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.