Favorite betrayal criterion: Difference between revisions

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It is passed by [[Approval voting]], [[Range voting]], and [[Majority Judgment]]. All these are examples of [[cardinal voting systems]].

On the other hand, most [[Ranked voting systems|ordinal voting systems]] do not pass this criterion. For instance, [[Borda Count]], [[Copeland's method]], [[Instant runoff voting]] (IRV, known in the UK as the Alternative Vote), [[Kemeny-Young method|Kemeny-Young]], [[Minimax Condorcet]], [[Ranked Pairs]], and [[Schulze method|Schulze]] all fail this criterion. A few ordinal methods, like [[weighted positional method|Antiplurality]], pass it.

On the other hand, most [[Ranked voting systems|ordinal voting systems]] do not pass this criterion. For instance, [[Borda Count]], [[Copeland's method]], [[Instant runoff voting]] (IRV, known in the UK as the Alternative Vote), [[Kemeny-Young method|Kemeny-Young]], [[Minimax Condorcet]], [[Ranked Pairs]], and [[Schulze method|Schulze]] all fail this criterion. A few ordinal methods, like [[weighted positional method|Antiplurality]], pass it. Some [[Condorcet methods]] pass it when combined with the [[tied at the top]] rule, though this means they may not be Condorcet-efficient when some voters equally rank multiple candidates.

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

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#Ideal Party

== Notes ==

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.

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

25 A>B

26 B

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

!

!B

!C

!A

|-

|B

| ---

|'''51'''

|'''26'''

|-

|C

|49

| ---

|'''49'''

|-

|A

|25

| ---

|}

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

== Further reading ==