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==Beatpath Order==
The Schwartz set is the union of all of the cycle equivalence classes that are [http://en.wikipedia.org/wiki/Maximal_element maximal] in the [[../Beatpath#
This characterization of the Schwartz set follows from two characteristics of any set S that fullfills the first property of a Schwartz set component:
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Other characteristics of the Schwartz set include:
* If a [[Condorcet Criterion |Condorcet winner]] exists, it is the one and only candidate in the Schwartz set.
* All [http://en.wikipedia.org/wiki/Condorcet_method#Related_terms weak Condorcet winners] are in the Schwartz set. The weak Condorcet winners are the candidates in the Schwartz set that are not in a cycle, i.e. they are each in their own Schwartz set component.
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