 | This article needs additional citations for verification .(April 2022) |
Anti-plurality voting describes an electoral system in which each voter votes against a single candidate, and the candidate with the fewest votes against wins. Anti-plurality voting is an example of a positional voting method. [1] [2]
Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities and that everyone wants to live as near to the capital as possible.
The candidates for the capital are:
The preferences of the voters would be divided like this:
| 42% of voters (close to Memphis) | 26% of voters (close to Nashville) | 15% of voters (close to Chattanooga) | 17% of voters (close to Knoxville) |
|---|---|---|---|
|
|
|
|
In this electoral system, each voter marks a vote against his or her fourth preference. In this case, it would be a tie between Nashville and Chattanooga, both receiving zero votes. If the tie is to be resolved with anti-plurality voting as well, Nashville would win, as it has less second-to-last place votes (32%) than Chattanooga (42%). Ties could also be resolved through a second subsequent runoff election.
As can be seen from the example, in the absence of tactical voting, this system tends to favor middle-of-the-road candidates. However, it is very sensitive to tactical voting, as any candidate perceived beforehand as a potential winner will attract more countervotes from partisans of their opponents. This creates the paradoxical situation for the candidates that, in order to win, you need to appear not to be winning. For this reason, few would advocate this system for general high-stakes use, though for its simplicity it can be useful in specific situations (where voters are not motivated to use tactical voting).
APV satisfies the monotonicity criterion, the participation criterion and the consistency criterion. It does not satisfy the Condorcet loser criterion, the independence of irrelevant alternatives criterion, the independence of clones criterion or reversal symmetry.
Approval voting is a single-winner electoral system in which each voter may choose ("approve") any number of candidates, and the winner is the candidate approved by the largest number of voters. A ballot on which multiple candidates may be marked is called an approval ballot. The use of this is what makes it different from other common single-winner systems:
Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added, and the candidate with the highest total is elected. It has been described by various other names including evaluative voting, utilitarian voting, interval measure voting, the point system, ratings summation, 0-99 voting, average voting and utilityvoting. It is a type of cardinal voting electoral system, and aims to implement the utilitarian social choice rule.
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.
In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion.
In voting systems, the Minimax Condorcet method is one of several Condorcet methods used for tabulating votes and determining a winner when using ranked voting in a single-winner election. It is sometimes referred to as the Simpson–Kramer method, and the successive reversal method.
Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is never worth more. A valid progression of points or weightings may be chosen at will or it may form a mathematical sequence such as an arithmetic progression, a geometric one or a harmonic one. The set of weightings employed in an election heavily influences the rank ordering of the candidates. The steeper the initial decline in preference values with descending rank, the more polarised and less consensual the positional voting system becomes.
The Kemeny–Young method is an electoral system that uses preferential ballots and pairwise comparison counts to identify the most popular choices in an election. It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice.
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.
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, single transferable voting, or in the United States, ranked-choice voting (RCV), though these names are also used for other systems.
Majority judgment (MJ) is a single-winner voting system proposed in 2007 by Michel Balinski and Rida Laraki. It is a highest median rule, i.e., a cardinal voting system that elects the candidate with the highest median rating.
The later-no-help 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 win. Voting systems that fail the later-no-help criterion are vulnerable to the tactical voting strategy called mischief voting, which can deny victory to a sincere Condorcet winner.
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.
STAR voting is an electoral system for single-seat elections. Variations also exist for multi-winner and proportional representation elections. The name stands for "Score then Automatic Runoff", referring to the fact that this system is a combination of score voting, to pick two finalists with the highest total scores, followed by a "virtual runoff" in which the finalist who is preferred on more ballots wins. It is a type of cardinal voting electoral system.