Condorcet methods
113-506: 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 Mixed-member proportional representation ( MMP or MMPR ) is a type of representation provided by some mixed electoral systems which combine local winner-take-all elections with
226-497: A compensatory tier with party lists , in a way that produces proportional representation overall. Like proportional representation , MMP is not a single system, but a principle and goal of several similar systems. Some systems designed to achieve proportionality are still called mixed-member proportional, even if they generally fall short of full proportionality. In this case, they provide semi-proportional representation . In typical MMP systems, voters get two votes: one to decide
339-501: 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
452-400: 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
565-585: A candidate-based PR system, has only rarely been used to elect more than 21 in a single contest. Some PR systems use at-large pooling or regional pooling in conjunction with single-member districts (such as the New Zealand MMP and the Scottish additional member system ). Other PR systems use at-large pooling in conjunction with multi-member districts ( Scandinavian countries ). Pooling is used to allocate leveling seats (top-up) to compensate for
678-547: 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
791-436: A divisor of 8 (7 seats + 1 per the method's divisor formula) instead of 1. The resulting table would then give 7 seats for Scotland and 4 seats for Wales to the parties possessing the highest averages on the table, although both devolved parliaments do not use a table, instead using a sequential method. The compensatory effect characteristic of MMP is in the fact that a party that won constituency seats would have lower averages on
904-475: A few list-PR systems). A country-wide pooling of votes to elect more than a hundred members is used in Angola, for example. Where PR is desired at the municipal level, a city-wide at-large districting is sometimes used, to allow as large a district magnitude as possible. For large districts, party-list PR is often used, but even when list PR is used, districts sometimes contain fewer than 40 or 50 members. STV,
1017-491: A longtime supporter of MMP. The Green Party of Canada has generally been a staunch supporter of a move to a proportional electoral system. In June 2016, the Canadian House of Commons Special Committee on Electoral Reform was formed to examine potential changes to the voting system with MMP being one of the options examined. The committee presented its report to Parliament on 1 December of the same year. In early 2017,
1130-673: A member with a 'safe' constituency seat is therefore a tremendous asset to a minor party in New Zealand. In elections for the Scottish Parliament, there is no threshold set, because the district magnitude of each electoral region is small enough to impose an inherent threshold in the seat distribution calculations. The following countries currently have MMP representation. Countries which nominally use or have used MMP, but in practice had highly disproportional representation or it as otherwise not implemented are discussed in
1243-433: A nationwide representative, parties may be required to achieve a minimum number of constituency seats, a minimum percentage of the nationwide party vote, or both. MMP differs from mixed-member majoritarian representation (often achieved by parallel voting ) in that the nationwide seats are allocated to political parties in a compensatory manner in order to achieve proportional election results across all seats (not just
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#17327982586941356-480: A number of seats roughly based on its population size (see degressive proportionality ) and in each member state, the election must also be held using a PR system (with proportional results based on vote share). The most widely used families of PR electoral systems are party-list PR, used in 85 countries; mixed-member PR (MMP), used in 7 countries; and the single transferable vote (STV), used in Ireland, Malta,
1469-575: A party must earn at least a certain percentage of the total party vote, or no candidates will be elected from the party list. Candidates having won a constituency will still have won their seat. In New Zealand the threshold is 5%, in Bolivia 3%, in Germany 5% for elections for federal parliament and most state parliaments. A party can also be eligible for list seats if it wins at least three constituency seats in Germany, or at least one in New Zealand. Having
1582-601: A party wins too many constituency seats. The problem of ticket splitting strategies can be solved either by eliminating at least one of the two mechanisms that create the opportunity for abuse: This sort of strategy for a coalition of parties to capture a larger share of list seats may be adopted formally as a strategy. By way of example, in Albania's 2005 parliamentary election , the two main parties did not expect to win any list seats, so they encouraged voters to use their list votes for allied minor parties. This tactic distorted
1695-532: 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
1808-523: 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
1921-427: 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
2034-504: Is allocated seats based on its party share. Some party-list PR systems use overall country-wide vote counts; others count vote shares in separate parts of the country and allocate seats in each part according to that specific vote count. Some use both. List PR involves parties in the election process. Voters do not primarily vote for candidates (persons), but for electoral lists (or party lists ), which are lists of candidates that parties put forward. The mechanism that allocates seats to
2147-407: 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
2260-420: Is also randomness – a party that receives more votes than another party might not win more seats than the other. Any such dis-proportionality produced by the district elections is addressed, where possible, by the allocation of the compensatory additional members. (Number of districts won) (party-list PR seats) under MMP MMP gives only as many compensatory seats to a party as they need to have
2373-499: 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
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#17327982586942486-411: 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;
2599-412: 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
2712-531: Is called MMP, while in other countries similar systems are known under other names. The seat linkage compensatory mixed system often referred to as MMP originates in Germany , and was later adopted with modifications under the name of MMP in New Zealand. In Germany, where is was differentiated from a different compensatory mixed system it was always known as personalized proportional representation (PPR) ( German : personalisiertes Verhältniswahlrecht ). Since
2825-419: Is described here. The mixed-member proportional system combines single member plurality voting (SMP), also known as first-past-the-post (FPTP), with party-list PR in a way that the overall result of the election is supposed to be proportional. The voter may vote for a district candidate as well as a party. The main idea behind MMP is compensation , meaning that the list-PR seat allocation is not independent of
2938-401: 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
3051-513: 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
3164-456: Is more complicated than first-past-the-post voting , but the following example shows how the vote count is performed and how proportionality is achieved in a district with 3 seats. In reality, districts usually elect more members than that in order to achieve more proportional results. A risk is that if the number of seats is larger than, for example, 10 seats, the ballot will be so large as to be inconvenient and voters may find it difficult to rank
3277-551: Is no need for a single office (e.g. a president, or mayor) to be elected proportionately if no votes are for parties (subgroups). In the European Parliament , for instance, each member state has a number of seats that is (roughly) proportional to its population, enabling geographical proportional representation. For these elections, all European Union (EU) countries also must use a proportional electoral system (enabling political proportional representation): When n % of
3390-440: 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
3503-489: Is not considered to make an electoral system "proportional" the way the term is usually used. For example, the US House of Representatives has 435 members, who each represent a roughly equal number of people; each state is allocated a number of members in accordance with its population size (aside from a minimum single seat that even the smallest state receives), thus producing equal representation by population. But members of
Mixed-member proportional representation - Misplaced Pages Continue
3616-510: 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
3729-607: Is the number of constituency seats that party won, so that the additional seats are compensatory (top-up). If a party wins more FPTP seats than the proportional quota received by the party-list vote, these surplus seats are called overhang seats ( Überhangmandate in German), which may be an obstacle to achieving full proportionality. When a party wins more constituency seats than it would be entitled to from its proportion of (party list) votes, most systems allow for these overhang seats to be kept by those candidates who earned it in
3842-404: 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
3955-580: Is used with 5-member districts, it is common for successful candidates to receive 16.6 percent of the vote in the district. This produces a high effective threshold in the districts, and the country maintains a very strong two-party system. However, about 4000 voters in a district would be enough to elect a third-party candidate if voters desired but this seldom happens. Conversely, New South Wales, which uses STV to elect its legislative council in 21-seat contests, sees election of representatives of seven or eight parties each time. In this election about 1/22nd of
4068-700: The 2008 New Zealand general election the Māori Party won 2.4% of the party vote, which would entitle them to 3 seats in the House, but won 5 constituency seats, leaving an overhang of 2 seats, which resulted in a 122-member house. If the party vote for the Māori Party had been more in proportion with the constituency seats won, there would have been a normal 120-member house. To combat disproportionalities caused by overhang seats, in most German states leveling seats ( Ausgleichsmandate in German) are added to compensate for
4181-651: The 2012 election , the voting system was adjusted to link the local and list seats to limit the decoy lists' effectiveness, resulting in an almost perfectly proportionate election result for the competing parties. 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] )
4294-653: The Australian Senate , and Indian Rajya Sabha . Proportional representation systems are used at all levels of government and are also used for elections to non-governmental bodies, such as corporate boards . All PR systems require multi-member election contests, meaning votes are pooled to elect multiple representatives at once. Pooling may be done in various multi-member voting districts (in STV and most list-PR systems) or in single countrywide – a so called at-large – district (in only
4407-480: 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
4520-645: The South Wales West region, and every election in the South Wales Central region apart from the 2003 election. This situation arises because Labour has continued to hold the overwhelming majority of constituency seats in these regions, and only around one-third of the total number of seats are available for distribution as additional regional seats. ( MMM ) ( Gallagher ) number of overhang seats As in numerous proportional systems , in order to be eligible for list seats in many MMP models,
4633-595: The United Kingdom the sometimes less proportional implementation of MMP used in Scotland and the London Assembly is referred to as the additional member system . In South Africa, MMP is generally referred to as a "mixed-system". The Scandinavian countries have a long history of using both multi-member districts (members elected through party-list PR) and nationally-based compensatory top-up seats using
Mixed-member proportional representation - Misplaced Pages Continue
4746-608: The representative for their single-seat constituency , and one for a political party, but some countries use single vote variants . Seats in the legislature are filled first by the successful constituency candidates, and second, by party candidates based on the percentage of nationwide or region-wide votes that each party received. The constituency representatives are usually elected using first-past-the-post voting (FPTP). The nationwide or regional party representatives are, in most jurisdictions, drawn from published party lists , similar to party-list proportional representation . To gain
4859-410: The "best near-winner" method in a four-region model, where the regional members are the local candidates of the under-represented party in that region who received the most votes in their local constituency without being elected in it ( Zweitmandat , literally "second mandate"). At the regional or national level (i.e. above the constituency level) several different calculation methods have been used, but
4972-543: The 200-seat legislature as large as in the examples that follow, about 67 three-seat districts would be used. Districts with more seats would provide more proportional results – one form of STV in Australia uses a district with 21 members being elected at once. With a larger district magnitude, it is more likely that more than two parties will have some of their candidates elected. For example, in Malta , where STV
5085-544: 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
5198-464: 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
5311-555: 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
5424-508: The Government announced that it would accept only some of the committee's recommendations, and would not pursue the issue of electoral reform any further. The pan-European party VOLT Europa proposes transnational mixed-member proportional representation with the combination of Majority Judgment and party-list PR . In other cases, a party may be so certain of winning a large number of constituency seats that it expects no extra seats in
5537-510: The House are elected in single-member districts generally through first-past-the-post elections : a single-winner contest does not produce proportional representation as it has only one winner. Conversely, the representation achieved under PR electoral systems is typically proportional to a district's population size (seats per set amount of population), votes cast (votes per winner), and party vote share (in party-based systems such as party-list PR ). The European Parliament gives each member state
5650-640: 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
5763-670: The US House of Representatives). Votes and seats often cannot be mathematically perfectly allocated, so some amount of rounding has to be done. The various methods deal with this in different ways, although the difference is reduced if there are many seats – for example, if the whole country is one district. Party-list PR is also more complicated in reality than in the example, as countries often use more than one district, multiple tiers (e.g. local, regional and national), open lists or an electoral threshold . This can mean that final seat allocations are frequently not proportional to
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#17327982586945876-433: The absence or insufficient number of leveling seats (in list PR, MMP or AMS) may produce disproportionality. Other sources are electoral tactics that may be used in certain systems, such as party splitting in some MMP systems. Nonetheless, PR systems approximate proportionality much better than other systems and are more resistant to gerrymandering and other forms of manipulation. Proportional representation refers to
5989-564: The additional seats). Under MMP, two parties that each receive 25% of the votes end up with about 25% of the seats, even if one party wins more constituency seats than the other. Depending on the exact system implemented in a country and the results of a particular election, the proportionality of an election may vary. Overhang seats may reduce the proportionality of the system, although this can be compensated for by allocating additional party list seats to cover any proportionality gap. The specific system of New Zealand for electing its parliament
6102-536: The basic characteristic of the MMP is that the total number of seats in the assembly, including the single-member seats and not only the party-list ones, are allocated to parties proportionally to the number of votes the party received in the party portion of the ballot. This can be done by different apportionment methods : such as the D'Hondt method or the Sainte-Laguë method . Subtracted from each party's allocation
6215-411: 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
6328-412: The candidates determine the winner. This is done using a preferential ballot . The ranking is used to instruct election officials of how the vote should be transferred in case the first preference is marked for an un-electable candidate or for an already elected candidate. Each voter casts one vote and the district used elects multiple members (more than one, usually 3 to 7). Because parties play no role in
6441-605: 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
6554-617: The compensation mechanism was manipulated by decoy lists. Countries with systems which have been confused with mixed-member proportional representation: In March 2004, the Law Commission of Canada proposed a system of MMP, with only 33% of MPs elected from regional open lists, for the House of Commons of Canada but Parliament's consideration of the Report in 2004–05 was stopped after the 2006 election. The New Democratic Party has been
6667-496: 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
6780-680: The constituency elections. A counter-example would be the In Germany's Bundestag , where constituency winners may not always keep their seats since the latest modification of the electoral law. In an MMP variant used in Romania in the 2008 and 2012 legislative elections , where constituency seats could only be earned by the winning candidate if they also achieved an absolute majority in their district, thereby eliminating overhang seats. In New Zealand House of Representatives , all members elected for constituencies keep their seats. For example, in
6893-424: 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
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#17327982586947006-510: The context of voting systems, PR means that each representative in an assembly is elected by a roughly equal number of voters. In the common case of electoral systems that only allow a choice of parties, the seats are allocated in proportion to the vote tally or vote share each party receives. The term proportional representation may be used to mean fair representation by population as applied to states, regions, etc. However, representation being proportional with respect solely to population size
7119-529: The disproportional results produced in single-member districts using FPTP or to increase the fairness produced in multi-member districts using list PR. PR systems that achieve the highest levels of proportionality tend to use as general pooling as possible (typically country-wide) or districts with large numbers of seats. Due to various factors, perfect proportionality is rarely achieved under PR systems. The use of electoral thresholds (in list PR or MMP), small districts with few seats in each (in STV or list PR), or
7232-504: The elected body. The concept applies mainly to political divisions ( political parties ) among voters. The essence of such systems is that all votes cast – or almost all votes cast – contribute to the result and are effectively used to help elect someone. Under other election systems, a bare plurality or a scant majority are all that are used to elect candidates. PR systems provide balanced representation to different factions, reflecting how votes are cast. In
7345-410: The election are as follows (popular vote). Under party-list PR, every party gets a number of seats proportional to their share of the popular vote. This is done by a proportional formula or method; for example, the Sainte-Laguë method – these are the same methods that may be used to allocate seats for geographic proportional representation (for example, how many seats each states gets in
7458-432: The electorate support a particular political party or set of candidates as their favourite, then roughly n % of seats are allotted to that party or those candidates. All PR systems aim to provide some form of equal representation for votes but may differ in their approaches on how they achieve this. Party-list PR is the most commonly used version of proportional representation. Voters cast votes for parties and each party
7571-474: 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
7684-450: The example below, the Droop quota is used and so any candidate who earns more than 25 percent of the vote is declared elected. Note that it is only possible for 3 candidates to each achieve that quota. In the first count, the first preference (favourite candidate) marked on each of the ballots is counted. Candidates whose vote tally equals or passes the quota are declared elected as shown in
7797-497: The example below. (first preferences) Next, surplus votes belonging to those already elected, votes the candidates received above the quota (votes that they did not need to be elected), are transferred to the next preference marked by the voters who voted for them. Continuing the example, suppose that all voters who marked first preference for Jane Doe marked John Citizen as their second choice. Based on this, Jane Doe's surplus votes are transferred to John Citizen, John Citizen passes
7910-470: 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
8023-530: The general principle found in any electoral system in which the popularly chosen subgroups (parties) of an electorate are reflected proportionately in the elected body. To achieve that intended effect, proportional electoral systems need to either have more than one seat in each district (e.g. single transferable vote ), or have some form of compensatory seats (e.g. mixed-member proportional representation apportionment methods ). A legislative body (e.g. assembly, parliament) may be elected proportionally, whereas there
8136-454: 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,
8249-569: The individual candidate vote in a clearly distinct fashion from open-list systems, it may still be considered mixed-member proportional in the sense of a proportional system having two kinds of MP: one (may be) elected by personal (candidate) votes, one elected by (closed list) votes. Previously, the federal elections used a flexible number of additional compensatory seats, also known as leveling seats , which essentially guaranteed mixed-member proportional representation even with extremely disproportional constituency results, but dramatically increased
8362-401: The many candidates, although 21 are elected through STV in some elections with no great difficulty. (In many STV systems, voters are not required to mark more choices than desired. Even if all voters marked only one preference, the resulting representation would be more balanced than under single-winner FPTP.) Under STV, an amount that guarantees election is set, which is called the quota . In
8475-425: The nature of the calculations used to distribute the regional list seats, overhang seats are not possible; the list allocation works like a mixed-member majoritarian system, but in using the d'Hondt method 's divisors to find the averages for the allocation, the first divisor for each party takes into account the number of constituency seats won by the party; i.e. a party that won 7 constituency seats would start with
8588-464: The next section. Though not all overhang seats are perfectly compensated for, New Zealand is widely considered to be a typical example of mixed-member proportional representation due to the high proportionality of the system (disregarding the electoral threshold). MMP replaced (modified): There are several other countries which attempted to introduce MMP by seat linkage compensation , but either not enough leveling seats were provided to achieve it, or
8701-469: The number of list seats or "overhang" seats, Albania subsequently decided to change to a pure-list system. In an abusive gambit similar to that used in Albania, major parties feeling that they are unlikely to win a large number of list seats because of their advantage at the constituency level might choose to split their party in two, with one subdivision of the party contesting the constituency seats, while
8814-442: The number of seats of each party be proportional. Another way to say this is that MMP focuses on making the outcome proportional. Compare the MMP example to a mixed-member majoritarian system, where the party-list PR seat allocation is independent of the district results (this is also called parallel voting ). There is no compensation (no regard to how the district seats were filled) when allocating party-list seats so as to produce
8927-425: 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
9040-419: 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
9153-434: The other contests the list seats—assuming this is allowed by electoral law. The two linked parties could then co-ordinate their campaign and work together within the legislature, while remaining legally separate entities. The result of this approach, if it is used by all parties, would be to transform MMP into a de facto parallel voting mechanism . An example could be seen in the 2007 Lesotho general election . In this case
9266-470: The overhang seats and thereby achieve complete proportionality. For example, the provincial parliament ( Landtag ) of North Rhine Westphalia has, instead of the usual 50% compensatory seats, only 29% unless more are needed to balance overhangs. If a party wins more local seats than its proportion of the total vote justifies, the size of the Landtag increases so that the total outcome is fully proportional to
9379-619: The paradox of voting means that it is still possible for a circular ambiguity in voter tallies to emerge. Proportional representation 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 Proportional representation ( PR ) refers to any type of electoral system under which subgroups of an electorate are reflected proportionately in
9492-419: The parties' vote share. The single transferable vote is an older method than party-list PR, and it does not need to formally involve parties in the election process. Instead of parties putting forward ordered lists of candidates from which winners are drawn in some order, candidates run by name, each voter marks preferences for candidates, with only one marked preference used to place the vote, and votes cast for
9605-408: The parties/lists is how these systems achieve proportionality. Once this is done, the candidates who take the seats are based on the order in which they appear on the list. This is the basic, closed list version of list PR. An example election where the assembly has 200 seats to be filled is presented below. Every voter casts their vote for the list created by their favourite party and the results of
9718-634: The party's regional list: Bavaria uses seven regions for this purpose. A regional open-list method was recommended for the United Kingdom by the Jenkins Commission (where it is known as AMS) and for Canada by the Law Commission of Canada ; neither recommendation was ever implemented. In contrast, the open-list method of MMP was chosen in November 2016 by voters in the 2016 Prince Edward Island electoral reform referendum . In Baden-Württemberg , there were no lists prior to 2022; they used
9831-511: The party's seats. 81 percent of the voters saw their first choice elected. At least 15 percent of them (the Doe first, Citizen second voters) saw both their first and second choices elected – there were likely more than 15 percent if some "Citizen first" votes gave their second preference to Doe. Every voter had satisfaction of seeing someone of the party they support elected in the district. for candidates of party Under STV, to make up
9944-493: The plurality winner. In German, this localized list system now shares the name of PPR with the mixed systems still used in the federal states of Germany that are referred to as MMP in English. In English, due to this change, the system is no longer considered to be MMP in the sense of a mixed member system combining proportional and majoritarian representation , but it would be a personalized/localized version of PR. As it retains
10057-426: 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
10170-617: The proportional top-up (list seats). Some voters may therefore seek to achieve double representation by voting tactically for another party in the regional vote, as a vote for their preferred party in the regional vote would be wasted. This tactic is much less effective in MMP models with a relatively large share of list seats (50% in most German states , and 40% in the New Zealand House of Representatives ) and/or ones which add " balancing seats ", leading to fewer opportunities for overhangs and maintaining full proportionality, even when
10283-409: The quota and so is declared elected to the third and last seat that had to be filled. Even if all of Fred Rubble's surplus had gone to Mary Hill, the vote transfer plus Hill's original votes would not add up to quota. Party B did not have two quotas of votes so was not due two seats, while Party A was. It is possible, in realistic STV elections, for a candidate to win without quota if they are still in
10396-488: The representative is by default chosen using a single winner method (though this is not strictly necessary), typically first-past-the-post : that is, the candidate with the most votes (plurality) wins. Most systems used closed party lists to elect the non-constituency MPs (also called list MPs). In most jurisdictions, candidates may stand for both a constituency and on a party list (referred to in New Zealand as dual candidacy ). In Wales between 2006 and 2014 dual candidacy
10509-528: The results of the district level voting. First-past-the-post is a single winner system and cannot be proportional (winner-takes-all), so these disproportionalities are compensated by the party-list component. A simple, yet common version of MMP has as many list-PR seats as there are single-member districts. In the example it can be seen, as is often the case in reality, that the results of the district elections are highly disproportional: large parties typically win more seats than they should proportionally, but there
10622-421: The running when the field of candidates has thinned to the number of remaining open seats. In this example, the district result is balanced party-wise. No one party took all the seats, as frequently happens under FPTP or other non-proportional voting systems. The result is fair – the most popular party took two seats; the less popular party took just one. The most popular candidates in each party won
10735-662: The same method as MMP, however because the local MPs are also elected using PR, these systems are not usually considered MMP as they are not mixed systems . As especially mixed electoral systems can be quite different, sometimes there is no consensus on their classification as mixed-member proportional, mixed majoritarian or something between the two. These cases include partially or conditionally compensatory systems such as those of Hungary, Mexico and South Korea, which are typically said to be supermixed systems or partially compensatory systems, but sometimes inaccurately referred to as MMP even though they are highly disproportional. In MMP,
10848-469: 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
10961-426: 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
11074-610: The size of the Bundestag. This meant that it was potentially the most proportional MMP system used after the one in New Zealand , where only overhang seats are added back as list seats, which resulted in minor flexibility of the parliament size. In the Canadian province of Quebec , where an MMP model was studied in 2007, it is called the compensatory mixed-member voting system ( système mixte avec compensation or SMAC). In
11187-558: The table than it would if the election used MMM. Because of no provision for overhang seats, there have been cases where a party ended up with fewer total seats than its proportional entitlement. This occurred, for example, in the elections in the South East Wales electoral region in both 2007 ( Welsh Conservatives under-represented) and in 2016 ( Welsh Labour over-represented, Plaid Cymru under-represented). Labour has also been over-represented on this basis in every election in
11300-753: The two leading parties, the Lesotho Congress for Democracy (LCD) and the All Basotho Convention (ABC) used decoy lists, respectively named the National Independent Party and the Lesotho Workers' Party to avoid the compensatory mechanisms of MMP. As a result, the LCD and its decoy were able to take 69.1% of the seats with only 51.8% of the vote. ABC leader Tom Thabane called the vote "free, but not fair." In
11413-475: The two-vote variant to make local members of parliament (MPs) more personally accountable. Voters can thus vote for the local person they prefer for local MP without regard for party affiliation, since the partisan make-up of the legislature is determined only by the party vote. In the 2017 New Zealand election , 27.33% of voters split their vote (voted for a local candidate of a different party than their party vote) compared to 31.64% in 2014. In each constituency,
11526-420: The variants used in Germany almost always produce very proportional results, the proportionality is emphasized over the mixed nature of the electoral system, and it is essentially considered a localized or personalized form of PR, used instead of conventional open-list systems . The new modified federal election system does not allow overhang seats at all, therefore not all local districts are guaranteed to elect
11639-402: The vote count, STV may be used for nonpartisan elections, such as the city council of Cambridge, Massachusetts . A large proportion of the votes cast are used to actually elect someone so the result is mixed and balanced with no one voting block taking much more than its due share of the seats. Where party labels are indicated, proportionality party-wise is noticeable. Counting votes under STV
11752-481: The vote in the state is enough to take a seat, and seven or eight parties take at least that many votes, demonstrating a different voting pattern than Malta exhibits. Mixed-member proportional representation combines election of district members with election of additional members as compensatory top-up. Often MMP systems use single-member districts (SMDs) to elect district members. (Denmark, Iceland and Sweden use multi-member districts in their MMP systems.) MMP with SMDs
11865-407: The voter casts two votes: one for a constituency representative and one for a party. In the original variant used in Germany, citizens gave only one vote, so that voting for a representative automatically meant also voting for the representative's party, which is still used in some MMP elections today and is more robust against tactical voting than typical two-vote versions. Most of Germany changed to
11978-486: 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
12091-420: 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
12204-448: 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
12317-464: The votes, with other parties receiving additional list seats to achieve proportionality. The leveling seats are added to the normal number of seats for the duration of the electoral period. In the German state of Bavaria , the constituency vote and party vote are combined to determine the distribution of seats. Scotland uses a modified variant of MMP known as the additional member system where due to
12430-532: 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
12543-523: 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
12656-626: The working of the model to the point that the parties that won list seats were almost always different from the parties that won constituency seats. Only one constituency member was elected from parties that won list seats. The election was condemned by the Organization for Security and Co-operation in Europe which said it failed to comply with international standards because of "serious irregularities", intimidation, vote-buying and "violence committed by extremists on both sides." Rather than increasing
12769-402: Was banned, i.e. candidates were restricted to contend either for a constituency or for a party list, but not both. If a candidate is on the party list, but wins a constituency seat, they do not receive two seats; they are instead crossed off the party list and the party seat goes to the next candidate down. In Bavaria , the second vote is not simply for the party but for one of the candidates on
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