Procedures
Each voter rank-orders all of the candidates on their ballot. Otherwise, the candidate ranked last by the largest number (plurality) of voters is eliminated, making each individual round equivalent to anti-plurality voting. Conversely, under instant-runoff voting, the candidate ranked first (among non-eliminated candidates) by the fewest voters is eliminated.
In some sources, the elimination proceeds regardless of whether any candidate is ranked first by a majority of voters, and the last candidate to be eliminated is the winner. [5] This variant of the method can result in a different winner than the former one (unlike in instant-runoff voting, where checking to see if any candidate is ranked first by a majority of voters is only a shortcut that does not affect the outcome).
Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other are elected.
The two-round system, also called ballotage, top-two runoff, or two-round plurality, is a single winner voting method. It is sometimes called plurality-runoff, although this term can also be used for other, closely-related systems such as ranked-choice voting or the exhaustive ballot. It falls under the class of plurality-based voting rules, together with instant-runoff and first-past-the-post (FPP). In a two-round system, both rounds are held under choose-one voting, where the voter marks a single favorite candidate. The two candidates with the most votes in the first round proceed to a second round, where all other candidates are excluded.
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, whenever there is such a candidate. A candidate with this property, the pairwise champion or beats-all winner, is formally called the Condorcet winner or Pairwise Majority Rule Winner (PMRW). The head-to-head elections need not be done separately; a voter's choice within any given pair can be determined from the ranking.
A Condorcet winner is a candidate who would receive the support of more than half of the electorate in a one-on-one race against any one of their opponents. Voting systems where a majority winner will always win are said to satisfy the Condorcet winner criterion. The Condorcet winner criterion extends the principle of majority rule to elections with multiple candidates.
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.
In single-winner voting system theory, the Condorcet loser criterion (CLC) is a measure for differentiating voting systems. It implies the majority loser criterion but does not imply the Condorcet winner criterion.
In social choice theory, the best-is-worst paradox occurs when a voting rule declares the same candidate to be both the best and worst possible winner. The worst candidate can be identified by reversing each voter's ballot, then applying the voting rule to the reversed ballots find a new "anti-winner".
The exhaustive ballot is a voting system used to elect a single winner. Under the exhaustive ballot the elector casts a single vote for his or her chosen candidate. However, if no candidate is supported by an overall majority of votes then the candidate with the fewest votes is eliminated and a further round of voting occurs. This process is repeated for as many rounds as necessary until one candidate has a majority.
The contingent vote is an electoral system used to elect a single representative in which a candidate requires a majority of votes to win. It is a form of preferential voting. The voter ranks the candidates in order of preference, and when the votes are counted, the first preference votes only are counted. If no candidate has a majority of the votes cast, then all but the two leading candidates are eliminated and the votes received by the eliminated candidates are distributed among the two remaining candidates according to voters' preferences.
Runoff voting can refer to:
Later-no-harm is a property of some ranked-choice voting systems, first described by Douglas Woodall. In later-no-harm systems, increasing the rating or rank of a candidate ranked below the winner of an election cannot cause a higher-ranked candidate to lose.
Instant-runoff voting (IRV) is a winner-takes-all multi-round elimination voting system that uses ranked voting to simulate a series of runoff elections, where the last-place finisher according to a plurality vote is eliminated in each round and the votes supporting the eliminated choice are transferred to their next available preference until one of the options reaches a majority of the remaining votes. Its purpose is to elect the candidate in single-member districts with majority support even when there are more than two candidates. IRV is most closely related to two-round runoff election.
The majority loser criterion is a criterion to evaluate single-winner voting systems. The criterion states that if a majority of voters give a candidate no support, i.e. do not list that candidate on their ballot, that candidate must lose.
The 2009 Burlington mayoral election was the second mayoral election since the city's 2005 change to instant-runoff voting (IRV), also known as ranked-choice voting (RCV), after the 2006 mayoral election. In the 2009 election, incumbent Burlington mayor won reelection as a member of the Vermont Progressive Party, defeating Kurt Wright in the final round with 48% of the vote.
An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect 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.
Ranked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked system is one that depends only on which of two candidates is preferred by a voter, and as such does not incorporate any information about intensity of preferences. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them very different properties.
There are a number of different criteria which can be used for voting systems in an election, including the following
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.
A final-four or final-five primary is an electoral system using a nonpartisan primary by multi-winner plurality in the first step.
In social choice, a center squeeze is a kind of spoiler effect in which the Condorcet winner is eliminated before the final round of an election. Candidates focused on appealing to a small base of core supporters can "squeeze" Condorcet winners out of the race, by splitting the first-round vote needed to survive earlier rounds. The effect was first predicted by social choice theorists in the 1940s and has since been confirmed empirically by studies of politics. Famous examples of center squeezes include the 2022 Alaska special election, where Nick Begich III was eliminated in the first round by right-wing spoiler Sarah Palin, and the 2009 Burlington mayoral election, where results were criticized by mathematicians and voting theorists for several pathologies associated with ranked-choice voting.
Mathematicsportal 
