#### Definitions

A sincere vote is one with no falsified preferences or preferences left unspecified when the election method allows them to be specified (in addition to the preferences already specified).

One candidate is preferred over another candidate if, in a one-on-one competition, more voters prefer the first candidate than prefer the other candidate.

The Smith set is the smallest set of candidates such that every member of the set is preferred to every candidate not in the set. If the Smith set consists of only one candidate, that candidate is the Ideal Democratic Winner (IDW).

#### Statement of Criterion

*If a majority prefers a member of the Smith set to another candidate who is not in the Smith set, then the other candidate should not win if that majority votes sincerely and no other voter falsifies any preferences.*

#### Complying Methods

The Condorcet method complies with the Generalized Strategy-Free Criterion, but none of the other methods in the compliance table above comply.

#### Commentary

GSFC generalizes the Strategy-Free Criterion (SFC) to the case in which no Ideal Democratic winner (IDW) exists, thereby covering all possible cases. If no IDW exists, then a cyclical ambiguity exists among the members of the Smith set and must be resolved. The commentary for SFC above applies here also.