In voting systems, the Schwartz set is the union of all Schwartz set components. A Schwartz set component is any non-empty set S of candidates such that
- Every candidate inside the set S is pairwise unbeaten by every candidate outside S; and
- No non-empty proper subset of S fulfills the first property.
A set of candidates that meets the first requirement is also known as an undominated set.
The Schwartz set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Schwartz set pass the Schwartz criterion. The Schwartz set is named for political scientist Thomas Schwartz.
Read more about Schwartz Set: Properties, Smith Set Comparison, Algorithms, Complying Methods
Famous quotes containing the word set:
“Although knaves win in every political struggle, although society seems to be delivered over from the hands of one set of criminals into the hands of another set of criminals, as fast as the government is changed, and the march of civilization is a train of felonies, yet, general ends are somehow answered.”
—Ralph Waldo Emerson (1803–1882)