# Generalized Strategy-Free criterion

## Contents

#### 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 called "Condorcet candidate" or "Condorcet winner".

#### 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

Schulze complies with the Generalized Strategy-Free Criterion, while Approval voting, Cardinal Ratings, Borda count, Plurality voting, and Instant-Runoff Voting do not comply.

The practical significance of the Strategy-Free Criterion can be questioned. For example, approval voting may be said to bear a Gray Hat Syndrome, but this not not remotely as pernicious as a Black Hat Syndrome. See the First Past the Post electoral system entry, in the subheading on *3.2 Tactical voting*.

#### Commentary

GSFC generalizes the Strategy-Free criterion (SFC) to the case in which no Condorcet candidate exists, thereby covering all possible cases. If no Condorcet candidate 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.

*Some parts of this article are derived with permission from text at http://electionmethods.org*

## See Also

- Voting system
- Monotonicity criterion
- Condorcet Criterion
- Generalized Condorcet criterion
- Strategy-Free criterion
- Strong Defensive Strategy criterion
- Weak Defensive Strategy criterion
- Favorite Betrayal criterion
- Participation criterion
- Summability criterion

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