View source for Generalized Strategy-Free criterion

<h4 class=left>Definitions</h4>

<p>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).</p>

<p>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.</p>

<p>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".</p>

<h4 class=left>Statement of Criterion</h4>

<p><em>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.</em></p>

<h4 class=left>Complying Methods</h4>

<p>[[Schulze method|Schulze]] complies with the Generalized Strategy-Free
Criterion, while [[Approval voting]], [[Cardinal Ratings]], [[Borda count]], [[Plurality voting]], and [[Instant-Runoff Voting]] do not comply.</p>

<h4 class=left>Commentary</h4>

<p>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.</p>

''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]]

== External Links ==

* [http://electionmethods.org/ Election Methods Education and Research Group]

[[Category:Voting system criteria]]

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