Voting criterion requiring a kind of majority rule
The Smith criterion (sometimes the generalized Condorcet criterion) is a voting system criterion that formalizes the concept of a majority rule. A voting system satisfies the Smith criterion if it always elects a candidate from the Smith set, which generalizes the idea of a "Condorcet winner" to cases where there may be cycles or ties, by allowing for several who together can be thought of as being "Condorcet winners." A Smith method will always elect a candidate from the Smith set.
The Smith criterion is also called the top (Condorcet) cycle criterion, but this can be slightly misleading: the Smith set sometimes consists of a degenerate cycle with only one candidate who "cycles" with themselves (a Condorcet winner), or a pair of tied candidates who "cycle" with each other.[1]
An alternative, stricter criterion is given by the Landau set.
The Smithcriterion (sometimes the generalized Condorcet criterion) is a voting system criterion that formalizes the concept of a majority rule. A voting...
the Smith set is also called the smallest dominating set. An alternative generalization of the Condorcet criterion (which is stricter than the Smith criterion)...
said to satisfy the majority-rule principle, also known as the Condorcet criterion. Condorcet voting methods extend majority rule to elections with more...
The Criterion Collection, Inc. (or simply Criterion) is an American home-video distribution company that focuses on licensing, restoring and distributing...
utility or benefit, and j represents the player. Efficiency is an important criterion for judging behavior in a game. In a notable and often analyzed game known...
majority criterion, the monotonicity criterion, the Smithcriterion (which implies the Condorcet criterion), the Condorcet loser criterion, and the independence...
exists, is known as Condorcet consistent or as satisfying the Condorcet criterion. Such systems are referred to as Condorcet methods. However, in elections...
The monotonicity criterion, also called positive response or positive vote weight, is a principle of social choice theory that says that increasing a...
matchings. Some cycle resolution methods are Smith-efficient, meaning that they pass the Smithcriterion. This guarantees that when there is a cycle (and...
voting and minimax Condorcet. The Smithcriterion implies the Condorcet loser criterion, because no candidate in the Smith set can lose a head-to-head matchup...
Note that although this criterion is classed here as nominee-relative, it has a strong absolute component in excluding Smith-dominated candidates from...
account in 2-candidate elections. STAR voting satisfies the monotonicity criterion, i.e. raising your vote's score for a candidate can never hurt their chances...
monotonicity criterion, the participation criterion, the consistency criterion, independence of irrelevant alternatives, resolvability criterion, and reversal...
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...
The participation criterion, also called vote or population monotonicity, is a voting system criterion that says that a candidate should never lose an...
disadvantages (for example, it fails the participation criterion, and can fail the majority criterion arbitrarily badly). The tie-breaking formula of the...
go.jp. Archived from the original on 2022-08-08. Retrieved 2022-06-06. Smith, Sydney (1839). Ballot . London: Longman, Orme, Brown, Green and Longmans...
candidates. It implies a voting procedure which satisfies the Condorcet criterion but is computationally burdensome. The Borda count is particularly susceptible...
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