Ranked Pairs: Difference between revisions
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# Sort (rank) each pair, by the largest margin of victory first to smallest last.
# "Lock in" each pair, starting with the one with the largest number of winning votes, and add one in turn to a graph as long as they do not create a cycle (which would create an ambiguity). The completed graph shows the winner.
See the [[Ranked pairs#Notes|Notes]] section for information on finding the Ranked Pairs winner without constructing a graph.
RP can also be used to create a sorted list of preferred candidates.
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== Notes ==
The RP winner can be found using only a pairwise comparison table. Example:
Ranked Pairs passes the [[Independence of Smith-dominated Alternatives]] criterion. Because of this, all candidates not in the Smith set can be eliminated before starting the procedure, reducing the number of operations needed to be done to find the winner. In addition, Ranked Pairs, like [[Schulze]], is equivalent to [[Minimax]] when there are 3 or fewer candidates with no pairwise ties between them, so if the Smith set has 3 or fewer candidates in it with no pairwise ties between them, then after eliminating all candidates not in the Smith set, Minimax can be done instead to find the Ranked Pairs winner. ▼
4 A>B>C
3 B>C>A
5 C>A>B
The pairwise comparison table looks like this (victories are bolded, defeats are underlined):
{| class="wikitable"
|+
!
!A
!B
!C
|-
|A
| -
|'''9'''
|<u>4</u>
|-
|B
|<u>3</u>
| -
|'''7'''
|-
|C
|'''8'''
|<u>5</u>
| -
|}
All candidates suffer at least one pairwise defeat, so the RP procedure must be done. The pairwise victories can be ordered from largest to smallest as A > B 9, C > A 8, and B > C 7. The first two victories are locked in, and then the third defeat is thrown away, resulting in the following pairwise comparison table:
{| class="wikitable"
!
!A
!B
!C
|-
|A
| -
|'''9'''
|<u>4</u>
|-
|B
|<u>3</u>
| -
|'''7'''
|-
|C
|'''8'''
|<u><s><small>5</small></s></u>
| -
|}
When ignoring struckthrough (non-locked in) pairwise victories, C is the only candidate with no pairwise defeats, and thus is the RP winner.
▲Ranked Pairs passes the [[Independence of Smith-dominated Alternatives]] criterion. Because of this, all candidates not in the Smith set can be eliminated before starting the procedure, reducing the number of operations needed to be done to find the winner. In addition, Ranked Pairs, like [[Schulze]], is equivalent to [[Minimax]] when there are 3 or fewer candidates with no pairwise ties between them, so if the Smith set has 3 or fewer candidates in it with no pairwise ties between them,
== External Resources ==
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