Smith Set - Properties

Properties

  • The Smith set always exists and is well-defined. There is only one smallest dominating set since dominating sets are nested, non-empty, and the set of candidates is finite.
  • The Smith set can have more than one candidate, either because of pair-wise ties or because of cycles, such as in Condorcet's paradox.
  • The Condorcet winner, if one exists, is the sole member of the Smith set. If weak Condorcet winners exist, they are in the Smith set.

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