Schwartz Set - Properties

Properties

  • The Schwartz set is always non-empty—there is always at least one Schwartz set component.
  • Any two distinct Schwartz set components are disjoint.
  • If there is a Condorcet winner, it is the only member of the Schwartz set. If there is only one member in the Schwartz set, it is at least a weak Condorcet winner.
  • If a Schwartz set component contains only a single candidate, that candidate is a weak Condorcet winner. If a Schwartz set component contains multiple candidates, they are all in a beatpath cycle with each other, a top cycle.
  • Any two candidates that are in different Schwartz set components are pairwise tied with each other.

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