Approval voting is a single-winner electoral system in which voters mark all the candidates they support, instead of just choosing one. The candidate with the highest approval rating is elected. Approval voting is currently in use for government elections in St. Louis, Missouri, Fargo, North Dakota and in the United Nations to elect the Secretary General.
Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other are elected.
Score voting, sometimes called range voting, is an electoral system for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected. Score voting includes the well-known approval voting, but also lets voters give partial (in-between) approval ratings to candidates.
Strategic or tactical voting is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results. For example, in plurality or instant-runoff, a voter may recognize their favorite candidate is unlikely to win and so instead support a candidate they think is more likely to win.
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.
Vote swapping, also called co-voting or vote pairing, occurs when 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 that candidate has a greater possibility of winning in that district.
The Gibbard–Satterthwaite theorem is a theorem in voting theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner, and shows that for every voting rule of this form, at least one of the following three things must hold:
- The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or
- The rule limits the possible outcomes to two alternatives only; or
- The rule is not straightforward, i.e. there is no single always-best strategy.
The lesser of two evils principle, also referred to as the lesser evil principle and lesser-evilism, is the principle that when faced with selecting from two immoral options, the least immoral one should be chosen. The principle is most often invoked in reference to binary political choices under systems that make it impossible to express a sincere preference for one's favorite.
A Condorcet winner is a candidate who more than half of all voters would support them 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 majority-rule principle, because they extend the principle of majority rule to elections with multiple candidates.
In social choice, a no-show paradox is a pathology in some voting rules, where a candidate loses an election as a result of having too many supporters. More formally, a no-show paradox occurs when adding voters who prefer Alice to Bob causes Alice to lose the election to Bob. Voting systems without the no-show paradox are said to satisfy the participation criterion.
The median voter theorem in political science and social choice theory, developed by Duncan Black, states that if voters and candidates are distributed along a one-dimensional spectrum and voters have single-peaked preferences, any voting method that is compatible with majority-rule will elect the candidate preferred by the median voter. The median voter theorem thus shows that under a realistic model of voter behavior, Arrow's theorem, which essentially suggests that ranked-choice voting systems cannot eliminate the spoiler effect, does not apply, and therefore that rational social choice is in fact possible if the election system is using a Condorcet method.
The majority favorite criterion is a voting system criterion that says that, if a candidate would win more than half the vote in a first-preference plurality election, that candidate should win. Equivalently, if only one candidate is ranked first by a over 50% of voters, that candidate must win. It is occasionally referred to simply as the "majority criterion", but this term is more often used to refer to Condorcet's majority-rule principle.
Bullet, single-shot, or plump voting is when a voter supports only a single candidate, typically to show strong support for a single favorite.
The Kemeny–Young method is an electoral system that uses ranked 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.
Instant-runoff voting (IRV) is a multi-round elimination rule. The rule works by simulating a series of runoff elections, where the last-place finisher according to a plurality vote is eliminated in each round. IRV is most closely related to two-round runoff election. It is also known as Ranked-Choice Voting (RCV), preferential voting (PV), the alternative vote (AV), or Hare system.
In game theory and political science, Poisson games are a class of games often used to model the behavior of large populations. One common application is determining the strategic behavior of voters with imperfect information about each others' preferences. Poisson games are most often used to model strategic voting in large electorates with secret and simultaneous voting.
There are a number of different criteria which can be used for voting systems in an election, including the following
The Tideman Alternative method, also called Alternative-Smithvoting, is a voting rule developed by Nicolaus Tideman which selects a single winner using ranked ballots. This method is Smith-efficient, making it a kind of Condorcet method, and uses the alternative vote (RCV) to resolve any cyclic ties.
The sincere favorite or no favorite-betrayal criterion is a property of some voting systems, that says voters should have no incentive to vote for someone else over their favorite. It protects voters from having to engage in lesser-evil voting or a strategy called "decapitation".
Lesser-evil voting (LEV) refers to a kind of strategic voting where a voter supports a less-preferred candidate in an election rather than their actual favorite candidate, when this candidate is unlikely to win.
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