Other Criteria
Any election method that complies with the Smith criterion also complies with the Condorcet criterion, since if there is a Condorcet winner, then it is the only candidate in the Smith set. Obviously, this means that failing the Condorcet criterion automatically implies the non-compliance with the Smith criterion as well. Additionally, such sets comply with the Condorcet loser criterion. This is notable, because even some Condorcet methods do not (Minimax). It also implies the mutual majority criterion, since the Smith set is a subset of the MMC set.
The Smith set and Schwartz set are sometimes confused in the literature. Miller (1977, p. 775) lists GOCHA as an alternate name for the Smith set, but it actually refers to the Schwartz set. The Schwartz set is actually a subset of the Smith set (and equal to it if there are no pairwise ties between members of the Smith set).
Read more about this topic: Smith Criterion
Famous quotes containing the word criteria:
“The Hacker Ethic: Access to computers—and anything which might teach you something about the way the world works—should be unlimited and total.
Always yield to the Hands-On Imperative!
All information should be free.
Mistrust authority—promote decentralization.
Hackers should be judged by their hacking, not bogus criteria such as degrees, age, race, or position.
You can create art and beauty on a computer.
Computers can change your life for the better.”
—Steven Levy, U.S. writer. Hackers, ch. 2, “The Hacker Ethic,” pp. 27-33, Anchor Press, Doubleday (1984)
“There are ... two minimum conditions necessary and sufficient for the existence of a legal system. On the one hand those rules of behavior which are valid according to the system’s ultimate criteria of validity must be generally obeyed, and on the other hand, its rules of recognition specifying the criteria of legal validity and its rules of change and adjudication must be effectively accepted as common public standards of official behavior by its officials.”
—H.L.A. (Herbert Lionel Adolphus)