It has been suggested that this article be
merged into
Round-robin voting and
Tournament (graph theory). (
Discuss) Proposed since May 2024. |
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Electoral systems |
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A tournament solution is a function that maps an oriented complete graph to a nonempty subset of its vertices. It can informally be thought of as a way to find the "best" alternatives among all of the alternatives that are "competing" against each other in the tournament. Tournament solutions originate from social choice theory, [1] [2] [3] [4] but have also been considered in sports competition, game theory, [5] multi-criteria decision analysis, biology, [6] [7] webpage ranking, [8] and dueling bandit problems. [9]
In the context of social choice theory, tournament solutions are closely related to Fishburn's C1 social choice functions, [10] and thus seek to show who are the strongest candidates in some sense.
A tournament graph is a tuple where is a set of vertices (called alternatives) and is a connex and asymmetric binary relation over the vertices. In social choice theory, the binary relation typically represents the pairwise majority comparison between alternatives.
A tournament solution is a function that maps each tournament to a nonempty subset of the alternatives (called the choice set [2]) and does not distinguish between isomorphic tournaments:
Common examples of tournament solutions are the: [1] [2]
It has been suggested that this article be
merged into
Round-robin voting and
Tournament (graph theory). (
Discuss) Proposed since May 2024. |
Part of the Politics series |
Electoral systems |
---|
Politics portal |
A tournament solution is a function that maps an oriented complete graph to a nonempty subset of its vertices. It can informally be thought of as a way to find the "best" alternatives among all of the alternatives that are "competing" against each other in the tournament. Tournament solutions originate from social choice theory, [1] [2] [3] [4] but have also been considered in sports competition, game theory, [5] multi-criteria decision analysis, biology, [6] [7] webpage ranking, [8] and dueling bandit problems. [9]
In the context of social choice theory, tournament solutions are closely related to Fishburn's C1 social choice functions, [10] and thus seek to show who are the strongest candidates in some sense.
A tournament graph is a tuple where is a set of vertices (called alternatives) and is a connex and asymmetric binary relation over the vertices. In social choice theory, the binary relation typically represents the pairwise majority comparison between alternatives.
A tournament solution is a function that maps each tournament to a nonempty subset of the alternatives (called the choice set [2]) and does not distinguish between isomorphic tournaments:
Common examples of tournament solutions are the: [1] [2]