Electoral methods This series is part of the Politics and the Election series. Politics Politics is the process by which groups of people make decisions An election is a Decision-making process by which a population chooses an individual to hold formal office

Single member Plurality (first-past-the-post) Two-round system Exhaustive ballot Preferential systems Satisfy Condorcet criterion Condorcet method Copeland's method Kemeny-Young method Minimax Condorcet Nanson's method Ranked Pairs Schulze method Other systems Bucklin voting Coombs' method Instant-runoff Borda count Non-rank methods Approval voting Range voting Multi-member Proportional representation Cumulative voting Mixed-member Party-list (Open and Closed) D'Hondt method Highest averages method Largest remainder method Sainte-Laguë method Single transferable vote Quota Borda system Matrix vote Semi-proportional representation Additional Member System Parallel voting Cumulative voting Single non-transferable vote Non-proportional multi-member representation Bloc voting Limited voting Random selection Sortition

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A voting system allows voters to choose between options, often in an election where candidates are selected for public office. The plurality voting system is a Single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member The two-round system (also known as the second ballot or runoff voting) is a Voting system used to elect a single winner The exhaustive ballot is a Voting system used to elect a single winner This article is about voting systems that use ranked ballots For alternative meanings see Preferential voting (disambiguation. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate Copeland's method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories The Kemeny-Young method is a Voting system that uses Preferential ballots Pairwise comparison counts and sequence scores to identify the Minimax is often considered to be the simplest of the Condorcet methods It is also known as the Simpson-Kramer method, and the successive reversal method The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Ranked Pairs (RP or Tideman (named after its developer Nicolaus Tideman) is a Voting method that selects a single winner using votes that express The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. Bucklin voting is the name of a Voting system that can be used for single-member and multi-member districts. The Coombs' method, also called the Coombs rule is a Voting system created by Clyde Coombs used for single-winner Elections in which Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of The Borda count is a single-winner election method in which voters rank candidates in order of preference Approval voting is a single-winner voting system used for Elections Each voter may vote for (approve of as many of the candidates as they wish Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score A voting system allows voters to choose between options often in an Election where candidates are selected for public office. Proportional representation (sometimes referred to as full representation or PR is a category of electoral formula aiming at a close match between the percentage of votes Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation Mixed member proportional representation, also termed mixed-member proportional voting and commonly abbreviated to MMP, is an ' additional member ' Party-list proportional representation systems are a family of Voting systems used in multiple-winner Elections (e Open list describes any variant of Party-list proportional representation where voters have at least some influence on the order in which a party's candidates are elected Closed list describes the variant of Party-list proportional representation where voters can (effectively only vote for political parties as a whole and thus The D'Hondt method (mathematically but not operationally equivalent to Jefferson's method, and Bader-Ofer method) is a Highest averages method for The highest averages method is one way of allocating seats proportionally for representative assemblies with party list Voting systems. The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list Voting systems. The Sainte-Laguë method of the highest average (equivalent to Webster's method or divisor method with standard rounding is one way of allocating seats proportionally for Single transferable vote (STV is a preferential Voting system designed to minimize Wasted votes and provide Proportional representation The Quota Borda System or Quota Preference Score is a Voting system that was devised by the British philosopher Michael Dummett and first published in 1984 in his The matrix vote can be used when one group of people wishes to elect a smaller number of persons each of whom is to have a different assignment The Additional Member System (AMS is a branch of Voting systems in which some representatives are elected from geographic constituencies and others are elected under Parallel voting describes a mixed Voting system where voters in effect participate in two separate elections using different systems and where the results in one election have Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation The single non-transferable vote or SNTV is an Electoral system used in multi-member constituency elections Limited voting is a Voting system in which electors have fewer votes than there are positions available Sortition, also known as allotment, is an equal-chance method of selection by some form of lottery such as drawing coloured pebbles from a bag An election is a Decision-making process by which a population chooses an individual to hold formal office Public administration can be broadly described as the development implementation and study of branches of government Policy. Voting can be also used to award prizes, to select between different plans of action, or by a computer program to find a solution to a problem. Computer programs (also software programs, or just programs) are instructions for a Computer. Voting can be contrasted with consensus decision making. WikipediaConsensus here as this is the article namespace and that information is irrelevant to the reader

A voting system contains rules for valid voting, and how votes are aggregated to yield a final result. The study of formally defined voting systems is called voting theory, a subfield of political science, economics or mathematics. Political science is a branch of Social sciences that deals with the theory and practice of Politics and the description and analysis of Political systems Economics is the social science that studies the production distribution, and consumption of goods and services. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Voting theory began formally in the 18th century and many proposals for voting systems have been made.

Voting systems are either majority rule, proportional representation or plurality voting. Majority rule is a decision rule that makes one of two alternatives the "winner" based on which has more than half the votes Proportional representation (sometimes referred to as full representation or PR is a category of electoral formula aiming at a close match between the percentage of votes The plurality voting system is a Single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member Given the simplicity of majority rule, those who are unfamiliar with voting theory are often surprised that another voting system exists, or that "majority rule" systems can produce results not supported by a majority. If every election had only two choices, the winner would be determined using majority rule alone. However, when there are three or more options, there may not be a single option that is preferred by a majority. Different voting systems may give very different results, particularly in cases where there is no clear majority preference.

Further information: effects of different voting systems under similar circumstances

Contents 1 Aspects of voting systems 1.1 The ballot 1.2 Weight of votes 1.3 Status quo 1.4 Constituencies 2 Single-winner methods 2.1 Single or sequential vote methods 2.2 Ranked voting methods 2.3 Rated voting methods 3 Multiple-winner methods 3.1 Non-proportional and semi-proportional methods 3.2 Proportional methods 3.3 Semi-proportional methods 4 Criteria in evaluating single winner voting systems 5 History 5.1 Early democracy 5.2 Foundations of voting theory 5.3 The single-winner revival 5.4 Influence of game theory 5.5 Post-1980 developments 6 See also 7 References 7.1 General references 7.2 Notes 7.3 References 8 External links 8.1 General 8.2 Advocacy 8.3 Research papers

Aspects of voting systems

A voting system specifies the form of the ballot, the set of allowable votes, and the tallying method, an algorithm for determining the outcome. This article describes an example election using geographical proximity to create hypothetical preferences of a group of voters and then compares the results of such preferences with ten different A ballot is a device (originally a small ball—see blackball) used to record choices made by Voters Each voter uses one ballot and ballots are not In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation This outcome may be a single winner, or may involve multiple winners such as in the election of a legislative body. A legislature is a type of representative Deliberative assembly with the power to create amend and change Laws The law created by a legislature is called Legislation The voting system may also specify how voting power is distributed among the voters, and how voters are divided into subgroups (constituencies) whose votes are counted independently. A constituency is any cohesive corporate unit or body bound by shared structures goals or loyalty

The real-world implementation of an election is generally not considered part of the voting system. For example, though a voting system specifies the ballot abstractly, it does not specify whether the actual physical ballot takes the form of a piece of paper, a punch card, or a computer display. Electronic voting (also known as e-voting) is a term encompassing several different types of Voting, embracing both electronic means of casting a vote and electronic A voting system also does not specify whether or how votes are kept secret, how to verify that votes are counted accurately, or who is allowed to vote. Suffrage (from the Latin suffragium, meaning "voting tablet" and figuratively "right to vote" probably from suffrago "hough" and originally These are aspects of the broader topic of elections and election systems. A voting system allows voters to choose between options often in an Election where candidates are selected for public office.

The ballot

Different voting systems have different forms for allowing the individual to express his or her vote. In ranked ballot or "preference" voting systems, such as Instant-runoff voting, the Borda count, or a Condorcet method, voters order the list of options from most to least preferred. This article is about voting systems that use ranked ballots For alternative meanings see Preferential voting (disambiguation. Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of The Borda count is a single-winner election method in which voters rank candidates in order of preference A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate In range voting, voters rate each option separately on a scale. Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score In plurality voting (also known as "first-past-the-post"), voters select only one option, while in approval voting, they can select as many as they want. The plurality voting system is a Single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member Approval voting is a single-winner voting system used for Elections Each voter may vote for (approve of as many of the candidates as they wish In voting systems that allow "plumping", like cumulative voting, voters may vote for the same candidate multiple times. Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation

Some voting systems include additional choices on the ballot, such as write-in candidates, a none of the above option, or a no confidence in that candidate option. A write-in candidate is a candidate in an Election whose name does not appear on the Ballot, but for whom voters may Vote nonetheless by writing in the None of the Above ( NOTA) or against all is a Ballot choice in some Jurisdictions or Organizations placed so as to allow the

Weight of votes

Many elections are held to the ideal of "one person, one vote," meaning that every voter's votes should be counted with equal weight. This is not true of all elections, however. Corporate elections, for instance, usually weight votes according to the amount of stock each voter holds in the company, changing the mechanism to "one share, one vote". A corporation is a separate legal entity usually used to conduct business Votes can also be weighted unequally for other reasons, such as increasing the voting weight of higher-ranked members of an organization.

Voting weight is not the same thing as voting power. In situations where certain groups of voters will all cast the same vote (for example, political parties in a parliament), voting power measures the ability of a group to change the outcome of a vote. A political party is a Political organization that seeks to attain and maintain political power within Government, usually by participating in electoral TalkParliament#Screen-size. -->A  parliament is a Legislature, especially in those Groups may form coalitions in order to maximize their voting power. A coalition is an alliance among individuals during which they cooperate in joint action, each in their own Self-interest.

Status quo

Some voting systems are weighted in themselves, for example if a supermajority is required to change the status quo. A supermajority or a qualified majority is a requirement for a proposal to gain a specified level or type of support which exceeds a simple Majority in order to have An extreme case of this is unanimous consent, where changing the status quo requires the support of every voting member. In Parliamentary procedure, unanimous consent, also known as general consent, or in the case of the parliaments under the Westminster system leave of the house If the decision is whether to accept a new member into an organization, failure of this procedure to admit the new member is called blackballing. Blackballing was a rejection technique used in elections to membership of a Gentlemen's club (as well as similarly organised institutions such as Freemasonry

A different mechanism that favors the status quo is the requirement for a quorum, which ensures that the status quo remains if not enough voters participate in the vote. In Law, a quorum is the minimum number of members of a Deliberative body necessary to conduct the business of that group Quorum requirements often depend only on the total number of votes rather than the number of actual votes cast for the winning option; however, this can sometimes encourage dissenting voters to refrain from voting entirely in order to prevent a quorum.

Constituencies

Main article: Constituency

Often the purpose of an election is to choose a legislative body made of multiple winners. A constituency is any cohesive corporate unit or body bound by shared structures goals or loyalty A legislature is a type of representative Deliberative assembly with the power to create amend and change Laws The law created by a legislature is called Legislation This can be done by running a single election and choosing the winners from the same pool of votes, or by dividing up the voters into constituencies that have different options and elect different winners.

Some countries, like Israel, fill their entire parliament using a single multiple-winner district (constituency) or multiple member electorate, while others, like the Republic of Ireland or Belgium, break up their national elections into smaller multiple-winner districts, and yet others, like the United States or the United Kingdom, hold only single-winner elections. For a topic outline on this subject see List of basic Israel topics. A constituency is any cohesive corporate unit or body bound by shared structures goals or loyalty Ireland ( Irish: Éire, ˈeːrʲə is a country in north-western Europe. The Kingdom of Belgium is a Country in northwest Europe. It is a founding member of the European Union and hosts its headquarters as well as those The United States of America —commonly referred to as the The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located Some systems, like the Additional member system, embed smaller districts within larger ones. The Additional Member System (AMS is a branch of Voting systems in which some representatives are elected from geographic constituencies and others are elected under

The way in which constituencies are created and assigned seats can dramatically affect the results. Apportionment is the process by which states, regions, or larger districts are awarded seats, usually according to population changes as a result of a census. Apportionment is the process of allocating political power among a set of principles (or defined constituencies A census is the procedure of acquiring information about every member of a given population Redistricting is the process by which the borders of constituencies are redrawn once apportioned. Redistricting, a form of redistribution, is the process of changing of political Borders in the United States Both procedures can become highly politically contentious due to the possibility of both malapportionment, where there are unequal representative to population ratios across districts, and gerrymandering, where electoral districts are manipulated for political gain. Apportionment is the process of allocating political power among a set of principles (or defined constituencies Gerrymandering is a form of redistribution in which electoral district or Constituency boundaries are manipulated for electoral advantage A particularly ill case was the English Rotten Boroughs, abandoned towns who still were represented in parliament. The term "rotten" or "decayed" borough referred to a parliamentary borough or Constituency in Great Britain and Ireland

Single-winner methods

Main article: Single-winner voting systems

Single-winner systems can be classified based on their ballot type. One vote systems are those in which a voter picks one choice at a time. In ranked voting systems, each voter ranks the candidates in order of preference. In rated voting systems, voters give a score to each candidate.

Single or sequential vote methods

The most prevalent single-winner voting method, by far, is plurality (also called "first-past-the-post", "relative majority", or "winner-take-all"), in which each voter votes for one choice, and the choice that receives the most votes wins, even if it receives less than a majority of votes. The plurality voting system is a Single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member

Runoff methods hold multiple rounds of plurality voting to ensure that the winner is elected by a majority. Top-two runoff voting, the second most common method used in elections, holds a runoff election between the top two options if there is no majority. In elimination runoff elections, the weakest candidate is eliminated until there is a majority. Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of In an exhaustive runoff election, no candidates are eliminated, so voting is simply repeated until there is a majority.

A nonpartisan primary election is also used as a two round runoff process. A primary election ( nominating primary) also referred to simply as a primary, is an election in which voters in a Jurisdiction select candidates The two candidates with the most votes in the open primary pass to the general election. The difference between a runoff and an open primary is that a winner is never chosen in the primary, while the first round of a runoff can result in a winner if one candidate has over 50% of the vote.

Random ballot is a method in which each voter votes for one option, and a single ballot is selected at random to determine the winner. The random ballot Voting method takes the one person one vote principle to an extreme by only counting the vote of one person This is mostly used as a tiebreaker for other methods.

Ranked voting methods

Main article: Preferential voting

Also known as preferential voting methods, these methods allow each voter to rank the candidates in order of preference. Often it is not necessary to rank all the candidates: unranked candidates are usually considered to be tied for last place. Some ranked ballot methods also allow voters to give multiple candidates the same ranking.

The most common ranked voting method is instant-runoff voting (IRV), also known as the "alternative vote" or simply "preferential voting", which uses voters' preferences to simulate an elimination runoff election without multiple voting events. Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of As the votes are tallied, the option with the fewest first-choice votes is eliminated. In successive rounds of counting, the next preferred choice still available from each eliminated ballot is transferred to candidates not yet eliminated. The least preferred option is eliminated in each round of counting until there is a majority winner, with all ballots being considered in every round of counting.

The Borda count is a simple ranked voting method in which the options receive points based on their position on each ballot. The Borda count is a single-winner election method in which voters rank candidates in order of preference A class of similar methods is called positional voting systems. A positional voting system is a ranked voting method in which the options receive points based on their position on each ballot and the option with the most points wins

Other ranked methods include Coombs' method, Supplementary voting, Bucklin voting, and Condorcet method. The Coombs' method, also called the Coombs rule is a Voting system created by Clyde Coombs used for single-winner Elections in which The contingent vote is an electoral system used to elect a single winner in which the voter ranks the candidates in order of preference Bucklin voting is the name of a Voting system that can be used for single-member and multi-member districts. A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate

Condorcet methods, or pairwise methods, are a class of ranked voting methods that meet the Condorcet criterion. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters These methods compare every option pairwise with every other option, one at a time, and an option that defeats every other option is the winner. An option defeats another option if a majority of voters rank it higher on their ballot than the other option.

These methods are often referred to collectively as Condorcet methods because the Condorcet criterion ensures that they all give the same result in most elections, where there exists a Condorcet winner. The differences between Condorcet methods occur in situations where no option is undefeated, implying that there exists a cycle of options that defeat one another, called a Condorcet paradox or Smith set. The voting paradox (also known as Condorcet's paradox or the paradox of voting) is a situation noted by the Marquis de Condorcet in the late 18th century In Voting systems the Smith set is the smallest non-empty set of candidates in a particular election such that each member beats every other candidate outside the set in a pairwise Considering a generic Condorcet method to be an abstract method that does not resolve these cycles, specific versions of Condorcet that select winners even when no Condorcet winner exists are called Condorcet completion methods.

A simple version of Condorcet is Minimax: if no option is undefeated, the option that is defeated by the fewest votes in its worst defeat wins. Minimax is often considered to be the simplest of the Condorcet methods It is also known as the Simpson-Kramer method, and the successive reversal method Another simple method is Copeland's method, in which the winner is the option that wins the most pairwise contests, as in many round-robin tournaments. Copeland's method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories A round-robin tournament or all-play-all tournament is a type of group tournament in which each participant plays every other participant an equal number of times The Schulze method (also known as "Schwartz sequential dropping", "cloneproof Schwartz sequential dropping" or the "beatpath method") and Ranked Pairs are two recently designed Condorcet methods that satisfy a large number of voting system criteria. The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. Ranked Pairs (RP or Tideman (named after its developer Nicolaus Tideman) is a Voting method that selects a single winner using votes that express

The Kemeny-Young method is a Condorcet method that fully ranks all the candidates from most popular to least popular. The Kemeny-Young method is a Voting system that uses Preferential ballots Pairwise comparison counts and sequence scores to identify the

Rated voting methods

Rated ballots allow even more flexibility than ranked ballots, but few methods are designed to use them. Each voter gives a score to each option; the allowable scores could be numeric (for example, from 0 to 100) or could be "grades" like A/B/C/D/F.

In range voting, voters give numeric ratings to each option, and the option with the highest total score wins. Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score

Approval voting where voters may vote for as many candidates as they like can be seen as an instance of range voting where the allowable ratings are 0 and 1. Approval voting is a single-winner voting system used for Elections Each voter may vote for (approve of as many of the candidates as they wish

Rated ballots can be used for ranked voting methods, as long as the ranked method allows tied rankings. Some ranked methods assume that all the rankings on a ballot are distinct, but many voters would be likely to give multiple candidates the same rating on a rated ballot.

Multiple-winner methods

A vote with multiple winners, such as the election of a legislature, has different practical effects than a single-winner vote. Often, participants in a multiple winner election are more concerned with the overall composition of the legislature than exactly which candidates get elected. For this reason, many multiple-winner systems aim for proportional representation, which means that if a given party (or any other political grouping) gets X% of the vote, it should also get approximately X% of the seats in the legislature. Proportional representation (sometimes referred to as full representation or PR is a category of electoral formula aiming at a close match between the percentage of votes Not all multiple-winner voting systems are proportional.

Non-proportional and semi-proportional methods

Many multiple-winner voting methods are simple extensions of single-winner methods, without an explicit goal of producing a proportional result. Bloc voting, or plurality-at-large, has each voter vote for N options and selects the top N as the winners. Because of its propensity for landslide victories won by a single winning slate of candidates, bloc voting is non-proportional. In Politics, a landslide victory (or landslide) is the victory of a candidate or Political party by an overwhelming margin in an Election Two similar plurality-based methods with multiple winners are the Single Non-Transferable Vote or SNTV method, where the voter votes for only one option, and cumulative voting, described above. The single non-transferable vote or SNTV is an Electoral system used in multi-member constituency elections Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation Unlike bloc voting, elections using the Single Nontransferable Vote or cumulative voting may achieve proportionality if voters use tactical voting or strategic nomination. In Voting systems tactical voting (or strategic voting or sophisticated voting) occurs when a voter supports a candidate other than his or her Strategic nomination is the manipulation of an Election through its candidate set (compare this to Tactical voting, where the manipulation comes from the voters

Because they encourage proportional results without guaranteeing them, the Single Nontransferable Vote and cumulative voting methods are classified as semi-proportional. Other methods that can be seen as semi-proportional are mixed methods, which combine the results of a plurality election and a party-list election (described below). Parallel voting is an example of a mixed method because it is only proportional for a subset of the winners. Parallel voting describes a mixed Voting system where voters in effect participate in two separate elections using different systems and where the results in one election have

Proportional methods

Main article: Proportional representation

Truly proportional methods make some guarantee of proportionality by making each winning option represent approximately the same number of voters. Proportional representation (sometimes referred to as full representation or PR is a category of electoral formula aiming at a close match between the percentage of votes This number is called a quota. For example, if the quota is 1000 voters, then each elected candidate reflects the opinions of 1000 voters, within a margin of error. This can be measured using the Gallagher Index. The Gallagher Index (or least squares index) is used to measure the disproportionality of an electoral outcome that is the difference between the percentage of votes received

Most proportional systems in use are based on party-list proportional representation, in which voters vote for parties instead of for individual candidates. Party-list proportional representation systems are a family of Voting systems used in multiple-winner Elections (e For each quota of votes a party receives, one of their candidates wins a seat on the legislature. The methods differ in how the quota is determined or, equivalently, how the proportions of votes are rounded off to match the number of seats.

The methods of seat allocation can be grouped overall into highest averages methods and largest remainder methods. The highest averages method is one way of allocating seats proportionally for representative assemblies with party list Voting systems. The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list Voting systems. Largest remainder methods set a particular quota based on the number of voters, while highest averages methods, such as the Sainte-Laguë method and the d'Hondt method, determine the quota indirectly by dividing the number of votes the parties receive by a sequence of numbers. The Sainte-Laguë method of the highest average (equivalent to Webster's method or divisor method with standard rounding is one way of allocating seats proportionally for The D'Hondt method (mathematically but not operationally equivalent to Jefferson's method, and Bader-Ofer method) is a Highest averages method for

Independently of the method used to assign seats, party-list systems can be open list or closed list. In an open list system, voters decide which candidates within a party win the seats. Open list describes any variant of Party-list proportional representation where voters have at least some influence on the order in which a party's candidates are elected In a closed list system, the seats are assigned to candidates in a fixed order that the party chooses. Closed list describes the variant of Party-list proportional representation where voters can (effectively only vote for political parties as a whole and thus The Mixed Member Proportional system is a mixed method that only uses a party list for a subset of the winners, filling other seats with the winners of regional elections, thus having features of open list and closed list systems. Mixed member proportional representation, also termed mixed-member proportional voting and commonly abbreviated to MMP, is an ' additional member '

In contrast to party-list systems, the Single Transferable Vote is a proportional representation system in which voters rank individual candidates in order of preference. Single transferable vote (STV is a preferential Voting system designed to minimize Wasted votes and provide Proportional representation Unlike party-list systems, STV does not depend on the candidates being grouped into political parties. Votes are transferred between candidates in a manner similar to instant runoff voting, but in addition to transferring votes from candidates who are eliminated, excess votes are also transferred from candidates who already have a quota. Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of

Semi-proportional methods

A simpler method called Cumulative voting (CV) is a semi-proportional voting system in which each voter has n votes, where n is the number of seats to be elected. Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation Voters can distribute portions of their vote between a set of candidates, fully upon one candidate, or a mixture. It is considered a proportional system in allowing a united coalition representing a m/(n+1) fraction of the voters to be guaranteed to elect m seats of an n-seat election. For example in a 3-seat election, 3/4 of the voters (if united on 3 candidates) can guarantee control over all three seats. (In contrast, plurality at large, which allows a united coalition (majority) (50%+1) to control all the seats. )

Cumulative voting is a common way of holding elections in which the voters have unequal voting power, such as in corporate governance under the "one share, one vote" rule. Cumulative voting is also used as a multiple-winner method, such as in elections for a corporate board.

Cumulative voting is not fully proportional because it suffers from the same spoiler effect of plurality without a run-off process. The " spoiler effect " is a term to describe the effect a Minor party candidate with little chance of winning can have on a close Election, in which their A group of like-minded voters divided among "too many" candidates may fail to elect any winners, or elect fewer than they deserve by their size. The level of proportionality depends on how well-coordinated the voters are.

Limited voting is a multi-winner system that gives voters fewer votes than the number of seats to be decided. Limited voting is a Voting system in which electors have fewer votes than there are positions available The simplest and most common form of limited voting is Single Non-Transferable Vote (SNTV). The single non-transferable vote or SNTV is an Electoral system used in multi-member constituency elections It can be considered a special variation of cumulative voting where a full vote cannot be divided among more than one candidate. It depends on a statistical distributions of voters to smooth out preferences that CV can do by individual voters.

For example, in a 4-seat election a candidate needs 20% to guarantee election. A coalition of 40% can guarantee 2-seats in CV by perfectly splitting their votes as individuals between 2 candidates. In comparison, SNTV tends towards collectively dividing 20% between each candidate by assuming every coalition voter flipped a coin to decide which candidate to support with their single vote. This limitation simplifies voting and counting, at the cost of more uncertainty of results.

Criteria in evaluating single winner voting systems

In the real world, attitudes toward voting systems are highly influenced by the systems' impact on groups that one supports or opposes. This can make the objective comparison of voting systems difficult. In order to compare systems fairly and independently of political ideologies, voting theorists use voting system criteria, which define potentially desirable properties of voting systems mathematically.

It is impossible for one voting system to pass all criteria in common use. Economist Kenneth Arrow proved Arrow's impossibility theorem, which demonstrates that several desirable features of voting systems are mutually contradictory. Kenneth Joseph Arrow (born August 23, 1921) is an American Economist and joint winner of the Nobel Memorial Prize in Economics In Social choice theory, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can convert the ranked preferences of individuals For this reason, someone implementing a voting system has to decide which criteria are important for the election.

Using criteria to compare systems does not make the comparison completely objective. For example, it is relatively easy to devise a criterion that is met by one's preferred voting method, and by very few other methods. Doing this, one can then construct a biased argument for the criterion, instead of arguing directly for the method. No one can be the ultimate authority on which criteria should be considered, but the following are some criteria that are accepted and considered to be desirable by many voting theorists:

• Majority criterion — If there exists a majority that ranks (or rates) a single candidate higher than all other candidates, does that candidate always win?
• Monotonicity criterion — Is it impossible to cause a winning candidate to lose by ranking him higher, or to cause a losing candidate to win by ranking him lower?
• Consistency criterion — If the electorate is divided in two and a choice wins in both parts, does it always win overall?
• Participation criterion — Is it always better to vote honestly than to not vote? (This is grouped with the distinct but similar Consistency Criterion in the table below. The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer This article is about a voting system criterion See Monotonic function for a mathematical notion A Voting system is consistent if when the electorate is divided arbitrarily into two (or more parts and separate elections in each part result in the same choice being selected The participation criterion is a Voting system criterion for evaluating Voting systems and is also known as the No show paradox. ^[1])
• Condorcet criterion — If a candidate beats every other candidate in pairwise comparison, does that candidate always win?
• Condorcet loser criterion — If a candidate loses to every other candidate in pairwise comparison, does that candidate always lose?
• Independence of irrelevant alternatives — Is the outcome the same after adding or removing non-winning candidates?
• Independence of clone candidates — Is the outcome the same if candidates identical to existing candidates are added?
• Reversal symmetry — If individual preferences of each voter are inverted, does the original winner never win?

The following table shows which of the above criteria are met by several single-winner systems. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate In single-winner Voting system theory the Condorcet loser criterion is a measure for differentiating voting systems Independence of irrelevant alternatives (IIA is a term for an Axiom of Decision theory and various social sciences Strategic nomination is the manipulation of an Election through its candidate set (compare this to Tactical voting, where the manipulation comes from the voters Reversal symmetry is a Voting system criterion that is stated as follows If a candidate A is the unique winner and the individual preferences of each voter are inverted then

	Majority	Monotone	Consistency & Participation	Condorcet	Condorcet loser	IIA	Clone independence	Reversal symmetry
Approval	Ambiguous	Yes	Yes	No	No	Yes	Ambiguous[2]	Yes
Borda count	No	Yes	Yes	No	Yes	No	No (teaming)	Yes
IRV	Yes	No	No	No	Yes	No	Yes[3]	No
Kemeny-Young	Yes	Yes	No	Yes	Yes	No	No
Minimax	Yes	Yes	No	Yes	No	No	No (vote-splitting)	No
Plurality	Yes	Yes	Yes	No	No	No	No (vote-splitting)
Range voting	No	Yes	Yes	No	No	Yes	Yes	Yes
Ranked Pairs	Yes	Yes	No	Yes	Yes	No (see local IIA note)	Yes
Runoff voting	Yes	No	No	No	Yes	No	No (vote-splitting)
Schulze	Yes	Yes	No	Yes	Yes	No (see local IIA note)	Yes	Yes

In addition to the above criteria, voting systems are judged using criteria that are not mathematically precise but are still important, such as simplicity, speed of vote-counting, the potential for fraud or disputed results, the opportunity for tactical voting or strategic nomination, and, for multiple-winner methods, the degree of proportionality produced. The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer This article is about a voting system criterion See Monotonic function for a mathematical notion A Voting system is consistent if when the electorate is divided arbitrarily into two (or more parts and separate elections in each part result in the same choice being selected The participation criterion is a Voting system criterion for evaluating Voting systems and is also known as the No show paradox. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters In single-winner Voting system theory the Condorcet loser criterion is a measure for differentiating voting systems Independence of irrelevant alternatives (IIA is a term for an Axiom of Decision theory and various social sciences In voting systems theory the Independence of Clones Criterion is a criterion that measures an election method's robustness to Strategic nomination. Reversal symmetry is a Voting system criterion that is stated as follows If a candidate A is the unique winner and the individual preferences of each voter are inverted then Approval voting is a single-winner voting system used for Elections Each voter may vote for (approve of as many of the candidates as they wish The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters The Borda count is a single-winner election method in which voters rank candidates in order of preference The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters Strategic nomination is the manipulation of an Election through its candidate set (compare this to Tactical voting, where the manipulation comes from the voters Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters The Kemeny-Young method is a Voting system that uses Preferential ballots Pairwise comparison counts and sequence scores to identify the The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters Minimax is often considered to be the simplest of the Condorcet methods It is also known as the Simpson-Kramer method, and the successive reversal method The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters Vote splitting is an electoral effect in which the distribution of votes among multiple similar candidates reduces the chance of winning for any of the similar candidates and The plurality voting system is a Single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters Vote splitting is an electoral effect in which the distribution of votes among multiple similar candidates reduces the chance of winning for any of the similar candidates and Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters Ranked Pairs (RP or Tideman (named after its developer Nicolaus Tideman) is a Voting method that selects a single winner using votes that express The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters Ranked Pairs (RP or Tideman (named after its developer Nicolaus Tideman) is a Voting method that selects a single winner using votes that express The two-round system (also known as the second ballot or runoff voting) is a Voting system used to elect a single winner The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters Vote splitting is an electoral effect in which the distribution of votes among multiple similar candidates reduces the chance of winning for any of the similar candidates and The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. The majority criterion is a single-winner Voting system criterion, used to objectively compare such systems The criterion states that if a majority of voters prefer The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. In Voting systems tactical voting (or strategic voting or sophisticated voting) occurs when a voter supports a candidate other than his or her Strategic nomination is the manipulation of an Election through its candidate set (compare this to Tactical voting, where the manipulation comes from the voters The Gallagher Index (or least squares index) is used to measure the disproportionality of an electoral outcome that is the difference between the percentage of votes received

It is also possible to simulate large numbers of virtual elections on a computer and see how various voting systems compare in terms of voter satisfaction. Such simulations are sensitive to their assumptions, particularly with regards to voter strategy, but by varying the assumptions they can give repeatable measures that bracket the best and worst cases for a voting system. To date, the only such simulation to compare a wide variety of voting systems was run by a range-voting advocate and has not been peer-reviewed. ^[4]

The New Zealand Royal Commission on the Electoral System listed ten criteria for their evaluation of possible new electoral systems for New Zealand. New Zealand is an Island country in the south-western Pacific Ocean comprising two main landmasses (the North Island and the South Island The Royal Commission on the Electoral System was formed in New Zealand in 1985, and reported in 1986. Electoral Reform in New Zealand has in recent years become a political issue as major changes have been made to both Parliamentary and local government elections These included fairness between political parties, effective representation of minority or special interest groups, political integration, effective voter participation and legitimacy.

Bayesian regret is an objective numerical measure of quality of a voting system that is sensitive to subjective assumptions about the candidates and electorate. In Statistics, Decision theory and Economics, a loss function is a function that maps an event (technically an element of a Sample space Its least contentious use is to give best-case and worst-case values for a given system.

History

Early democracy

Voting has been used as an essential feature of democracy since the 6th century BC, when democracy was introduced by the Athenian democracy. Democracy is a form of government in which the supreme power is held completely by the people under a free electoral system Athenian democracy developed in the Greek City-state of Athens One of the earliest recorded elections in Athens was a plurality vote that it was undesirable to "win": in the process called ostracism, voters chose the citizen they most wanted to exile for ten years. The plurality voting system is a Single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member Ostracism ( ostrakismos) was a procedure under the Athenian democracy in which a prominent Citizen could be expelled from the City-state Most elections in the early history of democracy were held using plurality voting or some variant, but as an exception, the state of Venice in the 13th century adopted the system we now know as approval voting to elect their Great Council. Democracy is a political system in which all the members of the society have an equal share of formal political power Venice ( Italian: Venezia, Venetian: Venesia or Venexia) is a city in Northern Italy, the capital of the Approval voting is a single-winner voting system used for Elections Each voter may vote for (approve of as many of the candidates as they wish ^[5]

The Venetians' system for electing the Doge was a particularly convoluted process, consisting of five rounds of drawing lots and five rounds of approval voting. The Doge ( Venetian language, also Doxe, derived from Latin Dux military leader duke cf By drawing lots, a body of 30 electors was chosen, which was further reduced to 9 electors by drawing lots again. The electoral college of 9 members elected 40 people by approval voting; those 40 were reduced to form a second electoral college of 12 members by drawing lots again. The second electoral college elected 25 people by approval voting, which were reduced to form a third electoral college of 9 members by drawing lots. The third electoral college elected 45 people, which were reduced to form a fourth electoral college of 11 by drawing lots. They in turn elected a final electoral body of 41 members, who ultimately elected the Doge. Despite its complexity, the system had certain desirable properties such as being hard to game and ensuring that the winner reflected the opinions of both majority and minority factions. ^[6] This process was used with little modification from 1268 until the end of the Republic of Venice in 1797, and was one of the factors contributing to the durability of the republic. The Most Serene Republic of Venice ((Serenìsima Repùblica Vèneta or Repùblica de Venesia Serenissima Repubblica

Foundations of voting theory

Voting theory became an object of academic study around the time of the French Revolution. The French Revolution (1789–1799 was a period of political and social upheaval in the History of France, during which the French governmental structure previously an ^[5] Jean-Charles de Borda proposed the Borda count in 1770 as a method for electing members to the French Academy of Sciences. Jean-Charles chevalier de Borda ( May 4, 1733 – February 19, 1799) was a French Mathematician, Physicist The Borda count is a single-winner election method in which voters rank candidates in order of preference The French Academy of Sciences ( French: Académie des sciences) is a Learned society, founded in 1666 by Louis XIV at the His system was opposed by the Marquis de Condorcet, who proposed instead the method of pairwise comparison that he had devised. Implementations of this method are known as Condorcet methods. A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate He also wrote about the Condorcet paradox, which he called the intransitivity of majority preferences. The voting paradox (also known as Condorcet's paradox or the paradox of voting) is a situation noted by the Marquis de Condorcet in the late 18th century ^[7]

While Condorcet and Borda are usually credited as the founders of voting theory, recent research has shown that the philosopher Ramon Llull discovered both the Borda count and a pairwise method that satisfied the Condorcet criterion in the 13th century. Ramon Llull (1232 &ndash June 29, 1315) (sometimes Raymond Lully, Raymond Lull, in Latin Raimundus or The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters The manuscripts in which he described these methods had been lost to history until they were rediscovered in 2001. ^[8]

Later in the 18th century, the related topic of apportionment began to be studied. Apportionment is the process of allocating political power among a set of principles (or defined constituencies The impetus for research into fair apportionment methods came, in fact, from the United States Constitution, which mandated that seats in the United States House of Representatives had to be allocated among the states proportionally to their population, but did not specify how to do so. The Constitution of the United States of America is the supreme Law of the United States. The United States House of Representatives is one of the two chambers of the United States Congress; the other is the Senate. ^[9] A variety of methods were proposed by statesmen such as Alexander Hamilton, Thomas Jefferson, and Daniel Webster. Thomas Jefferson (April 13 1743 – July 4 1826 was the third President of the United States (1801–1809 the principal author of the Declaration of Independence Daniel Webster (January 18 1782 &ndash October 24 1852 was a leading American Statesman during the nation's Antebellum Period. Some of the apportionment methods discovered in the United States were rediscovered in Europe in the 19th century, as seat allocation methods for the newly proposed system of party-list proportional representation. The United States of America —commonly referred to as the Party-list proportional representation systems are a family of Voting systems used in multiple-winner Elections (e The result is that many apportionment methods have two names: for instance, Jefferson's method is the same as the d'Hondt method, and Webster's method is the Sainte-Laguë method. The D'Hondt method (mathematically but not operationally equivalent to Jefferson's method, and Bader-Ofer method) is a Highest averages method for The Sainte-Laguë method of the highest average (equivalent to Webster's method or divisor method with standard rounding is one way of allocating seats proportionally for ^[10]

The Single Transferable Vote system was devised by Carl Andrae in Denmark in 1855, and also in England by Thomas Hare in 1857. Single transferable vote (STV is a preferential Voting system designed to minimize Wasted votes and provide Proportional representation Carl Christoffer Georg Andræ ( 14 October 1812 &ndash 2 February 1893) was a Danish Politician and Mathematician The Kingdom of Denmark ( ˈd̥ænmɑɡ̊ (archaic ˈd̥anmɑːɡ̊ commonly known as Denmark, is a country in the Scandinavian region of northern Europe England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland Thomas Hare (born in England 28 March 1806; died 6 May 1891) was a British proponent of electoral reform Their discoveries may or may not have been independent. STV elections were first held in Denmark in 1856, and in Tasmania in 1896 after its use was promoted by Andrew Inglis Clark. Tasmania is an Australian island and state of the same name It is located south of the eastern side of the Continent, being separated from it by Bass Andrew Inglis Clark (24 February 1848–14 November 1907 was an Australian politician Party-list proportional representation was first implemented to elect European legislatures in the early 20th century, with Belgium implementing it first in 1900. The Kingdom of Belgium is a Country in northwest Europe. It is a founding member of the European Union and hosts its headquarters as well as those Since then, proportional and semi-proportional methods have come to be used in almost all democratic countries, with most exceptions being former British colonies. The British Empire was the largest empire in history and for over a century was the foremost global power. ^[11]

The single-winner revival

Perhaps influenced by the rapid development of multiple-winner voting methods, theorists began to publish new findings about single-winner methods in the late 19th century. This began around 1870, when William Robert Ware proposed applying STV to single-winner elections, yielding instant runoff voting. William Robert Ware ( 27 May 1832 &ndash 9 June 1915) born in Cambridge Massachusetts into a family of the Unitarian Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of ^[12] Soon, mathematicians began to revisit Condorcet's ideas and invent new methods for Condorcet completion. Edward J. Nanson combined the newly described instant runoff voting with the Borda count to yield a new Condorcet method called Nanson's method. Edward John Nanson (1850-1936 was a mathematician known for devising Nanson's method, a variation of the Borda count using successive elimination down to the winner Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of The Borda count is a single-winner election method in which voters rank candidates in order of preference The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Charles Dodgson, better known as Lewis Carroll, published pamphlets on voting theory, focusing in particular on Condorcet voting. Charles Lutwidge Dodgson (ˈdɒdsən (27 January 1832 &ndash 14 January 1898 better known by the Pen name Lewis Carroll (/ˈkærəl/ was an English He introduced the use of matrices to analyze Condorcet elections, though this, too, had already been done in some form in the then-lost manuscripts of Ramon Llull. In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally Ramon Llull (1232 &ndash June 29, 1315) (sometimes Raymond Lully, Raymond Lull, in Latin Raimundus or He also proposed the straightforward Condorcet method known as Dodgson's method.

Ranked voting systems eventually gathered enough support to be adopted for use in government elections. In Australia, IRV was first adopted in 1893, and continues to be used along with STV today. In the United States in the early 20th century, various municipalities began to use Bucklin voting, but the results were not satisfying to voters. The United States of America —commonly referred to as the Bucklin voting is the name of a Voting system that can be used for single-member and multi-member districts. Bucklin is no longer used in any government elections, and has even been declared unconstitutional in Minnesota. Minnesota ( Native Americans demonstrated the name to early settlers ^[13]

Influence of game theory

After John von Neumann and others developed the mathematical field of game theory in the 1940s, new mathematical tools were available to analyze voting systems and strategic voting. Game theory is a branch of Applied mathematics that is used in the Social sciences (most notably Economics) Biology, Engineering, This led to significant new results that changed the field of voting theory. ^[5] The use of mathematical criteria to evaluate voting systems was introduced when Kenneth Arrow showed in Arrow's impossibility theorem that certain intuitively desirable criteria were actually mutually contradictory, demonstrating the inherent limitations of voting theorems. Kenneth Joseph Arrow (born August 23, 1921) is an American Economist and joint winner of the Nobel Memorial Prize in Economics In Social choice theory, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can convert the ranked preferences of individuals Arrow's theorem is easily the single most cited result in voting theory, and it inspired further significant results such as the Gibbard-Satterthwaite theorem, which showed that strategic voting is unavoidable in certain common circumstances.

The use of game theory to analyze voting systems also led to discoveries about the emergent strategic effects of certain systems. Duverger's Law is a prominent example of such a result, showing that plurality voting often leads to a two-party system. In Political science, Duverger's law is a principle which asserts that a plurality rule election system tends to favor a Two-party system. The plurality voting system is a Single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member A two-party system is a form of Party system where two major Political parties dominate voting in nearly all Elections at every Further research into the game theory aspects of voting led Steven Brams and Peter Fishburn to formally define and promote the use of approval voting in 1977. Steven J Brams (born November 28, 1940) is a game theorist and Political scientist at the New York University department of politics Peter C Fishburn (born 1936 is known as a pioneer in the field of decision making processes Approval voting is a single-winner voting system used for Elections Each voter may vote for (approve of as many of the candidates as they wish While approval voting had been used before that, it had not been named or considered as an object of academic study, particularly because it violated the assumption made by most research that single-winner methods were based on preference rankings.

Post-1980 developments

Voting theory has come to focus on voting system criteria almost as much as it does on particular voting systems. Now, any description of a benefit or weakness in a voting system is expected to be backed up by a mathematically defined criterion. Recent research in voting theory has largely involved devising new criteria and new methods devised to meet certain criteria.

Political scientists of the 20th published many studies on the effects that the voting systems have on voters choices and political parties,^[14][15][16] and on political stability. This is a list of notable political scientists See the List of political theorists for those who study politics without using the Scientific method. ^[17][18] A few scholars also studied what effects caused a nation to change for a particular voting system. ^{[19][20][21][22][23]} One prominent current voting theorist is Nicolaus Tideman, who formalized concepts such as strategic nomination and the spoiler effect in the independence of clones criterion. T Nicolaus Tideman (born August 11, 1943 in Chicago Illinois) is a Professor of Economics at Virginia Polytechnic Institute Strategic nomination is the manipulation of an Election through its candidate set (compare this to Tactical voting, where the manipulation comes from the voters The " spoiler effect " is a term to describe the effect a Minor party candidate with little chance of winning can have on a close Election, in which their In voting systems theory the Independence of Clones Criterion is a criterion that measures an election method's robustness to Strategic nomination. Tideman also devised the ranked pairs method, a Condorcet method that is not susceptible to clones. Ranked Pairs (RP or Tideman (named after its developer Nicolaus Tideman) is a Voting method that selects a single winner using votes that express A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate In voting systems theory the Independence of Clones Criterion is a criterion that measures an election method's robustness to Strategic nomination. Also, Donald G. Saari has brought renewed interest to the Borda count with the books he has published since 2001. Donald Gene Saari (born March 1940 in Houghton Michigan, US) is the Distinguished Professor of Mathematics and Economics and director of the Institute for Mathematical The Borda count is a single-winner election method in which voters rank candidates in order of preference Saari and uses geometric models of positional voting systems to promote the Borda count. A positional voting system is a ranked voting method in which the options receive points based on their position on each ballot and the option with the most points wins

The increased availability of computer processing has increased the practicality of using the Kemeny-Young, ranked pairs, and Schulze methods that fully rank all the choices from most popular to least popular. The Kemeny-Young method is a Voting system that uses Preferential ballots Pairwise comparison counts and sequence scores to identify the Ranked Pairs (RP or Tideman (named after its developer Nicolaus Tideman) is a Voting method that selects a single winner using votes that express The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences.

The advent of the Internet has increased the interest in voting systems. Unlike many other mathematical fields, voting theory is generally accessible enough to non-experts that new results can be discovered by amateurs, and frequently are. As such, many recent discoveries in voting theory come not from published papers, but from informal discussions among hobbyists on online forums and mailing lists.

The study of voting systems has influenced a new push for electoral reform that is going on today, with proposals being made to replace plurality voting in governmental elections with other methods. Electoral reform is change in Electoral systems to improve how public desires are expressed in election results Various municipalities in the United States have begun to adopt instant-runoff voting in the 2000s. The United States of America —commonly referred to as the Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of New Zealand adopted Mixed Member Proportional for Parliamentary elections in 1993 and Single Transferable Vote for some local elections in 2004 (see Electoral reform in New Zealand). New Zealand is an Island country in the south-western Pacific Ocean comprising two main landmasses (the North Island and the South Island Mixed member proportional representation, also termed mixed-member proportional voting and commonly abbreviated to MMP, is an ' additional member ' Members of New Zealand 's House of Representatives, commonly called " Parliament " normally gain their parliamentary seats through nationwide general Single transferable vote (STV is a preferential Voting system designed to minimize Wasted votes and provide Proportional representation Electoral Reform in New Zealand has in recent years become a political issue as major changes have been made to both Parliamentary and local government elections The Canadian province of British Columbia will hold a second referendum on adopting STV in 2008. Country to "Dominion of Canada" or "Canadian Federation" or anything else please read the Talk Page British Columbia (ˌbrɪtɨʃ kəˈlʌmbiə ( BC) ( (la Colombie-Britannique C Single transferable vote (STV is a preferential Voting system designed to minimize Wasted votes and provide Proportional representation The Province of Ontario will hold a Referendum on October 10, 2007, on whether to adopt a Mixed Member Proportional system. Events 680 - Battle of Karbala: Shia Imam Husayn bin Ali, the grandson of the Prophet Muhammad, is decapitated Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Moreover, on September 2007, the United New Democratic Party of South Korea started the world's first Mobile Voting System to use their presidential primary. The United New Democratic Party ( Hangul: 대통합민주신당 Hanja: 大統合民主新黨 Abbreviation: UNDP was a political party of South Korea South Korea, officially the Republic of Korea and often referred to as Korea ( Korean: 대한민국 tɛː ^[24] An even wider range of voting systems is now seen in non-governmental organizations.

See also

• E-democracy
• Electoral reform
• Poll
• Social choice theory
• Table of voting systems by nation
• Vote counting system
• Voting machine

References

General references

• Arrow, Kenneth J. E-democracy, a combination of the words " electronic " and " Democracy," comprises the use of electronic Communications Technologies Electoral reform is change in Electoral systems to improve how public desires are expressed in election results Polymerase (DNA directed lambda, also known as POLL, is a human Gene. Social choice theory studies voting rules that govern and describe how individual preferences are aggregated to form a collective preference This table deals with voting to select candidates for office not for the passing of legislation There exist various methods through which the Ballots cast at an Election may be counted prior to applying a Voting system to obtain one or more winners Voting machines are the total combination of mechanical electromechanical or electronic equipment (including Software, Firmware, and documentation required to program (1951, 2nd ed. , 1963), Social Choice and Individual Values. Kenneth Arrow 's Monograph Social Choice and Individual Values (1951 2nd ed New Haven: Yale University Press. ISBN 0-300-01364-7
• Colomer, Josep M. ed. (2004). Handbook of Electoral System Choice. London and New York: Palgrave-Macmillan. ISBN 1-4039-0454-5.  
• Cretney, Blake. Election Methods Resource. condorcet. org. Retrieved on October 3, 2005.
• Cranor, Lorrie. Vote Aggregation Methods. Declared-Strategy Voting: An Instrument for Group Decision-Making. Retrieved on October 3, 2005.
• Farrell, David M. (2001). Electoral Systems: A Comparative Introduction. New York: St. Martin's Press. ISBN 0-333-80162-8.  

Notes

References

• Boix, Carles 1999. Setting the Rules of the Game: The Choice of Electoral Systems in Advanced Democracies American Political Science Review 93, 609-624. </ref>
• Duverger, Maurice. 1954. Political Parties. New York: Wiley.
• Hermens, Ferdinand A. 1941. Democracy or Anarchy? A Study of Proportional Representation. Notre Dame: University of Notre Dame.
• Lijphart, Arend
  • 1985 The Field of Electoral Systems Research: A Critical Survey, Electoral Studies 4:
  • 1992 Democratization and Constitutional Choices in Czecho-Slovakia, Hungary and Poland, 1989-1991, Journal of Theoretical Politics 4: 207-223. Arend d'Angremond Lijphart (born 17 August 1936, Apeldoorn, The Netherlands) is a world renowned Political scientist specializing
  • 1994 Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945-1990. Oxford: Oxford University Press, 1994. ISBN 0-19-828054-8.
• Rae, Douglas W. 1971. The Political Consequences of Electoral Laws. New Haven: Yale University Press.
• Rogowski, Ronald. 1987. Trade and the Variety of Democratic Institutions, International Organization

41: 203-224.

• Rokkan, Stein. 1970. Citizens, Elections, Parties: Approaches to the Comparative Study of the Process of Development. Oslo: Universitetsforlaget.
• Taagapera, Rein and Matthew S. Shugart. 1989. Seats and Votes: The Effects and Determinants of Electoral Systems. New Haven: Yale University Press.

External links

General

• ACE Electoral Knowledge Network Expert site providing encyclopedia on Electoral Systems and Management, country by country data, a library of electoral materials, latest election news, the opportunity to submit questions to a network of electoral experts, and a forum to discuss all of the above
• A handbook of electoral system Design from International IDEA
• Accurate Democracy: electoral and legislative voting rules
• Election methods list A mailing list for technical discussions about election methods.
• Electowiki A wiki that focuses on voting theory.
• National Brainstorming project Canadian site.
• Descriptions of Single-Winner Voting Systems Paper by Warren D. Smith.
• Evaluating Voting Methods by Matt Corks
• Open Directory Project category on voting systems
• OpenSTV Software for computing a variety of voting systems including IRV, STV, and Condorcet.
• Ranked Ballot Voting Methods: tutorial, evaluation, and calculator
• Student's Social Choice by Alex Bogomolny. Illustrates various concepts of choice using Java applets. A Java applet is an Applet delivered in the form of Java bytecode.
• Voting, Arbitration, and Fair Division by Marcus Pivato.
• Voting and Election Reform: election calculator and other resources
• Voting Systems by Paul E. Johnson. A textbook-style overview of voting methods and their mathematical properties.
• U.S. Voting System Analysis
• A New Nation Votes: American Elections Returns 1787–1825
• Logicracy Freely available on-line referendum engine, competence vs. opinion scatter plots, competence-weighted voting, analysis tools, and fraud reduction methods.
• Criteria by Blake Cretney
• Evaluation of ranked ballot voting methods by Rob LeGrand
• Voting Methods: Tutorial and essays by James Green-Armytage
• Electoral systems and the protection and participation of minorities, report by Minority Rights Group, 2006

Advocacy

• Citizens for Approval Voting
• Center for Range Voting CRV simplified entry page
• Center for Voting and Democracy Advocates using IRV in the United States. Minority Rights Group International (MRG is an organisation founded with the objective of promoting respect for the Human rights of ethnic religious and linguistic Minorities
• California LocalParty.Org Advocates proportional elections in local elections.
• condorcet.org Advocates Condorcet voting and provides links to vote-tallying software.
• The De Borda Institute A Northern Ireland-based organisation promoting inclusive voting procedures
• May the Best Man Lose A Discover article on Approval voting and the Borda Count, by Dana Mackenzie.

Research papers

• Analysis and Design of Electoral Systems Proceedings of a seminar at the Mathematical Research Institute at Oberwolfach, Germany.
• Analysis of Democratic Institutions: Structure, Conduct and Performance An article by Roger B. Myerson that analyzes voting systems economically.
• PhD seminar on Choice Theory by Robert Nau.
• Common Voting Rules as Maximum Likelihood Estimators by Vincent Conitzer and Tuomas Sandholm.
• A New Monotonic and Clone-Independent Single-Winner Election Method by Markus Schulze (mirror1, mirror2). Introduces the Schulze method and its use in the Debian project. The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. Debian ( pronounced) is a computer Operating system composed entirely of Free and open source software.
• Hybrid Voting Protocols and Hardness of Manipulation by Edith Elkind and Helger Lipmaa.
• On the impact of indifferent voters on the likelihood of some voting paradoxes by Vincent Merlin and Fabrice Valognes.
• In Praise of Manipulation by Martin van Hees and Keith Dowding. Examines strategic voting from an ethical point of view.
• Universal voting protocol tweaks to make manipulation hard by Vincent Conitzer and Tuomas Sandholm.
• Voting by Adaptive Agents in Multi-candidate Elections by Scott Moser.
• Range Voting by Warren D. Smith. After the mathematical advocacy of Range Voting, there is a good monte-carlo comparison of voting systems in virtual elections, which, despite a rudimentary approach to strategy and polling, gives interesting best-case (honest) and worst-case (overstrategic) social utilities for various systems. In economics a social welfare function can be defined as a real-valued function that ranks conceivable social states (alternative complete descriptions of the society
• Safe Votes, Sincere Votes and Strategizing by Rohit Parikh and Eric Pacuit.

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