Favorite betrayal criterion: Difference between revisions

: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>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>

=== Current Definition of FBC: ===

Michael Ossipoff definition:

'''Requirements:'''

The voting system must allow the voter to vote at top as many candidates as s/he wishes.

If the winner is a candidate who is top-voted by you, then moving an additional candidate to top on your ballot shouldn't change the winner to a candidate who is not then top-voted by you.

'''Supplementary definition:'''

A candidate is "top-voted" by you, and is "at top" on your ballot, if you don't vote anyone over him/her.

===Earlier Definition===

The definition written below is the one that FBC's initial proponent had originally written and used. Its problem was that it led to the question of "What if the way of voting that optimizes your outcome without favorite-burial is some complicated, difficult-to-find strategy?". That question led to a better definition, written above on this page. Some time ago, someone else, too, had written that definition, and a link to it is given at the bottom of this page, under a different name (Sincere Favorite Criterion).

'''Supplementary Definition:'''

A voter optimizes the outcome (from his/her own perspective) if his vote causes the election of the best possible candidate that can be elected, based on his own preferences, given all the votes cast by other voters.

'''Earlier FBC definition:'''

<em>For any voter who has a unique favorite, there should be no possible set of votes cast by the other voters such that the voter can optimize the outcome (from his own perspective) only by voting someone over his favorite.</em>

==Complying methods==

[[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]].

[[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.

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>