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.
Read more about this topic: Schwartz Set
Famous quotes containing the word properties:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)