Favorite betrayal criterion: Difference between revisions
Cut alternate definitions, as Small's seems to be canonical. Add references to Condorcet methods failing FBC.
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It is defined as follows:
:A [[voting system]] satisfies the Favorite Betrayal Criterion (FBC) if there do not exist situations where a voter is only able to obtain a more preferred outcome (i.e. the election of a candidate that he or she prefers to the current winner) by insincerely listing another candidate ahead of his or her sincere favorite.<ref name="small">Alex Small, “Geometric construction of voting methods that protect voters’ first choices,” arXiv:1008.4331 (August 22, 2010), http://arxiv.org/abs/1008.4331.</ref>
The criterion permits the strategy of insincerely ranking another candidate equal to one's favorite. A related but stronger criterion, the ''strong favorite betrayal criterion'' disallows this.<ref name="small" />
==Complying methods==▼
[[Approval voting]], [[range voting]], [[Majority Judgment]], [[MMPO|MinMax(pairwise opposition)]], [[MCA]] (except MCA-A and some versions of MCA-R), [[MAMPO]], [[Majority Defeat Disqualification Approval]], and [[Improved Condorcet Approval]] comply with the favorite betrayal criterion, as do ICT and [[Symmetrical ICT]]. ▼
▲==Complying methods==
[[Borda count]], [[plurality voting]], [[Condorcet criterion|Condorcet methods]] (except for Improved Condorcet methods, such as Kevin Venzke's [[ICA]], and Chris Benham's ICT, and [[Symmetrical ICT]]) and [[instant-runoff voting]] do not comply.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-May/081273.html|title=WV methods fail FBC with 3 candidates|website=Election-methods mailing list archives|date=2005-05-13|last=Venzke|first=K.}}</ref><ref>{{cite web|url=https://munsterhjelm.no/km/yahoo_lists_archive/RangeVoting/web/2005-October/msg00059.html|title=I told why CC is incompatible with FBC. Why the continuing debate?|date=2005-10-18|last=Ossipoff|first=M.|website=RangeVoting Yahoo list mirror}}</ref>
▲[[Approval voting]], [[range voting]], [[Majority Judgment]], [[MMPO|MinMax(pairwise opposition)]], [[MCA]] (except MCA-A and some versions of MCA-R), [[MAMPO]], and [[Improved Condorcet Approval]] comply with the favorite betrayal criterion, as do ICT and [[Symmetrical ICT]].
== Examples ==
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== Stronger forms of the criterion ==
FBC simply requires that for a given election, a voter always has some kind of [[strategy]] they can use to vote in such a way that they most support their favorite candidate. However, this means that some voting methods that fail FB can allow a voter to benefit by doing FB, even though they didn't actually have to. For example, several voting methods which pass FBC because they allow a voter to protect themselves by equally ranking multiple candidates 1st (implying that the voter has a simple way to always avoid FB i.e. equal-ranking, as opposed to some FBC-compliant voting methods where the non-FB strategy may be opaque or difficult to figure out and thus less useful for avoiding FB) are like this. [[Score voting]] passes a stronger form of FBC, which says that voters can never benefit by doing FB i.e. there is no possible strategy involving FB that can benefit a voter.<ref>{{Cite web|url=https://rangevoting.org/FBCexecSumm.html|title=RangeVoting.org - Favorite betrayal (executive summary)|last=|first=|date=|website=rangevoting.org|url-status=live|archive-url=|archive-date=|access-date=2020-05-14|quote=We've come a long way since the days when range and approval voting were the only known methods in which betraying your favorite is strategically avoidable. Now many other methods also are known with that "FBC property." [...] However, it appears Range and Approval satisfy FBC in a stronger and more obvious sense than these other methods. Specifically, with Range and Approval, betraying your favorite simply never is useful. With the other methods it can be strategically useful (cause X to win instead of Y, where the betrayers prefer X) but if so there is always a way to get the same effect (i.e. make X win) by some other dishonest vote not involving favorite betrayal.}}</ref>
== Notes ==
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