Smith set: Difference between revisions
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(However, the definitions should be used cautiously when the voting method does not allow a vote to contain the voter's order of preference, because the pairwise comparisons will undercount voters and thus be misleading.) |
(However, the definitions should be used cautiously when the voting method does not allow a vote to contain the voter's order of preference, because the pairwise comparisons will undercount voters and thus be misleading.) |
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The "Sincere Smith set", (also mentioned below on this page)is the basis for a definition of the Smith Criterion that is applicable to all voting systems, including Plurality and Approval. |
The "Sincere Smith set", (also mentioned below on this page) is the basis for a definition of the Smith Criterion that is applicable to all voting systems, including Plurality and Approval. |
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Definition of sincere Smith set: |
Definition of sincere Smith set: |
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X is socially preferred to Y if more voters prefer X to Y than prefer Y to X. |
X is socially preferred to Y if more voters prefer X to Y than prefer Y to X. |
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The sincere Smith set is the smallest set of candidates such that every candidate in the set is socially preferred to every candidate outside the set. |
The sincere Smith set is the smallest set of candidates such that every candidate in the set is socially preferred to every candidate outside the set. |
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Smith Criterion: |
Smith Criterion: |