I wanted to express the beatpath definition of the Schwartz set in a simpler and more compelling or appealing way, and the cycle definition (that I've posted here) seemed such a simplification.
But the cycle definition doesn't define the Schwartz set. A candidate that doesn't have a defeat that isn't in a cycle isn't necessarily in the Scwhartz set (as defined by the unbeaten set definition and the beatpath definition]. Of the two definitions (unbeaten set and beatpath), the beatpath definition desn't have much compellingness. For compellingness, I much prefer the unbeaten set definition. Let me state both definitions here: Unbeaten set definition of the Schwartz set:: 1. An unbeaten sets is a set of alternatives none of which are beaten by anything outside the set. 2. An innermost unbeaten set is an unbeaten set that doesn't contain a smaller unbeaten set. 3.The Schwartz set is the set of alternatives that are in innermost unbeaten sets. [end of unbeaten set definition of Schwartz set] --------------------------------------- Beatpath definition of Schwartz set: There is a beatpath from X to Y if X beats Y, or if X beats A and there is a beatpath from A to Y. If there is a beatpath from Y to X, but not from X to Y, then X is not in the Schwartz set. Otherwise X is in the Schwartz set. [end of beatpath definition of the Schwartz set] Michael Ossipoff ---- Election-Methods mailing list - see http://electorama.com/em for list info
