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.
Read more about this topic: Smith Set
Famous quotes containing the word properties:
“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)
“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)