A voting system is a means of choosing between a number of options, based on the input of a number of voters. Voting is perhaps best known for its use in elections, where political candidates are selected for public office. Voting can also be used to award prizes, to select between different plans of action, or by a computer program to determine a solution to a complex problem. Voting can be contrasted with consensus decision making. It has been suggested that this article or section be merged into Plurality. ... An example of runoff voting. ... Instant-runoff voting (IRV) (also known as the Alternative Vote and by several other names) is an electoral system used for single winner elections in which voters rank candidates in order of preference. ... A preferential voting system (or preference voting system) is an electoral system in which voters rank a list of candidates or group of candidates in order of preference. ... Proportional representation (sometimes referred to as full representation, or PR), is an electoral system delivering a close match between the percentage of votes that the political parties obtain in elections and the percentage of seats they receive in legislative assemblies. ... Ballot for electoral district 252, Würzburg, for the 2005 German federal election. ... Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e. ... This STV ballot for the Australian Senate illustrates group voting tickets. ... 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 little or no impact on the results of the other. ... The Single Non-Transferable Vote or SNTV is an electoral system used in multi-member constituency elections. ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ... Bloc voting (or block voting) (also called Plurality-at-large) refers to a class of voting systems which can be used to elect several representatives from a single constituency. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Choice consists of that mental process of thinking involved with the process of judging the merits of multiple options and selecting one for action. ... It has been suggested that ballot be merged into this article or section. ... An election is a decision making process where people vote for preferred political candidates or parties to act as representatives in government. ... It has been suggested that public management be merged into this article or section. ... A prize is an award given to a person or a group of people to recognise and reward actions or achievements. ... The terms computer program, software program, applications program, system software, or just program are used to refer to either an executable program by both lay people and computer programmers or the collection of source code from which an executable program is created (eg, compiled). ... Consensus decision-making is a decision process that not only seeks the agreement of most participants, but also to resolve or mitigate the objections of the minority to achieve the most agreeable decision. ...

A voting system consists of the rules for how voters express their desires, and how these desires 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. Voting theory began in the 18th century and has led to several proposals for voting systems. Political science is an academic and research discipline that deals with the theory and practice of politics and the description and analysis of political systems and political behavior. ... Face-to-face trading interactions among on the New York Stock Exchange trading floor In the social sciences, economics is the study of human choice behavior and how it effects the production, distribution, and consumption of scarce resources. ... For other meanings of mathematics or math, see mathematics (disambiguation). ...

Most voting systems are based on the concept of majority rule, or the principle that more than half of the voters should get the outcome they want. Given the simplicity of majority rule, those who are unfamiliar with voting theory are often surprised that such a variety of voting systems exists, or that popular voting systems can produce results not supported by more than half the voters. 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. Thus, the choice of voting system(s) is one important component of a democratic government. Majoritarianism (often also called majority rule) is a political philosophy or agenda which asserts that a majority (sometimes categorized by religion, language or some other identifying factor) of the population is entitled to a certain degree of primacy in society, and has the right to make decisions that affect the...

Further information: effects of different voting systems under similar circumstances

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 voting systems. ...

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 outcome may be a single winner, or may involve multiple winners such as in the election of a legislative body. The voting system may also specify how voting power is distributed among the voters, and how voters are divided into (constituencies) whose votes are counted independently. A ballot is a device used to record choices made by voters. ... Flowcharts are often used to graphically represent algorithms. ... A legislature is a governmental deliberative body with the power to adopt laws. ... 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. 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. These are aspects of the broader topic of elections and election systems. Electronic voting machine used in all Brazilian elections and plebiscites. ... Suffrage is the civil right to vote, or the exercise of that right. ...

In a simple plurality ballot, the voter is expected to mark only one selection.

Image File history File links Plurality_ballot. ... Image File history File links Plurality_ballot. ... It has been suggested that this article or section be merged into Plurality. ...

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, like Instant-runoff voting, the Borda count, or a Condorcet method, voters order the list of options from most to least preferred. In range voting, voters rate each option separately on a scale. 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. In voting systems that allow "plumping", like cumulative voting, voters may vote for the same candidate multiple times. Term preferential voting (also known as the preference voting) has several different meanings: (1) A ranked ballot or preferential voting system is a type of voting system in which each voter casts their vote by ranking candidates in order of preference. ... Instant-runoff voting (IRV) (also known as the Alternative Vote and by several other names) is an electoral system used for single winner elections in which voters rank candidates in order of preference. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... Range voting (also called ratings summation, or average voting, or cardinal ratings, or 0-99 voting, or the score system or point system) is a voting system used for single-seat elections. ... It has been suggested that this article or section be merged into Plurality. ... On an approval ballot, the voter can vote for any number of candidates. ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ...

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 persons name. ... None of the Above (NOTA) is a ballot choice in some jurisdictions or organizations, placed so as to allow the voter to indicate his disapproval with all of the candidates in any voting system. ...

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 legal person which, while being composed of natural persons, exists completely separately from them. ...

Votes can also be weighted unequally for other reasons, such as increasing the voting weight of higher-ranked members of an organization. A special case of this is a tie-breaking vote, a privilege given to one voter to resolve what would otherwise be a tie. The voter who holds the tie-breaking vote may or may not be able to cast an ordinary vote as well; if he cannot cast an ordinary vote, then he effectively has a vote with less weight than an ordinary vote. A well-known example of this occurs in the United States Senate, where the Vice President does not have an ordinary vote, but votes only to break a tie. Electoral ties can also be resolved through other tie-breaking methods, such as by tossing a coin. Seal of the U.S. Senate The United States Senate is one of the two chambers of the Congress of the United States, the other being the House of Representatives. ... The Vice President of the United States is the second-highest executive official of the United States government. ... To tie or draw is to finish a competition with identical or inconclusive results. ... Coin flipping or coin tossing is the practice of throwing a coin in the air to resolve a dispute between two parties or otherwise choose between two alternatives. ...

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. Groups may form coalitions in order to maximize their voting power. A political party is an organization that seeks to attain political power within a government, usually by participating in electoral campaigns. ... States currently utilizing parliamentary systems are denoted in orange and red—the former being constitutional monarchies where authority is vested in a parliament, and the latter being parliamentary republics whose parliaments are effectively supreme over a separate head of state. ... A coalition is an alliance among entities, 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. An extreme case of this is unanimous consent, where changing the status quo requires the support of every voting member. 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. 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 effect. ... Unanimous consent, in parliamentary procedure, refers to situations in which a motion can pass if no one present objects. ... The blackball was used in elections to membership of a Gentlemens club (and 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. 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. In law, a quorum is the minimum number of members of a deliberative body necessary to conduct the business of that group. ...

Constituencies

Main article: Constituency

Often the purpose of an election is to choose a legislative body made of multiple winners. 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. A constituency is any cohesive corporate unit or body bound by shared structures, goals or loyalty. ... A legislature is a governmental deliberative body with the power to adopt laws. ...

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. Some systems, like the Additional member system, embed smaller districts within larger ones. A constituency is any cohesive corporate unit or body bound by shared structures, goals or loyalty. ... The Additional Member System (AMS) is a voting system in which some representatives are elected from geographic constituencies and others are elected under proportional representation from party lists. ...

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. Redistricting is the process by which the borders of constituencies are redrawn once apportioned. 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. A particularly ill case was the English Rotten Boroughs, abandoned towns who still were represented in parliament. Apportionment, or reapportionment, is the process of determining representation in politics within a legislative body by creating constituencies. ... 1870 US Census for New York City A census is the process of obtaining information about every member of a population (not necessarily a human population). ... The process known as redistricting in the United States and redistribution in many Commonwealth countries is the changing of political borders (in many countries, specifically the electoral district/constituency boundaries) usually in response to periodic census results. ... Malapportionment is broad and systematic variance in the size of electoral constituencies (at least within electoral systems which have them). ... Gerrymandering is a controversial form of redistricting in which electoral district or constituency boundaries are manipulated for an electoral advantage. ... The term rotten borough refers to a parliamentary borough or constituency in the Kingdom of England (pre-1707), the Kingdom of Great Britain (1707-1801), the Kingdom of Ireland (1536-1801) and the United Kingdom of Great Britain and Ireland (from 1801 until their final abolition in 1867) which due...

Single-winner methods

Single-winner systems can be classified based on their ballot type. Binary voting systems are those in which a voter either votes or does not vote for a given candidate. In ranked voting systems, each voter ranks the candidates in order of preference. In rated voting systems, voters give a score to each candidate.

On an approval ballot, the voter may vote for any number of options.

Image File history File links Approval_ballot. ... Image File history File links Approval_ballot. ... On an approval ballot, the voter can vote for any number of candidates. ...

Binary voting 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. It has been suggested that this article or section be merged into Plurality. ...

Approval voting is another binary voting method, where voters may vote for as many candidates as they like. The choice that receives the most approval votes wins. On an approval ballot, the voter can vote for any number of candidates. ...

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. In an exhaustive runoff election, no candidates are eliminated, so voting is simply repeated until there is a majority. An example of runoff voting. ... Runoff voting is a voting system used in single-seat elections. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

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. This is mostly used as a tiebreaker for other methods.
The random ballot voting method takes the one person one vote principle to an extreme by only counting the vote of one person. ...

Ranked voting methods

Main article: Preferential voting

In a typical ranked ballot, a voter is instructed to place the candidates in order of preference.

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. A preferential voting system (or preference voting system) is an electoral system in which voters rank a list of candidates or group of candidates in order of preference. ... Image File history File links Preferential_ballot. ... Image File history File links Preferential_ballot. ...

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. 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. Instant-runoff voting (IRV) (also known as the Alternative Vote and by several other names) is an electoral system used for single winner elections in which voters rank candidates in order of preference. ...

The Borda count is a simple ranked voting method in which the options receive points based on their position on each ballot. A class of similar methods is called positional voting systems. The Borda count is a single winner election method in which voters rank candidates in order of preference. ... A Positional voting system is a voting method that selects a winner based on information about voters preference rankings. ...

Other ranked methods include Coombs' method, Supplementary voting, and Bucklin voting, as well as the specific kinds of ranked methods listed below. The Coombs method, created by Clyde Coombs, is a voting system used for single-winner elections in which each voter rank-orders the candidates. ... The Supplementary Vote (SV) is a voting system used for the election of a single candidate. ... Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ...

Condorcet methods

Main article: Condorcet method

Condorcet methods, or pairwise methods, are a class of ranked voting methods that meet the Condorcet criterion. 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. Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ...

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. 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. The voting paradox is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i. ... In voting systems, the Smith set is the smallest set of candidates in a particular election who, when paired off in pairwise elections, can beat all other candidates outside the set. ...

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. 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. 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. Minimax is often considered to be the simplest of the Condorcet methods. ... Copelands 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 is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ... Cloneproof Schwartz Sequential Dropping (CSSD) is a voting system developed by Markus Schulze that selects a single winner using votes that express preferences. ... Cloneproof Schwartz Sequential Dropping (CSSD) 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. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ...

This ballot design, used in cumulative voting, allows a voter to split his vote among multiple candidates.

Image File history File links Cumulative_ballot. ... Image File history File links Cumulative_ballot. ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ...

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. A grade may refer to many different concepts, including: in various contexts: Each item in a (generally ordered and finite) collection of symbols or designators used as a particular grade system to distinguish and rank corresponding groups, where distinct members or instances of each group are regarded as sufficiently similar...

In range voting, voters give numeric ratings to each option, and the option with the highest total score wins. Approval voting can be seen as an instance of range voting where the allowable ratings are 0 and 1. Range voting (also called ratings summation, or average voting, or cardinal ratings, or 0-99 voting, or the score system or point system) is a voting system used for single-seat elections. ...

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

Seats won by each party in the 2005 German federal election, an example of a proportional voting system.

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. Not all multiple-winner voting systems are proportional. Image File history File links German_federal_election,_2005_-_Final. ... Image File history File links German_federal_election,_2005_-_Final. ... German federal elections took place on September 18, 2005 to elect the members of the 16th German Bundestag, the federal parliament of Germany. ... Proportional representation (sometimes referred to as full representation, or PR), is an electoral system delivering a close match between the percentage of votes that the political parties obtain in elections and the percentage of seats they receive in legislative assemblies. ...

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. Two similar plurality-based methods with multiple winners are the Single Non-Transferable Vote method, where the voter votes for only one option, and cumulative voting, described above. Unlike bloc voting, elections using the Single Non-Transferable Vote or cumulative voting may achieve proportionality if voters use tactical voting or strategic nomination. Bloc voting (or block voting) (also called Plurality-at-large) refers to a class of voting systems which can be used to elect several representatives from a single constituency. ... In politics, a landslide victory (or just a landslide) is the victory of a candidate or political party by an overwhelming majority in an election. ... The Single Non-Transferable Vote or SNTV is an electoral system used in multi-member constituency elections. ... A points method ballot design like this one is the most common for governmental elections using cumulative voting. ... In voting systems, tactical voting (or strategic voting) occurs when a voter misrepresents his or her sincere preferences in order to gain a more favorable outcome. ... 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 Non-Transferable 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 little or no impact on the results of the other. ...

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. 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. Proportional representation (sometimes referred to as full representation, or PR), is an electoral system delivering a close match between the percentage of votes that the political parties obtain in elections and the percentage of seats they receive in legislative assemblies. ... The Gallagher Index (or least squares) can be used to measure the disproportionality of electoral systems, in particular majoritarian systems. ...

Most proportional systems in use are based on party-list proportional representation, in which voters vote for parties instead of for individual candidates. 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. Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e. ...

The methods of seat allocation can be grouped overall into highest averages methods and largest remainder methods. 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 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 largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The highest averages method is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The Sainte-Laguë method of the highest average (sometimes identified with Websters method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. ... The DHondt method is a highest averages method for allocating seats in party-list proportional representation. ...

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. In a closed list system, the seats are assigned to candidates in a fixed order that the party chooses. 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. Open list describes any variant of party-list proportional representation where voters have at least some influence on the (by the political party itself supplied) order in which party 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 have no influence on the (party-supplied) order in which party candidates are elected. ... The Additional Member System (AMS) is a voting system where some representatives are elected from geographic constituencies and others are elected under proportional representation from party lists. ...

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. 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. This STV ballot for the Australian Senate illustrates group voting tickets. ... When the single transferable vote voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. ...

Semiproportional methods

A simpler method called Cumulative voting (CV) is a semiproportional voting system that allows voter to distribute portions of their 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.) A points method ballot design like this one is the most common for governmental elections using cumulative voting. ... Bloc voting (or block voting) (also called Plurality-at-large) refers to a class of voting systems which can be used to elect several representatives from a single constituency. ...

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 runoff process. 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 spoiler effect is a term to describe the effect a candidate can have on a close election, in which their candidacy results in the election being won by a candidate dissimilar to them, rather than a candidate similar to them. ... A plurality (or relative majority) is the largest share of something, which may or may not be a majority. ...

Even simpler than Cumulative Voting, is the semiproportional method called Single non-transferable vote (SNTV). It can be considered a special variation of Cumulative Voting where a full vote can't 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. The Single Non-Transferable Vote or SNTV is an electoral system used in multi-member constituency elections. ...

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 will tend 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.

Single Transferable Vote can be considered as a specialized form of cumulative voting with fractional votes that maximizes the preferences of all the voters, although up to a fraction 1/(n+1) may still have no representation.

Criteria in evaluating voting systems

It has been suggested that this article or section be merged with Voting system criteria. (Discuss)

Main article: Voting system criteria

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. Wikipedia does not have an article with this exact name. ... Wikipedia does not yet have an article with this exact name. ... Wikipedia does not yet have an article with this exact name. ...

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. For this reason, someone implementing a voting system has to decide which criteria are important for the election. Kenneth Arrow Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. ...

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 preferring a single candidate, does he always win if that majority votes sincerely?
• 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)
• 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?

The following table shows which of the above criteria are met by several single-winner systems, listed approximately in order of how commonly they are used. The majority criterion is a voting system criterion, used to objectively compare voting systems. ... A voting system is monotonic if it satisfies the monotonicity criterion, given below. ... A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same alternative being selected, an election of the entire electorate also selects that alternative. ... Statement of Criterion Adding one or more ballots that vote X over Y should never change the winner from X to Y. Complying Methods Plurality voting, Approval voting, Cardinal Ratings, Borda count, and Woodalls DAC method all pass the Participation Criterion. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... Given a vote where voters rank options in order of preference, a Condorcet loser is an option that loses all of its pairwise comparisons. ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... Independence of irrelevant alternatives (IIA) is an axiom often adopted by social scientists as a basic condition of rationality. ... Strategic nomination is the manipulation of an election through its candidate set (compare this to tactical voting, where the manipulation comes from the voters). ...

In addition to the above criteria, voting systems are also judged with 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 voting system criterion, used to objectively compare voting systems. ... A voting system is monotonic if it satisfies the monotonicity criterion, given below. ... A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same alternative being selected, an election of the entire electorate also selects that alternative. ... Statement of Criterion Adding one or more ballots that vote X over Y should never change the winner from X to Y. Complying Methods Plurality voting, Approval voting, Cardinal Ratings, Borda count, and Woodalls DAC method all pass the Participation Criterion. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ... Given a vote where voters rank options in order of preference, a Condorcet loser is an option that loses all of its pairwise comparisons. ... Independence of irrelevant alternatives (IIA) is an axiom often adopted by social scientists as a basic condition of rationality. ... 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 first-past-the-post electoral system is a voting system for single-member districts, variously called first-past-the-post (FPTP or FPP), winner-take-all, plurality voting, or relative majority. ... This article or section should be merged with Spoiler effect A split vote, or vote splitting, occurs in an election when the existence of two or more candidates that represent relatively similar viewpoints among voters reduces the votes received by each of them, reducing the chances of any one of... An example of runoff voting. ... This article or section should be merged with Spoiler effect A split vote, or vote splitting, occurs in an election when the existence of two or more candidates that represent relatively similar viewpoints among voters reduces the votes received by each of them, reducing the chances of any one of... When the single transferable vote voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. ... On an approval ballot, the voter can vote for any number of candidates. ... Range voting (also called ratings summation, or average voting, or cardinal ratings, or 0-99 voting, or the score system or point system) is a voting system used for single-seat elections. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... Strategic nomination is the manipulation of an election through its candidate set (compare this to tactical voting, where the manipulation comes from the voters). ... Minimax is often considered to be the simplest of the Condorcet methods. ... This article or section should be merged with Spoiler effect A split vote, or vote splitting, occurs in an election when the existence of two or more candidates that represent relatively similar viewpoints among voters reduces the votes received by each of them, reducing the chances of any one of... 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. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... In voting systems, tactical voting (or strategic voting) occurs when a voter misrepresents his or her sincere preferences in order to gain a more favorable outcome. ... 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) can be used to measure the disproportionality of electoral systems, in particular majoritarian systems. ...

It is also possible to simulate large numbers of virtual elections on a computer and see how various voting systems compare. Since, unlike real elections, in these elections it is possible to "see inside the voters' minds" one can then score the results on how much they satisfy the voters, a measure referred to as "bayesian regret". Such simulations are sensitive to their assumptions about candidate quality, voter strategy, and pre-election "polls"; and they cannot measure the effect a voting system has on the campaign; but if they can give relatively-objective best and worst cases for a voting system. The largest such simulation [1], run by a range voting advocate, found that the the only systems above potentially significantly better (that is, if they lead to less tactical voting, something not measurable by this model) than range voting were range voting itself, Borda, Minimax, Schulze, and Ranked Pairs. Most systems showed some potential advantage over Plurality, in many cases greater than the advantages of Plurality over monarchy. In voting systems, tactical voting (or strategic voting) occurs when a voter misrepresents his or her sincere preferences in order to gain a more favorable outcome. ... Range voting (also called ratings summation, or average voting, or cardinal ratings, or 0-99 voting, or the score system or point system) is a voting system used for single-seat elections. ... Range voting (also called ratings summation, or average voting, or cardinal ratings, or 0-99 voting, or the score system or point system) is a voting system used for single-seat elections. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... Minimax is often considered to be the simplest of the Condorcet methods. ... The Schulze method is a voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... It has been suggested that this article or section be merged into Plurality. ... It has been suggested that this article or section be merged into Plurality. ... Places where monarchies maintain rule appear in blue. ...

The New Zealand Royal Commission on the Electoral System listed ten criteria for their evaluation of possible new electoral systems for New Zealand. These included fairness between political parties, effective representation of minority or special interest groups, political integration, effective voter participation and legitimacy. The Royal Commission on the Electoral System was formed in New Zealand in 1985, and reported in 1986. ... Until 1996, New Zealand used the British system of first past the post (FPP) for parliamentary elections . ...

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. 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. 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.^[3] (2nd millennium BC - 1st millennium BC - 1st millennium) The 6th century BC started on January 1, 600 BC and ended on December 31, 501 BC. // Overview Monument 1, an Olmec colossal head at La Venta The 5th and 6th centuries BC were a time of empires, but more importantly, a... The speakers platform in the Pnyx, the meeting ground of the assembly where all the great political struggles of Athens were fought during the Golden Age. Here Athenian statesmen stood to speak, such as Pericles and Aristides in the 5th century BC and Demosthenes and Aeschines in the 4th... It has been suggested that this article or section be merged into Plurality. ... Ostracism was a procedure under the Athenian democracy in which a prominent citizen could be expelled from the city-state of Athens for ten years. ... The history of democracy traces back from its origins in prehistoric times to its re-emergence and rise from the 17th century to the present day. ... Country Italy Region Veneto Province Venice (VE) Mayor Massimo Cacciari (since April 18, 2005) Elevation m Area 412 km² Population  - Total (as of December 31, 2004) 271,251  - Density 646/km² Time zone CET, UTC+1 Coordinates Gentilic Veneziani Dialing code 041 Postal code 30100 Frazioni Chirignago, Favaro Veneto, Mestre... On an approval ballot, the voter can vote for any number of candidates. ...

Jean-Charles de Borda, an early voting theorist.

The Marquis de Condorcet, another early voting theorist.

Image File history File links Borda182x244. ... Image File history File links Borda182x244. ... Jean-Charles de Borda (May 4, 1733 - February 19, 1799) was a French mathematician, physicist, political scientist, and sailor. ... This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years. ... This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years. ... Marie Jean Antoine Nicolas Caritat, marquis de Condorcet (September 17, 1743 - March 28, 1794) was a French philosopher, mathematician, and early political scientist who devised the concept of a Condorcet method. ...

Foundations of voting theory

Voting theory became an object of academic study around the time of the French Revolution.^[3] Jean-Charles de Borda proposed the Borda count in 1770 as a method for electing members to the French Academy of Sciences. 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. He also wrote about the Condorcet paradox, which he called the intransitivity of majority preferences.^[4] The French Revolution (1789–1799) was a pivotal period in the history of French, European and Western civilization. ... Jean-Charles de Borda (May 4, 1733 - February 19, 1799) was a French mathematician, physicist, political scientist, and sailor. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... Louis XIV visiting the Académie in 1671 The French Academy of Sciences (Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. ... Marie Jean Antoine Nicolas Caritat, marquis de Condorcet (September 17, 1743 - March 28, 1794) was a French philosopher, mathematician, and early political scientist who devised the concept of a Condorcet method. ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... The voting paradox is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i. ...

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. The manuscripts in which he described these methods had been lost to history until they were rediscovered in 2001.^[5] Ramon Llull. ... The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate. ...

Later in the 18th century, the related topic of apportionment began to be studied. The impetus for research into fair apportionment methods came, in fact, from the United States Constitution, which mandated that seats in the House of Representatives had to be allocated among the states proportionally to their population, but did not specify how to do so.^[6] A variety of methods were proposed by statesmen such as Alexander Hamilton, Thomas Jefferson, and Daniel Webster. 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 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.^[7] Apportionment, or reapportionment, is the process of determining representation in politics within a legislative body by creating constituencies. ... The United States Constitution is the supreme law of the United States of America. ... House of Representatives is a name used for legislative bodies in many countries. ... Alexander Hamilton (January 11, 1755 or 1757 — July 12, 1804) was an American politician, leading statesman, financier, intellectual, military officer, and founder of the Federalist Party. ... Thomas Jefferson (April 13, 1743 N.S. – July 4, 1826) was the third President of the United States (1801–1809), principal author of the Declaration of Independence (1776), and an influential founder of the United States. ... Daniel Webster (1782–1852) Daniel Webster (January 18, 1782 – October 25, 1852) was a United States Senator and Secretary of State. ... World map showing Europe Political map (neighboring countries in Asia and Africa also shown) Europe is one of the seven traditional continents of the Earth. ... Party-list proportional representation systems are a family of voting systems used in multiple-winner elections (e. ... The DHondt method is a highest averages method for allocating seats in party-list proportional representation. ... The Sainte-Laguë method of the highest average (sometimes identified with Websters method or divisor method with standard rounding) is one way of allocating seats proportionally for representative assemblies with party list voting systems. ...

The Single Transferable Vote system was devised by Carl Andrae in Denmark in 1855, and also in England by Thomas Hare in 1857. 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. Party-list proportional representation was first implemented to elect European legislatures in the early 20th century, with Belgium implementing it first in 1900. Since then, proportional and semi-proportional methods have come to be used in almost all democratic countries, with most exceptions being former British colonies.^[8] This STV ballot for the Australian Senate illustrates group voting tickets. ... Carl Christoffer Georg Andræ (14 October 1812–2 February 1893) was a Danish politician and mathematician. ... Motto: (French for God and my right) Anthem: Multiple unofficial anthems Capital London Largest city London Official language(s) English (de facto) Government Constitutional monarchy  - Queen Queen Elizabeth II  - Prime Minister Tony Blair MP Unification    - by Athelstan AD 927  Area    - Total 130,395 km² (1st in UK)   50,346 sq... Thomas Hare (March 28, 1806 - May 6, 1891) was an English barrister who was involved in the theory and advocacy of election methods. ... Emblems: {{{Emblems}}} Motto: Ubertas et Fidelitas (Fertility and Faithfulness) Slogan or Nickname: The Apple Isle Other Australian states and territories Capital Hobart Government Const. ... Andrew Inglis Clark was born in Hobart, Tasmania on February 24, 1848, 5 years before the end of convict transportation to Tasmania. ...

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.^[9] 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. Charles Dodgson, better known as Lewis Carroll, published pamphlets on voting theory, focusing in particular on Condorcet voting. 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. He also proposed the straightforward Condorcet method known as Dodgson's method. William Robert Ware (27 May 1832 - 9 June 1915), born in Cambridge, Massachusetts into a family of the Unitarian clergy, was an architect who received his professional education at Harvard College and Harvards Lawrence Scientific School. ... When the single transferable vote voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. ... Edward John Nanson, 1850-1936, was born in England and received his professional education at Trinity College from 1870-1874. ... When the single transferable vote voting system is applied to a single-winner election it is sometimes called instant-runoff voting (IRV), as it is much like holding a series of runoff elections in which the lowest polling candidate is eliminated in each round until someone receives majority vote. ... 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. ... Photograph of Lewis Carroll taken by himself, with assistance Charles Lutwidge Dodgson (January 27, 1832 – January 14, 1898), better known by the pen name Lewis Carroll, was a British author, mathematician, Anglican clergyman, logician, and amateur photographer. ... In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. ... Ramon Llull. ...

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. Bucklin is no longer used in any government elections, and has even been declared unconstitutional in Minnesota.^[10] Bucklin is a voting system that can be used for single-member districts and also multi-member districts. ... Capital Saint Paul Largest city Minneapolis Area  Ranked 12th  - Total 87,014 sq mi (225,365 km²)  - Width 250 miles (400 km)  - Length 400 miles (645 km)  - % water 8. ...

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. This led to significant new results that changed the field of voting theory.^[3] 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. 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. John von Neumann in the 1940s. ... Game theory is a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ... Kenneth Arrow Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. ... The Gibbard-Satterthwaite theorem is a result about voting systems designed to choose a single winner from the preferences of certain individuals, where each individual ranks all candidates in order of preference. ...

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. 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. 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. Duvergers Law is a principle which asserts that a first-past-the-post election system or in other words, a Single-member, Simple-plurality system, naturally leads to a two-party system. ... It has been suggested that this article or section be merged into Plurality. ... This article or section does not cite its references or sources. ... Steven J. Brams (born November 28, 1940) is a political scientist and professor at New York University. ... Peter C. Fishburn (1936_) is known as a pioneer in the field of decision making processes. ... On an approval ballot, the voter can vote for any number of candidates. ...

Current 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. Wikipedia does not yet have an article with this exact name. ...

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. Tideman also devised the ranked pairs method to be a Condorcet method that is not susceptible to clones. Also, Donald G. Saari has brought renewed interest to the Borda count with the books he has published since 2001. Saari created geometric models of positional voting systems, and uses these models to promote the use of the Borda count. T. Nicolaus Tideman (born August 11, 1943 in Chicago, Illinois) is a Professor of Economics at Virginia Polytechnic Institute and State University. ... 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 candidate can have on a close election, in which their candidacy results in the election being won by a candidate dissimilar to them, rather than a candidate similar to them. ... Strategic nomination is the manipulation of an election through its candidate set (compare this to tactical voting, where the manipulation comes from the voters). ... It has been suggested that Maximize Affirmed Majorities be merged into this article or section. ... Any election method conforming to the Condorcet criterion is known as a Condorcet method. ... In the analysis of voting systems, a clone is an additional candidate who appears as attractive to each voter as an existing candidate. ... Donald G. Saari (born March 1940 in Houghton, Michigan, USA) is the Distinguished Professor of Mathematics and Economics at the University of California Irvine. ... The Borda count is a single winner election method in which voters rank candidates in order of preference. ... A Positional voting system is a voting method that selects a winner based on information about voters preference rankings. ...

The advent of the Internet has increased the interest in voting systems. Unlike many other mathematical fields, voting theory is generally accessible enough to nonexperts 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. Various municipalities in the United States have begun to adopt instant-runoff voting in the 2000s. New Zealand adopted Mixed Member Proportional for Parliamentary elections in 1993 and Single Transferable Vote for some local elections in 2004. The Canadian province of British Columbia will hold a second referendum on adopting STV in 2008. An even wider range of voting systems is now seen in non-governmental organizations. A new approach towards voting is vote swapping. First time voteswapping was used was in 2000 at the US presidential election. The voteswapping website Voteswap2000 was closed because of a court trial which filed it to be illegal. Another advanced voteswap system to put the voter into the 'pre-political arena' to support strategic voting and minimize wasted votes is The king's hub. Electoral reform projects seek to change the way that public desires are reflected in elections through electoral systems. ... Instant-runoff voting (IRV) (also known as the Alternative Vote and by several other names) is an electoral system used for single winner elections in which voters rank candidates in order of preference. ... Until 1996, New Zealand used the British system of first past the post (FPP) for parliamentary elections . ... The Additional Member System (AMS) is a voting system where some representatives are elected from geographic constituencies and others are elected under proportional representation from party lists. ... New Zealands House of Representatives, commonly called Parliament, is chosen by nationwide election. ... This STV ballot for the Australian Senate illustrates group voting tickets. ... Motto: Splendor Sine Occasu (Latin: Splendour without diminishment) Official languages none stated in law; English is de facto Flower Pacific dogwood Tree Western Redcedar Bird Stellers Jay Capital Victoria Largest city Vancouver Lieutenant-Governor Iona Campagnolo Premier Gordon Campbell (BC Liberal) Parliamentary representation  - House seat  - Senate seats 36 6... To meet Wikipedias quality standards, this article or section may require cleanup. ... This STV ballot for the Australian Senate illustrates group voting tickets. ... Vote swapping is the method where a voter in one district agrees to vote tactically for a less-preferred candidate or party who has a greater chance of winning in their district, in exchange for a voter from another district voting tactically for the candidate the first voter prefers, because...

See also

• E-democracy
• Electoral reform
• Poll
• Social choice theory
• Social Choice and Individual Values
• Sortition, decision by randomness
• Table of voting systems by nation
• Vote counting system
• Voting machine

E-democracy (a neologism and contraction of electronic democracy) is the utilization of electronic communications technologies, such as the Internet, in enhancing democratic processes within a democratic republic or representative democracy. ... Electoral reform projects seek to change the way that public desires are reflected in elections through electoral systems. ... A poll is either an election or a survey of a particular group. ... Social choice theory studies how individual preferences are aggregated to form a collective choice, such as, for example in voting systems (also known as social choice functions or systems). ... Social Choice and Individual Values is a book written by Kenneth Arrow first published in 1951. ... Sortition is the method of random selection, particularly in relation to the selection of decision makers also known as allotment. ... These tables deal 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. ... A voting machine is a device to record and register votes to be counted as per any voting system, with or without printing a ballot for the voter to verify. ...

References

General references

• Arrow, Kenneth J. (1951, 2nd ed., 1963), Social Choice and Individual Values. 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.

October 3 is the 276th day of the year (277th in leap years) in the Gregorian Calendar. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... October 3 is the 276th day of the year (277th in leap years) in the Gregorian Calendar. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ...

Notes and sources

1. ^ Provided a tie-breaker method is used that provides for the elimination of only one of the tied candidates.
2. ^ ^a b The original independence of clones criterion applied only to ranked voting methods.^{[citation needed]} There is some disagreement about how to extend it to unranked methods, and this disagreement affects whether approval and range voting are considered independent of clones.
3. ^ ^a b c J. J. O'Connor and E. F. Robertson. The history of voting. The MacTutor History of Mathematics Archive. Retrieved on October 12, 2005.
4. ^ J. J. O'Connor and E. F. Robertson. Marie Jean Antoine Nicolas de Caritat Condorcet. The MacTutor History of Mathematics Archive. Retrieved on October 12, 2005.
5. ^ G. Hägele and F. Pukelsheim (2001). "Llull's writings on electoral systems". Studia Lulliana 3: 3-38.
6. ^ Joseph Malkevitch. Apportionment. AMS Feature Columns. Retrieved on October 13, 2005.
7. ^ Joseph Malkevitch. Apportionment II. AMS Feature Columns. Retrieved on October 13, 2005.
8. ^ Proportional Voting Around the World. FairVote.org. Retrieved on October 13, 2005.
9. ^ The History of IRV. FairVote.org. Retrieved on November 9, 2005.
10. ^ Tony Anderson Solgård and Paul Landskroener. Municipal Voting System Reform: Overcoming the Legal Obstacles. Bench & Bar of Minnesota. Retrieved on November 16, 2005.

Strategic nomination is the manipulation of an election through its candidate set (compare this to tactical voting, where the manipulation comes from the voters). ... On an approval ballot, the voter can vote for any number of candidates. ... Range voting (also called ratings summation, or average voting, or cardinal ratings, or 0-99 voting, or the score system or point system) is a voting system used for single-seat elections. ... October 12 is the 285th day of the year in the Gregorian calendar (286th in leap years). ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... October 12 is the 285th day of the year in the Gregorian calendar (286th in leap years). ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... October 13 is the 286th day of the year (287th in leap years) in the Gregorian calendar. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... October 13 is the 286th day of the year (287th in leap years) in the Gregorian calendar. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... October 13 is the 286th day of the year (287th in leap years) in the Gregorian calendar. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... November 9 is the 313th day of the year (314th in leap years) in the Gregorian Calendar, with 52 days remaining. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ... November 16 is the 320th day of the year (321st in leap years) in the Gregorian Calendar, with 45 days remaining. ... 2005 (MMV) was a common year starting on Saturday of the Gregorian calendar. ...

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
• 11 Worst Places to Vote in America an article in Mother Jones Magazine
• A handbook of electoral system Design from International IDEA
• Election methods list A mailing list for technical discussions about election methods.
• Electowiki A wiki that focuses on voting theory.
• 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.
• Student's Social Choice by Alex Bogomolny. Illustrates various concepts of choice using Java applets.
• Voting, Arbitration, and Fair Division by Marcus Pivato.
• Voting Systems by Paul E. Johnson. A textbook-style overview of voting methods and their mathematical properties.
• U.S. Voting System Analysis

A Java applet is an applet delivered in the form of Java bytecode. ...

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.
• 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.
• 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.