Ranked Pairs: Difference between revisions
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To create a sorted list, repeatedly use RP to select a winner,
remove that winner from the list of candidates,
and repeat (to find the next runner up, and so forth). A simpler way to create the sorted list is simply to run RP once, and then use the resulting [[Condorcet ranking]] (when ignoring the defeats that were ignored by the RP procedure) as the RP ranking.
=== Tally ===
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== Notes ==
The RP winner can be found using only a pairwise comparison table. Example: <blockquote>4 A>B>C
3 B>C>A
5 C>A>B </blockquote>The pairwise comparison table looks like this (victories are bolded, defeats are underlined): ▼
▲The pairwise comparison table looks like this (victories are bolded, defeats are underlined):
{| class="wikitable"
|+
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| -
|}
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 (A>B creates no cycle, since it's the first defeat added, and B>C also creates no cycle, since for A, it shows A>B>C), and then the third defeat is thrown away (because adding C>A would result in, for A, an A>B>C>A [[beatpath]] cycle), resulting in the following pairwise comparison table:
{| class="wikitable"
!
!C▼
!A
!B
|-▼
▲!C
|C▼
| -▼
|'''8'''▼
|<u><s><small>5</small></s></u>▼
|-
|A
|<u>4</u>▼
| -
|'''9'''
▲|<u>4</u>
|-
|B
|'''<s>7</s>'''▼
|<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. The RP ranking is C>A>B, since C pairwise beats all others, A pairwise beats everyone except C, and B pairwise loses to everyone (when ignoring the defeats ignored by the RP procedure).
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, [[Smith//Minimax]] can be run instead to find the RP winner.
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