An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Elections and referenda have been organized by governments, business, non-profit organisations and informal organisations. There are many variations in electoral systems, with the most common systems being first-past-the-post voting, the two-round (runoff) system and proportional representation.
The study of electoral methods is called social choice theory or voting theory, and this study can take place within the field of political science, economics, or mathematics, and specifically within the subfields of game theory and mechanism design.
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A chronological list of discovery, invention, development, description, or first known adoption and major use of electoral systems.
Single transferable vote (STV) is a type of multi-winner ranked-choice voting method; an electoral system in which voter may rank the candidates according to their preferences, so their single vote can be transferred to other candidates based on these rankings to avoid votes being wasted. STV aims to provide proportional representation for every constituency, meaning each vote is effectively worth about the same, unlike majoritarian systems, no one party or voting bloc can take all the seats in a district.
A Condorcet method is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner. The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
Copeland's method is a ranked voting method based on a scoring system of pairwise "wins", "losses", and "ties". The method has a long history:
Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the Georgist politician James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system.
Ranked pairs (RP) or the Tideman method is an electoral system developed in 1987 by Nicolaus Tideman that selects a single winner using votes that express preferences. RP can also be used to create a sorted list of winners.
An electoral system satisfies the Condorcet winner criterion if it always chooses the Condorcet winner when one exists. The candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, that is, a candidate preferred by more voters than any others, is the Condorcet winner, although Condorcet winners do not exist in all cases. It is sometimes simply referred to as the "Condorcet criterion", though it is very different from the "Condorcet loser criterion". Any voting method conforming to the Condorcet winner criterion is known as a Condorcet method. The Condorcet winner is the person who would win a two-candidate election against each of the other candidates in a plurality vote. For a set of candidates, the Condorcet winner is always the same regardless of the voting system in question, and can be discovered by using pairwise counting on voters' ranked preferences.
The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion. The criterion states that if there is a subset S of the candidates, such that more than half of the voters strictly prefer every member of S to every candidate outside of S, this majority voting sincerely, the winner must come from S. This is similar to but stricter than the majority criterion, where the requirement applies only to the case that S contains a single candidate. This is also stricter than the majority loser criterion, where the requirement applies only to the case that S contains all but one candidate. The mutual majority criterion is the single-winner case of the Droop proportionality criterion.
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
Resolvability criterion can refer to any voting system criterion that ensures a low possibility of tie votes.
CPO-STV, or the Comparison of Pairs of Outcomes by the Single Transferable Vote, is a ranked voting system designed to achieve proportional representation. It is a more sophisticated variant of the Single Transferable Vote (STV) system, designed to overcome some of that system's perceived shortcomings. It does this by incorporating some of the features of Condorcet's method, a voting system designed for single-winner elections, into STV. As in other forms of STV, in a CPO-STV election more than one candidate is elected and voters must rank candidates in order of preference. As of February 2021, it has not been used for a public election.
The later-no-harm criterion is a voting system criterion formulated by Douglas Woodall. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to lose. Voting systems that fail the later-no-harm criterion are vulnerable to the tactical voting strategies called bullet voting and burying, which can deny victory to a sincere Condorcet winner.
The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the next-lowest gets 1 point, etc., and the highest-ranked candidate gets n − 1 points, where n is the number of candidates. Once all votes have been counted, the option or candidate with the most points is the winner. The Borda count is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.
Schulze STV is a draft single transferable vote (STV) ranked voting system designed to achieve proportional representation. It was invented by Markus Schulze, who developed the Schulze method for resolving ties using a Condorcet method. Schulze STV is similar to CPO-STV in that it compares possible winning candidate pairs and selects the Condorcet winner. It is not used in parliamentary elections.
Instant-runoff voting (IRV) is a type of ranked preferential vote counting method used in single-seat elections with more than two candidates. IRV is also sometimes referred to as the alternative vote (AV), preferential voting, or in the United States, ranked-choice voting (RCV), though these names are also used for other systems.
The majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters prefers every other candidate over a given candidate, then that candidate must not win.
An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Political electoral systems are organized by governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.
The term "ranked voting" refers to any voting system in which voters rank their candidates in a sequence of first or second on their respective ballots. Ranked voting systems differ on the basis of how the ballots are tabulated and how many seats are filled. The many electoral systems that use ranked voting use one of the many available counting methods to select the winning candidate or candidates. There is also variation among ranked voting electoral systems in that in some ranked voting systems, officials require voters to rank a set number of candidates, sometimes all of them; in others, citizens may rank as many candidates as they see fit.
Homogeneity is a common property for voting systems. The property is satisfied if, in any election, the result depends only on the proportion of ballots of each possible type. Specifically, if every ballot is replicated the same number of times, then the result should not change.
Electoral systems are the rules for conducting elections, a main component of which is the algorithm for determining the winner from the ballots cast. This article discusses methods and results of comparing different electoral systems, both those which elect a unique candidate in a 'single-winner' election and those which elect a group of representatives in a multiwinner election.
Tideman's Alternative Methods, including Alternative Smith and Alternative Schwartz, are two electoral systems developed by Nicolaus Tideman which select a single winner using votes that express preferences. These methods can also create a sorted list of winners.