round of voting featuring the top two parties or coalitions if there is no majority in the first round. The winner of the second round
605-448: A waste of votes due to vote splitting , a two-party system and political polarization due to electing candidates that do not support centrism . To understand why a race using First-past-the-post voting tends to favor less-centric candidates, consider a simple lab experiment where students in a class vote for their favorite marble. If five marbles are assigned names and are placed "up for election", and if three of them are green, one
726-501: A 'cycle'. This situation emerges when, once all votes have been tallied, the preferences of voters with respect to some candidates form a circle in which every candidate is beaten by at least one other candidate ( Intransitivity ). For example, if there are three candidates, Candidate Rock, Candidate Scissors, and Candidate Paper , there will be no Condorcet winner if voters prefer Candidate Rock over Candidate Scissors and Scissors over Paper, but also Candidate Paper over Rock. Depending on
847-400: A 68% majority of 1st choices among the remaining candidates and won as the majority's 1st choice. As noted above, sometimes an election has no Condorcet winner because there is no candidate who is preferred by voters to all other candidates. When this occurs the situation is known as a 'Condorcet cycle', 'majority rule cycle', 'circular ambiguity', 'circular tie', 'Condorcet paradox', or simply
968-512: A basic understanding of current issues, the liberal–conservative ideological dimension, and the relative ideological dilemma that are important to understand when making political decisions. Studies from other institutions have suggested that the physical appearance of candidates is a criterion upon which voters base their decision. Voting advice applications can increase political knowledge enabling to cast informed votes. Christadelphians , Jehovah's Witnesses , Old Order Amish , Rastafarians ,
1089-493: A candidate or party listed on the ballot, or a write-in where they write out the name of their preferred candidate (if it is not listed). An alternative method that is still paper-based known as ballot letters is used in Israel, where polling booths contain a tray with ballots for each party running in the elections; the ballots are marked with the letter(s) assigned to that party. Voters are given an envelope into which they put
1210-547: A contest between candidates A, B and C using the preferential-vote form of Condorcet method, a head-to-head race is conducted between each pair of candidates. A and B, B and C, and C and A. If one candidate is preferred over all others, they are the Condorcet Winner and winner of the election. Because of the possibility of the Condorcet paradox , it is possible, but unlikely, that a Condorcet winner may not exist in
1331-627: A country's constitution or electoral law . Participatory rules determine candidate nomination and voter registration , in addition to the location of polling places and the availability of online voting , postal voting , and absentee voting . 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 , but there are differences on
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#17327804819771452-419: A decision peacefully. The right to vote is usually restricted to certain people. Members of a society or club, or shareholders of a company, but not outsiders, may elect its officers, or adopt or change its rules, in a similar way to the election of people to official positions. A panel of judges, either formal judicial authorities or judges of the competition, may decide by voting. A group of friends or members of
1573-569: A different number of votes - only one (single voting as in First-past-the-post voting , Single non-transferable voting and Single transferable voting ); as many as are being elected in a multiple-member district (multiple voting as used in Plurality block voting ; more than one but fewer than are being elected in a multiple-member district ( Limited voting ). Most allow a voter to put just one vote on each candidate, but others allow
1694-579: A different system, as in contingent elections when no candidate wins a majority of the United States Electoral College . 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
1815-442: A different voter or electorate who will vote in his stead. In South Africa, there is a strong presence of anti-voting campaigns by poor citizens. They make the structural argument that no political party truly represents them. This resulted in the " No Land! No House! No Vote! " campaign, which becomes very prominent each time the country holds elections. The campaign is prominent among three of South Africa's largest social movements:
1936-565: A family may decide which film to see by voting. The method of voting can range from formal submission of written votes, through show of hands , voice voting or audience response systems, to informal noting which outcome seems to be preferred by more people. Some votes are carried out in person if all the people eligible to vote are present. This could be by a show of hands or keypad polling . Deliberative assemblies —bodies that use parliamentary procedure to arrive at decisions —use several methods when voting on motions (formal proposals by
2057-400: 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
2178-493: A majority of votes to be elected, either in a runoff election or final round of voting. This is sometimes referred to as a type of majority voting, although usually only a plurality is required in the last round, and sometimes even in the first round winners can avoid a second round without achieving a majority. In social choice theory, runoff systems are not called majority voting, as this term refers to Condorcet-methods . There are two main forms of runoff systems, one conducted in
2299-422: A member or members of a deliberative assembly). The regular methods of voting in such bodies are a voice vote, a rising vote, and a show of hands. Additional forms of voting include a recorded vote and balloting. The assembly can decide on the voting method by adopting a motion on it. The most common voting method uses paper ballots on which voters mark their preferences. This may involve marking their support for
2420-578: A number between one and ten (the upper and lower bounds may vary). See cardinal voting systems . Some "multiple-winner" systems such as the Single Non-Transferable Vote, SNTV, used in Afghanistan and Vanuatu give a single vote or one vote per elector per available position. STV uses single ranked votes; block voting ( Plurality-at-large voting ) are often used for at-large positions such as on some city councils. Finally,
2541-535: A number of seats approximately 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;
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#17327804819772662-877: A president, or a group, such as a committee or a parliament. In electing a parliament, either each of many small constituencies can elect a single representative, as in Britain; or each of a lesser number of multi-member constituencies may elect two or more representatives, as in Ireland; or multi-member districts and some single-member districts can be used; or the entire country can be treated as one "at-large" district, as in The Netherlands. Different voting systems use different ballot designs. Some ballots allow only one choice to be selected (single X voting); others allow ranking or selecting multiple options ( Ranked ballots ). Different voting systems allow each voter to cast
2783-445: A quota of 1st preferences; to any pair of candidates with two quotas of 1st/2nd preferences; and if seats are still to be filled, to those candidates with the highest MBC scores. In a voting system that uses multiple votes ( Plurality block voting ), the voter can vote for any subset of the running candidates. So, a voter might vote for Alice, Bob, and Charlie, rejecting Daniel and Emily. Approval voting uses such multiple votes. In
2904-532: A result of a kind of tie known as a majority rule cycle , described by Condorcet's paradox . The manner in which a winner is then chosen varies from one Condorcet method to another. Some Condorcet methods involve the basic procedure described below, coupled with a Condorcet completion method, which is used to find a winner when there is no Condorcet winner. Other Condorcet methods involve an entirely different system of counting, but are classified as Condorcet methods, or Condorcet consistent, because they will still elect
3025-454: 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 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
3146-492: A single party, with the party receiving the most votes winning all seats. This is used in five countries as part of mixed systems. Plurality voting is a system in which the candidate(s) with the highest number of votes wins, with no requirement to get a majority of votes. In cases where there is a single position to be filled, it is known as first-past-the-post ; this is the second most common electoral system for national legislatures, with 58 countries using it for this purpose,
3267-498: A single round of voting using ranked voting and the other using multiple elections, to successively narrow the field of candidates. Both are primarily used for single-member constituencies. Runoff can be achieved in a single election using instant-runoff voting (IRV), whereby voters rank candidates in order of preference; this system is used for parliamentary elections in Australia and Papua New Guinea . If no candidate receives
3388-523: A specific election. This is sometimes called a Condorcet cycle or just cycle and can be thought of as Rock beating Scissors, Scissors beating Paper, and Paper beating Rock . Various Condorcet methods differ in how they resolve such a cycle. (Most elections do not have cycles. See Condorcet paradox#Likelihood of the paradox for estimates.) If there is no cycle, all Condorcet methods elect the same candidate and are operationally equivalent. For most Condorcet methods, those counts usually suffice to determine
3509-415: A system used in eight countries. Approval voting is a choose-all-you-like voting system which aims to increase the number of candidates that win with majority support. Voters are free to pick as many candidates as they like and each choice has equal weight, independent of the number of candidates a voter supports. The candidate with the most votes wins. A runoff system in which candidates must receive
3630-427: A voter's choice within any given pair can be determined from the ranking. Some elections may not yield a Condorcet winner because voter preferences may be cyclic—that is, it is possible that every candidate has an opponent that defeats them in a two-candidate contest. The possibility of such cyclic preferences is known as the Condorcet paradox . However, a smallest group of candidates that beat all candidates not in
3751-423: A voter's votes to be piled on to one candidate. Different voting systems require different levels of support to be elected. Plurality voting ( First-past-the-post voting ) elects the candidate with more votes than any other single candidate. It does not require the winner to achieve a voting majority, to have more than half of the total votes cast. In First-past-the-post voting , when more than two candidates run,
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3872-470: A voting system that uses a ranked vote , the voter ranks the candidates in order of preference. For example, they might mark a preference for Bob in the first place, then Emily, then Alice, then Daniel, and finally Charlie. Ranked voting systems , such as those used in Australia and Ireland, use a ranked vote. In a voting system that uses a scored vote (or range vote ), the voter gives each alternative
3993-412: Is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote , who can stand as a candidate , how ballots are marked and cast , how
4114-407: Is also a Condorcet method, even though the voters do not vote by expressing their orders of preference. There are multiple rounds of voting, and in each round the vote is between two of the alternatives. The loser (by majority rule) of a pairing is eliminated, and the winner of a pairing survives to be paired in a later round against another alternative. Eventually, only one alternative remains, and it
4235-499: Is also referred to collectively as Condorcet's method. A voting system that always elects the Condorcet winner when there is one is described by electoral scientists as a system that satisfies the Condorcet criterion. Additionally, a voting system can be considered to have Condorcet consistency, or be Condorcet consistent, if it elects any Condorcet winner. In certain circumstances, an election has no Condorcet winner. This occurs as
4356-440: Is also used in a PR format. PR-STV is used in Australia, Ireland and Malta. Quota is calculated. In say a four-seat constituency, quota (if Droop quota is used) is 20 percent of the valid vote plus 1. Every candidate with quota (of 1st preferences alone or combination of first preferences and later preferences) will be elected. If a candidate has more than a quota and seats are yet to be filled, his/her surplus will be distributed to
4477-411: 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, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner , is formally called the Condorcet winner or Pairwise Majority Rule Winner (PMRW). The head-to-head elections need not be done separately;
4598-412: Is an election between four candidates: A, B, C, and D. The first matrix below records the preferences expressed on a single ballot paper, in which the voter's preferences are (B, C, A, D); that is, the voter ranked B first, C second, A third, and D fourth. In the matrix a '1' indicates that the runner is preferred over the 'opponent', while a '0' indicates that the runner is defeated. Using a matrix like
4719-475: Is an official none of the above option and it is counted as a valid vote. Usually, blank and null votes are counted (together or separately) but are not considered valid. Modern political science has questioned whether average citizens have sufficient political knowledge to cast meaningful votes. A series of studies coming out of the University of Michigan in the 1950s and 1960s argued that many voters lack
4840-627: Is another form of proportional representation. In STV, multi-member districts are used and each voter casts one vote, being a ranked ballot marked for individual candidates, rather than voting for a party list. STV is used in Malta and the Republic of Ireland . To be certain of being elected, candidates must pass a quota (the Droop quota being the most common). Candidates that pass the quota are elected. If necessary to fill seats, votes are transferred from
4961-410: 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 or Trinidad and Tobago , the post of President is elected by the legislature. In others like India , the vote is taken by an electoral college consisting of the national legislature and state legislatures. In
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5082-448: Is generally confined to periodic elections . In a democracy, the government is elected by the people who vote in an election : a way for an electorate to elect , that is choose , from several different candidates. It is more than likely that elections will be between two opposing parties. These two will be the most established and most popular parties in the country. For example, in the US,
5203-417: Is guaranteed 35 seats in the 60-seat Grand and General Council . In Greece the party receiving the most votes was given an additional 50 seats, a system which was abolished following the 2019 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
5324-417: 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 , apportionment or districting defines the area covered by each constituency. Where constituency boundaries are drawn has a strong influence on
5445-401: Is holding an election on the location of its capital . The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are: The preferences of each region's voters are: To find the Condorcet winner every candidate must be matched against every other candidate in a series of imaginary one-on-one contests. In each pairing
5566-414: Is impossible to design a straightforward voting system, i.e. one where it is always obvious to a strategic voter which ballot they should cast). The most common categorizations of electoral systems are: single-winner vs. multi-winner systems and proportional representation vs. winner-take-all systems vs. mixed systems . In all cases, where only a single winner is to be elected, the electoral system
5687-513: Is known as ambiguity resolution, cycle resolution method, or Condorcet completion method . Circular ambiguities arise as a result of the voting paradox —the result of an election can be intransitive (forming a cycle) even though all individual voters expressed a transitive preference. In a Condorcet election it is impossible for the preferences of a single voter to be cyclical, because a voter must rank all candidates in order, from top-choice to bottom-choice, and can only rank each candidate once, but
5808-440: Is no preference between candidates that were left unranked. Some Condorcet elections permit write-in candidates . The count is conducted by pitting every candidate against every other candidate in a series of hypothetical one-on-one contests. The winner of each pairing is the candidate preferred by a majority of voters. Unless they tie, there is always a majority when there are only two choices. The candidate preferred by each voter
5929-422: Is red, and one is blue, then a green marble will rarely win the election. The reason for the green's lack of success is vote splitting. The three green marbles will split the votes of those who prefer green. In fact, in this analogy, the only way that a green marble is likely to win is if more than three-fifths of the voters prefer green. If the same number of people prefer green as those who prefer red and blue, that
6050-510: Is taken to be the one in the pair that the voter ranks (or rates) higher on their ballot paper. For example, if Alice is paired against Bob it is necessary to count both the number of voters who have ranked Alice higher than Bob, and the number who have ranked Bob higher than Alice. If Alice is preferred by more voters then she is the winner of that pairing. When all possible pairings of candidates have been considered, if one candidate beats every other candidate in these contests then they are declared
6171-486: Is the two-round system , 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
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#17327804819776292-591: Is the case in Italy . Primary elections limit the risk of vote splitting by ensuring a single party candidate. In Argentina 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 . Some elections feature an indirect electoral system, whereby there
6413-415: Is the subject of a branch of welfare economics known as social choice theory . In smaller organizations, voting can occur in many different ways: formally via ballot to elect others for example within a workplace, to elect members of political associations, or to choose roles for others; or informally with a spoken agreement or a gesture like a raised hand. In larger organizations, like countries , voting
6534-404: Is the winner. This is analogous to a single-winner or round-robin tournament; the total number of pairings is one less than the number of alternatives. Since a Condorcet winner will win by majority rule in each of its pairings, it will never be eliminated by Robert's Rules. But this method cannot reveal a voting paradox in which there is no Condorcet winner and a majority prefer an early loser over
6655-490: Is thinned to the number of remaining open seats. In the Quota Borda System (QBS), the voters also cast their preferences, 1,2,3,4... as they wish. In the analysis, all 1st preferences are counted; all 2nd preferences are counted; after these preferences have been translated into points per the rules of a Modified Borda Count (MBC), the candidates' points are also counted. Seats are awarded to any candidates with
6776-409: Is to say, if one-third of the voters prefer green, one-third prefer blue, and one-third prefer red, then each green marble will only get one-ninth of the vote, if the green marbles each take same number of votes, while the red and blue marbles will each get one-third, putting the green marbles at a serious disadvantage. If the experiment is repeated with other colors, the color that is in the majority (if
6897-646: Is to try to achieve the most authentic outcome, without any risk of pressure, threat, or services linked to one's vote; this way, a person is able to express their actual preferences. Voting often takes place at a polling station but voting can also be done remotely by mail or using internet voting (such as in Estonia ). Voting is voluntary in some countries, like the UK, but it may be required by law in others, such as Australia. There are many electoral methods. The purpose of an election may be to choose one person, such as
7018-526: Is used in Kuwait , the Pitcairn Islands and Vanuatu . 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, members of a legislature are elected by two different methods; part of
7139-415: Is winner-take all. The same can be said for elections where only one person is elected per district, since the district elections are also winner-take-all, therefore the electoral system as a whole is also usually non-proportional. Some systems where multiple winners are elected at once (in the same district) are also winner-take-all. In party block voting , voters can only vote for the list of candidates of
7260-483: The Assemblies of Yahweh , and some other religious groups , have a policy of not participating in politics and this extends to voting. Rabbis from all Jewish denominations encourage voting and some even consider it a religious obligation. The Catholic Church teaches that it is morally obligatory to vote. Whenever several people who do not all agree need to make some decision, voting is a very common way of reaching
7381-597: The Borda count , each candidate is given a number of points equal to their rank, and the candidate with the least points wins. This system is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority. This system is used to elect the ethnic minority representatives seats in the Slovenian parliament. The Dowdall system is used in Nauru for parliamentary elections and sees voters rank
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#17327804819777502-529: The Coombs' method and positional voting . Among the Cardinal electoral systems , the most well known of these is range voting , where any number of candidates are scored from a set range of numbers. A very common example of range voting are the 5-star ratings used for many customer satisfaction surveys and reviews. Other cardinal systems include satisfaction approval voting , highest median rules (including
7623-480: The Marquis de Condorcet , who championed such systems. However, Ramon Llull devised the earliest known Condorcet method in 1299. It was equivalent to Copeland's method in cases with no pairwise ties. Condorcet methods may use preferential ranked , rated vote ballots, or explicit votes between all pairs of candidates. Most Condorcet methods employ a single round of preferential voting, in which each voter ranks
7744-480: The Netherlands , elections are carried out using 'pure' proportional representation, with the votes tallied on a national level before assigning seats to parties. However, in most cases several multi-member constituencies are used rather than a single nationwide constituency, giving an element of geographical representation; but this can result in the distribution of seats not reflecting the national vote totals. As
7865-530: The Swiss Federal Council . In some formats there may be multiple rounds held without any candidates being eliminated until a candidate achieves a majority. Positional systems like the Borda Count are ranked voting systems that assign a certain number of points to each candidate, weighted by position. The most popular such system is first-preference plurality . Another well-known variant,
7986-624: The United States , 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 . In addition to the various electoral systems currently in use for political elections, there are numerous others which have been used in
8107-742: The Western Cape Anti-Eviction Campaign , Abahlali baseMjondolo , and the Landless Peoples Movement . Other social movements in other parts of the world also have similar campaigns or non-voting preferences. These include the Zapatista Army of National Liberation and various anarchist-oriented movements. It is possible to make a blank vote , carrying out the act of voting, which may be compulsory, without selecting any candidate or option, often as an act of protest. In some jurisdictions, there
8228-404: 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
8349-550: The contingent vote where voters do not rank all candidates, but have a limited number of preference votes. If no candidate has a majority in the first round, all candidates are excluded except the top two, with the highest remaining preference votes from the votes for the excluded candidates then added to the totals to determine the winner. This system is used in Sri Lankan presidential elections, with voters allowed to give three preferences. The other main form of runoff system
8470-523: The majority judgment ), and the D21 – Janeček method 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 ), or by weighting the results of the vote. The latter system
8591-460: The Condorcet rule is used (sometimes) in decision-making. The voters or elected representatives cast their preferences on one, some, or all options, 1,2,3,4... as in PR-STV or QBS. In the analysis, option A is compared to option B, and if A is more popular than B, then A wins this pairing. Next, A is compared with option C, then D, and so on. Likewise, B is compared with C, D, etc. The option which wins
8712-493: The Condorcet winner if there is one. Not all single winner, ranked voting systems are Condorcet methods. For example, instant-runoff voting and the Borda count are not Condorcet methods. In a Condorcet election the voter ranks the list of candidates in order of preference. If a ranked ballot is used, the voter gives a "1" to their first preference, a "2" to their second preference, and so on. Some Condorcet methods allow voters to rank more than one candidate equally so that
8833-464: The Condorcet winner. As noted above, if there is no Condorcet winner a further method must be used to find the winner of the election, and this mechanism varies from one Condorcet consistent method to another. In any Condorcet method that passes Independence of Smith-dominated alternatives , it can sometimes help to identify the Smith set from the head-to-head matchups, and eliminate all candidates not in
8954-555: The Copeland winner has the highest possible Copeland score. They can also be found by conducting a series of pairwise comparisons, using the procedure given in Robert's Rules of Order described above. For N candidates, this requires N − 1 pairwise hypothetical elections. For example, with 5 candidates there are 4 pairwise comparisons to be made, since after each comparison, a candidate is eliminated, and after 4 eliminations, only one of
9075-640: The Schulze method, use the information contained in the sum matrix to choose a winner. Cells marked '—' in the matrices above have a numerical value of '0', but a dash is used since candidates are never preferred to themselves. The first matrix, that represents a single ballot, is inversely symmetric: (runner, opponent) is ¬(opponent, runner). Or (runner, opponent) + (opponent, runner) = 1. The sum matrix has this property: (runner, opponent) + (opponent, runner) = N for N voters, if all runners were fully ranked by each voter. [REDACTED] Suppose that Tennessee
9196-476: The allocation of seats in the multi-member constituencies is adjusted to achieve an overall seat allocation proportional to parties' vote share by taking into account the number of seats won by parties in the single-member constituencies. Vote linkage mixed systems are also compensatory, however they usually use different mechanism than seat linkage (top-up) method of MMP and usually aren't able to achieve proportional representation. Some electoral systems feature
9317-895: The ballot of the party they wish to vote for, before placing the envelope in the ballot box . The same system is also implemented in Latvia . The system is used commonly in open lists or primary elections , where voters must choose a single party whose candidates they are allowed to choose between. Machine voting uses voting machines , which may be manual (e.g. lever machines ) or electronic . Condorcet method Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results A Condorcet method ( English: / k ɒ n d ɔːr ˈ s eɪ / ; French: [kɔ̃dɔʁsɛ] )
9438-560: 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
9559-411: The basis for defining preference and determined that Memphis voters preferred Chattanooga as a second choice rather than as a third choice, Chattanooga would be the Condorcet winner even though finishing in last place in a first-past-the-post election. An alternative way of thinking about this example if a Smith-efficient Condorcet method that passes ISDA is used to determine the winner is that 58% of
9680-429: The branches of economics called social choice and mechanism design , but the question has also engendered substantial contributions from political scientists , analytic philosophers , computer scientists , and mathematicians . The field has produced several major results, including Arrow's impossibility theorem (showing that ranked voting cannot eliminate the spoiler effect ) and Gibbard's theorem (showing it
9801-605: The candidates from most (marked as number 1) to least preferred (marked with a higher number). A voter's ranking is often called their order of preference. Votes can be tallied in many ways to find a winner. All Condorcet methods will elect the Condorcet winner if there is one. If there is no Condorcet winner different Condorcet-compliant methods may elect different winners in the case of a cycle—Condorcet methods differ on which other criteria they satisfy. The procedure given in Robert's Rules of Order for voting on motions and amendments
9922-414: The candidates. First preference votes are counted as whole numbers, the second preferences by two, third preferences by three, and so on; this continues to the lowest possible ranking. The totals for each candidate determine the winners. Proportional representation is the most widely used electoral system for national legislatures, with the parliaments of over eighty countries elected by various forms of
10043-520: The competition is between the Republicans and the Democrats. In an indirect democracy, voting is the method by which the person elected (in charge) represents the people, whilst making decisions. Direct democracy is the complete opposite, the people make the policy decisions directly without selecting a representative to do it for them. A majority vote is when more than half of voters vote for
10164-496: The complete order of finish (i.e. who won, who came in 2nd place, etc.). They always suffice to determine whether there is a Condorcet winner. Additional information may be needed in the event of ties. Ties can be pairings that have no majority, or they can be majorities that are the same size. Such ties will be rare when there are many voters. Some Condorcet methods may have other kinds of ties. For example, with Copeland's method , it would not be rare for two or more candidates to win
10285-424: The context in which elections are held, circular ambiguities may or may not be common, but there is no known case of a governmental election with ranked-choice voting in which a circular ambiguity is evident from the record of ranked ballots. Nonetheless a cycle is always possible, and so every Condorcet method should be capable of determining a winner when this contingency occurs. A mechanism for resolving an ambiguity
10406-417: The district seats. Weighted systems are still used in corporate elections, with votes weighted to reflect stock ownership. 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 where the total number of votes is used to calculate
10527-474: The eventual winner (though it will always elect someone in the Smith set ). A considerable portion of the literature on social choice theory is about the properties of this method since it is widely used and is used by important organizations (legislatures, councils, committees, etc.). It is not practical for use in public elections, however, since its multiple rounds of voting would be very expensive for voters, for candidates, and for governments to administer. In
10648-410: The first preferences. If no single candidate has 50% of the vote, then the candidate with the fewest votes is excluded and their votes are redistributed according to the voter's nominated order of preference. The process repeats itself until a candidate has 50% or more votes. The system is designed to produce the same result as an exhaustive ballot but using only a single round of voting. Ranked voting
10769-470: The following sum matrix: When the sum matrix is found, the contest between each pair of candidates is considered. The number of votes for runner over opponent (runner, opponent) is compared with the number of votes for opponent over runner (opponent, runner) to find the Condorcet winner. In the sum matrix above, A is the Condorcet winner because A beats every other candidate. When there is no Condorcet winner Condorcet completion methods, such as Ranked Pairs and
10890-454: The group, known as the Smith set , always exists. The Smith set is guaranteed to have the Condorcet winner in it should one exist. Many Condorcet methods elect a candidate who is in the Smith set absent a Condorcet winner, and is thus said to be "Smith-efficient". Condorcet voting methods are named for the 18th-century French mathematician and philosopher Marie Jean Antoine Nicolas Caritat,
11011-420: The least successful candidates. Surplus votes held by successful candidates may also be transferred. Eventually all seats are filled by candidates who have passed the quota or there are only as many remaining candidates as the number of remaining seats. Under single non-transferable vote (SNTV) voters can vote for only one candidate, with the candidates receiving the most votes declared the winners; this system
11132-449: The majority is split among multiple candidates, proportionate results can still be produced if votes can be transferred, as under STV, or if multiple winners are elected and each voter has just one vote. Alternatives to First-past-the-post voting include approval voting , two-round , proportional representation , and instant-runoff voting . With approval voting , voters are encouraged to vote for as many candidates as they approve of, so
11253-447: The majority is split among multiple choices) will still rarely win. In other words, from a purely mathematical perspective, a single-winner system tends to favor a winner that is different from the majority, if the majority runs multiple candidates, and if the minority group runs just one candidate. This minority rule success can also result if multiple winners are elected and voters cast multiple votes ( Plurality block voting ). But even if
11374-506: 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 systems the results of the proportional vote are adjusted to balance the seats won in the constituency vote. The mixed-member proportional systems , in use in eight countries, provide enough compensatory seats to ensure that parties have
11495-452: The most individual votes (i.e. they may have lose the popular vote but still win the seat count). (It is also possible for a party to win plurality in a minority of constituencies (but more than any other one party) and thus win minority government.) All modern liberal democracies use voting by secret ballot to prevent individuals from becoming influenced by other people and to protect their political privacy . The objective of secret ballots
11616-605: The most pairings, (if there is one), is the Condorcet winner.--> When the citizens of a country are invited to vote, they are participating in an election. However, people can also vote in referendums and initiatives . Since the end of the eighteenth century, more than five hundred national referendums (including initiatives) were organized in the world; among them, more than three hundred were held in Switzerland . Australia ranked second with dozens of referendums. Most referendums are binary. The first multi-option referendum
11737-451: 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. For proportional systems that use ranked choice voting , there are several proposals, including CPO-STV , Schulze STV and the Wright system , which are each considered to be variants of proportional representation by means of
11858-425: The one above, one can find the overall results of an election. Each ballot can be transformed into this style of matrix, and then added to all other ballot matrices using matrix addition . The sum of all ballots in an election is called the sum matrix. Suppose that in the imaginary election there are two other voters. Their preferences are (D, A, C, B) and (A, C, B, D). Added to the first voter, these ballots would give
11979-419: The original 5 candidates will remain. To confirm that a Condorcet winner exists in a given election, first do the Robert's Rules of Order procedure, declare the final remaining candidate the procedure's winner, and then do at most an additional N − 2 pairwise comparisons between the procedure's winner and any candidates they have not been compared against yet (including all previously eliminated candidates). If
12100-450: The other candidates in proportion to all of that candidate's 2nd preferences, in line with secondary preferences marked on the vote if any. If there are still candidates to be elected and no surplus votes to be transferred, the least-popular is eliminated, as above in AV or IRV, and the process continues until four candidates have reached a quota or are declared elected when the field of candidates
12221-488: The paradox of voting means that it is still possible for a circular ambiguity in voter tallies to emerge. Voting system Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results An electoral or voting system
12342-453: The past, are only used in private organizations (such as electing the board members for a corporation or a student organization), or have only ever been made as proposals but not implemented. Among the Ranked systems these include Bucklin voting , the various Condorcet methods ( Copeland's , Dodgson's , Kemeny-Young , Maximal lotteries , Minimax , Nanson's , Ranked pairs , Schulze ),
12463-426: The procedure's winner does not win all pairwise matchups, then no Condorcet winner exists in the election (and thus the Smith set has multiple candidates in it). Computing all pairwise comparisons requires ½ N ( N −1) pairwise comparisons for N candidates. For 10 candidates, this means 0.5*10*9=45 comparisons, which can make elections with many candidates hard to count the votes for. The family of Condorcet methods
12584-469: The same number of pairings, when there is no Condorcet winner. A Condorcet method is a voting system that will always elect the Condorcet winner (if there is one); this is the candidate whom voters prefer to each other candidate, when compared to them one at a time. This candidate can be found (if they exist; see next paragraph) by checking if there is a candidate who beats all other candidates; this can be done by using Copeland's method and then checking if
12705-409: The same person or party. However, whilst it is usually said each individual's vote does count, many countries use a combination of factors to decide who has power, not the at-large "popular vote". Most influential of these factors are districts that divide the electorate. For example, in the UK a party winning plurality in a majority of constituencies wins majority government, but they may not always have
12826-423: 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 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 . In some cases, a runoff may be held using
12947-426: The set before doing the procedure for that Condorcet method. Condorcet methods use pairwise counting. For each possible pair of candidates, one pairwise count indicates how many voters prefer one of the paired candidates over the other candidate, and another pairwise count indicates how many voters have the opposite preference. The counts for all possible pairs of candidates summarize all the pairwise preferences of all
13068-661: The single transferable vote. Among the proportional voting systems that use rating are Thiele's voting rules and Phragmen's voting rule . A special case of Thiele's voting rules is Proportional Approval Voting . Some proportional systems that may be used with either ranking or rating include the Method of Equal Shares and the Expanding Approvals Rule . 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
13189-486: The system. Party-list proportional representation is the single most common electoral system and is used by 80 countries, and involves voters voting for a list of candidates proposed by a party. In closed list systems voters do not have any influence over the candidates put forward by the party, but in open list systems voters are able to both vote for the party list and influence the order in which candidates will be assigned seats. In some countries, notably Israel and
13310-529: The two candidates with the most significant plurality run again for the second round of voting. Variants exist regarding these two points: the requirement for being elected at the first round is sometimes less than 50%, and the rules for participation in the runoff may vary. With single-round ranked voting, such as instant-runoff voting system as used in some elections in Australia and the United States, voters rank each candidate in order of preference (1,2,3,4 etc.). Votes are distributed to each candidate according to
13431-556: 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, there are several types of plurality electoral systems. Under block voting (also known as multiple non-transferable vote or plurality-at-large), voters have as many votes as there are seats and can vote for any candidate, regardless of party,
13552-486: The voter might express two first preferences rather than just one. If a scored ballot is used, voters rate or score the candidates on a scale, for example as is used in Score voting , with a higher rating indicating a greater preference. When a voter does not give a full list of preferences, it is typically assumed that they prefer the candidates that they have ranked over all the candidates that were not ranked, and that there
13673-420: The voters, a mutual majority , ranked Memphis last (making Memphis the majority loser ) and Nashville, Chattanooga, and Knoxville above Memphis, ruling Memphis out. At that point, the voters who preferred Memphis as their 1st choice could only help to choose a winner among Nashville, Chattanooga, and Knoxville, and because they all preferred Nashville as their 1st choice among those three, Nashville would have had
13794-448: The voters. Pairwise counts are often displayed in a pairwise comparison matrix , or outranking matrix , such as those below. In these matrices , each row represents each candidate as a 'runner', while each column represents each candidate as an 'opponent'. The cells at the intersection of rows and columns each show the result of a particular pairwise comparison. Cells comparing a candidate to themselves are left blank. Imagine there
13915-409: The votes received by each party by a divisor or vote average that represents an idealized seats-to-votes ratio , then rounding normally. In the largest remainder system, parties' vote shares are divided by an electoral quota . This usually leaves some seats unallocated, which are awarded to parties based on which parties have the largest number of "leftover" votes. Single transferable vote (STV)
14036-628: The winner commonly has less than half of the vote, as few as 18 percent was recorded in 2014 in Toronto. In Instant-runoff voting , a candidate must have a majority of votes to be elected, although presence of exhausted votes may mean that the majority at time of final count is not majority of votes cast. In STV, any candidate who takes quota (usually set at much less than half of the votes) is elected; others without quota (but with more votes than any other single candidate) may be declared elected as well. Side effects of First-past-the-post voting include
14157-402: The winner is much more likely to be any one of the five marbles because people who prefer green will be able to vote for every one of the green marbles. With two-round elections, the field of candidates is thinned prior to the second round of voting. In most cases, the winner must receive a majority of the votes, which is more than half. If no candidate obtains a majority in the first round, then
14278-532: The winner is the candidate preferred by a majority of voters. When results for every possible pairing have been found they are as follows: The results can also be shown in the form of a matrix: ↓ 2 Wins ↓ 1 Win As can be seen from both of the tables above, Nashville beats every other candidate. This means that Nashville is the Condorcet winner. Nashville will thus win an election held under any possible Condorcet method. While any Condorcet method will elect Nashville as
14399-523: The winner, if instead an election based on the same votes were held using first-past-the-post or instant-runoff voting , these systems would select Memphis and Knoxville respectively. This would occur despite the fact that most people would have preferred Nashville to either of those "winners". Condorcet methods make these preferences obvious rather than ignoring or discarding them. On the other hand, in this example Chattanooga also defeats Knoxville and Memphis when paired against those cities. If we changed
14520-469: Was held in New Zealand in 1894, and most of them are conducted under a two-round system. New Zealand had a five-option referendum in 1992, while Guam had a six-option plebiscite in 1982, which also offered a blank option, in case some voters wanted to (campaign and) vote for a seventh option. Proxy voting is a form of voting in which a registered citizen who can legally vote passes on his or her vote to
14641-500: Was used in colonial Rhodesia for the 1962 and 1965 elections . The elections featured two voter rolls (the 'A' roll being largely European and the 'B' roll largely African); the seats of the House Assembly were divided into 50 constituency seats and 15 district seats. Although all voters could vote for both types of seats, 'A' roll votes were given greater weight for the constituency seats and 'B' roll votes greater weight for
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