Schwartz Set Comparison
The Schwartz set is closely related to and is always a subset of the Smith set. The Smith set is larger if and only if a candidate in the Schwartz set has a pair-wise tie with a candidate that is not in the Schwartz set.
The Smith set can be constructed from the Schwartz set by repeatedly adding two types of candidates until no more such candidates exist outside the set:
- candidates that have pair-wise ties with candidates in the set,
- candidates that beat a candidate in the set.
Note that candidates of the second type can only exist after candidates of the first type have been added.
Read more about this topic: Smith Set
Famous quotes containing the words set and/or comparison:
“A more secret, sweet, and overpowering beauty appears to man when his heart and mind open to the sentiment of virtue. Then he is instructed in what is set above him. He learns that his being is without bound; that to the good, to the perfect, he is born, low as he now lies in evil and weakness.”
—Ralph Waldo Emerson (18031882)
“What is man in nature? A nothing in comparison with the infinite, an all in comparison with the nothinga mean between nothing and everything.”
—Blaise Pascal (16231662)