Favorite betrayal criterion: Difference between revisions

The '''favorite betrayal criterion''' or(sometimes called '''sincere favorite criterion''') is a [[voting system criterion]] which requires that "voters should have no incentive to vote someone else over their favorite".<ref>{{Cite web|url=https://rangevoting.org/FBCsurvey.html|title=Survey of FBC (Favorite-Betrayal Criterion)|last=Ossipoff|first=Mike|last2=Smith|first2=Warren D.|date=Jan 2007|website=Center for Range Voting|url-status=live|archive-url=|archive-date=|access-date=2020-04-08}}</ref> Voting systems failing the criterion are vulnerable to a kind of strategy called '''decapitation''', i.e. removing the top ("head") of a ballot.<ref>{{Cite journal|last=Merrill|first=Samuel|last2=Nagel|first2=Jack|date=1987-06-01|title=The Effect of Approval Balloting on Strategic Voting under Alternative Decision Rules|url=https://www.cambridge.org/core/product/identifier/S0003055400194481/type/journal_article|journal=American Political Science Review|language=en|volume=81|issue=2|pages=509–524|doi=10.2307/1961964|issn=0003-0554}}</ref>

It is passed by [[Approval voting]], [[Range voting]], and [[Majority Judgment]]. All these are examples of [[cardinal voting systems]], though some voters may be reluctant to have a compromise candidate tied with their favorite candidate on their respective ballots.

It is also failed by [[Pluralityplurality voting]] and two-round [[runoff voting]].

: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>

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>

Though many voting methods fail FB, they tend to decrease the incentive to do FB relative to [[FPTP]]. Example for [[Condorcet]]: <blockquote>25 A>B

[[Condorcet=== methods]] can have theirReducing FB incentive eliminated in certaina scenarios.chicken Fordilemma example:===