Smith Set - Schwartz Set Comparison

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:

    You do not become a “dissident” just because you decide one day to take up this most unusual career. You are thrown into it by your personal sense of responsibility, combined with a complex set of external circumstances. You are cast out of the existing structures and placed in a position of conflict with them. It begins as an attempt to do your work well, and ends with being branded an enemy of society.
    Václav Havel (b. 1936)

    In comparison to the French Revolution, the American Revolution has come to seem a parochial and rather dull event. This, despite the fact that the American Revolution was successful—realizing the purposes of the revolutionaries and establishing a durable political regime—while the French Revolution was a resounding failure, devouring its own children and leading to an imperial despotism, followed by an eventual restoration of the monarchy.
    Irving Kristol (b. 1920)