Editing Ranked pairs (section)

== Example ==

=== The situation ===
{{Tenn voting example}}

The results are tabulated as follows:
{| class="wikitable"
|+Pairwise election results
!{{Diagonal split header|B|A|#ffe0e0|#e0e0ff}}
| bgcolor="#c0c0ff" |'''Memphis'''
| bgcolor="#c0c0ff" |'''Nashville'''
| bgcolor="#c0c0ff" |'''Chattanooga'''
| bgcolor="#c0c0ff" |'''Knoxville'''
|-
| bgcolor="#ffc0c0" |'''Memphis'''
|
| {{Diagonal split header|42%|58%|#e0e0ff}}
| {{Diagonal split header|42%|58%|#e0e0ff}}
| {{Diagonal split header|42%|58%|#e0e0ff}}
|-
| bgcolor="#ffc0c0" |'''Nashville'''
| {{Diagonal split header|58%|42%|#ffe0e0}}
|
| {{Diagonal split header|68%|32%|#ffe0e0}}
| {{Diagonal split header|68%|32%|#ffe0e0}}
|-
| bgcolor="#ffc0c0" |'''Chattanooga'''
| {{Diagonal split header|58%|42%|#ffe0e0}}
| {{Diagonal split header|32%|68%|#e0e0ff}}
|
| {{Diagonal split header|83%|17%|#ffe0e0}}
|-
| bgcolor="#ffc0c0" |'''Knoxville'''
| {{Diagonal split header|58%|42%|#ffe0e0}}
| {{Diagonal split header|32%|68%|#e0e0ff}}
| {{Diagonal split header|17%|83%|#e0e0ff}}
|
|}

* [A] indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption
* [B] indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column caption

=== Tally ===
First, list every pair, and determine the winner:
{| class="wikitable sortable"
!Pair
!Winner
|-
|Memphis (42%) vs. Nashville (58%)
|Nashville 58%
|-
|Memphis (42%) vs. Chattanooga (58%)
|Chattanooga 58%
|-
|Memphis (42%) vs. Knoxville (58%)
|Knoxville 58%
|-
|Nashville (68%) vs. Chattanooga (32%)
|Nashville 68%
|-
|Nashville (68%) vs. Knoxville (32%)
|Nashville 68%
|-
|Chattanooga (83%) vs. Knoxville (17%)
|Chattanooga 83%
|}
The votes are then sorted. The largest majority is "Chattanooga over Knoxville"; 83% of the voters prefer Chattanooga. Thus, the pairs from above would be sorted this way:
{| class="wikitable"
!Pair
!Winner
|-
|Chattanooga (83%) vs. Knoxville (17%)
|Chattanooga 83%
|-
|Nashville (68%) vs. Knoxville (32%)
|Nashville 68%
|-
|Nashville (68%) vs. Chattanooga (32%)
|Nashville 68%
|-
|Memphis (42%) vs. Nashville (58%)
|Nashville 58%
|-
|Memphis (42%) vs. Chattanooga (58%)
|Chattanooga 58%
|-
|Memphis (42%) vs. Knoxville (58%)
|Knoxville 58%
|}

=== Lock ===
The pairs are then locked in order, skipping any pairs that would create a cycle:

* Lock Chattanooga over Knoxville.
* Lock Nashville over Knoxville.
* Lock Nashville over Chattanooga.
* Lock Nashville over Memphis.
* Lock Chattanooga over Memphis.
* Lock Knoxville over Memphis.

In this case, no cycles are created by any of the pairs, so every single one is locked in.

Every "lock in" would add another arrow to the graph showing the relationship between the candidates. Here is the final graph (where arrows point away from the winner).

[[File:Tennessee-vote.svg]]

In this example, Nashville is the winner using the ranked-pairs procedure.  Nashville is followed by Chattanooga, Knoxville, and Memphis in second, third, and fourth places respectively.

=== Summary ===
In the example election, the winner is Nashville. This would be true for any [[Condorcet method]].

Under [[First-past-the-post voting|first-past-the-post]] and some other systems, Memphis would have won the election by having the most people, even though Nashville won every simulated pairwise election outright. Using [[instant-runoff voting]] in this example would result in Knoxville winning even though more people preferred Nashville over Knoxville.