Difference between revisions of "Kemeny–Young method"

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Each possible complete ranking of the candidates is given a "distance"
score. For each pair of candidates, find the number of ballots that
order them the the opposite way as the given ranking. The distance is
the sum across all such pairs. The ranking with the least distance wins.
 
==Strategic Vulnerability==
Kemeny-Young is vulnerable to [[Tactical voting|compromising]], [[Tactical voting|burying]], and [[Strategic nomination|crowding]]. It fails [[cloneproofness]] because adding a clone can cause a non-clone to be elected, and this effect increases as the number of clones increases.
 
==Example==
 
It can be shown that this ranking is the one with the lowest distance score (this is because this is the [[Condorcet ranking]], and therefore switching any pair of candidates would require overturning the majority of voters in that pairing rather than the minority). Therefore, the winning ranking is Nashville>Chattanooga>Knoxville>Memphis, and so the winning candidate is Nashville.
 
Example with a Condorcet cycle:
 
25 A>B>C
40 B>C>A
35 C>A>B
 
A>B: 60>40, B>C: 65>35, C>A:75>25. There are 6 main rankings to consider here:
A>B>C: A>B opposed by 40, A>C by 75, and B>C by 35. Score is 150. So the minimum score so far is 150.
A>C>B: A>C by 75, A>B by 40, C>B by 65. Score is 180. Since this is greater than the minimum (150) this is disqualified.
B>A>C: B>A by 60, B>C by 35, A>C by 75. Score is 170. Disqualified by 150.
B>C>A: B>C by 35, B>A by 60, C>A by 25. Score is 120. This is the new minimum, so A>B>C is now disqualified.
C>A>B: C>A by 25, C>B by 65, A>B by 40. Score is 130. Disqualified by 120.
C>B>A: C>B by 65, C>A by 25, B>A by 60. Score is 150. Disqualified by 120.
 
So the final ranking is B>C>A, with B winning.
 
== Notes ==
 
[[Category:Single-winner voting methods]]
[[Category:Ranked voting methods]]
[[Category:Condorcet methods]]
[[Category:Smith-efficient Condorcet methods]]
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