Kemeny–Young method: Difference between revisions

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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 ==