Favorite betrayal criterion: Difference between revisions

Line 388:

== Notes ==

=== Least favorite betrayal criterion ===

A criterion related to FB is whether or not a voter can be hurt by giving no support to their least favorite candidates. Approval and Score voting pass this criterion, since if never benefits you to help your least favorite beat other candidates on approvals/points.

=== Criterion failure rates ===

Though many voting methods fail FB, they tend to decrease the incentive to do FB relative to [[FPTP]]. Example for [[Condorcet]]:

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

25 A>B

26 B

⚫

49 C </blockquote>In FPTP, C would win with 49 votes to B's 26 and A's 25, so the A-top voters would have to vote B>A instead (i.e. put B as their 1st choice) to ensure B wins with 51 votes, rather than C with 49. In Condorcet methods, this isn't necessary, since the pairwise table is:

49 C

⚫

In FPTP, C would win with 49 votes to B's 26 and A's 25, so the A-top voters would have to vote B>A instead (i.e. put B as their 1st choice) to ensure B wins with 51 votes, rather than C with 49. In Condorcet methods, this isn't necessary, since the pairwise table is:

{| class="wikitable"

|+Wins are bolded

Line 423:

Line 422:

and B is the [[Condorcet winner]]. See also the [[chicken dilemma]].

~~[[Condorcet~~ ~~methods]] can have their~~ FB incentive ~~eliminated~~ in ~~certain~~ ~~scenarios.~~ ~~For~~ ~~example:~~

=== Reducing FB incentive in a chicken dilemma ===

<blockquote>26 A>B

26 A>B

25 B

49 C</blockquote>A [[pairwise]] beats B beats C beats A, so there is a [[cycle]]. C would win in several methods, such as some [[Condorcet methods]], and [[IRV]]. To prevent A-top voters from having to vote B>A to make B the [[CW]]/[[majority criterion]] winner, it can essentially be observed that they have the incentive to do so, and if they do this, nobody else has incentive/ability to vote differently to get a different outcome, so B would automatically win.

49 C

⚫

A ~~beats~~ B ~~beats C beats A. To prevent A-top voters from voting B>A to make B the CW~~, ~~it can essentially be observed~~ that ~~they have the incentive to do so, and if they do this, nobody else has incentive to vote differently, so B would automatically win. However,~~ if the 49 C voters instead had voted C>A, then they make it so that now the voting method recognizes the C-top voters have an incentive to do FB to elect A rather than B. So a cycle would be formed all over again. ~~This~~ ~~means~~ that this trick doesn't always work. ~~See~~ [[Algorithmic Asset Voting]].

C>A

⚫

However, for Condorcet methods, note that if the 49 C voters instead had voted C>A, then they make it so that now the voting method recognizes the C-top voters have an incentive to do FB to elect A rather than B. So a cycle would be formed all over again in terms of deciding which factions can force their preferences through strategic voting, meaning that this trick doesn't always work (see [[Algorithmic Asset Voting]] for discussion on this).

== Further reading ==