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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 ==

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